Practice English Speaking&Listening with: Lecture 7 - Dopants and impurities in GaAs and InP

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went through the details and discussed the crystal structure of gallium arsenide. In

fact, what we discussed for gallium arsenide holds good also for indium phosphide that

also has got zinc blend structure. Most of these three-five compounds have got zinc blend

structure. So, wherever gallium was supposed to be sitting, we will have indium; wherever

arsenic was supposed to be sitting we have phosphorus. So, general three-five elements

are sitting there to form the zinc blend structure.

Now, we saw the (1 1 1) plane again projecting it to you, to see that you have got on the

(1 1 1) plane. All these are arsenic atoms and this gallium atom is below that because

that is at a by 4, a by 4, a by 4 from this corner so, that is below that. This arsenic

atom is even below that. So, which means as you go along the (1 1 1) plane, we have arsenic

gallium arsenic gallium.

So, if you look at the entire wafer on one side of the (1 1 1) plane or (1 1 1) gallium

arsenide wafer. If you take a gallium arsenide wafer, you have gallium plane on one side

go on alternating at the other extreme end of the arsenic plane, because you can never

remain arsenic on both sides. It starts with gallium ends with arsenic on the other surface.

So, general even for indium phosphide starts with indium other end of the (1 1 1) plane

is phosphorus. So, sometimes to keep the general term these three five semiconductors when

you take (1 1 1) oriented wafer you call it as (1 1 1) A, top plane for one surface (1

1 1) A and (1 1 1) B. These two have distinct characteristics. They have distinct characteristics

because, the (1 1 1) A, the A phase. Let me take the example of gallium arsenide has got

gallium atoms which are having three valence electrons which are forming three bonds down;

they are attached to the crystal with the three bonds going down. So, out of the three

valence electrons all the three occupying down. There is no electron available on the

surface. The implication of that is if there are no free electrons available, because all

the three are busy forming the bonds with the crystal, because there are no free electrons

available that surface is less reactive means it will oxidize slowly. It will etch also

slowly because for any chemical reaction there must be electrons.

In the absence of that, all those reactions are slow. So x-rate is slow, oxidation rate

is slow in that (1 1 1) gallium plane or (1 1 1) A plane. If you go to (1 1 1) B plane

in the case of gallium arsenide it is (1 1 1) arsenic plane. That plane has also got

the out of five; three of them will be bonding into the crystal. If you look into the crystal

structure we will see it will be bonding into the wafer or crystal from bottom three bonds,

three electrons, but there are other two electrons which are there on the surface. At least one

will be free for chemical reaction. So, the arsenic phase will be quick to react chemically

it will be quick to oxidize compared to the gallium plane or (1 1 1) A plane. So, these

are the two differences. This property also reflects on the ability to polish the two

surfaces, mechanical polishing or chemical polishing whatever you want to do, in a polished

surface of a wafer it is easy to polish (1 1 1) B plane. That is arsenic plane because

it is more highly reactive. Whereas, the A plane A phase difficult to polish. So, if

you ask a vendor I want (1 1 1) gallium arsenide wafer with gallium surface polished, you will

not get it. But if you say (1 1 1) arsenic phase polished, you will very easily get it,

because it is easy to polish. These are some of the results, consequences of some of the

peculiarities of the compound semi-conductor.

In silicon, it does not matter when you take silicon if top phase or bottom phase three

are bonding there one is available for you for chemical reaction. So, whether you take

top or bottom it oxidizes the same way you can polish both in the same way. These are

some of the differences between the crucial or major differences apart from the crystal

structure the reactivity of the surfaces. Now, let us take a look at further having

seen these structures and differences, you also saw that the cleavage plane of three

five compounds particularly gallium arsenide and indium phosphide etc., are (1 1 0) planes.

That also, we explained why. Let us go further down. Having seen the crystal structure, we

would like to see how to make devices and to make devices you must have the ability

to dope them. You should be able to make PN functions you must be able to make P-type

material.

