1. Preface to the Chemistry of Electronic Materials 2. Background to Electronic Materials 1. Introduction to Semiconductors 2. Doped Semiconductors 3. Diffusion 4. Crystal Structure 5. Structures of Element and Compound Semiconductors 3. Device Fundamentals 1. Introduction to Bipolar Transistors 2. Basic MOS Structure 3. Introduction to the MOS Transistor and MOSFETs 4. Light Emitting Diode 5. Polymer Light Emitting Diodes 6. Laser 7. Solar Cells 4. Bulk Materials 1. Properties of Gallium Arsenide 2. Synthesis and Purification of Bulk Semiconductors 3. Growth of Gallium Arsenide Crystals 4. Ceramic Processing of Alumina 5. Piezoelectric Materials Synthesis 5. Wafer Formation and Processing 1. Formation of Silicon and Gallium Arsenide Wafers . Doping . Applications for Silica Thin Films . Oxidation of Silicon . Photolithography . Composition and Photochemical Mechanisms of Photoresists 8. Integrated Circuit Well and Gate Creation
NOUR WN
6. Thin Film Growth 1. Molecular Beam Epitaxy 2. Atomic Layer Deposition 3. Chemical Vapor Deposition 4. Liguid Phase Deposition 7. Chemical Vapor Deposition 1. Selecting a Molecular Precursor for Chemical Vapor Deposition 2. Determination of Sublimation Enthalpy and Vapor Pressure for Inorganic and Metal-Organic Compounds by Thermogravimetric Analysis 3. 13-15 (III-V) Semiconductor Chemical Vapor Deposition 1. Phosphine and Arsine 2. Mechanism of the Metal Organic Chemical Vapor Deposition of Gallium Arsenide 4. Oxide Chemical Vapor Deposition 1. Chemical Vapor Deposition of Silica Thin Films 2. Chemical Vapor Deposition of Alumina 5. Nitride Chemical Vapor Deposition 1. Introduction to Nitride Chemical Vapor Deposition 2. Chemical Vapor Deposition of Silicon Nitride and Oxynitride 3. Chemical Vapor Deposition of Aluminum Nitride 6. Metal Organic Chemical Vapor Deposition of Calcium Fluoride
8. Materials Characterization 1. Rutherford Backscattering of Thin Films to the Study of Crystal Surface Processes . 3. Atomic Force Microscopy
9. Nanotechnology 1. Introduction to Nanoparticle Synthesis 2. Semiconductor Nanomaterials 1. Synthesis of Semiconductor Nanoparticles 2. Optical Properties of Group 12-16 (II-VI) Semiconductor Nanoparticles 3. Characterization of Group 12-16 (II-VI) Semiconductor Nanoparticles by UV-visible Spectroscopy Semiconductor Nanoparticles by Fluorescence Spectroscopy 3. Carbon Nanomaterials 4. Graphene 5. Rolling Molecules on Surfaces Under STM Imaging 10. Economic and Environmental Issues 1. The Environmental Impact of the Manufacturing of Seminconductors
Preface to the Chemistry of Electronic Materials
The intention of this text is not to provide a comprehensive reference to all aspects of semiconductor device fabrication or a review of research results that, irrespective of their promise, have not been adopted into mainstream production. Instead it is aimed to provide a useful reference for those interested in the chemical aspects of the electronics industry.
Given the nature of Connexions, this course is fluid in structure and content. In addition, it contains modules by other authors where appropriate. The content will be updated and expanded with time. If any authors have suitable content, please contact me and I will be glad to assist in transforming the content to a suitable module structure.
Andrew R. Barron
Rice University, Houston, TX 77005. E-mail: arb@rice.edu
Introduction to Semiconductors Introduction to semiconductors, mainly looking at the behavior of electrons in a solid from a quantum mechanical point of view.
Note:This module is adapted from the Connexions module entitled Introduction to Semiconductors by Bill Wilson.
If we only had to worry about simple conductors, life would not be very complicated, but on the other hand we wouldn't be able to make computers, CD players, cell phones, i-Pods and a lot of other things which we have found to be useful. We will now move on, and talk about another class of conductors called semiconductors.
In order to understand semiconductors and in fact to get a more accurate picture of how metals, or normal conductors actually work, we really have to resort to quantum mechanics. Electrons in a solid are very tiny objects, and it turns out that when things get small enough, they no longer exactly following the classical "Newtonian" laws of physics that we are all familiar with from everyday experience. It is not the purpose of this course to teach quantum mechanics, so what we are going to do instead is describe the results which come from looking at the behavior of electrons in a solid from a quantum mechanical point of view.
Solids (at least the ones we will be talking about, and especially semiconductors) are crystalline materials, which means that they have their atoms arranged in a ordered fashion. We can take silicon (the most important semiconductor) as an example. Silicon is a group 14(IV) element, which means it has four electrons in its outer or valence shell. Silicon crystallizes in a structure called the diamond crystal lattice, shown in [link]. Each silicon atom has four covalent bonds, arranged in a tetrahedral formation about the atom center.
Crystal structure of silicon.
In two dimensions, we can schematically represent a piece of single-crystal silicon as shown in [link]. Each silicon atom shares its four valence electrons with valence electrons from four nearest neighbors, filling the shell to 8 electrons, and forming a stable, periodic structure. Once the atoms have been arranged like this, the outer valence electrons are no longer strongly bound to the host atom. The outer shells of all of the atoms blend together and form what is called a band. The electrons are now free to move about within this band, and this can lead to electrical conductivity as we discussed earlier.
<4 —— st ———
—Si = —si—Ssi —* =—
—3 dd
A 2-D representation of a silicon crystal.
This is not the complete story however, for it turns out that due to quantum mechanical effects, there is not just one band which holds electrons, but several of them. What will follow is a very qualitative picture of how the electrons are distributed when they are in a periodic solid, and there are necessarily some details which we will be forced to gloss over. On the other hand this will give you a pretty good picture of what is going on, and may enable you to have some understanding of how a semiconductor really works. Electrons are not only distributed throughout the solid crystal spatially, but they also have a distribution in energy as well. The potential energy function within the solid is periodic in nature. This potential function comes from the positively charged atomic nuclei which are arranged in the crystal in a regular array. A detailed analysis of how electron wave functions, the mathematical abstraction which one must use to describe how small quantum mechanical objects behave when they are in a periodic potential, gives rise to an energy distribution somewhat like that shown in [link].
vi, TF aoe eee ais Bo ey eee ee
Band Gap
Schematic of the first two bands in a periodic solid showing energy levels and bands.
Firstly, unlike the case for free electrons, in a periodic solid, electrons are not free to take on any energy value they wish. They are forced into specific energy levels called allowed states, which are represented by the cups in [link]. The allowed states are not distributed uniformly in energy either. They are grouped into specific configurations called energy bands. There are no allowed levels at zero energy and for some distance above that. Moving up from zero energy, we then encounter the first energy band. At the bottom of the band there are very few allowed states, but as we move up in energy, the number of allowed states first increases, and then falls off again. We then come to a region with no allowed states, called an energy band gap. Above the band gap, another band of allowed states exists. This goes on and on, with any given material having many such bands and band gaps. This situation is shown schematically in [link], where the small cups represent allowed energy levels, and the vertical axis represents electron energy.
It turns out that each band has exactly 2N allowed states in it, where N is the total number of atoms in the particular crystal sample we are talking about. (Since there are 10 cups in each band in the figure, it must represent a crystal with just 5 atoms in it. Not a very big crystal at all!) Into these bands we must now distribute all of the valence electrons associated with the atoms, with the restriction that we can only put one electron into each allowed state. This is the result of something called the Pauli exclusion principle. Since in the case of silicon there are 4 valence electrons per atom, we would just fill up the first two bands, and the next would be empty. If we make the logical assumption that the electrons will fill in the levels with the lowest energy first, and only go into higher lying levels if the ones below are already filled. This situation is shown in [link], in which we have represented electrons as small black balls with a "-" sign on them. Indeed, the first two bands are completely full, and the next is empty. What will happen if we apply an electric field to the sample of silicon? Remember the diagram we have at hand right now is an energy based one, we are showing how the electrons are distributed in energy, not how they are arranged spatially. On this diagram we can not show how they will move about, but only how they will change their energy as a result of the applied field. The
electric field will exert a force on the electrons and attempt to accelerate them. If the electrons are accelerated, then they must increase their kinetic energy. Unfortunately, there are no empty allowed states in either of the filled bands. An electron would have to jump all the way up into the next (empty) band in order to take on more energy. In silicon, the gap between the top of the highest most occupied band and the lowest unoccupied band is 1.1 eV. (One eV is the potential energy gained by an electron moving across an electrical potential of one volt.) The mean free path or distance over which an electron would normally move before it suffers a collision is only a few hundred angstroms (ca. 300 x 10°8 cm) and so you would need a very large electric field (several hundred thousand V/cm) in order for the electron to pick up enough energy to "jump the gap". This makes it appear that silicon would be a very bad conductor of electricity, and in fact, very pure silicon is very poor electrical conductor.
VAVAVAY! WAU vi
bands full
and the next
empty.
A metal is an element with an odd number of valence electrons so that a metal ends up with an upper band which is just half full of electrons. This is illustrated in [link]. Here we see that one band is full, and the next is just half full. This would be the situation for the Group 13(III) element aluminum for instance. If we apply an electric field to these carriers, those near the top of the distribution can indeed move into higher energy levels by acquiring some kinetic energy of motion, and easily move from one place to the next. In reality, the whole situation is a bit more complex than we have shown here, but this is not too far from how it actually works.
vi whe VATAVAY! wavs ws
Electron distributio
nfora metal or good conductor.
So, back to our silicon sample. If there are no places for electrons to "move' into, then how does silicon work as a "Semiconductor"? Well, in the first place, it turns out that not all of the electrons are in the bottom two bands. In silicon, unlike say quartz or diamond, the band gap between the top-most full band, the next empty one is not so large. As we mentioned above it is only about 1.1 eV. So long as the silicon is not at absolute zero temperature, some electrons near the top of the full band can acquire enough thermal energy that they can "hop" the gap, and end up in the upper band, called the conduction band. This situation is shown in [link].
UU?
Thermal excitation of electrons across the band gap.
In silicon at room temperature, roughly 10!” electrons per cubic centimeter are thermally excited across the band-gap at any one time. It should be noted that the excitation process is a continuous one. Electrons are being excited across the band, but then they fall back down into empty spots in the lower band. On average however, the 10!° in each cm? of silicon is what you will find at any given instant. Now 10 billion electrons per cubic centimeter seems like a lot of electrons, but lets do a simple calculation. The mobility of electrons in silicon is about 1000 cm?/V.s. Remember, mobility times electric field yields the average velocity of the carriers. Electric field has units of V/cm, so with these units we get velocity in cm/s as we should. The charge on an electron is 1.6 x 10°! coulombs. Thus from [link]:
Equation:
o = nqu = 10!° (1.6 x 10°!) 1000 = 1.6x 10° mhos/em
If we have a sample of silicon 1 cm long by (1 mm x 1mm) square, it would have a resistance, [link], which does not make it much of a "conductor". In fact, if this were all there was to the silicon story, we could pack up and move on, because at any reasonable temperature, silicon would conduct electricity very poorly.
Equation:
R =L/oA 1/(1.6 x 10°°)(0.1)? 1.6 x 10° MQ
Doped Semiconductors From the silicon's crystal structure to discuss how to make doped semiconductors and the mechanics.
Note:This module is adapted from the Connexions module entitled Doped Semiconductors by Bill Wilson.
To see how we can make silicon a useful electronic material, we will have to go back to its crystal structure ([link]). Suppose somehow we could substitute a few atoms of phosphorus for some of the silicon atoms.
L | | - — Si —Ssi—=si=si =SsSi7 I IE tl I eS |S ee nd | oe — e IY WT —_ Si — P=—Sj ——Si ——Si —
A two dimensional representation of a silicon crystal lattice "doped" with phosphorus.
If you sneak a look at the periodic table, you will see that phosphorus is a group V element, as compared with silicon which is a group 14(IV) element. What this means is the phosphorus atom has five outer or valence electrons, instead of the four which silicon has. In a lattice composed mainly of silicon, the extra electron associated with the phosphorus atom has no "mating" electron with which it can complete a shell, and so is left loosely dangling to the phosphorus atom, with relatively low binding energy. In fact, with the addition of just a little thermal energy (from the
natural or latent heat of the crystal lattice) this electron can break free and be left to wander around the silicon atom freely. In our "energy band" picture, we have something like what we see in [link]. The phosphorus atoms are represented by the added cups with P's on them. They are new allowed energy levels which are formed within the "band gap" near the bottom of the first empty band. They are located close enough to the empty (or "conduction") band, so that the electrons which they contain are easily excited up into the conduction band. There, they are free to move about and contribute to the electrical conductivity of the sample. Note also, however, that since the electron has left the vicinity of the phosphorus atom, there is now one more proton than there are electrons at the atom, and hence it has a net positive charge of 1q. We have represented this by putting a little "+" sign in each P-cup. Note that this positive charge is fixed at the site of the phosphorous atom called a donor since it "donates" an electron up into the conduction band, and is not free to move about in the crystal.
y y \ Conduction (ee
# Y ¥ ai Band Gap
Ue i lvage wAwi Band
Silicon doped with phosphorus.
How many phosphorus atoms do we need to significantly change the resistance of our silicon? Suppose we wanted our 1 mm by 1 mm square sample to have a resistance of one ohm as opposed to more than 60 MQ.
Turning the resistance equation around we get, [link]. And hence, if we continue to assume an electron mobility of 1000 cm?/volt.sec, [link]. Equation:
o = L/RA
= 1Q/1 x (0.1)
= 100 mho/cm Equation: n = O/qu
100/(1.6 x 10°!°)1000 = 6.25 x 10!7 cm?
Now adding more than 6 x 10!” phosphorus atoms per cubic centimeter might seem like a lot of phosphorus, until you realize that there are almost 10*4 silicon atoms in a cubic centimeter and hence only one in every 1.6 million silicon atoms has to be changed into a phosphorus one to reduce the resistance of the sample from several 10s of MQ down to only one Q. This is the real power of semiconductors. You can make dramatic changes in their electrical properties by the addition of only minute amounts of impurities. This process is called doping the semiconductor. It is also one of the great challenges of the semiconductor manufacturing industry, for it is necessary to maintain fantastic levels of control of the impurities in the material in order to predict and control their electrical properties.
Again, if this were the end of the story, we still would not have any calculators, cell phones, or stereos, or at least they would be very big and cumbersome and unreliable, because they would have to work using vacuum tubes. We now have to focus on the few "empty" spots in the lower, almost full band (called the valence band.) We will take another view of this band, from a somewhat different perspective. I must confess at this point that what I am giving you is even further from the way things really work, then the "cups at different energies" picture we have been using so far. The problem is, that in order to do things right, we have to get involved in momentum phase-space, a lot more quantum mechanics, and generally a bunch of math and concepts we don't really need in order to have some idea
of how semiconductor devices work. What follow below is really intended as a motivation, so that you will have some feeling that what we state as results, is actually reasonable.
Consider [link]. Here we show all of the electrons in the valence, or almost full band, and for simplicity show one missing electron. Let's apply an electric field, as shown by the arrow in the figure. The field will try to move the (negatively charged) electrons to the left, but since the band is almost completely full, the only one that can move is the one right next to the ony spot, or hole as it is called.
Sn
Band full of electrons, with one missing.
One thing you may be worrying about is what happens to the electrons at the ends of the sample. This is one of the places where we are getting a somewhat distorted view of things, because we should really be looking in momentum, or wave-vector space rather than "real" space. In that picture, they magically drop off one side and "reappear" on the other. This doesn't happen in real space of course, so there is no easy way we can deal with it.
A short time after we apply the electric field we have the situation shown in [link], and a little while after that we have [link]. We can interpret this motion in two ways. One is that we have a net flow of negative charge to the left, or if we consider the effect of the aggregate of all the electrons in the band we could picture what is going on as a single positive charge, moving to the right. This is shown in [link]. Note that in either view we have the same net effect in the way the total net charge is transported
through the sample. In the mostly negative charge picture, we have a net flow of negative charge to the left. In the single positive charge picture, we have a net flow of positive charge to the right. Both give the same sign for the current!
E
Motion of the "missing" electron with an electric field.
Further motion of the "missing electron" spot.
Motion of a "hole" due to an applied electric field.
Thus, it turns out, we can consider the consequences of the empty spaces moving through the co-ordinated motion of electrons in an almost full band as being the motion of positive charges, moving wherever these empty spaces happen to be. We call these charge carriers "holes" and they too can add to the total conduction of electricity in a semiconductor. Using p to represent the density (in cm” of spaces in the valence band and py, and pip, to represent the mobility of electrons and holes respectively (they are usually not the same) we can modify to give the conductivity 0, when both electrons’ holes are present, [link].
Equation:
Oo = nqu, + Pq,
How can we get a sample of semiconductor with a lot of holes in it? What if, instead of phosphorus, we dope our silicon sample with a group III element, say boron? This is shown in [link]. Now we have some missing orbitals, or places where electrons could go if they were around. This modifies our energy picture as follows in [link]. Now we see a set of new levels introduced by the boron atoms. They are located within the band gap, just a little way above the top of the almost full, or valence band. Electrons in the valence band can be thermally excited up into these new allowed levels, creating empty states, or holes, in the valence band. The excited
electrons are stuck at the boron atom sites called acceptors, since they "accept" an electron from the valence band, and hence act as fixed negative charges, localized there. A semiconductor which is doped predominantly with acceptors is called p-type, and most of the electrical conduction takes place through the motion of holes. A semiconductor which is doped with donors is called n-type, and conduction takes place mainly through the motion of electrons.
a ee ee ey — sol ol —— ool ott tl oH | <=B-— sisi B= Si-— (Ey | | | —=Si= BB Si =si si.
A two dimensional representation of a silicon crystal lattice doped with boron.
UB oF ee!
@ e up Band Gap a Valence Band
P-type silicon, due to boron acceptors.
In n-type material, we can assume that all of the phosphorous atoms, or donors, are fully ionized when they are present in the silicon structure. Since the number of donors is usually much greater than the native, or intrinsic electron concentration, (* 10'° cm”), if Ny is the density of donors in the material, then n, the electron concentration, ~ Ng. If an electron deficient material such as boron is present, then the material is called p-type silicon, and the hole concentration is just * N, the concentration of acceptors, since these atoms "accept" electrons from the valence band.
If both donors and acceptors are in the material, then which ever one has the higher concentration wins out. This is called compensation. If there are more donors than acceptors then the material is n-type and n * Nj, - Ng. If there are more acceptors than donors then the material is p-type and p * N, - Nq. It should be noted that in most compensated material, one type of impurity usually has a much greater (several order of magnitude) concentration than the other, and so the subtraction process described above usually does not change things very much, e.g., 10/8 - 1016 = 1018.
One other fact which you might find useful is that, again, because of quantum mechanics, it turns out that the product of the electron and hole concentration in a material must remain a constant. In silicon at room temperature:
Equation:
Thus, if we have an n-type sample of silicon doped with 10!” donors per cubic centimeter, then n, the electron concentration is just p , the hole concentration, is 102°/10!” = 10° cm’. The carriers which dominate a material are called majority carriers, which would be the electrons in the above example. The other carriers are called minority carriers (the holes in the example) and while 10° might not seem like much compared to 10!” the presence of minority carriers is still quite important and can not be ignored. Note that if the material is undoped, then it must be that n = p and n = p= 10"
The picture of "cups" of different allowed energy levels is useful for gaining a pictorial understanding of what is going on in a semiconductor, but becomes somewhat awkward when you want to start looking at devices which are made up of both n and p type silicon. Thus, we will introduce one more way of describing what is going on in our material. The picture shown in [link] is called a band diagram. A band diagram is just a representation of the energy as a function of position with a semiconductor device. In a band diagram, positive energy for electrons is upward, while for holes, positive energy is downwards. That is, if an electron moves upward, its potential energy increases just as a with a normal mass in a gravitational field. Also, just as a mass will "fall down" if given a chance, an electron will move down a slope shown in a band diagram. On the other hand, holes gain energy by moving downward and so they have a tendancy to "float" upward if given the chance - much like a bubble in a liquid. The line labeled E,, in [link] shows the edge of the conduction band, or the bottom of the lowest unoccupied allowed band, while E,, is the top edge of the valence, or highest occupied band. The band gap, E, for the material is obviously E, - Ey. The dotted line labeled E; is called the Fermi level and it tells us something about the chemical equilibrium energy of the material, and also something about the type and number of carriers in the material. More on this later. Note that there is no zero energy level on a diagram such as this. We often use either the Fermi level or one or other of the band edges as a reference level on lieu of knowing exactly where "zero energy" is
located. Energy (eV) Ec ———— Ej Ey Position
An electron band- diagram for a semiconductor.
The distance (in energy) between the Fermi level and either E,, and E,, gives us information concerning the density of electrons and holes in that region of the semiconductor material. The details, once again, will have to be begged off on grounds of mathematical complexity. It turns out that you can Say:
Equation:
Equation:
kT
p=Ne
Both N, and N,, are constants that depend on the material you are talking about, but are typically on the order of 10!9 cm’. The expression in the denominator of the exponential is just Boltzman's constant (8.63 x 10° eV/K), k, times the temperature T of the material (in absolute temperature or Kelvin). At room temperature kT = '/49 of an electron volt. Look carefully at the numerators in the exponential. Note first that there is a minus sign in front, which means the bigger the number in the exponent, the fewer carriers we have. Thus, the top expression says that if we have n-type material, then E must not be too far away from the conduction band, while if we have p-type material, then the Fermi level,E, must be down close to the valence band. The closer EF gets to E, the more electrons we have. The closer Ey gets to Ey, the more holes we have. [link] therefore must be for a sample of n-type material. Note also that if we know how heavily a sample is doped (i.e., we know what Nj is) and from the fact that n * Ng we can use [link] to find out how far away the Fermi level is from the conduction band, [link].
Equation:
N.
To help further in our ability to picture what is going on, we will often add to this band diagram, some small signed circles to indicate the presence of mobile electrons and holes in the material. Note that the electrons are spread out in energy. From our "cups" picture we know they like to stay in the lower energy states if possible, but some will be distributed into the higher levels as well. What is distorted here is the scale. The band-gap for silicon is 1.1 eV, while the actual spread of the electrons would probably only be a few tenths of an eV, not nearly as much as is shown in [link]. Lets look at a sample of p-type material, just for comparison. Note that for holes, increasing energy goes down not up, so their distribution is inverted from that of the electrons. You can kind of think of holes as bubbles in a glass of soda or beer, they want to float to the top if they can. Note also for both n and p-type material there are also a few "minority" carriers, or carriers of the opposite type, which arise from thermal generation across the band-gap.
