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Good morning. Today, we start our discussion on a series of lectures on high speed devices
and circuits. My name is K. N. Bhat from the microelectronic section in the Electronic
Engineering department, Indian Institute of Technology, Madras.
The reference books I think I can hand it over to you later. Just see, one of the books
that I am referring constantly for material properties will be: S.K. Gandhi book on VLSI
Fabrication Principles, second edition 1994, there is a book by Chang and Kat Gallium Arsenide
high speed devices: Physics Technology and circuit applications. There is a book by Beneking
high speed semiconductor devices circuit aspects and fundamental behavior. There are few things
it is a very thin book it contains somethings which you do not usually see otherwise which
are relevant to high speed circuits. That is another book we just can see, in fact this
book is available in library. I have a copy of these two books I bought it especially
for this course but, I do not know how much of it I follow but, still we will have material
from various literature borrowed here.
The other books which are available in library are: Michael Shur book on Gallium Arsenide
Devices and Circuits, slightly old book, 1987, but, good enough for the basic studies. S.M
sze, book 1990 which I think I am sure you have seen in the library for high speed semiconductor
devices. Lastly, there is one the first time when I was seeing these areas I saw the book
on VLSI electronics gallium arsenide microelectronics. This is also available in reference section.
These are some of the books which we can use as reference book but generally, I will be
giving you the summary or the list of various details related to the high speed devices
as well as circuits. There is lot of emphasis on devices but, definitely circuit part also
will be touched upon. I will not highlight what the syllabus is going to be, in fact,
if you go to website you will see the syllabus.
High speed devices and circuits when you say you can immediately see there are two classes
of devices and circuits, one class based on the silicon devices and when you say silicon
devices immediately you will see MOSFET and bipolar junction transistor circuit BJT that
is very popular both in digital and analog circuits. Further classifications we will
see later. Major device areas are these two. We will also see compound semiconductor devices;
we will see why we should move from here to here for high speed during our course of discussion.
When you deal with compound semiconductor devices, you will have MESFET that is metal
semiconductor field effect transistor; I suggest MOSFET in semiconductor integrated circuits.
Also you will have high electron mobility transistors as against MOSFET and JFET and
other one will be HBT hetero junction bipolar transistors which actually is a replacement
for the conventional bipolar transistors. We will definitely touch upon some of the
circuit aspects. For example; some concepts of logic families involving these types of
devices which are different from those MOSFET based logic circuits. Let me not name them
right now because there is no point so, these are the general ideas.
Now, we will see silicon based circuits dominate the VLSI applications. First, we will have
to see why it is so dominating, why it is all pervasive. Next, we would like to see
why we should look for other materials. Those are the two aspects we will discuss now.
So, you notice I just put it deliberately on the left hand side so that, some space
may be required for here if I shifted everything to the left slightly. Silicon is very omnipresent
because of various reasons; number one is you see silicon is the most abundant material
on the earth’s crust. It forms 0.238 weight fraction of earth’s crust. In fact, there
is a joke on this you can go to beach collect some sand that is silica and you can reduce
it to silicon, so plenty of silica means plenty of silicon that is one of the major reasons
why silicon is very popular. Now, apart from that, there are other reasons like the chemical
stability of silicon is extremely high, when you say chemical stability is high it means,
we can immerse silicon at room temperature particularly in all chemicals acids or alkalis.
For example, we can dip it in nitric acid, HCL (hydro chloric acid) or even we can dip
it in combination of HCL and HNO3 that is aqua regia. Even aqua regia the most dreaded
chemical which can eat or etch gold will not affect silicon. That is what we mean by saying
it is chemically very stable it becomes very easy to process because, we can dip it in
various chemicals. That is one of the major advantages that silicon has compared to most
of the other semiconductor materials. Unless we require them very badly we will not go
in for other semiconductor materials. Silicon surface can be oxidized to silicon dioxide
this is another advantage you put silicon into or just subject silicon to high temperature
like 1000 degree centigrade pass oxygen; you have immediately silicon plus oxygen gives
you silicon dioxide. Temperatures, we talk of are 900 degree centigrade to may be 1100
degree centigrade that is the range. So, you can easily convert it using oxygen or you
can oxidize in water vapor H20, result is the same silicon dioxide. Silicon converted
into silicon dioxide is called the native oxide. It has several uses why do we say oxidize
the silicon so what, if you see these here a slide you can see this silicon dioxide is
used as gate dielectric, in a MOSFET you have a gate and an oxide the gate dielectric is
very effective and very powerful with silicon dioxide. Metal oxide silicon that is MOS structure
you can make with the metal then, the silicon dioxide then, silicon the MOS structure. You
also have other advantages like the masking and passivation let us take a look one by
one. So, one is the gate dielectric Sio2 can act as gate dielectric and second one is the masking layer.