It is not enough if you have a gallium arsenide crystal, we must be able to make P-type gallium

arsenide N- type gallium arsenide. So, dopants or impurities in three five compounds: I will

take the example of gallium arsenide. What I discussed holds good for indium phosphide

also because they go hand in hand, they competed with each other for microelectronics and also

up to electronics. Now, in this gallium arsenide, gallium is from third group arsenic is from

fifth group. Now, if you take impurities from the group two from the periodic table, impurities

from group two are zinc, cadmium, beryllium, and magnesium. If you take any one of them,

if they are occupying the gallium site what will happen. In the gallium site, it calls

for three electrons, gallium of three valence electrons. It forms covalent bond with arsenic

with five electrons from arsenic, three electrons from gallium, so totally eight to form the

covalent bond. Now, if you put zinc and if it is occupying the gallium site, zinc is

from second group it has only two electrons. So when it is sitting on the arsenic gallium

site there is one deficient one electron. That is there is one vacancy, so it becomes

.P-type material. Absence of electron you say it is a hole that is equivalent of having

a plus charge that is actually P-type. Now numbers here are the numbers which will tell

you where that acceptor level is with respect to the valence band. After all, you would

like to see what the ionization energy is. For example, the vacancy, we can call it as

a hole, is that hole has to move from the vacancy to the valence band. How is it possible?

By transfer of electrons from the valence band to that point that vacancy can be occupied

by transferring electron from the valence band to that point that will be negatively

charged when it is ionized. So, energy required to ionize that acceptor level is the ionization

energy. Now it can be easily ionized if it is close to the valence band. Now, this is

our 31 milli electron volts. Gallium arsenide band gap is 1.43 electron volts. Out of that,

31 milli electrons are very small, very close to the valence band.

That is why EA is the acceptor level, EV is just for clarifying what I am implying EC

EV that is the band gap. Now, what we are telling is you have this acceptor level or

this when you introduce zinc or cadmium or beryllium that introduces a level. This is

actually the ionization energy, energy required to transfer electrons from here to here, in

other words to transfer the vacancy from here to here. That vacancy one electron moves from

here you have a plus charge there that is that plus charge which is available for current

transport. So, this is what we are talking of and this is the P-type. EA is due to any

one of the zinc, mostly it is zinc that is used and today people are using beryllium.

In fact, if you see on this table you are given some of the concentrations which have

been achieved. For example, zinc can be introduced at the

concentration of 10 to the power of 21 that means you can make P plus gallium arsenide,

P plus means very heavily doped P-type material P plus gallium arsenide by introducing zinc

to a level of 10 to the power of 21. Beryllium, it can go beyond 10 to the power of 19 but

actually upper limit I do not have these two there is no numbers variable at the moment.

Implying these can be used but, there are difficulties in realizing them using them,

so mostly zinc and beryllium. In fact, if you open up literature the most popular P-type

dopant in gallium arsenide and indium phosphide is zinc. Zinc doped gallium arsenide. It adds

just a doping concentration. Now on an average that energy difference is about 40 milli electron

volts which is almost similar to that of silicon. Silicon also if you introduce boron which

is third group element, silicon is fourth group, so one less electron in boron it introduces

a level similar to level at about 40 to 50 electron volts.

Let us take a look at the N- type impurities. N- type impurities introduces a level ED donor

level EC EV that is supposed to donate an electron to the conduction band that means

when it ionizes which should be possible even at room temperature. If he should be able

to ionize a donor even at room temperature the implication is very small energy, the

donor should donate electron to the conduction band.

That means, the donor level is located very close to conduction band if it should donate

that is the meaning of that. So, we put it as what is the meaning of this plus? The meaning

of the plus is when it has donated an electron it is like this a donor atom with an electron

attached to that and donor in the case of silicon is from the fifth group. So, the fifth

electron donates because it requires only four to form the covalent bond. Now, if you

take sixth group in the case of gallium arsenide, if it has six group elements, it has six valence

electrons. If it is sitting on the arsenic site, there is one extra electron. Arsenic

site requires 5 electrons you write it as 5 electrons, how? Instead of that if sixth

group elements like sulphur, selenium, and tellurium all of them belong to sixth group.

If they are occupying the arsenic site, then there is one extra electron which is very

loosely attached because, all other five electrons will be forming the bond. So, those are the

ones which formed the bond. So, the fifth one is available that will be donated to that.

So this one when it goes off once it is donated to the conduction band it is left to the positive

charge. So, that is why we put that donor level as plus there implying it is ionized.

What is ionization energy? Energy required over the electron to move from the donor level

that is the ED to the conduction band.

Now, noticed the difference. This is one of the things that we will note EC minus ED 6.1

mill electron volts. That is one of the major differences between donors in silicon and donors in gallium arsenide. In silicon,

it is something like 40 to 50 milli electron volts gallium arsenide. These ionization energies

of shallow donors are 6.1, 5.9, and 5.8 on an average 5 milli electron volts, very small.