© © CROMOMC CIOMONOKCRONS
© ©
Band diagram for an
n-type semiconductor.
Diffusion The module discusses the process of electrons moving across a p-n or n-p junction known as diffusion.
Note:This module is adapted from the Connexions module entitled Diffusion by Bill Wilson.
Introduction
Let us turn our attention to what happens to the electrons and holes once they have been injected across a forward-biased junction. We will concentrate just on the electrons which are injected into the p-side of the junction, but keep in mind that similar things are also happening to the holes which enter the n-side.
When electrons are injected across a junction, they move away from the junction region by a diffusion process, while at the same time, some of them are disappearing because they are minority carriers (electrons in basically p-type material) and so there are lots of holes around for them to recombine with. This is all shown schematically in [link].
Injection
Processes involved in electron transport across a p-n junction.
Diffusion process quantified
It is actually fairly easy to quantify this, and come up with an expression for the electron distribution within the p-region. First we have to look a little bit at the diffusion process however. Imagine that we have a series of bins, each with a different number of electrons in them. In a given time, we could imagine that all of the electrons would flow out of their bins into the neighboring ones. Since there is no reason to expect the electrons to favor one side over the other, we will assume that exactly half leave by each side. This is all shown in [link]. We will keep things simple and only look at three bins. Imagine there are 4, 6, and 8 electrons respectively in each of the bins. After the required "emptying time," we will have a net flux of exactly one electron across each boundary as shown.
A schematic representation of a diffusion problem.
Now let's raise the number of electrons to 8, 12 and 16 respectively ({link]). We find that the net flux across each boundary is now 2 electrons per emptying time, rather than one. Note that the gradient (slope) of the concentration in the boxes has also doubled from one per box to two per box. This leads us to a rather obvious statement that the flux of carriers is proportional to the gradient of their density. This is stated formally in what
is known as Fick's First Law of Diffusion, [link]. Where D, is simply a proportionality constant called the diffusion coefficient. Since we are talking about the motion of electrons, this diffusion flux must give rise to a current density J.,.... Since an electron has a charge —q associated with it, [link].
Equation: d een a oe ee d x Equation: dn ease = We au
A schematic representation of a diffusion from bins.
Now we have to invoke something called the continuity equation. Imagine we have a volume (V) which is filled with some charge (Q). It is fairly obvious that if we add up all of the current density which is flowing out of the volume that it must be equal to the time rate of decrease of the charge within that volume. This ideas is expressed in the formula below which uses a closed-surface integral, along with the all the other integrals to follow: Equation:
We can write @ as, [link], where we are doing a volume integral of the charge density (p ) over the volume (V). Now we can use Gauss' theorem which says we can replace a surface integral of a quantity with a volume integral of its divergence, [link].
Equation:
Q= $v) av
V
fras= | aiv(aav
S
Equation:
So, combining [link], [link] and [link], we have, [link]. Equation: dp div (J) dV =— | —dV / iv (J) / dt
Finally, we let the volume V shrink down to a point, which means the quantities inside the integral must be equal, and we have the differential form of the continuity equation (in one dimension), [Link].
Equation:
div (J) os
What about the electrons?
Now let's go back to the electrons in the diode. The electrons which have been injected across the junction are called excess minority carriers, because they are electrons in a p-region (hence minority) but their concentration is greater than what they would be if they were in a sample of p-type material at equilibrium. We will designate them as n', and since they could change with both time and position we shall write them as n'(x,¢). Now there are two ways in which n'(x,t) can change with time. One would be if we were to stop injecting electrons in from the n-side of the junction. A reasonable way to account for the decay which would occur if we were not supplying electrons would be to write:
Equation:
Where 7, called the minority carrier recombination lifetime. It is pretty easy to show that if we start out with an excess minority carrier concentration no' at t = 0, then n'(x,t) will go as, [link]. But, the electron concentration can also change because of electrons flowing into or out of the region x. The
p(x,t) q
electron concentration n'(x,t) is just . Thus, due to electron flow we
have, [Link].
Equation: n'(x,t) = n'jem Equation: n'(z,t) = a sole.t) = a div (J(z,t))
But, we can get an expression for J(, t) from [link]. Reducing the divergence in [link] to one dimension (we just have a oh) we finally end up
with, [Link]. Equation:
d? n'(z, t) d x?
Combining [link] and [link] (electrons will, after all, suffer from both recombination and diffusion) and we end up with: Equation:
d? n'(z, t) n' (a, t) / ? ’ —n (x,t) = De = 5 = :
This is a somewhat specialized form of an equation called the ambipolar diffusion equation. It seems kind of complicated but we can get some nice results from it if we make some simply boundary condition assumptions.
Using the ambipolar diffusion equation
For anything we will be interested in, we will only look at steady state solutions. This means that the time derivative on the LHS of [link] is zero, and so letting n’(x,t) become simply n‘(a) since we no longer have any time variation to worry about, we have:
Equation:
d? 1 Day
n'(x) =0
Picking the not unreasonable boundary conditions that n’(0) = no (the concentration of excess electrons just at the start of the diffusion region) and n'(a) —> 0. as 2 — oo (the excess carriers go to zero when we get far from the junction) then:
Equation:
The expression in the radical ./ D.7T, is called the electron diffusion length, L,, and gives us some idea as to how far away from the junction the excess electrons will exist before they have more or less all recombined. This will be important for us when we move on to bipolar transistors. A typical value for the diffusion coefficient for electrons in silicon would be D, = 25 cm?/sec and the minority carrier lifetime is usually around a microsecond. As shown in [link] this is not very far at all.
Equation:
Le JV Det — 4/25 x 10-6
— 5x10°cm
Crystal Structure
Introduction
In any sort of discussion of crystalline materials, it is useful to begin with a discussion of crystallography: the study of the formation, structure, and properties of crystals. A crystal structure is defined as the particular repeating arrangement of atoms (molecules or ions) throughout a crystal. Structure refers to the internal arrangement of particles and not the external appearance of the crystal. However, these are not entirely independent since the external appearance of a crystal is often related to the internal arrangement. For example, crystals of cubic rock salt (NaCl) are physically cubic in appearance. Only a few of the possible crystal structures are of concern with respect to simple inorganic salts and these will be discussed in detail, however, it is important to understand the nomenclature of crystallography.
Crystallography
Bravais lattice
The Bravais lattice is the basic building block from which all crystals can be constructed. The concept originated as a topological problem of finding the number of different ways to arrange points in space where each point would have an identical “atmosphere”. That is each point would be surrounded by an identical set of points as any other point, so that all points would be indistinguishable from each other. Mathematician Auguste Bravais discovered that there were 14 different collections of the groups of points, which are known as Bravais lattices. These lattices fall into seven different "crystal systems”, as differentiated by the relationship between the angles between sides of the “unit cell” and the distance between points in the unit cell. The unit cell is the smallest group of atoms, ions or molecules that, when repeated at regular intervals in three dimensions, will produce the lattice of a crystal system. The “lattice parameter” is the length between two points on the comers of a unit cell. Each of the various lattice parameters are designated by the letters a, b, and c. If two sides are equal,
such as in a tetragonal lattice, then the lengths of the two lattice parameters are designated a and c, with b omitted. The angles are designated by the Greek letters a, B, and y, such that an angle with a specific Greek letter is not subtended by the axis with its Roman equivalent. For example, a is the included angle between the b and c axis.
[link] shows the various crystal systems, while [link] shows the 14 Bravais lattices. It is important to distinguish the characteristics of each of the individual systems. An example of a material that takes on each of the Bravais lattices is shown in [link].
System Axial lengths and angles Parcel geometry
cubic a=b=c,a= B= y= 90°
tetragonal a=b#c,a=fB=~7y=90°
orthorhombic a#b#c,a= 68 = y= 90°
rhombohedral a=b=c,a=B=y77#90°
a=b4#c,a=B=90°, y=
h ] exagona 120° monoclinic ae ARE 90° triclinic a#%~b#c,azpFy
Geometrical characteristics of the seven crystal systems.
simple cubic body-centered face-centered cubic cubic
= C
le | -» i simple body-centered tetragonal tetragonal
simple body-centered orthorhombic orthorhombic
base-centered face-centered orthorhombic orthorhombic
rhombohedral hexagonal simple base-centered triclinic monoclinic monoclinic
Bravais lattices.
Crystal system Example
triclinic K S208
monoclinic As,S4, KNO> rhombohedral Hg, Sb hexagonal Zn, Co, NiAs orthorhombic Ga, Fe3C tetragonal In, TiO cubic Au, Si, NaCl
Examples of elements and compounds that adopt each of the crystal systems.
The cubic lattice is the most symmetrical of the systems. All the angles are equal to 90°, and all the sides are of the same length (a = b = c). Only the length of one of the sides (a) is required to describe this system completely. In addition to simple cubic, the cubic lattice also includes body-centered cubic and face-centered cubic ([{link]). Body-centered cubic results from the presence of an atom (or ion) in the center of a cube, in addition to the atoms (ions) positioned at the vertices of the cube. In a similar manner, a face- centered cubic requires, in addition to the atoms (ions) positioned at the vertices of the cube, the presence of atoms (ions) in the center of each of the cubes face.
The tetragonal lattice has all of its angles equal to 90°, and has two out of the three sides of equal length (a = b). The system also includes body- centered tetragonal ([link]).
In an orthorhombic lattice all of the angles are equal to 90°, while all of its sides are of unequal length. The system needs only to be described by three lattice parameters. This system also includes body-centered orthorhombic, base-centered orthorhombic, and face-centered orthorhombic ([link]). A base-centered lattice has, in addition to the atoms (ions) positioned at the
vertices of the orthorhombic lattice, atoms (ions) positioned on just two opposing faces.
The rhombohedral lattice is also known as trigonal, and has no angles equal to 90°, but all sides are of equal length (a = b = c), thus requiring only by one lattice parameter, and all three angles are equal (a = B = 4).
A hexagonal crystal structure has two angles equal to 90°, with the other angle ( y) equal to 120°. For this to happen, the two sides surrounding the 120° angle must be equal (a = b), while the third side (c) is at 90° to the other sides and can be of any length.
The monoclinic lattice has no sides of equal length, but two of the angles are equal to 90°, with the other angle (usually defined as B) being something other than 90°. It is a tilted parallelogram prism with rectangular bases. This system also includes base-centered monoclinic ([link]).
In the triclinic lattice none of the sides of the unit cell are equal, and none of the angles within the unit cell are equal to 90°. The triclinic lattice is chosen such that all the internal angles are either acute or obtuse. This crystal system has the lowest symmetry and must be described by 3 lattice parameters (a, b, and c) and the 3 angles (a, B, and ¥).
Atom positions, crystal directions and Miller indices
Atom positions and crystal axes
The structure of a crystal is defined with respect to a unit cell. As the entire crystal consists of repeating unit cells, this definition is sufficient to represent the entire crystal. Within the unit cell, the atomic arrangement is expressed using coordinates. There are two systems of coordinates commonly in use, which can cause some confusion. Both use a corner of the unit cell as their origin. The first, less-commonly seen system is that of Cartesian or orthogonal coordinates (X, Y, Z). These usually have the units of Angstroms and relate to the distance in each direction between the origin
of the cell and the atom. These coordinates may be manipulated in the same fashion are used with two- or three-dimensional graphs. It is very simple, therefore, to calculate inter-atomic distances and angles given the Cartesian coordinates of the atoms. Unfortunately, the repeating nature of a crystal cannot be expressed easily using such coordinates. For example, consider a cubic cell of dimension 3.52 A. Pretend that this cell contains an atom that has the coordinates (1.5, 2.1, 2.4). That is, the atom is 1.5 A away from the origin in the x direction (which coincides with the a cell axis), 2.1 A in the y (which coincides with the b cell axis) and 2.4 A in the z (which coincides with the c cell axis). There will be an equivalent atom in the next unit cell along the x-direction, which will have the coordinates (1.5 + 3.52, 2.1, 2.4) or (5.02, 2.1, 2.4). This was a rather simple calculation, as the cell has very high symmetry and so the cell axes, a, b and c, coincide with the Cartesian axes, X, Y and Z. However, consider lower symmetry cells such as triclinic or monoclinic in which the cell axes are not mutually orthogonal. In such cases, expressing the repeating nature of the crystal is much more difficult to accomplish.
Accordingly, atomic coordinates are usually expressed in terms of fractional coordinates, (x, y, z). This coordinate system is coincident with the cell axes (a, b, c) and relates to the position of the atom in terms of the fraction along each axis. Consider the atom in the cubic cell discussion above. The atom was 1.5 A in the a direction away from the origin. As the a axis is 3.52 A long, the atom is (17/352) or 0.43 of the axis away from the origin. Similarly, it is (*/3.59) or 0.60 of the b axis and (74/3) or 0.68 of the c axis. The fractional coordinates of this atom are, therefore, (0.43, 0.60, 0.68). The coordinates of the equivalent atom in the next cell over in the a direction, however, are easily calculated as this atom is simply 1 unit cell away ina. Thus, all one has to do is add 1 to the x coordinate: (1.43, 0.60, 0.68). Such transformations can be performed regardless of the shape of the unit cell. Fractional coordinates, therefore, are used to retain and manipulate crystal information.
Crystal directions
The designation of the individual vectors within any given crystal lattice is accomplished by the use of whole number multipliers of the lattice parameter of the point at which the vector exits the unit cell. The vector is indicated by the notation [hkl], where h, k, and ! are reciprocals of the point at which the vector exits the unit cell. The origination of all vectors is assumed defined as [000]. For example, the direction along the a-axis according to this scheme would be [100] because this has a component only in the a-direction and no component along either the b or c axial direction. A vector diagonally along the face defined by the a and b axis would be [110], while going from one corner of the unit cell to the opposite corner would be in the [111] direction. [link] shows some examples of the various directions in the unit cell. The crystal direction notation is made up of the lowest combination of integers and represents unit distances rather than actual distances. A [222] direction is identical to a [111], so [111] is used. Fractions are not used. For example, a vector that intercepts the center of the top face of the unit cell has the coordinates x = 1/2, y = 1/2,z = 1. All have to be inversed to convert to the lowest combination of integers (whole numbers); i.e., [221] in [link]. Finally, all parallel vectors have the same crystal direction, e.g., the four vertical edges of the cell shown in [link] all have the crystal direction [hk/] = [001].
Some common directions in a cubic unit cell.
Crystal directions may be grouped in families. To avoid confusion there exists a convention in the choice of brackets surrounding the three numbers to differentiate a crystal direction from a family of direction. For a direction, square brackets [hkl] are used to indicate an individual direction. Angle brackets <hkl> indicate a family of directions. A family of directions includes any directions that are equivalent in length and types of atoms encountered. For example, in a cubic lattice, the [100], [010], and [001] directions all belong to the <100> family of planes because they are equivalent. If the cubic lattice were rotated 90°, the a, b, and c directions would remain indistinguishable, and there would be no way of telling on which crystallographic positions the atoms are situated, so the family of directions is the same. In a hexagonal crystal, however, this is not the case, so the [100] and [010] would both be <100> directions, but the [001] direction would be distinct. Finally, negative directions are identified with a bar over the negative number instead of a minus sign.
Crystal planes
Planes in a crystal can be specified using a notation called Miller indices. The Miller index is indicated by the notation [hkl] where h, k, and | are reciprocals of the plane with the x, y, and z axes. To obtain the Miller indices of a given plane requires the following steps:
The plane in question is placed on a unit cell.
Its intercepts with each of the crystal axes are then found.
The reciprocal of the intercepts are taken.
These are multiplied by a scalar to insure that is in the simple ratio of whole numbers.
For example, the face of a lattice that does not intersect the y or z axis would be (100), while a plane along the body diagonal would be the (111) plane. An illustration of this along with the (111) and (110) planes is given in [Link].
1 _ Tepe = M10)
Examples of Miller indices notation for crystal planes.
As with crystal directions, Miller indices directions may be grouped in families. Individual Miller indices are given in parentheses (hkl), while braces {hkl} are placed around the indices of a family of planes. For example, (001), (100), and (010) are all in the {100} family of planes, for a cubic lattice.
Description of crystal structures
Crystal structures may be described in a number of ways. The most common manner is to refer to the size and shape of the unit cell and the positions of the atoms (or ions) within the cell. However, this information is sometimes insufficient to allow for an understanding of the true structure in three dimensions. Consideration of several unit cells, the arrangement of the
atoms with respect to each other, the number of other atoms they in contact with, and the distances to neighboring atoms, often will provide a better understanding. A number of methods are available to describe extended solid-state structures. The most applicable with regard to elemental and compound semiconductor, metals and the majority of insulators is the close packing approach.
Close packed structures: hexagonal close packing and cubic close packing
Many crystal structures can be described using the concept of close packing. This concept requires that the atoms (ions) are arranged so as to have the maximum density. In order to understand close packing in three dimensions, the most efficient way for equal sized spheres to be packed in two dimensions must be considered.
The most efficient way for equal sized spheres to be packed in two dimensions is shown in [link], in which it can be seen that each sphere (the dark gray shaded sphere) is surrounded by, and is in contact with, six other spheres (the light gray spheres in [link]). It should be noted that contact with six other spheres the maximum possible is the spheres are the same size, although lower density packing is possible. Close packed layers are formed by repetition to an infinite sheet. Within these close packed layers, three close packed rows are present, shown by the dashed lines in [link].
Schematic representation of a close packed layer of equal sized spheres. The close packed rows (directions) are shown by the dashed lines.
The most efficient way for equal sized spheres to be packed in three dimensions is to stack close packed layers on top of each other to give a close packed structure. There are two simple ways in which this can be done, resulting in either a hexagonal or cubic close packed structures.
Hexagonal close packed
If two close packed layers A and B are placed in contact with each other so
as to maximize the density, then the spheres of layer B will rest in the hollow (vacancy) between three of the spheres in layer A. This is demonstrated in [link]. Atoms in the second layer, B (shaded light gray), may occupy one of two possible positions ([link]a or b) but not both together or a mixture of each. If a third layer is placed on top of layer B such that it exactly covers layer A, subsequent placement of layers will
result in the following sequence ...ABABAB.... This is known as hexagonal
close packing or hcp.
(a) (b)
Schematic representation of two close packed layers arranged in A (dark grey) and B (light grey) positions. The alternative stacking of the B layer is
shown in (a) and (b).
The hexagonal close packed cell is a derivative of the hexagonal Bravais lattice system ({link]) with the addition of an atom inside the unit cell at the coordinates (1/3,7/3,'/9). The basal plane of the unit cell coincides with the close packed layers ({link]). In other words the close packed layer makes-up the {001} family of crystal planes.
A schematic projection of the basal plane of the hep unit cell on the close packed layers.
The “packing fraction” in a hexagonal close packed cell is 74.05%; that is 74.05% of the total volume is occupied. The packing fraction or density is derived by assuming that each atom is a hard sphere in contact with its nearest neighbors. Determination of the packing fraction is accomplished by calculating the number of whole spheres per unit cell (2 in hcp), the volume occupied by these spheres, and a comparison with the total volume of a unit cell. The number gives an idea of how “open” or filled a structure is. By comparison, the packing fraction for body-centered cubic ({link]) is 68% and for diamond cubic (an important semiconductor structure to be described later) is it 34%.
Cubic close packed: face-centered cubic
In a similar manner to the generation of the hexagonal close packed structure, two close packed layers are stacked ([link]) however, the third layer (C) is placed such that it does not exactly cover layer A, while sitting in a set of troughs in layer B ([link]), then upon repetition the packing sequence will be .. ABCABCABC.... This is known as cubic close packing or ccp.
Schematic representation of the three close packed layers in a cubic close packed arrangement: A (dark grey), B
(medium grey), and C (light grey).
The unit cell of cubic close packed structure is actually that of a face- centered cubic (fcc) Bravais lattice. In the fcc lattice the close packed layers constitute the {111} planes. As with the hcp lattice packing fraction in a cubic close packed (fcc) cell is 74.05%. Since face centered cubic or fcc is more commonly used in preference to cubic close packed (ccp) in describing the structures, the former will be used throughout this text.
Coordination number
The coordination number of an atom or ion within an extended structure is defined as the number of nearest neighbor atoms (ions of opposite charge) that are in contact with it. A slightly different definition is often used for atoms within individual molecules: the number of donor atoms associated with the central atom or ion. However, this distinction is rather artificial, and both can be employed.
The coordination numbers for metal atoms in a molecule or complex are commonly 4, 5, and 6, but all values from 2 to 9 are known and a few examples of higher coordination numbers have been reported. In contrast, common coordination numbers in the solid state are 3, 4, 6, 8, and 12. For example, the atom in the center of body-centered cubic lattice has a coordination number of 8, because it touches the eight atoms at the corners of the unit cell, while an atom in a simple cubic structure would have a coordination number of 6. In both fcc and hcp lattices each of the atoms have a coordination number of 12.
Octahedral and tetrahedral vacancies
As was mentioned above, the packing fraction in both fcc and hcp cells is 74.05%, leaving 25.95% of the volume unfilled. The unfilled lattice sites (interstices) between the atoms in a cell are called interstitial sites or vacancies. The shape and relative size of these sites is important in controlling the position of additional atoms. In both fcc and hcp cells most of the space within these atoms lies within two different sites known as octahedral sites and tetrahedral sites. The difference between the two lies in their “coordination number”, or the number of atoms surrounding each site. Tetrahedral sites (vacancies) are surrounded by four atoms arranged at the comers of a tetrahedron. Similarly, octahedral sites are surrounded by six atoms which make-up the apices of an octahedron. For a given close packed lattice an octahedral vacancy will be larger than a tetrahedral vacancy.
Within a face centered cubic lattice, the eight tetrahedral sites are positioned within the cell, at the general fractional coordinate of (°/4,"/4,"/4) where n = 1 or 3, e.g., (7/4, /4,!/4), (/4,"/4,7/4), etc. The octahedral sites are located at the center of the unit cell (1/5,"/5,'/5), as well as at each of the edges of the cell, e.g., (4/5,0,0). In the hexagonal close packed system, the tetrahedral sites are at (0,0,°/g) and (1/3,/3,’/g), and the octahedral sites are at (1/3,"/3,'/4) and all symmetry equivalent positions.
Important structure types
The majority of crystalline materials do not have a structure that fits into the one atom per site simple Bravais lattice. A number of other important crystal structures are found, however, only a few of these crystal structures are those of which occur for the elemental and compound semiconductors and the majority of these are derived from fcc or hcp lattices. Each structural type is generally defined by an archetype, a material (often a naturally occurring mineral) which has the structure in question and to which all the similar materials are related. With regard to commonly used elemental and compound semiconductors the important structures are diamond, zinc blende, Wurtzite, and to a lesser extent chalcopyrite. However, rock salt, B-tin, cinnabar and cesium chloride are observed as high pressure or high temperature phases and are therefore also discussed.