This is like this: you have a substrate of silicon on that you can have a thick oxide
and you have this that is the gate and then you have n plus do not know whether it is
visible. This is actually the basic MOSFET structure source drain a schematic representation.
So I am trying to say is you will have this portion which is colored that is actually
the gate oxide which already you know I am just re iterating just filling whatever information
you require. This is metal oxide semiconductor this is very effective as the gate dielectric.
This is called gate dielectric you see the field oxide this portion that also a silicon
dioxide. The second one is the masky layer for example when we do this n plus n plus
diffusion you use the oxide as the mask which will prevent the diffusion of dopants through
that layer. So, the silicon dioxide is a very effective masking agent against impurities
that is what implies when we say masking layer. The third one is passivation layer notice
here the junction is below oxide. The junction is protected by means of this oxide, so that
is what we mean by saying junction is passivated that is otherwise it is very highly reactive.
When we have the oxide on the junction its reactivity is reduced on surface, so contaminants
do not go and reach the surface. It is a protection layer or a passivated layer. In layman’s
language we can say it is a protective layer in electronic term we can say it is passivate.
Those are the advantages that we have for silicon dioxide. In fact, this is the major
advantage of using silicon because it is converted to oxide very easily.
Other benefits of silicon in integrated circuits are the energy band gap. The gap between the
conduction band and the valence band is 1.1 electron volts. In fact the energy gap 1.1
means it requires 1.1 electron volts energy to remove the electrons from the valence band
and make it available for the conduction. That means sufficient amount of energy must
be given to break the covalent bonds to remove the electrons from the bond. The big advantage
of this is for example if we take germanium its band gap is 0.728 electron volts. That
is one of the reasons, why germanium lost its market compared to silicon because this
energy band gap is small. Whole electron pairs can be created very easily. So, if you make
a junction, if the temperature goes up to 60 or 70 degree centigrade the junction becomes
very leaky. If the junction becomes very leaky it can no longer effectively rectify junction.
Result is the transistors etc., do not work properly the way you want them to behave.
That is why it is one of the advantages. In fact, going back to the previous slide, silicon
can be oxidized to get silicon dioxide for germanium we may ask, can you oxidize it?
You can oxidize germanium where, we get germanium dioxide or germanium tri oxide but, that oxide
is not chemically stable when you process it by dipping it into chemicals it just gets
washed out very easily even the dilutest of dilute chemicals will etch out the germanium
oxide. Whereas, silicon dioxide chemically very highly stable just like silicon the only
chemical which will etch silicon dioxide is hydrochloric acid. In fact, you should be
able to etch with some chemical otherwise we cannot handle it at least there must be
some boss to control that is hydrochloric acid.
Germanium oxide that is very weak, it can get etched very easily. So, on two counts
germanium lost its market though the transistor initially was invented in germanium within
a decade, silicon took over, because of: one, the advantage of high band gap 1.1 electron
volts, two is the advantage of the oxide. The other advantage is that, we see now I
am just putting it as an advantage, in the sense, since silicon was made use of for realizing
integrated circuits; the vendors who sell the wafers started going bigger and bigger
diameter wafers. In the sense grow a rod of silicon, slice them to get wafers, today you
can grow twelve inch diameter rod that Intel etc., use only twelve inch diameter wafer
by slicing them. In India, we have four inch diameter wafer BHEL semiconductor complex
Chandigarh six inch diameter wafer, ITI Bangalore, Fithar, they use six inch wafers, so these
are some of the companies. There are also other companies that deal with compound semiconductor.