They are virtually very close to conduction band. What is the consequence of this? The

consequence of that is you go down below room temperature there is no career freeze out.

If you take silicon for example, it requires certain energy of 50 milli electron volts

for donating the electrons. You go down below room temperature you would have calculated

in some places that has to go down in temperature number of donors which are ionized that decreases.

You go to much lower degree temperatures, less and less number of them is donated. What

does it mean? That means, the electron concentration goes down it is frozen into the donor atom

itself. It is not moving there, it is right here that is what we say imply when you say

it is frozen. If you take gallium arsenide the energy is 6 milli electron volts or 5

milli electron volts then even if you go down liquid nitrogen temperature even if you go

down to that temperature, the electron should remain there they are available for conduction,

because very little energy is sufficient to release those electrons to the conduction

band. So, even at much lower temperatures, you have these electrons which are available

for conduction; whereas, in the case of silicon you go down to much lower temperature liquid

nitrogen etc., the number of electrons which are available will be coming down drastically

reduced.

So, the conductivity goes down and if it is delivering certain current at room temperature

at lower temperature, the device will not be able to deliver much current, whereas;

here it can work. You can immediately see what will be the benefit of this. The benefit

of this is you can make use of gallium arsenide devices at lower temperature very confidently.

If you recall what we discussed earlier you would like to operate some of the devices

at lower temperatures to avoid scattering or to reduce the lattice scattering. So, if

you go down to lower temperature if the electron concentration is reducing no point where is

the question of scattering if the electrons are available for conduction. So, this is

one of the advantages, you are cutting down lattice scattering by going to lower temperature.

Now of course, you will have to be worrying what about ionized impurities scattering.

They have got methods of separating the donor and acceptor to prevent the ionized impurity

scattering that we will discuss when we go to high electron mobility transistor discussion.

So, main impurity that is used is sulphur. Selenium and tellurium are used you will see

selenium doped or tellurium doped gallium arsenide, we try to avoid that because it

forms some compounds. After all if you introduce tellurium it should remain as tellurium, so

that it acts as the donor there. If it is making a compound like tellurium and gallium

telluride like this, it is no longer a donor. It is an unwanted lump standing there in gallium

arsenide, so no use. So that is why they are finding difficulty in that, but still when

the doping concentration is low you can use that, but when it is higher you must use sulphur.

There are better impurities. We will go and see those things afterwards after seeing what

could be the reason for this low ionization energy.

Explanation for that because after all we would like to see why it is so low compared

to silicon. If you recall when you discussed the silicon ionization energy, there is a

simple model for this. The simple model is the fifth group impurity in silicon may be

represented by a nucleus with a single orbiting electron. When you say it is in silicon, if

you take gallium arsenide it is sixth group fitting on the arsenic side. So, what you

are telling is the donor. A donor, shallow donor can be represented by means of a nucleus

with a single orbiting electron like that.

This is the one which is orbiting. This is equivalent to hydrogen atom, hydrogen like

in character which has one electron which is orbiting. Now, there you find out what

is the ionization energy of that electron. There what you mean is the energy required

to remove it from the vacuum level that is calculated by this formula. Once you consider

the hydrogen atom what is ionization energy of the electron that is the energy required

to remove the electron away that is used by this formula. This is almost dealt at the

high school, let me not go into that where here m0 is the mass of the electron. When

you talk of hydrogen, we will talk of the free mass of the electron and q is of course

the charge, n is 1 depending upon energy level when you talk of hydrogen atom of the electron

that is n is 1 only 1 electron, h is Plancks constant, epsilon is permittivity of free

space. So, when you use that, it so turns out that substitute for m0h, n equal to 1

epsilon0 is 8.854 into 10 to the power of minus 14 farads per centimeter, m0 is the

mass you should have known what it is right now you can substitute that it is very small,

h is Plancks constant, substituted all that this turns out to be 13.6 electron volts.

Now, when you consider this silicon atom or gallium arsenide atom or for that matter indium

phosphide atom with the donor or a donor in these materials when you consider, you consider

this as just like hydrogen like atom.