The following provides a summary of these structures. Details of the full range of solid-state structures are given elsewhere.
Diamond Cubic
The diamond cubic structure consists of two interpenetrating face-centered cubic lattices, with one offset '/, of a cube along the cube diagonal. It may also be described as face centered cubic lattice in which half of the tetrahedral sites are filled while all the octahedral sites remain vacant. The diamond cubic unit cell is shown in [link]. Each of the atoms (e.g., C) is four coordinate, and the shortest interatomic distance (C-C) may be determined from the unit cell parameter (a).
Equation:
Unit cell structure of a diamond cubic lattice showing the two interpenetrating face- centered cubic lattices.
Zinc blende
This is a binary phase (ME) and is named after its archetype, a common mineral form of zinc sulfide (ZnS). As with the diamond lattice, zinc blende consists of the two interpenetrating fcc lattices. However, in zinc blende one lattice consists of one of the types of atoms (Zn in ZnS), and the other lattice is of the second type of atom (S in ZnS). It may also be described as face centered cubic lattice of S atoms in which half of the tetrahedral sites are filled with Zn atoms. All the atoms in a zinc blende structure are 4- coordinate. The zinc blende unit cell is shown in [link]. A number of inter- atomic distances may be calculated for any material with a zinc blende unit cell using the lattice parameter (a).
Equation:
Zn-S = av3 = 0.422a 4
Equation:
Zn-Zn = S-S = a_= 0.707 a v2
Unit cell structure of a
zinc blende (ZnS) lattice. Zinc atoms are shown in green (small), sulfur atoms shown in red (large), and the dashed lines show the unit cell.
Chalcopyrite
The mineral chalcopyrite CuFeS, is the archetype of this structure. The structure is tetragonal (a = b#c, a= 8 = y = 90°, and is essentially a superlattice on that of zinc blende. Thus, is easiest to imagine that the chalcopyrite lattice is made-up of a lattice of sulfur atoms in which the tetrahedral sites are filled in layers, ...FeCuCuFe..., etc. ({link]). In such an idealized structure c = 2a, however, this is not true of all materials with chalcopyrite structures.
Unit cell structure of a chalcopyrite lattice. Copper atoms are shown in blue, iron atoms are shown in green and sulfur atoms are shown in yellow. The dashed lines show the unit cell.
Rock salt
As its name implies the archetypal rock salt structure is NaCl (table salt). In common with the zinc blende structure, rock salt consists of two interpenetrating face-centered cubic lattices. However, the second lattice is offset 1/2a along the unit cell axis. It may also be described as face centered cubic lattice in which all of the octahedral sites are filled, while all the tetrahedral sites remain vacant, and thus each of the atoms in the rock salt
structure are 6-coordinate. The rock salt unit cell is shown in [link]. A number of inter-atomic distances may be calculated for any material with a rock salt structure using the lattice parameter (a).
Equation:
Na-Cl = a = 05a 2
Equation:
Na-Na = CI-Cl = a = 0.707a v2
Unit cell structure of a rock salt lattice. Sodium ions are shown in purple
(small spheres) and chloride ions are shown in red (large spheres).
Cinnabar
Cinnabar, named after the archetype mercury sulfide, Hg§S, is a distorted rock salt structure in which the resulting cell is rhombohedral (trigonal) with each atom having a coordination number of six.
Wurtzite
This is a hexagonal form of the zinc sulfide. It is identical in the number of and types of atoms, but it is built from two interpenetrating hcp lattices as opposed to the fcc lattices in zinc blende. As with zinc blende all the atoms in a wurtzite structure are 4-coordinate. The wurtzite unit cell is shown in [link]. A number of inter atomic distances may be calculated for any material with a wurtzite cell using the lattice parameter (a).
Equation:
Zn-S = av3/8 = 0.612a = 3c = 0375c¢ 8
Equation:
Zn-Zn = S-S = a = 1.632c
However, it should be noted that these formulae do not necessarily apply when the ratio a/c is different from the ideal value of 1.632.
Unit cell structure of a wurtzite lattice. Zinc atoms are shown in green (small spheres), sulfur atoms shown in red (large spheres), and the dashed lines show the unit cell.
Cesium Chloride
The cesium chloride structure is found in materials with large cations and relatively small anions. It has a simple (primitive) cubic cell ([link]) with a chloride ion at the corners of the cube and the cesium ion at the body center. The coordination numbers of both Cs* and Cl’, with the inner atomic distances determined from the cell lattice constant (a).
Equation:
Cs-Cl = ayv3 = 0.8664 2
Equation:
Cs-Cs = CI-Cl =a
B-Tin.
The room temperature allotrope of tin is B-tin or white tin. It has a tetragonal structure, in which each tin atom has four nearest neighbors (Sn- Sn = 3.016 A) arranged in a very flattened tetrahedron, and two next nearest neighbors (Sn-Sn = 3.175 A). The overall structure of B-tin consists of fused hexagons, each being linked to its neighbor via a four-membered Sn, ring.
Defects in crystalline solids
Up to this point we have only been concerned with ideal structures for crystalline solids in which each atom occupies a designated point in the crystal lattice. Unfortunately, defects ordinarily exist in equilibrium between the crystal lattice and its environment. These defects are of two general types: point defects and extended defects. As their names imply, point defects are associated with a single crystal lattice site, while extended defects occur over a greater range.
Point defects: “too many or too few” or “just plain wrong”
Point defects have a significant effect on the properties of a semiconductor, so it is important to understand the classes of point defects and the characteristics of each type. [link] summarizes various classes of native point defects, however, they may be divided into two general classes; defects with the wrong number of atoms (deficiency or surplus) and defects where the identity of the atoms is incorrect.
: -
(a) perfect lattice (b) interstitial impurity
:
(c) cation vacancy (d) anion vacancy
(e) substitution of cation (f) substitution of anion
(g) Ba antisite defect (h) Ag antisite defect
Point defects in a crystal lattice.
Interstitial Impurity
An interstitial impurity occurs when an extra atom is positioned in a lattice site that should be vacant in an ideal structure ([{link]b). Since all the adjacent lattice sites are filled the additional atom will have to squeeze itself into the interstitial site, resulting in distortion of the lattice and alteration in the local electronic behavior of the structure. Small atoms, such as carbon,
will prefer to occupy these interstitial sites. Interstitial impurities readily diffuse through the lattice via interstitial diffusion, which can result in a change of the properties of a material as a function of time. Oxygen impurities in silicon generally are located as interstitials.
Vacancies
The converse of an interstitial impurity is when there are not enough atoms in a particular area of the lattice. These are called vacancies. Vacancies exist in any material above absolute zero and increase in concentration with temperature. In the case of compound semiconductors, vacancies can be either cation vacancies ({link]c) or anion vacancies ([{link]d), depending on what type of atom are “missing”.
Substitution
Substitution of various atoms into the normal lattice structure is common, and used to change the electronic properties of both compound and elemental semiconductors. Any impurity element that is incorporated during crystal growth can occupy a lattice site. Depending on the impurity, substitution defects can greatly distort the lattice and/or alter the electronic structure. In general, cations will try to occupy cation lattice sites ([link]e), and anion will occupy the anion site ({link]f). For example, a zinc impurity in GaAs will occupy a gallium site, if possible, while a sulfur, selenium and tellurium atoms would all try to substitute for an arsenic. Some impurities will occupy either site indiscriminately, e.g., Si and Sn occupy both Ga and As sites in GaAs.
Antisite Defects
Antisite defects are a particular form of substitution defect, and are unique to compound semiconductors. An antisite defect occurs when a cation is misplaced on an anion lattice site or vice versa ([link]g and h). Dependant
on the arrangement these are designated as either Ap antisite defects or Ba antisite defects. For example, if an arsenic atom is on a gallium lattice site the defect would be an Asc, defect. Antisite defects involve fitting into a lattice site atoms of a different size than the rest of the lattice, and therefore this often results in a localized distortion of the lattice. In addition, cations and anions will have a different number of electrons in their valence shells, so this substitution will alter the local electron concentration and the electronic properties of this area of the semiconductor.
Extended Defects: Dislocations in a Crystal Lattice
Extended defects may be created either during crystal growth or as a consequence of stress in the crystal lattice. The plastic deformation of crystalline solids does not occur such that all bonds along a plane are broken and reformed simultaneously. Instead, the deformation occurs through a dislocation in the crystal lattice. [link] shows a schematic representation of a dislocation in a crystal lattice. Two features of this type of dislocation are the presence of an extra crystal plane, and a large void at the dislocation core. Impurities tend to segregate to the dislocation core in order to relieve strain from their presence.
extra net plane 0 . direction of slip —_____ >»
dislocation core
Dislocation in a crystal lattice.
Epitaxy
Epitaxy, is a transliteration of two Greek words epi, meaning "upon", and taxis, meaning "ordered". With respect to crystal growth it applies to the process of growing thin crystalline layers on a crystal substrate. In epitaxial growth, there is a precise crystal orientation of the film in relation to the substrate. The growth of epitaxial films can be done by a number of methods including molecular beam epitaxy, atomic layer epitaxy, and chemical vapor deposition, all of which will be described later.
Epitaxy of the same material, such as a gallium arsenide film on a gallium arsenide substrate, is called homoepitaxy, while epitaxy where the film and substrate material are different is called heteroepitaxy. Clearly, in homoepitaxy, the substrate and film will have the identical structure, however, in heteroepitaxy, it is important to employ where possible a substrate with the same structure and similar lattice parameters. For example, zinc selenide (zinc blende, a = 5.668 A) is readily grown on gallium arsenide (zinc blende, a = 5.653 A). Alternatively, epitaxial crystal growth can occur where there exists a simple relationship between the structures of the substrate and crystal layer, such as is observed between AlyO3 (100) on Si (100). Whichever route is chosen a close match in the lattice parameters is required, otherwise, the strains induced by the lattice mismatch results in distortion of the film and formation of dislocations. If the mismatch is significant epitaxial growth is not energetically favorable, causing a textured film or polycrystalline untextured film to be grown. As a general rule of thumb, epitaxy can be achieved if the lattice parameters of the two materials are within about 5% of each other. For good quality epitaxy, this should be less than 1%. The larger the mismatch, the larger the strain in the film. As the film gets thicker and thicker, it will try to relieve the strain in the film, which could include the loss of epitaxy of the growth of dislocations. It is important to note that the <100> directions of a film must be parallel to the <100> direction of the substrate. In some cases, such as Fe on MgO, the [111] direction is parallel to the substrate [100]. The epitaxial relationship is specified by giving first the plane in the film that is parallel to the substrate [100].
Bibliography
e International Tables for X-ray Crystallography. Vol. IV; Kynoch Press: Birmingham, UK (1974).
¢ B. F. G. Johnson, in Comprehensive Inorganic Chemistry, Pergamon Press, Vol. 4, Chapter 52 (1973).
e A. R. West, Solid State Chemistry and its Applications, Wiley, New York (1984).
Structures of Element and Compound Semiconductors
Introduction
A single crystal of either an elemental (e.g., silicon) or compound (e.g., gallium arsenide) semiconductor forms the basis of almost all semiconductor devices. The ability to control the electronic and opto- electronic properties of these materials is based on an understanding of their structure. In addition, the metals and many of the insulators employed within a microelectronic device are also crystalline.
Group IV (14) elements
Each of the semiconducting phases of the group IV (14) elements, C (diamond), Si, Ge, and a-Sn, adopt the diamond cubic structure ((link]). Their lattice constants (a, A) and densities (p, g/cm?) are given in [link].
Unit cell structure of a diamond cubic lattice showing the two interpenetrating face- centered cubic lattices.
Lattice parameter, a
Element Density (g/cm? carbon
(arsond) 3.56683(1) 3.51525
silicon 5.4310201(3) 2.319002 germanium 5.657906(1) 5.3234
tin (a-Sn) 6.4892(1) 7.285
Lattice parameters and densities (measured at 298 K) for the diamond cubic forms of the group IV (14) elements.
As would be expected the lattice parameter increase in the order C < Si < Ge < a-Sn. Silicon and germanium form a continuous series of solid solutions with gradually varying parameters. It is worth noting the high degree of accuracy that the lattice parameters are known for high purity crystals of these elements. In addition, it is important to note the temperature at which structural measurements are made, since the lattice parameters are temperature dependent ([link]). The lattice constant (a), in A, for high purity silicon may be calculated for any temperature (T) over the temperature range 293 - 1073 K by the formula shown below.
ay = 5.4304 + 1.8138 X 10° (T - 298.15 K) + 1.542 X 10°9 (T — 298.15 K)
(a) 5.447 5.444
5.44]
aA) 5 a3 5.435
5.432
5.429 0 100 200 300 400 500 600 700 800
Temperature (°C)
(b) 5.69
5.66
0 100 200 300 400 500 600 700 800 Temperature (°C)
Temperature dependence of the lattice parameter for (a) Si and (b) Ge.
Even though the diamond cubic forms of Si and Ge are the only forms of direct interest to semiconductor devices, each exists in numerous crystalline high pressure and meta-stable forms. These are described along with their interconversions, in [link].
Phase
Sil
Si II
Si III
Si TV
Si V
Si VI
Ge I
Ge II
Ge III
Ge IV
Structure diamond cubic
grey tin structure
cubic
hexagonal
unidentified
hexagonal close packed
diamond cubic
B-tin structure
tetragonal
body centered cubic
Remarks stable at normal pressure
formed from Si I or Si V above 14 GPa
metastable, formed from Si II above 10 GPa
stable above 34 GPa, formed from Si II above 16 GPa
stable above 45 GPa
low-pressure phase formed from Ge I above 10 GPa
formed by quenching Ge II at low pressure
formed by quenching Ge II to 1 atm at 200 K
High pressure and metastable phases of silicon and germanium.
Group ITI-V (13-15) compounds
The stable phases for the arsenides, phosphides and antimonides of aluminum, gallium and indium all exhibit zinc blende structures ([link]). In contrast, the nitrides are found as wurtzite structures (e.g., [link]). The structure, lattice parameters, and densities of the III-V compounds are given
in [link]. It is worth noting that contrary to expectation the lattice parameter of the gallium compounds is smaller than their aluminum homolog; for GaAs a = 5.653 A; AlAs a = 5.660 A. As with the group IV elements the lattice parameters are highly temperature dependent; however, additional variation arises from any deviation from absolute stoichiometry. These effects are shown in [link].
Unit cell structure of a zinc blende (ZnS) lattice. Zinc atoms are shown in
green (small), sulfur atoms shown in red
(large), and the dashed lines show the unit cell.
Unit cell structure of a wurtzite lattice. Zinc atoms are shown in green (small), sulfur atoms shown in red (large), and the dashed lines show the
unit cell. Compound Structure AIN wurtzite zinc og blende AlAs zinc
blende
Lattice parameter (A)
a = 3.11(1), c= 4.98(1)
a = 5.4635(4) a = 5.660
Density (g/cm?)
3.200
2.40(1)
3.760
AlSb zinc a = 6.1355(1) 4.26
blende GaN wurtzite ae Ee GaP ae - a = 5.4505(2) 4.138 GaAs ae a a = 5.65325(2) 5.3176(3) InN wurtzite ae oi 6.81 InP a a a = 5.868(1) 4.81 InAs he ” a = 6.0583 5.667 InSb ae 7 a = 6.47937 5.7747(4)
Lattice parameters and densities (measured at 298 K) for the II-V (13-15) compound semiconductors. Estimated standard deviations given in parentheses.
stoichiometric
a(A) 5.
0 10 20 30 8 40 50 60 70 Temperature (°C)
Temperature dependence of the lattice parameter for stoichiometric GaAs and crystals with either Ga or As excess.
The homogeneity of structures of alloys for a wide range of solid solutions to be formed between ITI-V compounds in almost any combination. Two classes of ternary alloys are formed: III,-II,_,-V (e.g., Al,-Ga,.,-As) and IT-V1_,-Vx (e.g., Ga-Asj_,-P,) . While quaternary alloys of the type III,- IIT,_,-V,-V1-y allow for the growth of materials with similar lattice parameters, but a broad range of band gaps. A very important ternary alloy, especially in optoelectronic applications, is Al,-Ga,_,-As and its lattice parameter (a) is directly related to the composition (x).
d = 5.6533 + 0.0078 x
Not all of the III-V compounds have well characterized high-pressure phases. however, in each case where a high-pressure phase is observed the coordination number of both the group III and group V element increases from four to six. Thus, AIP undergoes a zinc blende to rock salt transformation at high pressure above 170 kbar, while AlSb and GaAs form orthorhombic distorted rock salt structures above 77 and 172 kbar,
respectively. An orthorhombic structure is proposed for the high-pressure form of InP (>133 kbar). Indium arsenide (InAs) undergoes two-phase transformations. The zinc blende structure is converted to a rock salt structure above 77 kbar, which in turn forms a B-tin structure above 170 kbar.
Group II-VI (12-16) compounds
The structures of the II-VI compound semiconductors are less predictable than those of the III-V compounds (above), and while zinc blende structure exists for almost all of the compounds there is a stronger tendency towards the hexagonal wurtzite form. In several cases the zinc blende structure is observed under ambient conditions, but may be converted to the wurtzite form upon heating. In general the wurtzite form predominates with the smaller anions (e.g., oxides), while the zinc blende becomes the more stable phase for the larger anions (e.g., tellurides). One exception is mercury sulfide (HgS) that is the archetype for the trigonal cinnabar phase. [link] lists the stable phase of the chalcogenides of zinc, cadmium and mercury, along with their high temperature phases where applicable. Solid solutions of the II-VI compounds are not as easily formed as for the III-V compounds; however, two important examples are ZnS,Se,_, and Cd,Hg,. le:
Lattice Density Compound Structure parameter (A) (g/cm?) ZINC = 7nS Tae a=5.410 4.075 wurtzite ae 087
6.260
ZnSe Zinc a = 5.668 oa
blende Zinc - ZntTe eiende a= 6.10 5.636 : a = 4.136, c = CdS wurtzite 6.714 4.82 . a = 4.300, c = CdSe wurtzite 7011 5.81 Zinc _ CdTe Pleada a = 6.482 5.87 ; a=4.149,c= Hgs cinnabar 9.495 ane - a= 5.851 7.73 Zinc _ HgSe hewis a = 6.085 8.25 Zinc _ HgTe beade a = 6.46 8.07
Lattice parameters and densities (measured at 298 K) for the II-VI (12-16) compound semiconductors.
The zinc chalcogenides all transform to a cesium chloride structure under high pressures, while the cadmium compounds all form rock salt high- pressure phases ([link]). Mercury selenide (HgSe) and mercury telluride (HgTe) convert to the mercury sulfide archetype structure, cinnabar, at high pressure.
Unit cell structure of a rock salt lattice. Sodium ions are shown in purple
and chloride ions are shown in red.
I-III-VI, (11-13-16) compounds
Nearly all I-III-VI, compounds at room temperature adopt the chalcopyrite structure ([link]). The cell constants and densities are given in [link]. Although there are few reports of high temperature or high-pressure phases, AgInS> has been shown to exist as a high temperature orthorhombic polymorph (a = 6.954, b = 8.264, and c = 6.683 A), and AgInTe, forms a cubic phase at high pressures.
Unit cell structure of a chalcopyrite lattice. Copper atoms are shown in blue, iron atoms are shown in green and sulfur atoms are shown in yellow. The dashed lines show the unit cell.
Lattice Lattice Compound parameter a parameter c
(A) (A) (g.cm’)
Density
CuAlS> 5.02 10.430 3.45
CuAlSep 9.61 10.92 4.69 CuAlTe, 5.96 177 9.47 CuGaS» 9.39 10.46 4.38 CuGaSe» 9.61 11.00 rel CuGatTep 6.00 11.93 9.95 CulnS> Di02 11.08 4.74 CulnSe, 5.78 11.55 Deld- CulnTe, 6.17 12.34 6.10 AgAIS» 6.30 11.84 6.15 AgGaS» DLO 10.29 4.70 AgGaSe> 5.98 10.88 5.70 AgGatTeo 6.29 11.95 6.08 AgInS» 5.82 11.17 4.97 AgInSe> 6.095 11.69 5.82 AginTe> 6.43 12,09 6.96
Chalcopyrite lattice parameters and densities (measured at 298 K) for the I- II-VI compound semiconductors. Lattice parameters for tetragonal cell.
Of the I-ITI-VI, compounds, the copper indium chalcogenides (CuInE>) are certainly the most studied for their application in solar cells. One of the
advantages of the copper indium chalcogenide compounds is the formation of solid solutions (alloys) of the formula CulnE>_,E',, where the composition variable (x) varies from 0 to 2. The CulnS5_,Se, and CulnSe >. x le, systems have also been examined, as has the CuGa,Inj.yS7_,Sex quaternary system. As would be expected from a consideration of the relative ionic radii of the chalcogenides the lattice parameters of the CulnS>_,Se, alloy should increase with increased selenium content. Vergard's law requires the lattice constant for a linear solution of two semiconductors to vary linearly with composition (e.g., as is observed for Al,Ga;_,As), however, the variation of the tetragonal lattice constants (a and c) with composition for CulnS>_,S, are best described by the parabolic relationships.
a = 5.532 + 0.0801 x + 0.0260 x?
c = 11.156 + 0.1204 x + 0.0611 x?
A similar relationship is observed for the CulnSe_,Te, alloys. a = 5.783 + 0.1560 x + 0.0212 x?
c = 11.628 + 0.3340 x + 0.0277 x?
The large difference in ionic radii between S and Te (0.37 A) prevents formation of solid solutions in the CulnS»_,Te, system, however, the single alloy CulnS, 5Teg 5 has been reported.
Orientation effects
Once single crystals of high purity silicon or gallium arsenide are produced they are cut into wafers such that the exposed face of these wafers is either the crystallographic {100} or {111} planes. The relative structure of these surfaces are important with respect to oxidation, etching and thin film growth. These processes are orientation-sensitive; that is, they depend on the direction in which the crystal slice is cut.
Atom density and dangling bonds
The principle planes in a crystal may be differentiated in a number of ways, however, the atom and/or bond density are useful in predicting much of the chemistry of semiconductor surfaces. Since both silicon and gallium arsenide are fcc structures and the {100} and {111} are the only technologically relevant surfaces, discussions will be limited to fcc {100} and {111}.