We will come back to these later because we will see whether we will need them at all.
In fact there is one company in Hyderabad Getech, entirely deals with gallium arsenide
base devices or high speed devices, high speed integrated circuits monolithic micro integrated
circuits MMIC. That is the reality it is not a myth. So now, we know that, we can grow
twelve inch diameter wafers by using Czochralski technique. That is melting silicon from poly
crystal material dip inside crystal pull it to get that. This is I am sure you studied
in your technology course initially. So, these are the things which have projected silicon
into the forefront.
Now, let us see what are the parameters which limit the high frequency performance or high
speed performance of the devices. I think without telling anything, we will say the
parameters which kill the high speed operation of the devices are resistors and capacitors
because, wherever resistors are there combined with the capacitors, we will have the RC time
constant delays. It will affect the high frequency performance and also affect switching speeds
because; wherever there are capacitors you have to charge those capacitors. If they are
accompanied by the resistors they have to be charged through those resistors, so device
capacitance and routing capacitance. You may have the integrated circuits where, a number
of devices are there but those devices must be connected from one to another by means
of inter connecting leads or wires. Those wires are not just connected like that it
is routed on the surface of the oxide. Those wires will have capacitance to substrate and
those capacitance are called routing capacitance or you can pronounce it like routing capacitors
whichever way you like. It depends which part of the world you are
talking, if you are talking in America it is a routing capacitance. Other thing the
device capacitance like junction capacitance and also when we talk about MOSFET the MOS
gate itself has got the capacitance that has to be charged. Now, when it is getting charged
from a preceding stage, preceding devices will be driving the capacitors and the preceding
device if driving the capacitors, the ON resistance of the preceding device will come into the
picture that is the R of the previous device. For example, C MOS if we have the full of
transistors that is the one we are charging this next stage. So that resistor is ON resistance
of the device that ON resistance is the one that I am referring to here. That should be
kept low; if it is high the RC time constant is lost that is when you are using the digital
circuits. Now, there are some aspects which are known as the characteristics frequencies.
These are of course the parameter which control those frequencies really, apart from that
there are defined certain frequencies which will be the figure of merit of the device.
The characteristics frequencies of the devices particularly of a circuit, of that matter
for example: The cutoff frequencies related to power relationship. Cutoff frequencies
that are at low frequency get certain output power from device. Now, that power output
will become 50% that is 3 db.10 log half, 10 log half is minus 3 db logarithm 2 base
10, 2 is actually 0.3 into 10, 3 db. So the 3 db frequencies is called the cutoff frequencies
where the power output falls 50% 3 db point. Now, that one is evidently governed by the
rc time constant of the devices and circuits. Then you have the transit frequencies. In
fact, this may be slightly a different term which is related to transit time. Sometimes
we see people referring to the cutoff frequencies and the transit frequencies one under the
same thing they are different type. The transit frequencies are related to transit time which
is actually related entirely to the device and the cutoff frequencies are related to
not only device capacitances plus the series resistance or shunt resistance which come
across that device, we will see that.
We have already defined what the cutoff frequency is. The cutoff frequency that is at fc to
define that fc the power output P0 at cutoff frequency is 50% of its low frequency value
which is the maximum power output that you get. That is why; fc is 3 db frequency because,
at log P0 by Pm into 10, 10 log P0 by Pm is 10 log half that is finally minus 3 db at
fc 10 log P0 by Pm is equal to 10 log 0.5 is equal to minus 3 db. So that is the cutoff
frequency of the device. Now, what is the frequency, transit time, transit frequency?
The next thing that we will see is Transit time taut, this is I am sure very familiar
for those of you who have taken at least one course on devices; this is property of the
device. Transit time as the name itself indicates is actually the length divided by the velocity
of the carriers.
If there is the length L for example if we have the channel length here this is actually
the channel length that is the channel length. The carriers get transported from the source
to drain through these lengths with the velocity v. The transit time is the time required for
the carriers to move from the source to the drain through the path length of l. So that
is why that will be actually the length divided by the velocity and the velocity would depend
upon the transport mechanism. For example, if we take the base region of the transistor
there also you can talk of transit time. The mechanism by with the carriers transported
which is not by drift it is by diffusion. Velocities are smaller compared to drift.