So, if you want to compute the ionization energy of the donor what you do is you compute

this quantity. Meanwhile of course when it goes to conduction band, it is available for

free transport. It is freed from the donor, it is available. So, that is ionization energy.Now

what should we do to compute that n you can put it as 1 and m0 you replace by the effect

q mass, because the electron now is in a crystal. The way electron moves in a crystal is different

from the way it would move in the free space. Because, an electron moves under the action

of an external force plus it experiences the force within the lattice itself. Within the

lattice itself, there are electrostatic forces acting on them internal forces. So, the way

it moves is different, so people have simplified the whole thing so that we can apply Newtons

laws of force, force is equal to mass into acceleration. That force is actually the applied

force and the mass is the mass of the free space free electron if it is free space. So,

for a given force it will accelerate decided by the mass. Now, if that electron is moving

within a crystal where other forces also come if those forces are already aiding the movement

for a given force there will be different acceleration. So, we can still apply the Newtons

laws of force, the force is equal to mass into acceleration. The f is actually what

you see outside is applied force, but the electron experiences a force which is a combined

effect of external force and internal force. So, to accommodate that internal force still

you use force is equal to mass into acceleration you use a different mass that is called effective

mass. It will look as if the mass is different. Normally, if the mass is m0 when I apply a

force f acceleration is force divided by mass. Now, when I apply the same force if the acceleration

is more it appears as if mass is smaller. So, that is the effective mass that is because

in addition to the applied force there is internal force that is coming. So acceleration

is more still we can apply Newtons laws of force to use the effective mass concept.

Now, what you should do here is replace the m0 by effective mass you would have computed

that and this epsilon0 replace by epsilonr epsilon0 where, epsilonr is the relative directive

constant.

That is what is put here. Epsilonr for gallium arsenide is 12.8 and mn star effective mass

of electron divided by actual mass of electron is 0.067. You can see it looks as if it is

much lighter which will tell you that if you apply a force the electrons will run virtually

much faster than in the free space, because there are additional forces internally. A

mass of hole that may not get into the physics of this, we borrow this result straight away.

The effective mass of holes divided by the effective mass of an electron is 0.5. It is

not as light as an electron. So, ionization energy now what you do is just I will go back

once replace m0 by mn star. That means what I will do is whatever I get here is 13.6 divided

by m0 multiplied by mn star or what I do is 13.6 is there dividing by m0 multiply by mn

star. It is also to our convenience. I do not have to know the actual mass of an electron.

All that I have to know is mn star by m0. That ratio which is much smaller divided by

in the place of epsilon0 square the epsilonr also coming up so, that is there. So, this

number when you evaluate is 5.56 volts milli electron volts.

So, the ionization energy comes out to be very small because the effective mass of electrons

is very small. Whereas, the effective mass of holes if you see EA minus EV is much larger

than that because that is mp star by m0 is 0.5 for gallium arsenide mn star by m0 is

0.067. So, depending upon how small is the effective mass you will get smaller this energy.

This model is a very simplified model but it works out, it is amazing. A hydrogen-like

model can be applied for such a complicated structure crystal. Now, you can see the whole

lot of them. I hope this is clear enough. Exactly all that you do is 13.6 you multiply

mn star by m0 divided by epsilonr square. The entire ionization energy depends upon

that ratio of the effective mass to the actual mass.

Using that if you sum up and see I have listed here gallium arsenide, indium phosphide, and

gallium nitrate. Because these are the two, first two are the very popular ones. This

is the one which is finding its way in the gallium nitrate. I have just added that also

and they are almost comparable. What are not comparable, varying are effective mass of

electron mass of electron 0.067 for gallium arsenide and 0.077 for indium phosphide. In

fact, this also decides what the mobility is, mass is smaller the mobility is better.

So, you can see from here that mobility of electrons in gallium arsenide will be higher

than that of indium phosphide and that will higher than that of gallium nitrate. It is

true 8500, 4500, and 2000 that way it goes. Now, mp star by m0, almost 0.5 or 0.6 so,

that is why this ionization energy when you take a silicon, gallium arsenide, indium phosphide

they are almost same 40 to 50 milli electron volts. Whereas, if you take the ionization

energy of donors, silicon it is about 0.5 because this is much larger than that of gallium

arsenide etc., at least five to six times, so that when this is larger and in case of

gallium arsenide and indium phosphide that is small. Let us model to see what actually

the cause is for this. The cause is the lower effective mass which is decided by several

physical phenomena happening between the crystals itself.