The atom density of a surface may be defined as the number of atoms per unit area. [link] shows a schematic view of the {111} and {100} planes in a fcc lattice. The {111} plane consists of a hexagonal close packed array in which the crystal directions within the plane are oriented at 60° to each other. The hexagonal packing and the orientation of the crystal directions are indicated in [link]b as an overlaid hexagon. Given the intra-planar inter- atomic distance may be defined as a function of the lattice parameter, the area of this hexagon may be readily calculated. For example in the case of silicon, the hexagon has an area of 38.30 A*. The number of atoms within the hexagon is three: the atom in the center plus 1/3 of each of the six atoms at the vertices of the hexagon (each of the atoms at the hexagons vertices is shared by three other adjacent hexagons). Thus, the atom density of the {111} plane is calculated to be 0.0783 A’. Similarly, the atom density of the {100} plane may be calculated. The {100} plane consists of a square array in which the crystal directions within the plane are oriented at 90° to each other. Since the square is coincident with one of the faces of the unit cell the area of the square may be readily calculated. For example in the case of silicon, the square has an area of 29.49 A*. The number of atoms within the square is 2: the atom in the center plus 1/4 of each of the four atoms at the vertices of the square (each of the atoms at the corners of the square are shared by four other adjacent squares). Thus, the atom density of the {100} plane is calculated to be 0.0678 A-*. While these values for the atom density are specific for silicon, their ratio is constant for all diamond cubic and zinc blende structures: {100}:{111} = 1:1.155. In general, the fewer dangling bonds the more stable a surface structure.
Schematic representation of the (111) and (100) faces of a face centered cubic (fcc) lattice showing the relationship between the close packed rows.
An atom inside a crystal of any material will have a coordination number (n) determined by the structure of the material. For example, all atoms within the bulk of a silicon crystal will be in a tetrahedral four-coordinate environment (n = 4). However, at the surface of a crystal the atoms will not make their full compliment of bonds. Each atom will therefore have less nearest neighbors than an atom within the bulk of the material. The missing bonds are commonly called dangling bonds. While this description is not particularly accurate it is, however, widely employed and as such will be used herein. The number of dangling bonds may be defined as the difference between the ideal coordination number (determined by the bulk crystal structure) and the actual coordination number as observed at the surface.
[link] shows a section of the {111} surfaces of a diamond cubic lattice viewed perpendicular to the {111} plane. The atoms within the bulk have a coordination number of four. In contrast, the atoms at the surface (e.g., the atom shown in blue in [link]) are each bonded to just three other atoms (the atoms shown in red in [link]), thus each surface atom has one dangling bond. As can be seen from [link], which shows the atoms at the {100} surface viewed perpendicular to the {100} plane, each atom at the surface (e.g., the atom shown in blue in [link]) is only coordinated to two other atoms (the atoms shown in red in [link]), leaving two dangling bonds per
atom. It should be noted that the same number of dangling bonds are found for the {111} and {100} planes of a zinc blende lattice. The ratio of dangling bonds for the {100} and {111} planes of all diamond cubic and zinc blende structures is {100}:{111} = 2:1. Furthermore, since the atom densities of each plane are known then the ratio of the dangling bond densities is determined to be: {100}:{111} = 1:0.577.
A section of the {111} surfaces of a diamond cubic lattice viewed perpendicular to the {111} plane.
A section of the {100} surface of a diamond cubic lattice viewed perpendicular to the
{100} plane.
Silicon
For silicon, the {111} planes are closer packed than the {100} planes. As a result, growth of a silicon crystal is therefore slowest in the <111> direction, since it requires laying down a close packed atomic layer upon another layer in its closest packed form. As a consequence <111> Si is the easiest to grow, and therefore the least expensive.
The dissolution or etching of a crystal is related to the number of broken bonds already present at the surface: the fewer bonds to be broken in order to remove an individual atom from a crystal, the easier it will be to dissolve the crystal. As a consequence of having only one dangling bond (requiring three bonds to be broken) etching silicon is slowest in the <111> direction. The electronic properties of a silicon wafer are also related to the number of dangling bonds.
Silicon microcircuits are generally formed on a single crystal wafer that is diced after fabrication by either sawing part way through the wafer thickness or scoring (scribing) the surface, and then physically breaking. The physical breakage of the wafer occurs along the natural cleavage planes, which in the case of silicon are the {111} planes.
Gallium arsenide
The zinc blende lattice observed for gallium arsenide results in additional considerations over that of silicon. Although the {100} plane of GaAs is structurally similar to that of silicon, two possibilities exist: a face consisting of either all gallium atoms or all arsenic atoms. In either case the surface atoms have two dangling bonds, and the properties of the face are independent of whether the face is gallium or arsenic.
The {111} plane also has the possibility of consisting of all gallium or all arsenic. However, unlike the {100} planes there is a significant difference between the two possibilities. [link] shows the gallium arsenide structure represented by two interpenetrating fcc lattices. The [111] axis is vertical within the plane of the page. Although the structure consists of alternate layers of gallium and arsenic stacked along the [111] axis, the distance between the successive layers alternates between large and small. Assigning arsenic as the parent lattice the order of the layers in the [111] direction is
As— Ga-As— Ga-As~— Ga, while in the | 111 | direction the layers are
ordered, Ga-As-Ga— As-Ga— As ({link]). In silicon these two directions are of course identical. The surface of a crystal would be either arsenic, with three dangling bonds, or gallium, with one dangling bond. Clearly, the latter is energetically more favorable. Thus, the (111) plane shown in [link] is
called the (111) Ga face. Conversely, the fii plane would be either
gallium, with three dangling bonds, or arsenic, with one dangling bond.
Again, the latter is energetically more favorable and the fii plane is
therefore called the (111) As face.
The (111) Ga face of GaAs showing a surface layer containing gallium
atoms (green) with one dangling bond per gallium and three bonds to the arsenic atoms (red) in the lower layer.
The (111) As is distinct from that of (111) Ga due to the difference in the number of electrons at the surface. As a consequence, the (111) As face etches more rapidly than the (111) Ga face. In addition, surface evaporation below 770 °C occurs more rapidly at the (111) As face.
Bibliography
e M. Baublitz and A. L. Ruoff, J. Appl. Phys., 1982, 53, 6179.
J. C. Jamieson, Science, 1963, 139, 845.
C. C. Landry, J. Lockwood, and A. R. Barron, Chem. Mater., 1995, 7, 699.
e M. Robbins, J. C. Phillips, and V. G. Lambrecht, J. Phys. Chem. Solids, 1973, 34, 1205.
D. Sridevi and K. V. Reddy, Mat. Res. Bull., 1985, 20, 929.
Y. K. Vohra, S. T. Weir, and A. L. Ruoff, Phys. Rev. B, 1985, 31, 7344. e W. M. Yin and R. J. Paff, J. Appl. Phys., 1973, 45, 1456.
Introduction to Bipolar Transistors
Note:This module is adapted from the Connexions module entitled Introduction to Bipolar Transistors by Bill Wilson.
Let's leave the world of two terminal devices (which are all called diodes by the way; diode just means two-terminals) and venture into the much more interesting world of three terminals. The first device we will look at is called the bipolar transistor. Consider the structure shown in [link]:
+ Emitter | Base | Collector oe n+ p n
Structure of a npn bipolar transistor.
The device consists of three layers of silicon, a heavily doped n-type layer called the emitter, a moderately doped p-type layer called the base, and third, more lightly doped layer called the collector. In a biasing (applied DC potential) configuration called forward active biasing, the emitter-base junction is forward biased, and the base-collector junction is reverse biased. [link] shows the biasing conventions we will use. Both bias voltages are referenced to the base terminal. Since the base-emitter junction is forward biased, and since the base is made of p-type material, Vp must be negative. On the other hand, in order to reverse bias the base-collector junction Vcp will be a positive voltage.
Forward active biasing of a npn bipolar transistor.
Now, let's draw the band-diagram for this device. At first this might seem hard to do, but we know what forward and reverse biased band diagrams look like, so we'll just stick one of each together. We show this in [link], which is a very busy figure, but it is also very important, because it shows all of the important features in the operation the transistor. Since the base- emitter junction is forward biased, electrons will go from the (n-type) emitter into the base. Likewise, some holes from the base will be injected into the emitter.
‘Ee
Band diagram and carrier fluxes in a bipolar transistor.
In [link], we have two different kinds of arrows. The open arrows which are attached to the carriers, show us which way the carrier is moving. The solid arrows which are labeled with some kind of subscripted J, represent current flow. We need to do this because for holes, motion and current flow are in the same direction, while for electrons, carrier motion and current flow are in opposite directions.
Just as we saw in the last chapter, the electrons which are injected into the base diffuse away from the emitter-base junction towards the (reverse biased) base-collector junction. As they move through the base, some of the electrons encounter holes and recombine with them. Those electrons which do get to the base-collector junction run into a large electric field which sweeps them out of the base and into the collector. They "fall" down the large potential drop at the junction.
These effects are all seen in [link], with arrows representing the various currents which are associated with each of the carriers fluxes. I, represents the current associated with the electron injection into the base, i.e., it points in the opposite direction from the motion of the electrons, since electrons have a negative charge. Iz, represents the current associated with holes injection into the emitter from the base. Ip, represents recombination current in the base, while Jc, represents the electron current going into the collector. It should be easy for you to see that:
Equation: Ip = Ige + Len Equation: Ip = Ign + Lpr Equation: Ic = Ice
In a "good" transistor, almost all of the current across the base-emitter junction consists of electrons being injected into the base. The transistor engineer works hard to design the device so that very little emitter current is
made up of holes coming from the base into the emitter. The transistor is also designed so that almost all of those electrons which are injected into the base make it across to the base-collector reverse-biased junction. Some recombination is unavoidable, but things are arranged so as to minimize this effect.
Basic MOS Structure
Note:This module is adapted from the Connexions module entitled Basic MOS Structure by Bill Wilson.
[link] shows the basic steps necessary to make the MOS structure. It will help us in our understanding if we now rotate our picture so that it is pointing sideways in our next few drawings. [link] shows the rotated structure. Note that in the p-silicon we have positively charged mobile holes, and negatively charged, fixed acceptors. Because we will need it later, we have also shown the band diagram for the semiconductor below the sketch of the device. Note that since the substrate is p-type, the Fermi
level is located down close to the valance band. polysilicon
SiO» Op + heat ~ SiH4 + heat —— PELL EL ELIE ELD
Formation of the metal-oxide- semiconductor (MOS) structure.
Basic metal-oxide- semiconductor (MOS) structure.
Let us now place a potential between the gate and the silicon substrate. Suppose we make the gate negative with respect to the substrate. Since the substrate is p-type, it has a lot of mobile, positively charged holes in it. Some of them will be attracted to the negative charge on the gate, and move over to the surface of the substrate. This is also reflected in the band diagram shown in [link]. Remember that the density of holes is exponentially proportional to how close the Fermi level is to the valence band edge. We see that the band diagram has been bent up slightly near the surface to reflect the extra holes which have accumulated there.
Applying a negative gate voltage to a basic metal-oxide- semiconductor (MOS) structure.
An electric field will develop between the positive holes and the negative gate charge. Note that the gate and the substrate form a kind of parallel plate capacitor, with the oxide acting as the insulating layer in-between them. The oxide is quite thin compared to the area of the device, and so it is quite appropriate to assume that the electric field inside the oxide is a uniform one. (We will ignore fringing at the edges.) The integral of the electric field is just the applied gate voltage V,. If the oxide has a thickness Xox then since E,, is uniform, it is given by, [link].
Equation:
Vo
Lox
Fox =
If we focus in on a small part of the gate, we can make a little "pill" box which extends from somewhere in the oxide, across the oxide/gate interface and ends up inside the gate material someplace. The pill-box will have an area As. Now we will invoke Gauss' law which we reviewed earlier. Gauss' law simply says that the surface integral over a closed surface of the displacement vector D (which is, of course, € x E) is equal to the total charge enclosed by that surface. We will assume that there is a surface charge density -Q, Coulombs/cm? on the surface of the gate electrode ({link]). The integral form of Gauss' Law is just:
Equation:
f exk dS= Qencl
surface charge density Qg
Electric Field
‘pill box" with area 4s
Finding the surface charge density.
Note that we have used €,,F in place of D. In this particular set-up the integral is easy to perform, since the electric field is uniform, and only pointing in through one surface - it terminates on the negative surface charge inside the pill-box. The charge enclosed in the pill box is just - (QgAs), and so we have (keeping in mind that the surface integral of a vector pointing into the surface is negative), [link], or [link]. Equation:
fey E AS = —(€oxEoxA(s)) — (Q,A(s)) Equation: EoxEox = Qs
Now, we can use [link] to get [link] or [link].
Equation: EoxVg Q Lox Equation: Qs Eox __ Tr = “ox Vy Box
The quantity c,, is called the oxide capacitance. It has units of Farads/cm?, so it is really a capacitance per unit area of the oxide. The dielectric constant of silicon dioxide, €,,, is about 3.3 x 10°!8 F/cm. A typical oxide thickness might be 250 A (or 2.5 x 10° cm). In this case, c,, would be about 1.30 x 10°’ F/cm?. The units we are using here, while they might
seem a little arbitrary and confusing, are the ones most commonly used in the semiconductor business.
The most useful form of [link] is when it is turned around, [link], as it gives us a way to find the charge on the gate in terms of the gate potential. We will use this equation later in our development of how the MOS transistor really works.
Equation:
Qs = Con
It turns out we have not done anything very useful by apply a negative voltage to the gate. We have drawn more holes there in what is called an accumulation layer, but that is not helping us in our effort to create a layer of electrons in the MOSFET which could electrically connect the two n- regions together.
Let's turn the battery around and apply a positive voltage to the gate ([link]). Actually, let's take the battery out for now, and just let V, be a positive value, relative to the substrate which will tie to ground. Making V, positive puts positive Q, on the gate. The positive charge pushes the holes away from the region under the gate and uncovers some of the negatively- charged fixed acceptors. Now the electric field points the other way, and goes from the positive gate charge, terminating on the negative acceptor charge within the silicon.
SR WAWS INSNONG!
x
Increasing the voltage
extends the depletion
region further into the device.
The electric field now extends into the semiconductor. We know from our experience with the p-n junction that when there is an electric field, there is a shift in potential, which is represented in the band diagram by bending the bands. Bending the bands down (as we should moving towards positive charge) causes the valence band to pull away from the Fermi level near the surface of the semiconductor. If you remember the expression we had for the density of holes in terms of E, and E; it is easy to see that indeed, [link], there is a depletion region (region with almost no holes) near the region under the gate. (Once Fr - E, gets large with respect to kT, the negative exponent causes p — 0.)
Equation:
>
s
Le;
ON
>,
SS
SS
SS uv
2
WU
iA
SS
PFs
Threshold, E; is getting close to E,.
The electric field extends further into the semiconductor, as more negative charge is uncovered and the bands bend further down. But now we have to recall the electron density equation, which tells us how many electrons we have:
Equation:
Ec—Ef n= N.e~ kT
A glance at [link] reveals that with this much band bending, E, the conduction band edge, and E; the Fermi level are starting to get close to one another (at least compared to kT), which means that n, the electron concentration, should soon start to become significant. In the situation represented by [link], we say we are at threshold, and the gate voltage at this point is called the threshold voltage, Vr.
Now, let's increase V, above V7. Here's the sketch in [link]. Even though we have increased Vg beyond the threshold voltage, V;, and more positive charge appears on the gate, the depletion region no longer moves back into the substrate. Instead electrons start to appear under the gate region, and the additional electric field lines terminate on these new electrons, instead of on additional acceptors. We have created an inversion layer of electrons under the gate, and it is this layer of electrons which we can use to connect the
two n-type regions in our initial device.
J us
Inversion - electrons form under the gate.
Where did these electrons come from? We do not have any donors in this material, so they can not come from there. The only place from which electrons could be found would be through thermal generation. Remember, in a semiconductor, there are always a few electron hole pairs being generated by thermal excitation at any given time. Electrons that get created in the depletion region are caught by the electric field and are swept over to the edge by the gate. I have tried to suggest this with the electron generation event shown in the band diagram in the figure. In a real MOS device, we have the two n-regions, and it is easy for electrons from one or both to "fall" into the potential well under the gate, and create the inversion layer of electrons.
Introduction to the MOS Transistor and MOSFETs
Note:This module is adapted from the Connexions modules entitled Introduction to MOSFETs and MOS Transistor by Bill Wilson.
We now move on to another three terminal device - also called a transistor. This transistor, however, works on much different principles than does the bipolar junction transistor of the last chapter. We will now focus on a device called the field effect transistor, or metal-oxide-semiconductor field effect transistor or simply MOSFET.
In [link] we have a block of silicon, doped p-type. Into it we have made two regions which are doped n-type. To each of those n-type regions we attach a wire, and connect a battery between them. If we try to get some current, J, to flow through this structure, nothing will happen, because the n-p junction on the RHS is reverse biased, i.e., the positive lead from the battery going to the n-side of the p-n junction. If we attempt to remedy this by turning the battery around, we will now have the LHS junction reverse biased, and again, no current will flow. If, for whatever reason, we want current to flow, we will need to come up with some way of forming a layer of n-type material between one n-region and the other. This will then connect them together, and we can run current in one terminal and out the other.
p-type silicon
The start of a field effect
transistor.
To see how we will do this, let's do two things. First we will grow a layer of SiO, (silicon dioxide or silica, but actually refered to as "oxide") on top of the silicon. To do this the wafer is placed in an oven under an oxygen atmosphere, and heated to 1100 °C. The result is a nice, high-quality insulating SiO> layer on top of the silicon). On top of the oxide layer we then deposit a conductor, which we call the gate. In the "old days" the gate would have been a layer of aluminum; hence the "metal-oxide-silicon" or MOS name. Today, it is much more likely that a heavily doped layer of polycrystalline silicon (polysilicon, or more often just "poly") would be deposited to form the gate structure. Polysilicon is made from the reduction of a gas, such as silane (SiH,), [link].
Equation:
The silicon is polycrystalline (composed of lots of small silicon crystallites) because it is deposited on top of the oxide, which is amorphous, and so it does not provide a single crystal "matrix" which would allow the silicon to organize itself into one single crystal. If we had deposited the silicon on top of a single crystal silicon wafer, we would have formed a single crystal layer of silicon called an epitaxial layer. This is sometimes done to make structures for particular applications. For instance, growing a n-type epitaxial layer on top of a p-type substrate permits the fabrication of a very abrupt p-n junction.
Note:Epitaxy, is a transliteration of two Greek words epi, meaning "upon", and taxis. meaning "ordered". Thus an epitaxial layer is one that follows the order of the substrate on which it is grown.
Now we can go back now to our initial structure, shown in [link], only this time we will add an oxide layer, a gate structure, and another battery so that we can invert the region under the gate and connect the two n-regions together. Well also identify some names for parts of the structure, so we will know what we are talking about. For reasons which will be clear later, we call the n-region connected to the negative side of the battery the source, and the other one the drain. We will ground the source, and also the p-type substrate. We add two batteries, V;, between the gate and the source, and Vas between the drain and the source.
41] 1|IF-* IKV
Vgs
{I
p-type substrate
Biasing a MOSFET transistor
It will be helpful if we also make another sketch, which gives us a perspective view of the device. For this we strip off the gate and oxide, but we will imagine that we have applied a voltage greater than Vr to the gate, so there is a n-type region, called the channel which connects the two. We will assume that the channel region is Z long and W wide, as shown in [link].
BU dx
The inversion channel and its resistance.
Next we want to take a look at a little section of channel, and find its resistance a(R), when the little section is O(a) long, [link]. Equation:
We have introduced a slightly different form for our resistance formula here. Normally, we would have a simple o in the denominator, and an area A, for the cross-sectional area of the channel. It turns out to be very hard to figure out what that cross sectional area of the channel is however. The electrons which form the inversion layer crowd into a very thin sheet of surface charge which really has little or no thickness, or penetration into the substrate.
If, on the other hand we consider a surface conductivity (units: simply mhos), o, [link], then we will have an expression which we can evaluate. Here, jz; is a surface mobility, with units of cm2/V.sec, that is the quantity which represented the proportionality between the average carrier velocity and the electric field, [link] and [link].
Equation: Os = HsQ chan Equation: v=pE Equation: qT an
The surface mobility is a quantity which has to be measured for a given system, and is usually just a number which is given to you. Something around 300 cm?/V.sec is about right for silicon. Q chan is called the surface charge density or channel charge density and it has units of Coulombs/cm?. This is like a sheet of charge, which is different from the bulk charge density, which has units of Coulombs/cm2. Note that:
Equation: 2 Coul cm Coulombs __ sec Volt sec cm? “Volt ees —~ VY = mbhos
It turns out that it is pretty simple to get an expression for Q chan, the surface charge density in the channel. For any given gate voltage V,,, we know that the charge density on the gate is given simply as:
Equation:
Qo = Cox Ves
However, until the gate voltage V,., gets larger than Vr we are not creating any mobile electrons under the gate, we are just building up a depletion region. We'll define Q as the charge on the gate necessary to get to threshold. Q-7 = CoxVr. Any charge added to the gate above Q7 is matched by charge @ chan in the channel. Thus, it is easy to say: [link] or [link].
Equation:
OQ) saan = Q, _ Qr
Equation:
Q chan = Cox (V, _ Vr)
Thus, putting [link] and [link] into [link], we get: Equation:
_ al(x) 7 LsCox (Vas = Vr)W
If you look back at [link], you will see that we have defined a current Ig flowing into the drain. That current flows through the channel, and hence through our little incremental resistance a(R), creating a voltage drop a(V.) across it, where V; is the channel voltage, [link].
Equation:
al(V.(«))
Iydl(R) Izdl(x) [sCox(Ves—Vr)W
Let's move the denominator to the left, and integrate. We want to do our integral completely along the channel. The voltage on the channel V,(z) goes from 0 on the left to Vg, on the right. At the same time, z is going from 0 to L. Thus our limits of integration will be 0 and Vg, for the voltage integral Q(V.(x)) and from 0 to L for the z integral a/(z).
Equation:
Vas LT i [sCox (Ves - Vr Wd Ve = / Igdz 0 0
Both integrals are pretty trivial. Let's swap the equation order, since we usually want J/g as a function of applied voltages. Equation:
IgL = [LsCoxW (Vas ad Vr) Vas
We now simply divide both sides by Z, and we end up with an expression for the drain current Jg, in terms of the drain-source voltage, Vg;, the gate
voltage V,, and some physical attributes of the MOS transistor. Equation:
sCoxW i= ( eet Vee v1) Vai
Light Emitting Diode Light Emitting Diode
Note:This module is adapted from the Connexions module entitled Light Emitting Diode by Bill Wilson.
Let's talk about the recombining electrons for a minute. When the electron falls down from the conduction band and fills in a hole in the valence band, there is an obvious loss of energy. The question is; where does that energy go? In silicon, the answer is not very interesting. Silicon is what is known as an indirect band-gap material. What this means is that as an electron goes from the bottom of the conduction band to the top of the valence band, it must also undergo a significant change in momentum. This all comes about from the details of the band structure for the material, which we will not concern ourselves with here. As we all know, whenever something changes state, we must still conserve not only energy, but also momentum. In the case of an electron going from the conduction band to the valence band in silicon, both of these things can only be conserved if the transition also creates a quantized set of lattice vibrations, called phonons, or "heat". Phonons posses both energy and momentum, and their creation upon the recombination of an electron and hole allows for complete conservation of both energy and momentum. All of the energy which the electron gives up in going from the conduction band to the valence band (1.1 eV) ends up in phonons, which is another way of saying that the electron heats up the crystal.