So, length there is a base width divided by the velocity related to the diffusion that
will give a transit time. Apparently or evidently it is related to the base width and some parameters
which govern the velocity when it is drift the mechanism or the parameter which governs
the velocity is when drift the velocity v is equal to mobility. Mobility of the carriers into electric field so that
is called as the mun E where, E is the electric field mun is the mobility. Similarly, there
is a velocity and length is L channel length. Similarly, the bipolar transistor the velocity
is related to not mobility but diffusion coefficient because, the diffusion process is the driving
force, driving force is the concentration gradient. The force is Dn into Dn by dfx where
d is the diffusion coefficient, coefficients Dn by dfx is the concentration gradient here
it is mun is the driving force in the electric field, there diffusion coefficients into driving
force is the concentration gradient. So, it is the diffusion coefficient, diffusion coefficient
is also related to mobility. What you see is now the velocity of carriers whether it
is by drift or by diffusion it is proportional to, it depends upon mun or another parameter
which is related to mun that is diffusion coefficient because, you know that Dn by mun
is kT by q that is the Einstein’s relationship Dn is the diffusion coefficients. Driving force
in this case is diffusion coefficient in to Dn by dfx concentration gradient. These are
of course the basic things which I am just reiterating.
Now, let us go back and see what the transit frequency is taut is the length and velocity.
Now, let us just find out what happens here. Let me just go through a quick derivation
of that. How much is transit time and how is it related to the term known as the transit
Transit frequency is defined what it is, we will see afterwards physically meaning, if
it is defined as ft equals 1 by 2 pi taut where, taut is the transit time. Now, let
us find out the transit time. This is the definition; we will see soon what it implies
when you really see the equivalent circuit. Sometimes, we make a mistake of calling this
as cutoff frequency itself it is the ideal cutoff frequency. So taut is length divided
by velocity that is L divided by velocity. Now, the MOSFET, we will define this with
respect to MOSFET. In a MOSFET metal oxide field effect transistor v is equal to mun
into E, E along the channel electric field along the channel length source to drain,
so that is actually equal to mun into what is the electric field along the channel voltage
drop across the channel divide by length and voltage across the channel when it is in linear
region it is just VDS. But once it goes to saturation the voltage drop is VGS minus threshold
voltage that is VGS minus VTn divide by l that is the electric circuit voltage by voltage
across the channel divide by length of the channel that is the average electric field.
Now, in fact, I would write it one step mun into VDS divide by L which is actually equal
to mun into VGS minus VTn divide by L when ID is saturated. ID in saturation gives you
that what this actually is taut transit time is equal to L divided by V is actually equal
to L square divided by L square divided by mun into VGS minus VTn. Here, VTn is actually
VGS is gate to source voltage VTn threshold voltage those are the well-known definitions,
we do not mention that initially but, for the completeness that is that. So, the transit
time actually is this number. Now, let us take a look at the transit frequency by using
this as the transit time what is the transit frequency.
Transit frequency ft 1 by 2 pi taut therefore omegat which is actually 2 pi ft is 1 by taut.
Please note that is the definition that turns out to be then from here, from this equation
we get this as the transit frequency. Now, let us look at manipulation. You have finally
what you want to see is how this will be related to some of the circuit parameter which we
talk of because, a circuit engineer may not like to say mobility threshold voltage or
sort of things he may not like to analyse so let us see how. I remove this now. Notice
that, what the transit time depends upon channel length and the mobility mainly, I can rewrite
this as multiplied by C oxide. C oxide is the well-known term gate oxide capacitance
per unit area so many farad per centimeter square in fact, the value is about 35 nanofarads
per centimeter square if oxide thickness is 100 nanometers that is 1000 angstroms. If
it is 1000 angstroms then that is 35 nanofarads per centimeter square.
I multiply that and then I multiply by W in to VGS minus VTn I just multiplied by these
two and then I divide by that. So, why did I do that, this I can write it as mun C oxide
W into VGS minus VTn divided by L just pulling out and then I will write it as L into W into
C oxide. Here we should know what the various terminologies are. Let us just see that because,
in case you we are using different symbols mobility of electrons oxide capacitance per
unit area of the gate looking at the top, W is the channel width when I take the MOSFET.