Now, we have discussed the donors from the fifth group sitting on the arsenic side acceptors

from the second group of elements sitting on the gallium side forming acceptors elements

on the sixth group site forming donors. What about the fourth group elements? They are

amphoteric. Amphoteric meaning it can go either way. It is the greatest opportunist because

it has got a chance. It can go and sit in the gallium site. If you give a chance it

will go and sit in the arsenic side. What is the meaning of given a chance? If you say

given a chance you give a vacancy there, it will go and occupy that position gallium.

If you give a vacancy on the arsenic side it will go and occupy them. That is why it

becomes amphoteric, either way it can go. If it occupies in a gallium site what does

it behave? If silicon force group sitting in the gallium site behaves like a donor,

one extra electron. They require three they have got fourth group element. If it is sitting

on the arsenic site it is actually acceptor because one less electron, you need five electrons

whereas silicon has only four. So, it can become either P- type or N- type but it so

turns out. It has some sort of choice prefers to go act as donor and if the same setting

if donor what you mean if silicon prefers to go to gallium site unless you create a

special situation where arsenic vacancies are tremendously more. Normally, at room temperature

itself, there will be vacancies. If you raise the temperature the vacancy concentration

goes up. So, given any particular condition of a crystal growth there will be vacancies

both gallium and arsenic and they are more or less comparable numbers it will go and

occupy gallium site. I just deliberately put this table, just sort of theorized or observed

certain patterns. See here silicon, germanium, tin, and lead all these belong to fourth group.

All of them in gallium arsenide act as donors. When act as donors sometimes normal conditions

unless you create additional vacancies in arsenic. When there are both arsenic and gallium

vacancies present in comparable numbers it will become donor.

The reason, this is the table which I have put just for it is a hunch. It is just observation

that I have made. I do not see it actually mentioned in books, but generally you can

see radius of the gallium atom, tetrahedral radius of gallium atom is 1.26 angstroms,

about arsenic that is 1.18 angstroms. So, in gallium arsenide if you have vacancy of

gallium that vacancy site is slightly bigger. This is the physical phenomena which you can

observe; whereas, vacancies that of arsenic is slightly smaller. So, if a foreign atom

or if a guest is coming and sitting the guest atom will come and occupy where it is comfortable.

It will be comfortable if the vacancy site is bigger. This is the law of the nature.

So, observing that gallium vacancy is bigger than arsenic vacancy because gallium has bigger

atom size that becomes donor. Now, you may ask you are flouting the rules there is one

atom here called carbon it generally becomes acceptor.

Now, the carbon is small atom, tetrahedral radius you can see 0.77. So, it will go either

way. It turns out that the gaze you can see is the law of the nature a small atom the

bigger seats are there but tend to occupy which is a smaller one. It is just on the

lighter sense. This is just on a lighter sense. So you can see the carbon is occupying that

arsenic site and acts as an acceptor. It does not mean that it does not go to the gallium

site it also goes but most of them tend to go and occupy that. There will be other criterion

like electro negativity etc. But generally this is a basic. Now, let us take a look at

what we say how far it is true? Take a look at gallium antimonite. Gallium 1.26, antimony

1.36, gallium is bigger. Now all these atoms will tend to go into the bigger vacancy that

is antimony, all acceptors and n is neutral means it may be go either way, goes into both

so that it is rather you do not see the effect of that. People are not being able to observe

very clearly about Pb lead on gallium antimonite. Similarly, you can see indium arsenide. Which

is bigger? From here itself we can see it is indium. Indium is 1.44 bigger, much bigger

than gallium, and arsenic is 1.18. It goes and sits in the indium site. This is just

a curiosity, just made this table to see whether something tangible is there and it seems to

hold good like that and of course this one is neutral implying it goes either way. In

fact, lead is quite big so that why it does not matter where it goes between the two of

them that is indium arsenide; indium is 1.44 same as almost smaller than that. So, probably

it tries to squeeze in both indium and indium arsenide generally, but what I am trying to

tell is general law. Similarly, indium antimonite also generally follows similar rules, slightly

flouting out the rules is there. It is just an observation.

So, now if you put silicon into gallium arsenide while growing gallium arsenide keep on adding

silicon into that melt what happens is the carrier concentration becomes equal to silicon

concentration. For example 10 to the power of 17 silicon atoms and gallium arsenide will

go and occupy the gallium arsenide which is bigger than silicon. Silicon is 1.18 angstroms.