In some other semiconductors, something else occurs. In a class of materials called direct band-gap semiconductors, the transition from conduction band to valence band involves essentially no change in momentum. Photons, it turns out, possess a fair amount of energy (several eV/photon in some cases) but they have very little momentum associated with them. Thus, for a direct band gap material, the excess energy of the electron-hole recombination can either be taken away as heat, or more likely, as a photon of light. This radiative transition then conserves energy
and momentum by giving off light whenever an electron and hole recombine. This gives rise to the light emitting diode (LED). Emission of a photon in an LED is shown schematically in [link].
OVEOQO Eg ade Ey OHOOVE © © @°
Radiative recombination in a direct band-gap semiconductor.
It was Planck who postulated that the energy of a photon was related to its frequency by a constant, which was later named after him. If the frequency of oscillation is given by the Greek letter "nu" (v), then the energy of the photon is just given by, [link], where h is Planck's constant, which has a value of 4.14 x 10° eV.sec.
Equation:
E=hv
When we talk about light it is conventional to specify its wavelength, A, instead of its frequency. Visible light has a wavelength on the order of nanometers, e.g., red is about 600 nm, green about 500 nm and blue is in the 450 nm region. A handy "rule of thumb" can be derived from the fact that c = Av, where c is the speed of light (3 x 10° m/sec or 3 x 10!” nm/sec, [link].
Equation:
A(nm) = ev)
1242 E(eV)
Thus, a semiconductor with a 2 eV band-gap should give off light at about 620 nm (in the red). A 3 eV band-gap material would emit at 414 nm, in the violet. The human eye, of course, is not equally responsive to all colors ({link]). The materials which are used for important light emitting diodes (LEDs) for each of the different spectral regions are also shown in [link].
lnva!
I[EVE IME
350 400 450 500 550 600 650 700 750 wavelength in nanometers
Relative response of the human eye to various colors.
It is worth noting that a number of the important LEDs are based on the GaAsP system. GaAs is a direct band-gap semiconductor with a band gap of 1.42 eV (in the infrared). GaP is an indirect band-gap material with a band gap of 2.26 eV (550 nm, or green). Both As and P are group V elements. (Hence the nomenclature of the materials as III-V (or 13-15) compound semiconductors.) We can replace some of the As with P in GaAs and make a mixed compound semiconductor GaAsj_,P,. When the mole fraction of phosphorous is less than about 0.45 the band gap is direct, and so we can "engineer" the desired color of LED that we want by simply growing a crystal with the proper phosphorus concentration! The properties of the GaAsP system are shown in [link]. It turns out that for this system, there are actually two different band gaps, as shown in [link]. One is a direct gap (no change in momentum) and the other is indirect. In GaAs, the direct gap has lower energy than the indirect one (like in the inset) and so the transition is a radiative one. As we start adding phosphorous to the system, both the direct and indirect band gaps increase in energy. However, the direct gap energy increases faster with phosphorous fraction than does
the indirect one. At a mole fraction x of about 0.45, the gap energies cross over and the material goes from being a direct gap semiconductor to an indirect gap semiconductor. At x = 0.35 the band gap is about 1.97 eV (630 nm), and so we would only expect to get light up to the red using the GaAsP system for making LED's. Fortunately, people discovered that you could add an impurity (nitrogen) to the GaAsP system, which introduced a new level in the system. An electron could go from the indirect conduction band (for a mixture with a mole fraction greater than 0.45) to the nitrogen site, changing its momentum, but not its energy. It could then make a direct transition to the valence band, and light with colors all the way to the green became possible. The use of a nitrogen recombination center is depicted in the [link].
Conduction Band
= z a : 4 ] = — 5 =~ = = 3 o o2 O4 06 0.8 1 GaAs GaP
Mole Fraction Phosphorous
Band gap for the GaAsP system
Energy
hv \
Addition of a nitrogen recombination center to indirect GaAspP.
4 kaa
Momentum
If we want colors with wavelengths shorter than the green, we must abandon the GaAsP system and look for more suitable materials. A compound semiconductor made from the II-VI elements Zn and Se make up one promising system, and several research groups have successfully made blue and blue-green LEDs from ZnSe. SiC is another (weak) blue emitter which is commercially available on the market. Recently, workers at a tiny, unknown chemical company stunned the "display world" by announcing that they had successfully fabricated a blue LED using the II-V material GaN. A good blue LED was the "holy grail" of the display and CD ROM research community for a number of years. Obviously, adding blue to the already working green and red LED's completes the set of 3 primary colors necessary for a full-color flat panel display. Furthermore, using a blue LED or laser in a CD ROM would more than quadruple its data capacity, as bit diameter scales as A, and hence the area as A2.
Polymer Light Emitting Diodes
This module was developed as part of a Rice University course CHEM496: Chemistry of Electronic Materials. This module was prepared with the assistance of Pui Yee Hung.
Introduction
In 1990, electroluminescent (EL) from conjugated polymers was first reported by Burroughes et al. of Cambridge University. A layer of poly(para- phenylenevinylene) (PPV) was sandwiched between layers of indium tin oxide (ITO) and aluminum. When this device is under a 14 V dc bias, the PPV emits a yellowish-green light with a quantum efficiency of 0.05%. This report attracted a lot of attention, because the potential that polymer light emitting diodes (LEDs) could be inexpensively mass produced into large area display area. The processing steps in making polymer LEDs are readily scaleable. The industrial coating techniques is well developed to mass produce polymer layers of 100 nm thickness, and the device could be patterned onto large surface area by pixellation of metal.
Since the initial discovery, and increasing amount of researches has been performed, and significant progress has been made. In 1990 the polymer LED only emitted yellowish green color, now the emission color ranged from deep blue to near infra red. The efficiency of the multi-layer polymer LED even reached a quantum efficiency of >4% and the operating voltage has been reduced significantly. In term of efficiency, color selection and operating voltage, polymer LEDs have attained adequate levels for commercialization. But there are reliability problems that are symptomatic of any organic devices.
Device physics and materials science of polymer LEDs
A schematic diagram of a polymer LED is shown in [link]. A polymer LED can be divided into three different components:
A. Anode: the hole supplier, made of metal of high working function. Examples of the common anode are indium tin oxide (ITO), gold etc. The anode is usually transparent so that light can be emitted through.
B. Cathode: the electron supplier, made of metal of low working function. Examples of the common cathode are aluminum or calcium.
C. Polymer: made of conjugated polymer film with thickness of 100 nm.
Cathode (aluminum)
Anode (ITO)
Substrate (glass)
Emitted light
Schematic set-up of polymer LED.
When a polymer LED is under a direct current (dc) bias, holes are injected from the anode (ITO) and electrons are injected from the cathode (aluminum). Under the influences of the electrical field, the electrons and holes will migrate toward each other. When they recombine in the conjugated polymer layer, a bound excited states (excitons) will be formed. Some of the excitons (singlets) then decays in the conjugated polymer layer to emit light through the transparent substrates (glass). The emission color will be depended on the energy gap of the polymers. There is energy gap in a conjugated polymer because the m electron are not completely delocalized over the entire polymer chain. Instead there are alternate region in the polymer chain that has a higher electron density ({link]a). The chain length of this region is about 15-20 multiple bonds. The emission color can be controlled by tuning this energy band gap ((link]|b). It shows that bond alternation limits the extent of delocalization. [link] summarizes the structure and emission color of some common conjugated polymers.
(a)
Alternation of bond lengths along a conjugated polymer chain (a) results in a material with properties of a large band gap semiconductor (b), where CB is the conductive band gap, and VB is the valence band, and E, is the band
Polymer
PA
PDA
PPP
gap.
Chemical name
trans- polyacetylene
polydiacetylene
poly(para- phenylene)
Structure
m™1-Tt* energy gap (eV)
1.5
Emission peak (nm)
600
465
PPV Poly(para- Oat 2.5 565 phenylenevinylene) : (green) poly(2,5-dialkoxy- - 09
RO-PPV __p- +, (blue) 980 phenlyenevinylen) - :
; s 2.0
PT polythiophene an Th (red) Poly(3 ss “ye | 20
O yi 7} n .
ea alkythiophene) : (red) on Poly(2,5- :
raN thiophenevinylene) TUT, ae
i! PPy Polypyrrole an@r at 3.1 PAni Polyaniline so eo 3.2
Example of common conjugated polymers.
Approaches to improve the efficiency Efficiency for any LED is defined:
Next = Desc ~ int
where Nexis the external quantum efficiency, nj; is the internal efficiency (represents the fraction of injected carrier, usually electron, that is converted to photon), and n,,, is the escape efficiency (represent fraction of photons that can reach to the outside).
The most common way to improve the internal efficiency is to balance the number of electrons and holes which arrives at the polymer layer. Originally, there are more holes than electron that arrive of the polymer layer because conjugated polymers have a higher electron affinity, and as a consequence will favor the transport of hole than electron. There are two ways to maintains the balance:
1. Match the work function of electrode with the electron affinity and ionization potential of the polymer.
2. Tune the polymer’s electron affinity and ionization potential to match the work function of the electrode.
The escape efficiency is also important because a polymer LED is made up of layers of materials that have different refractive index, and some of the photon generated from the excition may be reflected at the boundary and trapped inside the device.
Improvement in internal quantum efficiency using low working function cathode
Conjugated polymer is electron rich, the mobility for hole is higher than electron, and more holes will arrive in the polymer layer than electrons. One way to increase the population of the electron is to use a lower working function metal as cathode. Braun and Heeger have replaced the aluminum cathode with calcium results in improved internal efficiency by a factor of ten, to 0.1%. This approach is direct and fast but low working function electrode like calcium will be oxidized easily and shorten the devices’ life.
Improvement in internal quantum efficiency using multiple polymer layers
A layer of poly[2,5-di(hexyloxy)cyanoterephthalylidene] (CN-PPYV, [link]) is coated on top of PPV to improve the transport and recombination of electron and holes ({link]).
CsH)30
Structure of CN-PPV.
Cathode (aluminum)
NOUN UN UN UN UN UN UN UN UN UN UN UNOS UN UN UN UN UN C4 OL OOOO LOE LOSS
Substrate (glass)
Anode (ITO)
Emitted light
Schematic representation of a CN-PPV and PPV multi-layer LED.
The nitrile group in the CN-PPV has two effect on the polymer.
1. It increases the electron affinity so electrons can travel more efficient from the aluminum to the polymer layer. And metal of relative high working function like aluminum and gold can be now be used as cathode instead of calcium.
2. It increases the binding energy of the occupied m and unoccupied m* state but maintain a similar m-1* gap. So when the PPV and CN-PPV is placed
together, holes and electron will be confined at the heterojunction.
The resulting energy levels are shown in [link].
PPV CN-PPV
Schematic energy-level diagram for a PPV and CN-PPV under foreword bias. Adapted from N. C. Greenham, S. C. Maratti, D. D. C. Bradley, R. H. Friend, and A. B. Holmes, Nature,1993, 365, 62.
The absolute energies of levels are not known accurately, but the diagram show the relative position of the HOMO and LUMO levels in the polymers, and the Fermi levels of the various possible metal contacts, the differences in electron affinity (AEA) and ionization potential (AIP) between PPV and CN-PPV are also shown ([link]).
At the polymers interface there is a sizable offset in the energies of HOMO and LUMO of PPV and CN-PPY, the holes transported from the ITO and the electrons transport from the aluminum will be confined in the heterojunction. The local charge density will be sufficiently high to ensure the holes and electrons will pass within a collision capture radius. This set-up increases the chance for an electrons to combine with holes to form an excition. In addition, the emission will be close to the junction, far away from the electrode junction which will quench the singlet excitions. The result is that a multi-layers LED has an internal quantum efficiency
of 10% and external quantum efficiency (for light emitted in foreword direction) of 25%.
Based on this approach, a couple of polymers have been developed or modified to produce the desirable emission color and processing property. The drawback of this method is that desirable properties may not be commentary to each other. For example, in MEH-PPV an alkoxy side group (RO) is introduced to PPV so that it can be dissolved in organic solvent. But the undesirable effect is that MEH-PPV is less thermally stable. Moreover in multiple layers LEDs, different polymer layers have different refractive indices and a fraction of the photons will undergo total internal reflection at the refractive boundaries and cannot escape as light. This problem can be overcome by Febry-Pert microcavity structure.
Improvement in external quantum efficiency using microcavity
Fabry-Perot resonant structures are also used in inorganic LED, and are is based on Fermi’s golden rule:
K,~ | <M > | tw
where M (the matrix element of the perturbation between final and initial states) depends on the nature of the material, and r;,) can be altered by changing the density of various density states, e.g. using a luminescent thin films to select certain value of V.
In building a microcavity for a polymer LED, the polymer is placed between two mirrors. ((link]), in which one of the mirrors is made up of aluminum, the other mirror (a Bragg Mirror) is form by epitaxial multilayer stacks of Si,Ny and SiOp.
Aluminum mirror
LEKI RAL AL REEL Polymer AN
Si,N, SiO,
Schematic set-up of micro-cavity.
Improvement in internal quantum efficiency: doping of polymer
Doping is a process that creates carrier by purposely introducing impurities and is very popular method in the semiconductor industry. However, this technique was not used in polymer LED until 1995, when a co-polymer polystyrene-poly(3- hexylthiphene) (PS-P3HT) was doped with FeCl; Doping of MEH-PPV with iodine has improved the efficiency by 200% and the polymer LED can be operated under both forward and reverse bias ([link]). The doping is accomplsihed by mixing 1 wt% MEH-PPV with 0.2 wt% Ip. The molar ratio of MEH-PPV to Ip is 5:1. That is a huge “doping “ ratio when you compare the doping concentration in the semiconductor.
Un-doped Doped Turn on voltage (V) 10 foreword 5, reversed 12
External efficiency (%) 4x 104 8x 10°
Results of iodine doping of an Al/MEH-PPV/ITO-based LED.
Polymer LEDs on a silicon substrate: an application advantage over inorganic LEDs
In the initial research polymer LEDs were in direct competition with the inorganic LEDs and tried to achieve the existing LED standard. This is a difficult task as polymer LEDs have a lower long term stability. However, there are some applications in which polymer LEDs have a clear advantage over their more traditional inorganic analogs. One of these is to incorporate LEDs with the silicon integrated circuits for inter-chip communication.
It is difficult to build inorganic LEDs on a silicon substrate, because of the thermal stress developing between the inorganic LED (usually a HI-V based device) and the silicon interface. But polymer LEDs offer a solution, since polymers can be easily spin-coated on the silicon. The operating voltage of polymer LED is less than 4 V, and the turn on voltage can be as low as 2 V. Together with a switching time of less than 50 ns, make polymer LED a perfect candidate.
Reliability and degradation of polymer LEDs
In terms of the efficiency, color selection, and driving voltage, polymer LED have attained adequate level for commercialization. However, the device lifetime is still far from satisfactory. Research into understanding the reliability and degredation mechanisms of polymer LEDs has generally been divided into two area:
1. Photo-degradation of polymer. 2. Interface degradation.
Polymer photo degradation
Photoluminescece (PL) studies of the photo-oxidation of PPV have been undertaken, since it is believes that EL is closely related with PL.
It was found that there is a rapid decay in emission when PPV is exposed to oxygen. Using time resolved FTIR spectroscopy an increase in the carbonyl signal and a decrease in C=C signal with time ((link]). It was suggested that the carbonyl
group has a strong electron affinity level to charge transfer between molecules segment in the polymer, thereby dissociating the excition and quenching the PL.
Change in absorbance (arb units)
1800 1700 1600 1500 , 1000 900
Frequency (cm!)
FTIR as a function of photo-oxidation of PPV. Adapted from M. Yan, L. J. Rothberg, F, Papadimitrakopoulos, M. E. Galvin and T.
M. Miller, Phys. Rev. Lett., 1994, 73, 744.
Similar research was performed by Cumpston and Jensen using BCHA-PPV and P30T ([link]) and exposing them to dry air in UV irradiation. In BCHA-PPV, there is an increase in carbonyl signal with time, while the P3OT remain intact. A mechanism proposed for the degradation of BCHA-PPV involves the transfer of energy from the excited triplet state of the PPV to oxygen to from singlet oxygen which attack the vinyl double bond in the PPV backbone. And P3O0T dose not has vinyl bond so it can resist the oxidation .
(a) (b)
Structure of (a) BCHA-PPV and (b) P30T.
The research described above was all performed on polymer thin films deposited on an inert surface. The presence of cathode and anode may also affect the oxidation mechanism. Scott et al. have taken IR spectra from a MEH-PPV LED in the absence of oxygen. They obtained similar result as in Yan et al., however, a decrease in ITO’s oxygen signal was noticed suggesting that the ITO anode acts like a oxygen reservoir and supplies the oxygen for the degradation process.
Polymer LED interface degradation
There are few interface degredation studies in polymer LEDs. One of them by Scott et al. took SEM image of the cathode from a failed polymer LED. The polymer LED used ITO as the anode, MEH-PPV as the polymer layer, and an aluminum calcium alloy as cathode. SEM images showed “craters” formed in the cathode. The craters are formed when the cathode metal is melted and pull away from the polymer layer. It was suggested that a high current density will generate heat and result in local hot spot. The temperature in the hot spot is high enough to melt the cathode. And when it melt, it will pull away from the polymer. This process will decrease the effective cathode area, and reduce the luminescence gradually.
Bibliography
D. R. Baigent, N. C. Greenham, J. Gruner, R. N. Marks, R. H. Friends, S. C. Moratti, and A. B. Holmes, Synth.Met., 1994, 67, 3.
B. H. Cumpston and K. F. Jensen, Synth. Met., 1995, 73, 195.
J. H. Burroughes, D. D. C. Bradley, A. R. Brown, R. N. Marks, K. Mackay, R. H. Friend, P. L. Burns, and A. B. Holmes, Nature, 1990, 347, 539.
N. C. Greenham, S. C.Maratti, D. D. C. Bradley, R. H. Friend, and A. B. Holmes, Nature, 1993, 365, 628.
J. Gruner, F. Cacialli, I. D. W. Samuel, R. H. Friend, Synth. Met, 1996, 76, 197.
M. Herold, J. Gmeiner, W. Riess, and M. Schwoerer, Synth. Met., 1996, 76, 109.
R. H. Jordan, A. Dodabalapur, L. J. Rothberg, and R. E. Slusher, Proceeding of SPIE, 1997, 3002, 92.
I. D. Parker and H. H. Kim, Appl. Phys. Lett., 1994, 64, 1774.
J. C. Scott, J. Kaufman, P. J. Brock, R. DiPietro, J. Salem, and J. A. Goitia, J. Appl. Phys., 1996, 79, 2745.
M. S. Weaver, D. G. Lidzaey, T. A. Fisher, M. A. Pate, D. O’Brien, A. Bleyer, A. Tajbakhsh, D. D. C. Bradley, M. S. Skolnick, and G. Hill, Thin solid Films, 1996, 273, 39.
M. Yan, L. J.Rothberg, F. Papadimitrakopoulos, M. E. Galvin, and T. M. Miller, Phys. Rev. Lett., 1994, 73, 744.
Laser LASER
Note:This module is adapted from the Connexions module entitled LASER by Bill Wilson.
What is the difference between an LED and a solid state laser? There are some differences, but both devices operate on the same principle of having excess electrons in the conduction band of a semiconductor, and arranging it so that the electrons recombine with holes in a radiative fashion, giving off light in the process. What is different about a laser? In an LED, the electrons recombine in a random and unorganized manner. They give off light by what is known as spontaneous emission, which simply means that the exact time and place where a photon comes out of the device is up to each individual electron, and things happen in a random way.
There is another way in which an excited electron can emit a photon however. If a field of light (or a set of photons) happens to be passing by an electron in a high energy state, that light field can induce the electron to emit an additional photon through a process called stimulated emission. The photon field stimulates the electron to emit its energy as an additional photon, which comes out in phase with the stimulating field. This is the big difference between incoherent light (what comes from an LED or a flashlight) and coherent light which comes from a laser. With coherent light, all of the electric fields associated with each phonon are all exactly in phase. This coherence is what enables us to keep a laser beam in tight focus, and to allow it to travel a large distance without much divergence or spreading out.
So how do we restructure an LED so that the light is generated by stimulated emission rather than spontaneous emission? Firstly, we build what is called a heterostructure. All this means is that we build up a sandwich of somewhat different materials, with different characteristics. In this case, we put two wide band-gap regions around a region with a
narrower band gap. The most important system where this is done is the AlGaAs/GaAs system. A band diagram for such a set up is shown in [link]. AlGaAs (pronounced "Al-Gas") has a larger band-gap then does GaAs. The potential "well" formed by the GaAs means that the electrons and holes will be confined there, and all of the recombination will occur in a very narrow strip. This greatly increases the chances that the carriers can interact, but we still need some way for the photons to behave in the proper manner. [Link] is a diagram of what a typical diode might look like. We have the active GaAs layer sandwich in-between the two heterostructure confinement layers, with a contact on top and bottom. On either end of the device, the crystal has been "cleaved" or broken along a crystal lattice plane. This results in a shiny "mirror-like" surface, which will reflect photons. The back surface (which we can not see here) is also cleaved to make a mirror surface. The other surfaces are purposely roughened so that they do not reflect light. Now let us look at the device from the side, and draw just the band diagram for the GaAs region ({link]). We start things off with an electron and hole recombining spontaneously. This emits a photon which heads towards one of the mirrors. As the photon goes by other electrons, however, it may cause one of them to decay by stimulated emission. The two (in phase) photons hit the mirror and are reflected and start back the other way . As they pass additional electrons, they stimulate them into a transition as well, and the optical field within the laser starts to build up. After a bit, the photons get down to the other end of the cavity. The cleaved facet, while it acts like a mirror, is not a perfect one. Some light is not reflected, but rather "leaks"; though, and so becomes the output beam from the laser. The details of finding what the ratio of reflected to transmitted light is will have to wait until later in the course when we talk about dielectric interfaces. The rest of the photons are reflected back into the cavity and continue to stimulate emission from the electrons which continue to enter the gain region because of the forward bias on the diode.
n-AlGaAs GaAs p-AlGaAs
The band diagram for a double heterostructure GaAs/AlGaAs laser.
A schematic diagram of a typical laser diode.
Build up of a photon field in a laser diode.
In reality, the photons do not move back and forth in a big "clump" as we have described here, rather they are distributed uniformly along the gain region ([link]). The field within the cavity will build up to the point where the loss of energy by light leaking out of the mirrors just equals the rate at which energy is replaced by the recombining electrons.
OOQOOQ90 O00 OO
y yy
g Qin
y ve OOOO OOOO 0000
Output coupling in a diode laser.
Solar Cells
Note:This module is adapted from the Connexions module entitled Solar Cells by Bill Wilson.
Now let us look at the opposite process of light generation for a moment. Consider the following situation where we have just a plain old normal p-n junction, only now, instead of applying an external voltage, we imagine that the junction is being illuminated with light whose photon energy is greater than the band-gap ({link]a). In this situation, instead of recombination, we will get photo-generation of electron hole pairs. The photons simply excite electrons from the full states in the valence band, and "kick" them up into the conduction band, leaving a hole behind. This is similiar to the thermal excitation process. As can be seen from [link]b, this creates excess electrons in the conduction band in the p-side of the diode, and excess holes in the valence band of the n-side. These carriers can diffuse over to the junction, where they will be swept across by the built-in electric field in the depletion region. If we were to connect the two sides of the diode together with a wire, a current would flow through that wire as a result of the electrons and holes which move across the junction.
A schematic representation of a p-n diode under illlumination.
Which way would the current flow? A quick look at [link]c shows that holes (positive charge carriers) generated on the n-side will float up to the p-side as they go across the junction. Hence positive current must be coming out of the anode, or p-side of the junction. Likewise, electrons generated on the p-side will fall down the junction potential, and come out the n-side, but since they have negative charge, this flow represents current going into the cathode. We have constructed a photovoltaic diode, or solar cell. [link] is a picture of what this would look like schematically. We might like to consider the possibility of using this device as a source of energy, but the way we have things set up now, since the voltage across the diode is zero, and since power equals current times voltage, we see that we are getting nada from the cell. What we need, obviously, is a load resistor, so let's put one in. It should be clear from [link] that the photo current flowing through the load resistor will develop a voltage which it biases the diode in the forward direction, which, of course will cause current to flow back into
the anode. This complicates things, it seems we have current coming out of the diode and current going into the diode all at the same time! How are we going to figure out what. what is going on?
=
photon flux
IK
Schematic representation of a photovoltaic cell.
+
€ Vv = out
Photovoltaic cell with a load resistor.
The answer is to make a model. The current which arises due to the photon flux can be conveniently represented as a current source. We can leave the diode as a diode, and we have the circuit shown in [link]. Even though we show I,,; coming out of the device, we know by the usual polarity convention that when we define V,,; as being positive at the top, then we should show the current for the photovoltaic, I,y as current going into the top, which is what was done in [Link]. Note that Ipy = Idiode - Iphoto, $0 all we need to do is to subtract the two currents; we do this graphically in [link].
Note that we have numbered the four quadrants in the I-V plot of the total PV current. In quadrant I and III, the product of I and V is a positive number, meaning that power is being dissipated in the cell. For quadrant IT and IV, the product of I and V is negative, and so we are getting power from the device. Clearly we want to operate in quadrant IV. In fact, without the addition of an external battery or current source, the circuit, will only run in the IV'th quadrant. Consider adjusting R;,, the load resistor from 0 (a short) to co (an open). With R;,, we would be at point A on [link]. As Rj, starts to increase from zero, the voltage across both the diode and the resistor will start to increase also, and we will move to point B, say. As Ry, gets bigger and bigger, we keep moving along the curve until, at point C, where Ry, is an open and we have the maximum voltage across the device, but, of
course, no current coming out! lout ————_»
A model of a PV cell.
| diode | photo
| pv
Combining the diode and the current source.
Power is VJ so at B for instance, the power coming out would be represented by the area enclosed by the two dotted lines and the coordinate axes. Someplace about where I have point B would be where we would be getting the most power out of out solar cell.
[link] shows you what a real solar cell would look like. They are usually made from a complete wafer of silicon, to maximize the usable area. A shallow (0.25 tm) junction is made on the top, and top contacts are applied as stripes of metal conductor as shown. An anti-reflection (AR) coating is applied on top of that, which accounts for the bluish color which a typical solar cell has ({link]).
Solar Cell Wafer
top contact AR coating
a
back contact Side View
A schematic diagram of a real solar cell.
A solar cell showing the blue tint due to the AR coating.
The solar power flux on the earth's surface is (conveniently) about 1 kW/m? or 100 mW/cm-. So if we made a solar cell from a 4 inch diameter wafer (typical) it would have an area of about 81cm? and so would be receiving a flux of about 8.1 Watts. Typical cell efficiencies run from about 10% to maybe 15% unless special (and costly) tricks are made. This means that we will get about 1.2 Watts out from a single wafer. Looking at B on 2.59 we could guess that Vout will be about 0.5 to 0.6 volts, thus we could expect to get maybe around 2.5 amps from a 4 inch wafer at 0.5 volts with 15% efficiency under the illumination of one sun.
Properties of Gallium Arsenide
Gallium: the element
The element gallium was predicted, as eka-aluminum, by Mendeleev in 1870, and subsequently discovered by Lecog de Boisbaudran in 1875; in fact de Boisbaudran had been searching for the missing element for some years, based on his own independent theory. The first experimental indication of gallium came with the observation of two new violet lines in the spark spectrum of a sample deposited on zinc. Within a month of these initial results de Boisbaudran had isolated 1 g of the metal starting from several hundred kilograms of crude zinc blende ore. The new element was named in honor of France (Latin Gallia), and the striking similarity of its physical and chemical properties to those predicted by Mendeleev ([link]) did much to establish the general acceptance of the periodic Law; indeed, when de Boisbaudran first stated that the density of Ga was 4.7 g/cm? rather than the predicted 5.9 g/cm?, Mendeleev wrote to him suggesting that he redetermine the value (the correct value is 5.904 g/cm?).
Mendeleev's Observed properties of
Property prediction (1871) for gallium (discovered eka-aluminum, M 1875)
eee ca. 68 69.72
weight
Density,
ee 5.9 5.904 g.cm Mens Low 29.78
point
Vapor Non-volatile 10° mmHg, 1000 °C pressure
Valence 3 3 Oxide M,O3 GayO3 Density of oxide 5.5 5.88 (g/cm?) : _ shoul d dissolve Ga metal dissolves Properties slowly in acids and
slowly in acids and
of metal alkalis and be stable in Albalie end Ge Seble ack
alr
Properties M(OH)3 should of dissolve in both acids hydroxide and alkalis
Ga(OH)3 dissolves in both acids and alkalis
M salts will tend to Ga salts readily
form basic salts; the hydrolyze and form basic
sulfate should form salts; alums are known; Properties alums; M>S3 should be GaS3 can be precipitated of salts precipitated by H2S or under special conditions
(NH,)2S; anhydrous by H2S or (NH,)2S,
MCl3 should be more anhydrous GaCl3 is more
volatile than ZnCl» volatile than ZnCl.
Comparison of predicted and observed properties of gallium.
Gallium has a beautiful silvery blue appearance; it wets glass, porcelain, and most other surfaces (except quartz, graphite, and Teflon®) and forms a brilliant mirror when painted on to glass. The atomic radius and first ionization potential of gallium are almost identical with those of aluminum and the two elements frequently resemble each other in chemical properties. Both are amphoteric, but gallium is less electropositive as indicated by its
lower electrode potential. Differences in the chemistry of the two elements can be related to the presence of a filled set of 3d orbitals in gallium.
Gallium is very much less abundant than aluminum and tends to occur at low concentrations in sulfide minerals rather than as oxides, although gallium is also found associated with aluminum in bauxite. The main source of gallium is as a by-product of aluminum refining. At 19 ppm of the earth's crust, gallium is about as abundant as nitrogen, lithium and lead; it is twice as abundant as boron (9 ppm), but is more difficult to extract due to the lack of any major gallium-containing ore. Gallium always occurs in association either with zinc or germanium, its neighbors in the periodic table, or with aluminum in the same group. Thus, the highest concentrations (0.1 - 1%) are in the rare mineral germanite (a complex sulfide of Zn, Cu, Ge, and As); concentrations in sphalerite (ZnS), bauxite, or coal, are a hundred-fold less.
Gallium pnictides
Gallium's main use is in semiconductor technology. For example, GaAs and related compounds can convert electricity directly into coherent light (laser diodes) and is employed in electroluminescent light-emitting diodes (LED's); it is also used for doping other semiconductors and in solid-state devices such as heterojunction bipolar transistors (HBTs) and high power high speed metal semiconductor field effect transistors (MESFETs). The compound MgGa>O, is used in ultraviolet-activated powders as a brilliant green phosphor used in Xerox copying machines. Minor uses are as high- temperature liquid seals, manometric fluids and heat-transfer media, and for low-temperature solders.
Undoubtedly the binary compounds of gallium with the most industrial interest are those of the Group 15 (V) elements, GaE (E = N, P, As, Sb). The compounds which gallium forms with nitrogen, phosphorus, arsenic, and antimony are isoelectronic with the Group 14 elements. There has been considerable interest, particularly in the physical properties of these compounds, since 1952 when Welker first showed that they had semiconducting properties analogous to those of silicon and germanium.
Gallium phosphide, arsenide, and antimonide can all be prepared by direct reaction of the elements; this is normally done in sealed silica tubes or in a graphite crucible under hydrogen. Phase diagram data is hard to obtain in the gallium-phosphorus system because of loss of phosphorus from the bulk material at elevated temperatures. Thus, GaP has a vapor pressure of more than 13.5 atm at its melting point; as compared to 0.89 atm for GaAs. The physical properties of these three compounds are compared with those of the nitride in [link]. All three adopt the zinc blende crystal structure and are more highly conducting than gallium nitride.
Property GaN GaP GaAs GaSb Mens > 1250 (dec) 1350 1240 712 point (°C) Density
3 ca. 6.1 4.138 9.3176 9.6137 (g/cm”) Crystal Wiirtzite zinc zinc zinc structure blende blende blende Cell dimen. a= 3.187,c= a= a= a= (A)? 5.186 5.4505 9.6532 6.0959 Renecuve 2.35 3.178 3.666 4.388 index k (ohm7!cm 9 4an7 10°? - 10 i 10° - 10 102 ia 6-13 Band eae 3.44 2.24 1.424 0.71
(ev)
Physical properties of 13-15 compound semiconductors. a Values given for 300 K. b Dependent on photon energy; values given for 1.5 eV incident photons. c Dependent on temperature; values given for 300 K.
Gallium arsenide versus silicon
Gallium arsenide is a compound semiconductor with a combination of physical properties that has made it an attractive candidate for many electronic applications. From a comparison of various physical and electronic properties of GaAs with those of Si ({link]) the advantages of GaAs over Si can be readily ascertained. Unfortunately, the many desirable properties of gallium arsenide are offset to a great extent by a number of undesirable properties, which have limited the applications of GaAs based devices to date.
Properties GaAs Si Formula weight 144.63 28.09 Crystal structure zinc blende diamond Lattice constant 5.6532 5.43095 Melting point (°C) 1238 1415 Density (g/cm?) 5.32 2.328 Thermal conductivity (W/cm.K) 0.46 1.5 Band gap (eV) at 300 K 1.424 1.12
Intrinsic carrier conc. (cm™) 1.79 x 10° 1.45 x 10/0
Intrinsic resistivity (ohm.cm) 108 2.3.x 10°
Breakdown field (V/cm) 4x 10° 3x 10° Minority carrier lifetime (s) 10" 2.5x 10° Mobility (cm?/V.s) 8500 1500
Comparison of physical and semiconductor properties of GaAs and Si.
Band gap
The band gap of GaAs is 1.42 eV; resulting in photon emission in the infra- red range. Alloying GaAs with Al to give Al,Ga,_,As can extend the band gap into the visible red range. Unlike Si, the band gap of GaAs is direct, i.e., the transition between the valence band maximum and conduction band minimum involves no momentum change and hence does not require a collaborative particle interaction to occur. Photon generation by inter-band radiative recombination is therefore possible in GaAs. Whereas in Si, with an indirect band-gap, this process is too inefficient to be of use. The ability to convert electrical energy into light forms the basis of the use of GaAs, and its alloys, in optoelectronics; for example in light emitting diodes (LEDs), solid state lasers (light amplification by the stimulated emission of radiation).
A significant drawback of small band gap semiconductors, such as Si, is that electrons may be thermally promoted from the valence band to the conduction band. Thus, with increasing temperature the thermal generation of carriers eventually becomes dominant over the intentionally doped level of carriers. The wider band gap of GaAs gives it the ability to remain ‘intentionally’ semiconducting at higher temperatures; GaAs devices are generally more stable to high temperatures than a similar Si devices.
Carrier density
The low intrinsic carrier density of GaAs in a pure (undoped) form indicates that GaAs is intrinsically a very poor conductor and is commonly referred to as being semi-insulating. This property is usually altered by adding dopants of either the p- (positive) or n- (negative) type. This semi- insulating property allows many active devices to be grown on a single substrate, where the semi-insulating GaAs provides the electrical isolation of each device; an important feature in the miniaturization of electronic circuitry, i.e., VLSI (very-large-scale-integration) involving over 100,000 components per chip (one chip is typically between 1 and 10 mm square).
Electron mobility
The higher electron mobility in GaAs than in Si potentially means that in devices where electron transit time is the critical performance parameter, GaAs devices will operate with higher response times than equivalent Si devices. However, the fact that hole mobility is similar for both GaAs and Si means that devices relying on cooperative electron and hole movement, or hole movement alone, show no improvement in response time when GaAs based.
Crystal growth
The bulk crystal growth of GaAs presents a problem of stoichiometric control due the loss, by evaporation, of arsenic both in the melt and the growing crystal (> ca. 600 °C). Melt growth techniques are, therefore, designed to enable an overpressure of arsenic above the melt to be maintained, thus preventing evaporative losses. The loss of arsenic also negates diffusion techniques commonly used for wafer doping in Si technology; since the diffusion temperatures required exceed that of arsenic loss.
Crystal Stress
The thermal gradient and, hence, stress generated in melt grown crystals have limited the maximum diameter of GaAs wafers (currently 6" diameter compared to over 12" for Si), because with increased wafer diameters the thermal stress generated dislocation (crystal imperfections) densities eventually becomes unacceptable for device applications.
Physical strength
Gallium arsenide single crystals are very brittle, requiring that considerably thicker substrates than those employed for Si devices.
Native oxide
Gallium arsenide's native oxide is found to be a mixture of non- stoichiometric gallium and arsenic oxides and elemental arsenic. Thus, the electronic band structure is found to be severely disrupted causing a breakdown in 'normal' semiconductor behavior on the GaAs surface. As a consequence, the GaAs MISFET (metal-insulator-semiconductor-field- effect-transistor) equivalent to the technologically important Si based MOSFET (metal-oxide-semiconductor-field-effect-transistor) is, therefore, presently unavailable.
The passivation of the surface of GaAs is therefore a key issue when endeavoring to utilize the FET technology using GaAs. Passivation in this discussion means the reduction in mid-gap band states which destroy the semiconducting properties of the material. Additionally, this also means the production of a chemically inert coating which prevents the formation of additional reactive states, which can effect the properties of the device.
Bibliography
e S.K. Ghandhi, VLSI Fabrication Principles: Silicon and Gallium Arsenide. Wiley-Interscience, New York, (1994).
e Properties of Gallium Arsenide. Ed. M. R. Brozel and G. E. Stillman. 3rd Ed. Institution of Electrical Engineers, London (1996).
Synthesis and Purification of Bulk Semiconductors
Introduction
The synthesis and purification of bulk polycrystalline semiconductor material represents the first step towards the commercial fabrication of an electronic device. This polycrystalline material is then used as the raw material for the formation of single crystal material that is processed to semiconductor wafers. The strong influence on the electric characteristics of a semiconductors exhibited by small amounts of some impurities requires that the bulk raw material be of very high purity (> 99.9999%). Although some level of purification is possible during the crystallization process it is important to use as high a purity starting material as possible. While a wide range of substrate materials are available from commercial vendors, silicon and GaAs represent the only large-scale commercial semiconductor substrates, and thus the discussion will be limited to the synthesis and purification of these materials.
Silicon
Following oxygen (46%), silicon (L. silicis flint) is the most abundant element in the earth's crust (28%). However, silicon does not occur in its elemental form, but as its oxide (SiO>) or as silicates. Sand, quartz, amethyst, agate, flint, and opal are some of the forms in which the oxide appears. Granite, hornblende, asbestos, feldspar, clay and mica, etc. are a few of the numerous silicate minerals. With such boundless supplies of the raw material, the costs associated with the production of bulk silicon is not one of abstraction and conversion of the oxide(s), but of purification of the crude elemental silicon. While 98% elemental silicon, known as metallurgical-grade silicon (MGS), is readily produced on a large scale, the requirements of extreme purity for electronic device fabrication require additional purification steps in order to produce electronic-grade silicon (EGS). Electronic-grade silicon is also known as semiconductor-grade silicon (SGS). In order for the purity levels to be acceptable for subsequent crystal growth and device fabrication, EGS must have carbon and oxygen impurity levels less than a few parts per million (ppm), and metal impurities at the parts per billion (ppb) range or lower. [link] and [link] give typical
impurity concentrations in MGS and EGS, respectively. Besides the purity, the production cost and the specifications must meet the industry desires.
Element Concentration Element Concentration (ppm) (ppm)
aluminum 1000-4350 manganese 90-120
boron 40-60 molybdenum < 20
calcium 245-500 nickel 10-105
chromium 50-200 phosphorus 20-50
copper 15-45 titanium 140-300
iron 1550-6500 vanadium 50-250
magnesium 10-50 zirconium 20
Typical impurity concentrations found in metallurgical-grade silicon (MGS).
Elenite Concentration Element Concentration (ppb) (ppb) pene < 0.001 gold < 0.00001
antimony < 0.001 iron 0.1-1.0
boron < 0.1 nickel 0.1-0.5
carbon 100-1000 oxygen 100-400 chromium < 0.01 phosphorus < 0.3 cobalt 0.001 silver 0.001 copper 0.1 zinc <0.1
Typical impurity concentrations found in electronic-grade silicon (EGS).
Metallurgical-grade silicon (MGS)
The typical source material for commercial production of elemental silicon is quartzite gravel; a relatively pure form of sand (SiO>). The first step in the synthesis of silicon is the melting and reduction of the silica in a submerged- electrode arc furnace. An example of which is shown schematically in [link], along with the appropriate chemical reactions. A mixture of quartzite gravel and carbon are heated to high temperatures (ca. 1800 °C) in the furnace. The carbon bed consists of a mixture of coal, coke, and wood chips. The latter providing the necessary porosity such that the gases created during the reaction (SiO and CO) are able to flow through the bed.
quartzite, coal submerged electrode
coke, wood chips CO, SiO, H,O naan ee ae alias Si0+2C >" form SiC from SiO and C melt SiO, KG co
te,
SiC + SiO, > Si+ SiO +CO
li id ili - re discharge of MGSC—>
Schematic of submerged-electrode arc furnace for the production of metallurgical-grade silicon (MGS).
The overall reduction reaction of SiO, is expressed in [link], however, the reaction sequence is more complex than this overall reaction implies, and involves the formation of SiC and SiO intermediates. The initial reaction between molten SiO» and C ([link]) takes place in the arc between adjacent electrodes, where the local temperature can exceed 2000 °C. The SiO and CO thus generated flow to cooler zones in the furnace where SiC is formed ({link]), or higher in the bed where they reform SiO, and C ([link]). The SiC reacts with molten SiO> ({link]) producing the desired silicon along with SiO and CO. The molten silicon formed is drawn-off from the furnace and
solidified. Equation:
SiO,(liquid) + 2 C(solid) > Si(liquid) + 2 CO (gas)
Equation:
>1700 °C Si0Q,+2C == Si0+CO <1600 °C
Equation: SiO0+2C > SiC +CO (1600 - 1700 °C) Equation:
SiC + SiO, > Si+ SiO + CO
The as-produced MGS is approximately 98-99% pure, with the major impurities being aluminum and iron ({link]), however, obtaining low levels of boron impurities is of particular importance, because it is difficult to remove and serves as a dopant for silicon. The drawbacks of the above process are that it is energy and raw material intensive. It is estimated that the production of one metric ton (1,000 kg) of MGS requires 2500-2700 kg quartzite, 600 kg charcoal, 600-700 kg coal or coke, 300-500 kg wood chips, and 500,000 kWh of electric power. Currently, approximately 500,000 metric tons of MGS are produced per year, worldwide. Most of the production (ca. 70%) is used for metallurgical applications (e.g., aluminum- silicon alloys are commonly used for automotive engine blocks) from whence its name is derived. Applications in a variety of chemical products such as silicone resins account for about 30%, and only 1% or less of the total production of MGS is used in the manufacturing of high-purity EGS for the electronics industry. The current worldwide consumption of EGS is approximately 5 x 10° kg per year.
Electronic-grade silicon (EGS)
Electronic-grade silicon (EGS) is a polycrystalline material of exceptionally high purity and is the raw material for the growth of single-crystal silicon. EGS is one of the purest materials commonly available, see [link]. The formation of EGS from MGS is accomplished through chemical purification
processes. The basic concept of which involves the conversion of MGS to a volatile silicon compound, which is purified by distillation, and subsequently decomposed to re-form elemental silicon of higher purity (i.e., EGS). Irrespective of the purification route employed, the first step is physical pulverization of MGS followed by its conversion to the volatile silicon compounds.
A number of compounds, such as monosilane (SiH,), dichlorosilane (SiH»Cl)), trichlorosilane (SiHCl3), and silicon tetrachloride (SiCl,), have been considered as chemical intermediates. Among these, SiHCl3 has been used predominantly as the intermediate compound for subsequent EGS formation, although SiH, is used to a lesser extent. Silicon tetrachloride and its lower chlorinated derivatives are used for the chemical vapor deposition (CVD) growth of Si and SiO>. The boiling points of silane and its chlorinated products ([link]) are such that they are conveniently separated from each other by fractional distillation.
Compound Boiling point (°C) SiH, -112.3
SiH3Cl -30.4
SiH>Cl> 8.3
SiHCl3 31.5
SiCl, 57.6
Boiling points of silane and chlorosilanes at 760 mmHg (1 atmosphere).
The reasons for the predominant use of SiHCl3 in the synthesis of EGS are as follows:
1. SiHCl; can be easily formed by the reaction of anhydrous hydrogen chloride with MGS at reasonably low temperatures (200 - 400 °C);
2. it is liquid at room temperature so that purification can be accomplished using standard distillation techniques;
3. it is easily handled and if dry can be stored in carbon steel tanks;
4. its liquid is easily vaporized and, when mixed with hydrogen it can be transported in steel lines without corrosion;
5. it can be reduced at atmospheric pressure in the presence of hydrogen; 6. its deposition can take place on heated silicon, thus eliminating contact with any foreign surfaces that may contaminate the resulting silicon;
and 7. it reacts at lower temperatures (1000 - 1200 °C) and at faster rates than does SiCly.