So both are same or 10 to the power of 18 it is almost linear. For 10 to the power of

19 start deviating from it is not 10 to the power of 19 it is smaller than that. So as

you go to higher and higher silicon concentration, the electron concentration does not increase

linearly, it is sub linear. Reason as you go on dumping more and more silicon, they

prefer to go to gallium site, but as you go beyond certain level they thought finding

that there are arsenic sites also they can go into that. So, they are getting filled

up the gallium vacancies starts getting into arsenic site. So what happens? From 10 to

the power of 18 or 10 to the power of 19 around that as you go, if you go beyond this point,

the additional silicon atoms do not go into gallium site. Many of them tend to go into

arsenic site, so the electron concentration does not increase linearly, it becomes sub

linear and beyond a certain point it saturates, because beyond that point it goes equally

both into this gallium and arsenic site. So, if you introduce them equally you have one

shallow donor, one acceptor; one donating one accepting. So, there is no continuity

that is why the electron concentration saturates out beyond that point.

Now, just a few examples where you can see TIN follow the same rule. It can go either

way and it contributes becomes n- type but there is a donor, the fourth group TIN sitting

in the third group site, gallium site and it becomes nonlinear sometimes. That is exactly

like in the case of silicon that is what we mean by that. So TIN also behaves sub linearly

implying TIN is located in both gallium and arsenic site as you increase the concentration.

Now, what I am trying to point out is going back to silicon, we said silicon prefers to

go and occupy gallium site and become donor. Now, that is under normal circumstances, but

when you grow the crystal by a method known as liquid phase epitaxy, then what happens

is maybe I will have to draw the diagram, I will go through these statements first.

See what happens? Liquid phase epitaxy LPE, take a gallium arsenide substrate and then

I try to grow gallium arsenide layer on that with some silicon doping. Physical means even

when it contaminates so with that when I do what happens is at lower temperature it gives

p- type gallium arsenide.

I have some gallium arsenide substrate. This may be undoped. It is a substrate which I

am using. On that I want to grow another layer. This is a layer which I am growing, epitaxial

layer. Maybe it is not visible as if it was not I will redraw that. That is epitaxial

layer, epi is arranged upon. You arrange atoms on top of that. So, this can be done by different

ways. In fact, we will have occasion to see in some detail immediately after this dopants

etc. in the next one of the lectures. So, this layer when you grow what you can do is

keep this gallium arsenide substrate in contact with the liquid of gallium arsenide. Let me

draw that diagram for they are completeness sake here. Let me put it down here separately.

If you take a look at the gallium arsenide phase diagram, I am drawing into metallurgy now. If I take temperature, now

if I

take a look at that the phase diagram is like this. It tells you the phase of liquid gas

or solid of the material that is existing at different temperature. So, if you draw

this is a composition. Here, it is totally gallium, here it is totally arsenic. I can

move into gallium arsenide, gallium rich gallium arsenide, and arsenic rich gallium arsenide

and here stoichiometric gallium arsenide truly. Now, if you take a look at that, draw a line

like this here, this is important because all those people who talk of gallium arsenide

indium phosphide shall talk of this phase diagram. Now, what does it tell you? I have

line here at 29.75 degree centigrade. What is that 29.5 degree centigrade? It is the

melting point of gallium. That means in Chennai if you take gallium, it will liquid because

it is never below 29 degree centigrade and even in this room may be cooler, but otherwise

it will just like a mercury it will look like and if you take arsenic, its melting point

is somewhere here 810 centigrade. In fact, it is volatile at that temperature. If you

take gallium arsenide what is the melting point? Very easy to remember, silicon you

know it is 1410 degree centigrade, gallium arsenide 1234, 1234 plus 4, 1238. Remembering

is easy. What is the melting point of gallium arsenide? 1234 plus 4, that is 1238. See the

phase diagram will give you the melting point here 1238 degree centigrade. So, this is a

melting point here that is a melting point there, this is the melting point. In fact, draw those lines together like this

crossly what is that line. This is liquid and this is solid. Liquid plus solid, this

is solid and that is solid. You have liquid as line below that it will be liquid plus

solid it will coexist and finally it will be solid here. Now, we will have as we move

from here to here, we will have for example if you come down from here, freeze from here.

This is solid actually. This whole thing in the phase diagram is solid telling you will

get gallium arsenide. So, freeze from melting point you will get salt gallium arsenide stoichiometric.