Chlorosilane (Seimens) process
Trichlorosilane is synthesized by heating powdered MGS with anhydrous hydrogen chloride (HCl) at around 300 °C in a fluidized-bed reactor, [link]. Equation:
ca. 300 °C Si(solid) + 3 HCl(gas) == SiHCI,(vapor) + H, (gas) >900 °C
Since the reaction is actually an equilibrium and the formation of SiHCl3 highly exothermic, efficient removal of generated heat is essential to assure a maximum yield of SiHCl3. While the stoichiometric reaction is that shown in Eq. 5, a mixture of chlorinated silanes is actually prepared which must be separated by fractional distillation, along with the chlorides of any impurities. In particular iron, aluminum, and boron are removed as FeCl; (b.p. = 316 °C), AICI, (m.p. = 190 °C subl.), and BCI (b.p. = 12.65 °C), respectively. Fractional distillation of SiHCl3 from these impurity halides result in greatly increased purity with a concentration of electrically active impurities of less than 1 ppb.
EGS is prepared from purified SiHCl3 in a chemical vapor deposition (CVD) process similar to the epitaxial growth of Si. The high-purity SiHCl3 is vaporized, diluted with high-purity hydrogen, and introduced into the Seimens deposition reactor, shown schematically in [link]. Within the reactor, thin silicon rods called slim rods (ca. 4 mm diameter) are supported by graphite electrodes. Resistance heating of the slim rods causes the decomposition of the SiHCl3 to yield silicon, as described by the reverse reaction shown in Eq. 5.
<—— reaction chamber
Si-bridge
Si-slim rod
Schematic representation of a Seimens deposition reactor.
The shift in the equilibrium from forming SiHCl; from Si at low temperature, to forming Si from SiHC]l; at high temperature is as a consequence of the temperature dependence ({link]) of the equilibrium constant ([link], where p = partial pressure) for [link]. Since the formation of SiHCl3 is exothermic, i.e., AH < 0, an increase in the temperature causes the partial pressure of SiHCls to decrease. Thus, the Siemens process is typically run at ca. 1100 °C, while the reverse fluidized bed process is carried out at 300 °C.
Equation:
InK, = -AH RT
Equation:
Psincl, °H,
PHC
The slim rods act as a nucleation point for the deposition of silicon, and the resulting polycrystalline rod consists of columnar grains of silicon (polysilicon) grown perpendicular to the rod axis. Growth occurs at less than 1 mm per hour, and after deposition for 200 to 300 hours high-purity (EGS) polysilicon rods of 150-200 mm in diameter are produced. For subsequent float-zone refining the polysilicon EGS rods are cut into long cylindrical rods. Alternatively, the as-formed polysilicon rods are broken into chunks for single crystal growth processes, for example Czochralski melt growth.
In addition to the formation of silicon, the HCl] coproduct reacts with the SiHCl3 reactant to form silicon tetrachloride (SiCl4) and hydrogen as major byproducts of the process, [link]. This reaction represents a major disadvantage with the Seimens process: poor efficiency of silicon and chlorine consumption. Typically, only 30% of the silicon introduced into CVD reactor is converted into high-purity polysilicon.
Equation:
HCl + SiHCl, > SiC, +H,
In order to improve efficiency the HCl, SiCl,, H», and unreacted SiHCl3 are separated and recovered for recycling. [link] illustrates the entire chlorosilane process starting with MGS and including the recycling of the reaction byproducts to achieve high overall process efficiency. As a consequence, the production cost of high-purity EGS depends on the commercial usefulness of the byproduct, SiCl,. Additional disadvantages of the Seimens process are derived from its relatively small batch size, slow
growth rate, and high power consumption. These issues have lead to the investigation of alternative cost efficient routes to EGS.
Si(MGS) HC] SiC, HCl
hydrochlorination chlorosilane| Hz, of Si (MGS) recovery fluidized bed
reactor SiHCl,
hydrogen and HCl revovery
SiHCl, (SIH, Cly.x)
H2
SiHCls vaporization H> and chemical vapor deposition
SiHCls
distillation
low boiling SiCly impurities Si (EGS)
Schematic representation of the reaction pathways for the formation of EGS using the chlorosilane process.
Silane process
An alternative process for the production of EGS that has begun to receive commercial attention is the pyrolysis of silane (SiH). The advantages of producing EGS from SiH, instead of SiHCls are potentially lower costs associated with lower reaction temperatures, and less harmful byproducts. Silane decomposes < 900 °C to give silicon and hydrogen, [Link]. Equation:
SiH,(vapor) > Si(solid) + 2 H, (gas)
Silane may be prepared by a number of routes, each having advantages with respect to purity and production cost. The simplest process involves the direct reaction of MGS powders with magnesium at 500 °C in a hydrogen atmosphere, to form magnesium silicide (Mg»Si). The magnesium silicide is then reacted with ammonium chloride in liquid ammonia below 0 °C, [link]. Equation:
Mg,Si+4NH,Cl > SiH, +2 MgCl, +5 NH,
This process is ideally suited to the removal of boron impurities (a p-type dopant in Si), because the diborane (B>H¢) produced during the reaction forms the Lewis acid-base complex, H3B(NH3), whose volatility is sufficiently lower than SiHy, allowing for the purification of the latter. It is possible to prepare EGS with a boron content of < 20 ppt using SiH, synthesized in this manner. However, phosphorus (another dopant) in the form of PH3 may be present as a contaminant requiring subsequent purification of the SiHy.
Alternative routes to SiH, involve the chemical reduction of SiCl, by either lithium hydride ([link]), lithium aluminum hydride ([link]), or via hydrogenation in the presence of elemental silicon ([link] - [link]). The hydride reduction reactions may be carried-out on relatively large scales (ca. 50 kg), but only batch processes. In contrast, Union Carbide has adapted the hydrogenation to a continuous process, involving disproportionation reactions of chlorosilanes ([link] - [link]) and the fractional distillation of silane ({link]).
Equation:
SiCl,+4LiH > SiH, +4 LiCl Equation: SiCl, +4 LiAIH, > SiH,+LiCl + AICI,
Equation:
SiCl, +2 H, + Si(98%) > 4 SiHCI, Equation:
2 SiHCI, > SiH,Cl, + SiCl, Equation:
3 SiH,Cl, > SiH,CI +2 SiHCI, Equation:
2 SiH,Cl > SiH, + SiH,Cl,
Pyrolysis of silane on resistively heated polysilicon filaments at 700-800 °C yields polycrystalline EGS. As noted above, the EGS formed has remarkably low boron impurities compared with material prepared from trichlorosilane. Moreover, the resulting EGS is less contaminated with transition metals from the reactor container because SiH, decomposition does not cause as much of a corrosion problem as is observed with halide precursor compounds.
Granular polysilicon deposition
Both the chlorosilane (Seimens) and silane processes result in the formation of rods of EGS. However, there has been increased interest in the formation of granular polycrystalline EGS. This process was developed in 1980’s, and relies on the decomposition of SiH, in a fluidized-bed deposition reactor to
produce free-flowing granular polysilicon.
Tiny silicon particles are fluidized in a SiH4/Hp flow, and act as seed crystal onto which polysilicon deposits to form free-flowing spherical particles. The size distribution of the particles thus formed is over the range from 0.1 to 1.5 mm in diameter with an average particle size of 0.7 mm. The fluidized-bed
seed particles are originally made by grinding EGS in a ball (or hammer) mill and leaching the product with acid, hydrogen peroxide, and water. This process is time-consuming and costly, and tended to introduce undesirable impurities from the metal grinders. In a new method, large EGS particles are fired at each other by a high-speed stream of inert gas and the collision breaks them down into particles of suitable size for a fluidized bed. This process has the main advantage that it introduces no foreign materials and requires no leaching or other post purification.
The fluidized-bed reactors are much more efficient than traditional rod reactors as a consequence of the greater surface area available during CVD growth of silicon. It has been suggested that fluidized-bed reactors require ‘7, to /19 the energy, and half the capital cost of the traditional process. The quality of fluidized-bed polysilicon has proven to be equivalent to polysilicon produced by the conventional methods. Moreover, granular EGS in a free-flowing form, and with high bulk density, enables crystal growers to obtain the high, reproducible production yields out of each crystal growth run. For example, in the Czochralski crystal growth process, crucibles can be quickly and easily filled to uniform loading with granular EGS, which typically exceed those of randomly stacked polysilicon chunks produced by the Siemens silane process.
Zone refining
The technique of zone refining is used to purify solid materials and is commonly employed in metallurgical refining. In the case of silicon may be used to obtain the desired ultimate purity of EGS, which has already been purified by chemical processes. Zone refining was invented by Pfann, and makes use of the fact that the equilibrium solubility of any impurity (e.g., Al) is different in the solid and liquid phases of a material (e.g., Si). For the dilute solutions, as is observed in EGS silicon, an equilibrium segregation coefficient (kp) is defined by kg = C./C), where C, and C; are the equilibrium concentrations of the impurity in the solid and liquid near the interface, respectively.
If kp is less than 1 then the impurities are left in the melt as the molten zone is moved along the material. In a practical sense a molten zone is established in a solid rod. The zone is then moved along the rod from left to right. If k < 1 then the frozen part left on the trailing edge of the moving molten zone will be purer than the material that melts in on the right-side leading edge of the moving molten zone. Consequently the solid to the left of the molten zone is purer than the solid on the right. At the completion of the first pass the impurities become concentrated to the right of the solid sample. Repetition of the process allows for purification to exceptionally high levels. [link]. lists the equilibrium segregation coefficients for common impurity and dopant elements in silicon; it should be noted that they are all less than 1.
Element ko Element ko aluminum 0.002 iron 8x 10° boron 0.8 oxygen 0.25 carbon 0.07 phosphorus 0.35 copper 4x 10° antimony 0.023
Segregation coefficients for common impurity and dopant elements in silicon.
Gallium arsenide
In contrast to electronic grade silicon (EGS), whose use is a minor fraction of the global production of elemental silicon, gallium arsenide (GaAs) is produced exclusively for use in the semiconductor industry. However, arsenic and its compounds have significant commercial applications. The
main use of elemental arsenic is in alloys of Pb, and to a lesser extent Cu, while arsenic compounds are widely used in pesticides and wood preservatives and the production of bottle glass. Thus, the electronics industry represents a minor user of arsenic. In contrast, although gallium has minor uses as a high-temperature liquid seal, manometric fluids and heat transfer media, and for low temperature solders, its main use is in semiconductor technology.
Isolation and purification of gallium metal
At 19 ppm gallium (L. Gallia, France) is about as abundant as nitrogen, lithium and lead; it is twice as abundant as boron (9 ppm), but is more difficult to extract due to the lack of any major gallium-containing ore. Gallium always occurs in association either with zinc or germanium, its neighbors in the periodic table, or with aluminum in the same group. Thus, the highest concentrations (0.1-1%) are in the rare mineral germanite (a complex sulfide of Zn, Cu, Ge, and As), while concentrations in sphalerite (ZnS), diaspore [AlO(OH)], bauxite, or coal, are a hundred-fold less. Industrially, gallium was originally recovered from the flue dust emitted during sulfide roasting or coal burning (up to 1.5% Ga), however, it is now obtained as side product of vast aluminum industry and in particular from the Bayer process for obtaining alumina from bauxite.
The Bayer process involves dissolution of bauxite, AlIO,OH3_>,, in aqueous NaOH, separation of insoluble impurities, partial precipitation of the trihydrate, Al(OH)3, and calcination at 1,200 °C. During processing the alkaline solution is gradually enriched in gallium from an initial weight ratio Ga/Al of about 1/5000 to about 1/300. Electrolysis of these extracts with a Hg cathode results in further concentration, and the solution of sodium gallate thus formed is then electrolyzed with a stainless steel cathode to give Ga metal. Since bauxite contains 0.003-0.01% gallium, complete recovery would yield some 500-1000 tons per annum, however present consumption is only 0.1% of this about 10 tons per annum.
A typical analysis of the 98-99% pure gallium obtained as a side product from the Bayer process is shown in [link]. This material is further purified to
99.99% by chemical treatment with acids and O> at high temperatures followed by crystallization. This chemical process results in the reduction of the majority of metal impurities at the ppm level, see [link]. Purification to seven nines 99.9999% is possible through zone refining, however, since the equilibrium distribution coefficient of the residual impurities kp ~ 1, multiple passes are required, typically > 500. The low melting point of gallium ensures that contamination from the container wall (which is significant in silicon zone refining) is minimized. In order to facilitate the multiple zone refining in a suitable time, a simple modification of zone refining is employed shown in [link]. The gallium is contained in a plastic tube wrapped around a rotating cylinder that is half immersed in a cooling bath. A heater is positioned above the gallium plastic coil. Thus, establishing a series of molten zones that pass upon rotation of the drum by one helical segment per revolution. In this manner, 500 passes may be made in relatively short time periods. The typical impurity levels of gallium zone refined in this manner are given in [link].
Element
aluminum calcium copper iron
lead
magnesium
Bayer process (ppm) 100-1,000 10-100 100-1,000 100-1,000 < 2000
10-100
After acid/base leaching (ppm)
7 not detected 2 7
30
500 zone Passes
(ppm)
<1
not detected <1
|
not detected
not detected
mercury
nickel
silicon
tin
titanium
zinc
10-100 10-100 10-100 10-100 10-100
30,000
not detected not detected
not detected not detected x1 not detected x1] not detected 1 <1
x] not detected
Typical analysis of gallium obtained as a side product from the Bayer
process.
heater . gallium contained ina
rotating drum
plastic tube
Schematic representation of a zone refining
apparatus.
Isolation and purification of elemental arsenic
Elemental arsenic (L. arsenicum, yellow orpiment) exists in two forms: yellow (cubic, As,) and gray or metallic (rhombohedral). At a natural abundance of 1.8 ppm arsenic is relatively rare, however, this is offset by its presence in a number of common minerals and the relative ease of isolation.
Arsenic containing minerals are grouped into three main classes: the sulfides realgar (As,4S,) and orpiment (As>S3), the oxide arsenolite (As,O3), and the arsenides and sulfaresenides of the iron, cobalt, and nickel. Minerals in this latter class include: loellinginite (FeAs>), safforlite (CoAs), niccolite (NiAs), rammelsbergite (NiAs>), ansenopyrite or mispickel (FeAsS), cobaltite (CoAsS), enargite (Cu3AsS,), gerdsorfite (NiAsS), and the quarturnary sulfide glaucodot [(Co,Fe)AsS]. [link] shows the typical impurities in arsenopyrite.
Element Concentration Element Concentration (ppm) (ppm)
silver 90 nickel < 3,000
gold 8 lead 50
cobalt 30,000 platinum 0.4
copper 200 rhenium 50
germanium 30 selenium 50
manganese 3,000 vanadium 300
molybdenum 60 zinc 400
Typical impurities in arsenopyrite.
Arsenic is obtained commercially by smelting either FeAs» or FeAsS at 650- 700 °C in the absence of air and condensing the sublimed element (Ts,4 = 613 °C), [link].
Equation:
650-700 °C <613 °C FeAsS > FeS+As(vapor) > As(solid)
The arsenic thus obtained is combined with lead and then sublimed (T,,, = 614 °C) which binds any sulfur impurities more strongly than arsenic. Any residual arsenic that remains trapped in the iron sulfide is separated by forming the oxide (As»O3) by roasting the sulfide in air. The oxide is sublimed into the flue system during roasting from where it is collected and reduced with charcoal at 700-800 °C to give elemental arsenic. Semiconductor grade arsenic (> 99.9999%) is formed by zone refining.
Synthesis and purification of gallium arsenide.
Gallium arsenide can be prepared by the direct reaction of the elements, [link]. However, while conceptually simple the synthesis of GaAs is complicated by the different vapor pressures of the reagents and the highly exothermic nature of the reaction. Furthermore, since the synthesis of GaAs at atmospheric pressure is accompanied by its simultaneous decomposes due to the loss by sublimation, of arsenic, the synthesis must be carried out under an overpressure of arsenic in order to maintain a stoichiometric composition of the synthesized GaAs.
Equation:
>1240 °C Ga(liquid) + As(vapor) > GaAs(solid)
In order to overcome the problems associated with arsenic loss, the reaction is usually carried out in a sealed reaction tube. However, if a stoichiometric quantity of arsenic is used in the reaction a constant temperature of 1238 °C must be employed in order to maintain the desired arsenic overpressure of 1 atm. Practically, it is easier to use a large excess of arsenic heated to a lower temperature. In this situation the pressure in the tube is approximately equal to the equilibrium vapor pressure of the volatile component (arsenic) at the lower temperature. Thus, an over pressure of 1 atm arsenic may be
maintained if within a sealed tube elemental arsenic is heated to 600-620 °C while the GaAs is maintained at 1240-1250 °C.
[link] shows the sealed tube configuration that is typically used for the synthesis of GaAs. The tube is heated within a two-zone furnace. The boats holding the reactants are usually made of quartz, however, graphite is also used since the latter has a closer thermal expansion match to the GaAs product. If higher purity is required then pyrolytic boron nitride (PBN) is used. One of the boats is loaded with pure gallium the other with arsenic. A plug of quartz wool may be placed between the boats to act as a diffuser. The tube is then evacuated and sealed. Once brought to the correct reaction temperatures ([link]), the arsenic vapor is transported to the gallium, and they react to form GaAs in a controlled manner. [link] gives the typical impurity concentrations found in polycrystalline GaAs.
arsenic gallium
VEZERY)
ITT) TTT
600 - 620 °C 1240 - 1260 °C
Schematic representation of a sealed tube
synthesis of GaAs. Ficmeni Concentration Ficnient Concentration (ppm) (ppm)
boron 0.1 silicon 0.02
carbon 0.7 phosphorus 0.1
nitrogen 0.1 sulfur 0.01 oxygen 0.5 chlorine 0.08 fluorine 0.2 nickel 0.04 magnesium 0.02 copper 0.01 aluminum 0.02 zinc 0.05
Impurity concentrations found in polycrystalline GaAs.
Polycrystalline GaAs, formed in from the direct reaction of the elements is often used as the starting material for single crystal growth via Bridgeman or Czochralski crystal growth. It is also possible to prepare single crystals of GaAs directly from the elements using in-situ, or direct, compounding within a high-pressure liquid encapsulated Czochralski (HPLEC) technique.
Bibliography
e K.G. Baraclough, K. G., in The Chemistry of the Semiconductor Industry, Eds. S. J. Moss and A. Ledwith, Blackie and Sons, Glasgow, Scotland (1987).
e L. D. Crossman and J. A. Baker, Semiconductor Silicon 1977, Electrochem. Soc., Princeton, New Jersey (1977).
e M. Fleisher, in Economic Geology, 50th Aniv. Vol., The Economic Geology Publishing Company, Lancaster, PA (1955).
e G. Hsu, N. Rohatgi, and J. Houseman, AIChE J., 1987, 33, 784.
e S.K. lya, R. N. Flagella, and F. S. Dipaolo, J. Electrochem. Soc., 1982, 129, 1531.
e J. Krauskopf, J.D. Meyer, B. Wiedemann, M. Waldschmidt, K. Bethge, G. Wolf, and W. Schiiltze, 5th Conference on Semi-insulating II-V Materials, Malmo, Sweden, 1988, Eds. G. Grossman and L. Ledebo, Adam-Hilger, New York (1988).
J. R. McCormic, Conf. Rec. 14th IEEE Photovolt. Specialists Conf., San Diego, CA (1980).
J. R. McCormic, in Semiconductor Silicon 1981, Ed. H. R. Huff, Electrochemical Society, Princeton, New Jersey (1981).
W. C. O’ Mara, Ed. Handbook of Semiconductor Silicon Technology, Noyes Pub., New Jersey (1990).
W. G. Pfann, Zone Melting, John Wiley & Sons, New York, (1966). F, Shimura, Semiconductor Silicon Crystal Technology, Academic Press (1989).
Growth of Gallium Arsenide Crystals
Introduction
When considering the synthesis of Group 13-15 compounds for electronic applications, the very nature of semiconductor behavior demands the use of high purity single crystal materials. The polycrystalline materials synthesized above are, therefore, of little use for 13-15 semiconductors but may, however, serve as the starting material for melt grown single crystals. For GaAs, undoubtedly the most important 13-15 (III - V) semiconductor, melt grown single crystals are achieved by one of two techniques: the Bridgman technique, and the Czochralski technique.
Bridgman growth
The Bridgman technique requires a two-zone furnace, of the type shown in [link]. The left hand zone is maintained at a temperature of ca. 610 °C, allowing sufficient overpressure of arsenic within the sealed system to prevent arsenic loss from the gallium arsenide. The right hand side of the furnace contains the polycrystalline GaAs raw material held at a temperature just above its melting point (ca. 1240 °C). As the furnace moves from left to right, the melt cools and solidifies. If a seed crystal is placed at the left hand side of the melt (at a point where the temperature gradient is such that only the end melts), a specific orientation of single crystal may be propagated at the liquid-solid interface eventually to produce a single crystal.
furnace zone 1 furnace zone 2
; seed GaAs arsenic crystal charge
Direction of furnace travel
A schematic diagram of a Bridgman two-zone furnace used for melt growths of single crystal GaAs.
Czochralski growth
The Czochralski technique, which is the most commonly used technique in industry, is shown in [link]. The process relies on the controlled withdrawal of a seed crystal from a liquid melt. As the seed is lowered into the melt, partial melting of the tip occurs creating the liquid solid interface required for crystal growth. As the seed is withdrawn, solidification occurs and the seed orientation is propagated into the grown material. The variable parameters of rate of withdrawal and rotation rate can control crystal diameter and purity. As shown in [link] the GaAs melt is capped by boron trioxide (B03). The capping layer, which is inert to GaAs, prevents arsenic loss when the pressure on the surface is above atmospheric pressure. The growth of GaAs by this technique is thus termed liquid encapsulated Czochralski (LEC) growth.
counter- clockwise rotation
seed crystal fused ‘
silica crucible R.F. Coils
single crystal graphite susceptor
\ ° |. © tone fo) pp cap (@) Ee | iii tii ce) oO O 1@) ce) te) liquid melt
clockwise rotation
A schematic diagram of the Czochralski technique as used for growth of GaAs single crystal bond.
While the Bridgman technique is largely favored for GaAs growth, larger diameter wafers can be obtained by the Czochralski method. Both of these melt techniques produce materials heavily contaminated by the crucible, making them suitable almost exclusively as substrate material. Another disadvantage of these techniques is the production of defects in the material caused by the melt process.
Bibliography
e W.G. Pfann, Zone Melting, John Wiley & Sons, New York (1966).
e R.E. Williams, Gallium Arsenide Processing Techniques. Artech House (1984).
Ceramic Processing of Alumina
Introduction
While aluminum is the most abundant metal in the earth's crust (ca. 8%) and aluminum compounds such as alum, K[AI(SO,)].12(H2O), were known throughout the world in ancient times, it was not until the isolation of aluminum in the late eighteenth century by the Danish scientist H. C. Oersted that research into the chemistry of the Group 13 elements began in earnest. Initially, metallic aluminum was isolated by the reduction of aluminum trichloride with potassium or sodium; however, with the advent of inexpensive electric power in the late 1800's, it became economically feasible to extract the metal via the electrolyis of alumina (Al,O3) dissolved in cryolite, Na3AlF¢, (the Hall-Heroult process). Today, alumina is prepared by the Bayer process, in which the mineral bauxite (named for Les Baux, France, where it was first discovered) is dissolved with aqueous hydroxides, and the solution is filtered and treated with CO> to precipitate alumina. With availability of both the mineral and cheap electric power being the major considerations in the economical production of aluminum, it is not surprising that the leading producers of aluminum are the United States, Japan, Australia, Canada, and the former Soviet Union.
Aluminum oxides and hydroxides
The many forms of aluminum oxides and hydroxides are linked by complex structural relationships. Bauxite has the formula Al,(OH)3.9, (0 < x < 1) and is thus a mixture of Al5O3 (a-alumina), Al(OH) 3 (gibbsite), and AlO(OH) (boehmite). The latter is an industrially important compound which is used in the form of a gel as a pre-ceramic in the production of fibers and coatings, and as a fire retarding agent in plastics.
Heating boehmite and diaspore to 450 °C causes dehydration to yield forms of alumina which have structures related to their oxide-hydroxide precursors. Thus, boehmite produces the low-temperature form y-alumina, while heating diaspore will give a-alumina (corundum). y-alumina converts to the hcp structure at 1100 °C. A third form of Al»O3 forms on the surface of the clean aluminum metal. The thin, tough, transparent oxide layer is the
reason for much of the usefulness of aluminum. This oxide skin is rapidly self-repairing because its heat of formation is so large (AH = -3351 kJ/mol). Equation:
4Al +30, > 2A1,0,
Ternary and mixed-metal oxides
A further consequence of the stability of alumina is that most if not all of the naturally occurring aluminum compounds are oxides. Indeed, many precious gemstones are actually corundum doped with impurities. Replacement of aluminum ions with trace amounts of transition-metal ions transforms the formerly colorless mineral into ruby (red, Cr°*), sapphire (blue, Fe**/3*, Ti**), or topaz (yellow, Fe**). The addition of stoichiometric amounts of metal ions causes a shift from the a-Al,O3 hcp structure to the other common oxide structures found in nature. Examples include the perovskite structure for ABO3 type minerals (e.g., CeTiO7 or LaAlO3) and the spinel structure for AB»O, minerals (e.g., beryl, BeAl Ox).
Aluminum oxide also forms ternary and mixed-metal oxide phases. Ternary systems such as mullite (AlgSi,O;3), yttrium aluminum garnet (YAG, Y3AI150 >), the B-aluminas (e.g., NaAl,;;0,7) and aluminates such as hibonite (CaAl,»019) possessing B-alumina or magnetoplumbite-type structures can offer advantages over those of the binary aluminum oxides.
Applications of these materials are found in areas such as engineering composite materials, coatings, technical and electronic ceramics, and catalysts. For example, mullite has exceptional high temperature shock resistance and is widely used as an infrared-transparent window for high temperature applications, as a substrate in multilayer electronic device packaging, and in high temperature structural applications. Hibonite and other hexaluminates with similar structures are being evaluated as interfacial coatings for ceramic matrix composites due to their high thermal stability and unique crystallographic structures. Furthermore, aluminum oxides doped with an alkali, alkaline earth, rare earth, or transition metal are
of interest for their enhanced chemical and physical properties in applications utilizing their unique optoelectronic properties.
Synthesis of aluminum oxide ceramics
In common with the majority of oxide ceramics, two primary synthetic processes are employed for the production of aluminum oxide and mixed metal oxide materials:
1. The traditional ceramic powder process. 2. The solution-gelation, or "sol-gel" process.
The environmental impact of alumina and alumina-based ceramics is in general negligible; however, the same cannot be said for these methods of preparation. As practiced commercially, both of the above processes can have a significant detrimental environmental impact.
Traditional ceramic processing
Traditional ceramic processing involves three basic steps generally referred to as powder-processing, shape-forming, and densification, often with a final mechanical finishing step. Although several steps may be energy intensive, the most direct environmental impact arises from the shape- forming process where various binders, solvents, and other potentially toxic agents are added to form and stabilize a solid ("green") body ({link]).
Volume
Function Composition (%)
Powder alumina (Al,O3) 27
Solvent 1,1,1-trichloroethane/ethanol 58 Deflocculant menhaden oil 1.8 Binder poly(vinyl butyrol) 4.4
poly(ethylene glycol)/octyl
phthalate oe
Plasticizer
Typical composition of alumina green body
The component chemicals are mixed to a slurry, cast, then dried and fired. In addition to any innate health risk associated with the chemical processing these agents are subsequently removed in gaseous form by direct evaporation or pyrolysis. The replacement of chlorinated solvents such as 1,1,1-trichloroethylene (TCE) must be regarded as a high priority for limiting environmental pollution. The United States Environmental Protection Agency (EPA) included TCE on its 1991 list of 17 high-priority toxic chemicals targeted for source reduction. The plasticizers, binders, and alcohols used in the process present a number of potential environmental impacts associated with the release of combustion products during firing of the ceramics, and the need to recycle or discharge alcohols which, in the case of discharge to waterways, may exert high biological oxygen demands in the receiving communities. It would be desirable, therefore, to be able to use aqueous processing; however, this has previously been unsuccessful due to problems associated with batching, milling, and forming. Nevertheless, with a suitable choice of binders, etc., aqueous processing is possible. Unfortunately, in many cast-parts formed by green body processing the liquid solvent alone consists of over 50 % of the initial volume, and while this is not directly of an environmental concern, the resultant shrinkage makes near net shape processing difficult.
Sol-gel
Whereas the traditional sintering process is used primarily for the manufacture of dense parts, the solution-gelation (sol-gel) process has been
applied industrially primarily for the production of porous materials and coatings.
Sol-gel involves a four stage process: dispersion, gelation, drying, and firing. A stable liquid dispersion or sol of the colloidal ceramic precursor is initially formed in a solvent with appropriate additives. By changing the concentration (aging) or pH, the dispersion is "polymerized" to form a solid dispersion or gel. The excess liquid is removed from this gel by drying and the final ceramic is formed by firing the gel at higher temperatures.
The common sol-gel route to aluminum oxides employs aluminum hydroxide or hydroxide-based material as the solid colloid, the second phase being water and/or an organic solvent, however, the strong interactions of the freshly precipitated alumina gels with ions from the precursor solutions makes it difficult to prepare these gels in pure form. To avoid this complication, alumina gels are also prepared from the hydrolysis of aluminum alkoxides, Al(OR)3.
Equation:
AI(OR), + H,O/Ht > Al-gel
Equation:
A Al-gel > ALO,
The exact composition of the gel in commercial systems is ordinarily proprietary, however, a typical composition will include an aluminum compound, a mineral acid, and a complexing agent to inhibit premature precipitation of the gel, e.g., [link].
Function Composition
Boehmite precursor ASB [aluminum sec-butoxide, Al(OC4Ho)3] Electrolyte HNO3 0.07 mole/mole ASB Complexing agent glycerol ca. 10 wt.%
Typical composition of an alumina sol-gel for slipcast ceramics.
The principal environmental consequences arising from the sol-gel process are those associated with the use of strong acids, plasticizers, binders, solvents, and sec-butanol formed during the reaction. Depending on the firing conditions, variable amounts of organic materials such as binders and plasticizers may be released as combustion products. NO,’s may also be produced in the off-gas from residual nitric acid or nitrate salts. Moreover, acids and solvents must be recycled or disposed of. Energy consumption in the process entails “upstream” environmental emissions associated with the production of that energy.
Bibliography
e Advances in Ceramics, Eds. J. A. Mangels and G. L. Messing, American Ceramic Society, Westville, OH, 1984, Vol. 9.
e Adkins, J. Am. Chem. Soc., 1922, 44, 2175.
e A.R. Barron, Comm. Inorg. Chem., 1993, 14, 123.
e M. K. Cinibulk, Ceram. Eng. Sci., Proc., 1994, 15, 721.
e F. A. Cotton and G. Wilkinson, Advanced Inorganic Chemistry, 5th Ed., John Wiley and Sons, New York (1988).
e N. N. Greenwood and A. Earnshaw, Chemistry of the Elements, Pergamon Press, Oxford (1984).
e P.H. Hsu and T. F. Bates, Mineral Mag., 1964, 33, 749.
e W. D. Kingery, H. K. Bowen, and D. R. Uhlmann, Introduction to Ceramics, 2nd Ed. Wiley, New York (1976).
e H. Schneider, K. Okada, and J. Pask, Mullite and Mullite Ceramics, Wiley (1994).
e R. V. Thomas, Systems Analysis and Water Quality Management, McGraw-Hill, New York (1972).
e J.C. Williams, in Treatise on Materials Science and Technology, Ed. F. F. Y. Wang, Academic Press, New York (1976).
Piezoelectric Materials Synthesis
This module was developed as part of the Rice University course CHEM-496: Chemistry of Electronic Materials. This module was prepared with the assistance of Ilse Y. Guzman-Jimenez.
Introduction
Piezoelectricity is the generation of an electric moment by a change of stress applied to a solid. The word piezoelectricity literally means “pressure electricity”; the prefix piezo is derived from the Greek word piezein, “to press”. The piezoelectric effect was discovered in 1880 by the brothers Jacques and Pierre Curie. Not only did they demonstrate the phenomenon, but they also established the criteria for its existence in a given crystal. Of the thirty-two crystal classes, twenty-one are non-centrosymmetric (not having a centre of symmetry), and of these, twenty exhibit direct piezoelectricity.
The first practical application of the piezoelectric effect was developed when ground quartz crystals were placed between the plates of a tuning capacitor in order to stabilize oscillating circuits in radio transmitters and receivers; however, the phenomenon of piezoelectricity was not well exploited until World War I, when Langevin used piezoelectrically excited quartz plates to generate sounds waves in water for use in submarine detection.
Piezoelectricity can also occur in polycrystalline or amorphous substances which have become anisotropic by external agents. Synthetic piezoelectric materials became available near the end of World War II, with the accidental discovery of the fact that materials like barium titanate and rare earth oxides become piezoelectric when they are polarized electrically. During the postwar years, when germanium and silicon were revolutionizing the electronics industry, piezoceramics appeared for a while to be joining the revolution, but the limited availability of materials and components, made the piezoelectric phenomenon failed to lead mature applications during the 1950s. It is only now that a variety of piezoelectric materials are being synthesized and optimized. As a consequence piezoelectric-based devices are undergoing a revolutionary development, specially for medicine and aerospace applications.
Piezoelectric ceramics
Most piezoelectric transducers are made up of ceramic materials for a broad range of electromechanical conversion tasks as transmitters, ranging from buzzers in alarm clocks to sonars, and as receivers, ranging from ultra high frequency (UHF) filters to hydrophones.
Most of the piezoelectric materials in usage are from the lead zirconate titanate (PZT) family, because of their excellent piezoelectric parameters, thermal stability, and dielectric properties. Additionally the properties of this family can be modified by changing the zirconium to titanium ratio or by addition of both metallic and non-metallic elements. PZT (PbZr,_,TixO3) ceramics and their solid solutions with several complex perovskite oxides have been studied; among the various complex oxide materials, niobates have attracted special attention. Ternary ceramic materials, lead metaniobate, as well as, barium and modified lead titanates complete the list of piezoceramic materials.
Selective parameters for piezoceramic materials are given in [link], where Q,, is the mechanical quality factor, T, is the Curie point, d3; is the the transverse charge coefficient, and kp, k;, and k3, are the electromechanical coupling factors for planar, thickness, and transversal mode respectively.
Material PZT Lead PSZNT PZT, PSN- TsTS- PZT,
property modified metaniobate 31/40/29 x= PLT 42-1 x= 0.5 50/50 0.48
Qn 350 40 222 74 41 887
T. (°C) 290 462 369 152 355
CN 50
kp 0.5 60 0.428 30.7 46.5
k 0.32 0.438 -
k31 0.21 0.263 17.9
Selective parameters for illustrative piezoceramic materials.
Recently, sol-gel processing has been used to prepare ceramics, making possible the preparation of materials that are difficult to obtain by conventional methods. Both, inorganic and organic precursor have been reported. Additionally, new techniques for the production of ceramic fibers have been developed. Better processing and geometrical and microestructural control are the main goals in the production of fibers.
The latest development in piezoceramic fibers is the modification of the viscous-suspension-spinning process (VSSP) for the production of continuos piezoelectric ceramic fibers for smart materials and active control devices, such as transducers, sensor/actuators and structural-control devices. The VSSP utilizes conventional synthesized ceramic powders and cellulose, as the fugitive carrier, to produce green ceramic fiber at a reasonable cost. [link] shows the schematic representation of the VSSP.
Regeneration
bath Ceramic ——— Wash drum dispersion os ————— Dryer Take-up
Mix Filter and de-air 1S) <= 5 { drum reel
} 4) | an
: list — hy fre oe Gas —_e— SF = Metering pump Spin bath Finish bath
The viscous-suspension-spinning process (VSSP) for the production of continuous piezoceramic fiber.
Synthesis of reactive PZT precursor powder by the oxalate coprecipitation technique has also been developed. The precursor transforms to phase pure PZT at or above 850 °C the PZT obtained by this technique showed a Curie temperature of 355 °C. The advantages of the coprecipitation technique are the lack of moisture sensitive and special handling precursors.
Although new materials have been investigated with the purpose of create replacements for ceramics, there has been a great improvement in their properties and, current research is focused in the development of
new techniques for both synthesis and processing.
Piezoelectric single crystals.
The recent progress of the electronic technology requires new piezoelectric crystals with a high thermal stability and large electromechanical coupling factors. Single-crystal materials have been considered as replacements for polycrystalline ceramics. Ideally single-crystals of lead zirconate titanate (PZT) itself would be the main choice as it is the most prevailing piezoelectric material, but it is difficult to grow large single crystals. On the other hand, the fact that single-crystals offer many advantages over polycrystalline systems has been recognized. Materials such as lithium niobate present essentially no aging, no mechanical creep and excellent performance in high temperature conditions.
New piezoelectric single crystals grown by conventional RF-heating Czochralski (CZ) technique have been synthesized. High purity starting materials, mainly oxides powders, and Ar atmosphere are required. La3GasSiOj4, Lag3Nbg 5Gas.5O14 and La3Tag.5Gas.5O1,4 single crystals have been grown by using this method. However, the CZ technique can be applied only to materials that can be synthesized by ordinary solid-state reaction and can undergo the pulling method.
BaBe)Si,O7 (barylite) has been known as material with a strong piezoelectricity, however, it can not be obtained by solid-state reaction and CZ technique therefore is not applicable. As an alternative for piezoelectric crystals growth hydrothermal synthesis has been developed. [link] shows the experimental apparatus for the growth of barylite. Eventhough, crystals can be obtained using this technique, high pressure (500 - 1000 bar) and a solvent for the raw materials are required.
Experimental apparatus for the hydrothermal synthesis of barylite. H = heater, F = furnace, S = specimen vessel, G = growth capsule, P = pressure gauge, and T = thermocouples.
Adapted from M. Maeda, T. Uehara, H. Sato and T. Ikeda, Jpn. J. Appl. Phys., 1991, 30, 2240.
While the piezoceramics dominate the single crystal materials in usage, single crystals piezoelectrics continue to make important contributions both in price-conscious consumer market and in performance- driven defense applications. Areas such as frequency stabilized oscillators, surface acoustic wave devices and filters with a wide pass band, are still dominated by single crystals.
Piezoelectric thin films
Recently, there has been great interest in the deposition of piezoelectric thin films, mainly for microelectronical systems (MEMS) applications; where the goal is to integrate sensors and actuators based on PZT films with Si semiconductor-based signal processing; and for surface acoustic wave (SAW) devices; where the goal is to achieve higher electromechanical coupling coefficient and temperature stability. Piezoelectrical microcantilevers, microactuators, resonators and SAW devices using thin films have been reported.
Several methods have been investigated for PZT thin films. In the metallo-organic thin film deposition, alkoxides are stirred during long periods of time (up to 18 hours). After pyrolisis, PZT amorphous films are formed and then calcination between 400 — 600 °C for 80 hours leads to PZT crystallization (perovskita phase) by a consecutive phase transformation process, which involves a transitional pyrochlore phase.
A hybrid metallorganic decomposition (MOD) route has also been developed to prepare PZT thin films. Lead and titanium acetates and, zirconium acetylacetonate are used. The ferroelectric piezoelectric and dielectric properties indicate that the MOD route provides PZT films of good quality and comparable to literature values. In addition to being simple, MOD has several advantages which include: homogeneity at molecular level and ease composition control.
Metalorganic chemical vapor deposition (MOCVD) has been applied to PZT thin films deposition also. It has been proved that excellent quality PZT films can be grown by using MOCVD, but just recently the control of microstructure the deposition by varying the temperature, Zr to Ti ratio and precursors flow has been studied. Recent progress in PZT films deposition has led to lower temperature growth and it is expected that by lowering the deposition temperature better electrical properties can be achieved. Additionally, novel techniques such as KrF excimer laser ablation and, ion and photo-assisted depositions, have also been used for PZT films synthesis.
On the other hand, a single process to deposit PZT thin film by a hydrothermal method has been reported recently. Since the sol-gel method, sputtering and chemical vapor deposition techniques are useful only for making flat materials, the hydrothermal method offers the advantage of making curved shaped materials. The hydrothermal method utilizes the chemical reaction between titanium and ions melted in solution. A PZT thin film has been successfully deposited directly on a titanium substrate and the optimum ion ratio in the solution is being investigated to improve the piezoelectric effect.
Among the current reported piezoelectric materials, the Pb(Ni,/3Nb2/3)9.2Zro,4Tig. 403 (PNNZT, 2/4/4) ferroelectric ceramic has piezoelectric properties that are about 60 and 3 times larger than the reported values for ZnO and PZT. A sol-gel technique has been developed for the deposition of a novel piezoelectric
PNNZT thin film. A 2-methoxyethanol based process is used. In this process precursors are heated at lower temperature than the boiling point of the solvent, to distill off water. Then prior high temperature annealing, addition of excess Pb precursor in the precursor solution is required to compensate the lead loss. The pure perovskite phase is then obtained at 600 °C, after annealing.
Thin films of zinc oxide (ZnO), a piezoelectric material and n-type wide-bandgap semiconductor, have been deposited. ZnO films are currently used in SAW devices and in electro-optic modulators. ZnO thin films have been grown by chemical vapor deposition and both d.c. and r.f. sputtering techniques. Recently, optimization of ZnO films by r.f. magnetron sputtering has been developed. However, homogeneity is one of the main problems when using this technique, since films grown by this optimized method, showed two regions with different piezoelectric properties.
DC magnetron sputtering is other technique for piezoelectric thin film growth, recently aluminum nitride, a promising material for use in thin-film bulk acoustic wave resonators for applications in RF bandpass filters, has been grown by this method. The best quality films are obtained on Si substrates. In order to achieve the highest resonator coupling, the AIN must be grown directly on the electrodes. The main problem in the AIN growth is the oxygen contamination, which leads to the formation of native oxide on the Al surface, preventing crystalline growth of AIN.
Piezoelectric polymers
The discovery of piezoelectricity in polymeric materials such as polyvinylidene difluoride (PVF), was considered as an indication of a renaissance in piezoelectricity. Intensive research was focused in the synthesis and functionalization of polymers. A potential piezoelectric polymer has to contain a high concentration of dipoles and also be mechanically strong and film-forming. The degree of crystallinity and the morphology of the crystalline material have profound effects on the mechanical behavior of polymers. Additionally, in order to induce a piezoelectric response in amorphous systems the polymer is poled by application of a strong electric field at elevated temperature sufficient to allow mobility of the molecular dipoles in the polymer. Recent approaches have been focused in the development of cyano-containing polymers, due to the fact that cyano polymers could have many dipoles which can be aligned in the same direction.
Phase transfer catalyzed reaction has been used for piezoelectric polymer preparation from malonitrile, however this method leads to low molecular weight, and low yield of impure vinylidene cyanide units containing material. The use of solid K>CO3 and acetonitrile without added phase transfer catalyst shows excellent yields for polyester possessing backbone gem-dinitriles and for polyamide synthesis. The polyester and polyamide obtained contained a dinitrile group net dipole which can be align in the same direction as the carbonyl groups.
The pursuit for better piezoelectric polymers has led to molecular modeling which indicates that one cyano substituent should be almost as effective as two geminal cyano substituents, opening a new area of potential materials having an acrylonitrile group as the basic building block. However, polyacrilonitrile itself is not suitable because it forms a helix. Thus acrylonitrile copolymers have been investigated.
Most of the piezoelectric polymers available are still synthesized by conventional methods such as polycondensation and radical polymerization. Therefore piezoelectric polymer synthesis has the same problems as the commercial polymer preparation, such as controlling the degree of polymerization and crystallinity.
A novel technique of vapor deposition polymerization has been reported as an alternative method to copolymeric thin films. Aliphatic polyurea 9 was synthesized by evaporating monomers of 1,9- diaminononano and 1,9-diisocyanatononano onto glass substrate in vacuum. Deposition rates were improved at temperatures below 0 °C. After poling treatment films showed fairly large piezoelectric
activities. Additionally, a completely novel approach to piezoelectric polymers has been presented. This approach, consists in the synthesis of ordered piezoelectric polymer networks via crosslinking of liquid- crystalline monomers. The main goal in this approach is to achieve a polymer network which combines the long term stability of piezoelectric single-crystals with the ease of processability and fabrication of conventional polymers. [link] shows the schematic representation of this approach.
a. F ae. S SSSSSSSE Orient layers LEITIITIPPR hv ANAANAAASASSS E field across plates LAGI p> Polymerize in-situ Chiral S,* monomers Poled S.* monomers Crosslinked network Local helical symmetry Uniform bulk C, symmetry Bulk C, symmetry Fluid Fluid Non-centrosymmetric solid
Scheme of a ordered piezoelectric networks via a liquid-crystalline monomer strategy. Adapted from D. L. Gin and B. C. Baxter, Polymer Preprints, 1996, 38, 211.
Piezoelectric polymers are becoming increasingly important commercially because of their easier processability, lower cost, and higher impact resistance than ceramics, but the lack of high temperature stability and the absence of a solid understanding of the molecular level basis for the electrical properties are limitations. The requirements for strong piezoelectricity in a polymer are: the polymer chain has a larger resultant dipole moment normal to the chain axis; p