Now, in liquid phase epitaxy what to do is, you freeze somewhere here; take this gallium

arsenide, keep it in contact with the liquid, slightly reduce the temperature. When you

start reducing the temperature that is the liquid phase epitaxy, the composition from

here will start freezing or crystallizing. The very interesting thing if I go across to Anna

University, they will do the liquid phase epitaxy for gallium arsenide. We do not do

it in IIT, Chennai. So, this is the method. You freeze it, you will get liquid plus solid,

solid in contact with that, and the solid will set along, but long time it will take

and the freezing solid has a composition decided by this. You just freeze here the composition

of solid is decided by that and this has relevance to what we are talking of here. Why it becomes

p- type? Why it becomes n- type? Now, if you expand this portion alone; this is not a single

line. This is called congruent transformation from here to here that is just suddenly from

liquid to solid; whereas, here liquid plus solid, here it is only solid totally. So,

we have deviated from electrical engineering physics gone into metallurgy totally, but

this is important to understand some of these things what are happening.

If you see that what happens is, you have that line, what we saw is something like that;

this is that line and this is 0.5 gallium, 0.5 arsenic. This is stoichiometric gallium

arsenide means 50% gallium, 50% arsenide that is how the stoichiometric is. If you come

away from that, if I come down from this side what happens. This is 50% gallium, 50% arsenic,

zero arsenic full gallium. If I come here, it is gallium rich, arsenic deficient. When

you say gallium arsenide with gallium rich less arsenic what does it mean? That are arsenic

vacancies. This is another way of telling gallium rich means arsenic vacancy. One is

rich other one is poor automatically, arsenic vacancies present. So, if I freeze from here

to here onto this point here. Freezing solid has got that composition that means I am coming

down to this side and what is here, gallium rich that means arsenic vacancy is present

and if arsenic vacancy is present, the silicon contaminated, unwanted silicon or silicon

if you introduced along with that liquid if I introduced silicon that silicon will go

and sit in arsenic vacancy, that is p- type. Go to higher temperature right up to this

point then I am putting it to expand it here, freezing compound has got that composition.

What is that composition? Is it arsenic rich or gallium rich, it is arsenic rich, because

this is the 50% point that is arsenic rich that means gallium vacancy, less arsenic gallium

vacancy? It means it goes and sits in the gallium vacancy. Now, you have provided forced

a situation where either you have got arsenic vacancy or a gallium vacancy. If there is

a gallium vacancy you get high temperature and n- type. So what we are trying to tell

is relative vacancy concentration depends upon the growth temperature and arsenic over-pressure.

So depending upon the relative vacancy concentration you can make p- type or n- type.

This is one of the approaches people used to make some of the p-n junctions by just

the varying temperature. If you grow up to certain depth at that temperature, suddenly

jack up the temperature quickly to that you will get n- type. So you can get a p-n junction.

In fact light emitting diodes of that nature can be made we can get very high pure material

with liquid phase epitaxy. So, this is one of the advantages and this tells you it is

not necessary that silicon will go and make n- type only in gallium arsenide; it will

also make p and n depending upon the opportunity. That is why I said it is an opportunist. If

given opportunity it will grab it. Here you are giving an opportunity of gallium vacancies

or arsenic vacancies you get p- type or n- type. So, this is the situation that you have

got. So, that is actually as far as the impurities are concerned. So, today what we have done

is we have talked about the p- type impurities and n- type impurities in gallium arsenide.

Same impurities will be p- type and n- type in indium phosphide. In fact, even when you

go to gallium nitrate you will see silicon can be used for doping gallium nitrate. So,

impurities are same type and also we have seen I am summing up what we have said today,

we have seen that ionization energy of donors is very small in the case of gallium arsenide

and indium phosphide etc., but will not be as small in the case of gallium nitrate because

effective mass is not so low. So because of this, it is very easy to use these materials

at lower temperature because there is no career freeze out. This is one of the key things

that one should remember that is n- type. What about P-type? We are not concerned about

P-type or making F E Ts etc., because, P-type is no use in switching over to gallium

arsenide because gallium arsenide whole mobility is not better. So, we talk of only the devices

which deal with the electron transport so that is why you talk of that type of impurities.

In next lecture, we will just discuss some other impurities which have been a very popular

for realizing semi-insulating gallium arsenide because semi-insulating gallium arsenide is

important for making integrated circuits, that we will see in the next lecture.

The Description of Lecture 7 - Dopants and impurities in GaAs and InP