I just unfortunately rubbed of that, MOSFET has the depth and channel length, so channel
length is L, W is the channel width MOSFET and gate source voltage, threshold voltage.
What this quantity is L into W the area of the gate and C oxide is the capacitance for
the unit area. L into W total gate capacitance, we can call it as input capacitance. This
is actually equal to so L W in to C oxide
is gate capacitance. I got Ci input capacitance we call Cg or Ci just called input capacitance.
What this quantity is in terms of trans-conductance if you take. ID in saturation for MOSFET is mun C oxide
W divided by 2 L into standard square law simplified version of this MOSFET characteristic
that is
that square law.
Therefore, gm, which is trans conductance is equal to delta ID by delta VGS will be
equal to differentiate that minus, so now you can see what is omegat we defined it as
1 by taut and we finally come up to this and this portion we know it is equal to Ci gate
capacitance or input capacitance and this portion is nothing but gm. This actually is
equal to gm divided by Ci. In many places, we will see that, the figure of merit of this
transistor is gm divided by the input capacitance. In fact, we can show, I will leave it to you
to show as exercise for a bipolar transistor also if we define the transit frequency as
1 by taut that omegat will be equal to gm by Ci that is why I put Ci to keep a general
term. In a case of the transistors common emitter configuration it is the diffusion
capacitance between the base and the emitter gm divided by the capacitance that will be
the cutoff frequency if not cutoff frequency the transit frequency which will be actually
the 1 by taut. That is why I just kept it as Ci not Cg to keep it general. What is gm
in the case of bipolar transistors is Vt by Ic is R Ic by Vt is the trans-conductance
current divide by thermal voltage kT by q. If you have 1 milliampere current flowing
Vt that is kT by q is 25 millivolts so 1 by 25 that is 40 milliamperes per volt that is
the trans conductance for a bipolar. Here, you can see it depends upon this quantity.
I can have better and better value of that pi if a better value of this gm and smaller
value of the gate capacitance. These are some of the guidelines which are being used, gm
can be improved by increasing W but that are affecting capacitance also. So, by increasing
the area you will have the driving capability improved but, the capacitance also goes up
that is not the way to improve the speed of the device. We cannot make it W but, we can
make L smaller gm goes up capacitance goes down. The way to increase the speed is reduce
the channel length without affecting the capacitance, we are increasing the speed of the device.
This is one of the key things more importantly you can improve the speed of the device if
you can improve the mobility. How do you improve the mobility, for a given material we are
stuck with that mobility, but mobility is better when the doping concentrations are
low but, if we go to doping levels of ten to the power of seventeen of that level the
mobility will start falling. You must be guarded in the conventional applications not to go
to very high doping levels, we must remain at low doping levels it has its own repulsion,
we will see as we go on. You need to go higher doping concentrations in certain cases, so
one way is to change over the material which has better mobility or better velocity.
Now, let us take a look at the other aspects what we are telling, what the cutoff frequency
is let us see that how is it different from this transit frequency. of something is not
very clear so I have the symbols are clear enough the gm by Ci is the figure of this
is not only the device will talk circuit people will also talk. I am sure Prof. Radha Krishna
should have mentioned gm by C. That is the transit frequency which is omegat f with 1
by taut.
Now, let us see the cutoff frequencies. See the transit frequency is totally dependent
on the transit time totally depending on device structure and the transport mechanism because
that decides the velocity. Now, for this we will see the MOSFET example we will take MOSFET
transit frequency of MOSFET equivalent circuit. Gate and then you have some resistor which
may be the resistance of the gate region itself and also the contact resistance, so that comes
up to the point and then we have a capacitor that is the gate capacitance Ci which were
are talking of. Ci is the total gate capacitance which is equal to W into L into C oxide this
is R is the gate resistance. It could be also when rest of the resistance call this as the
g. So, this is the input point. Now, if this is Vi after all we are talking of small signals
equivalent circuit now, which would mean that, when I apply ac signal the ac signal appearing
across the gate capacitance the whole thing will appear here if this is zero. But it will
never be 0 from finite resistance contact resistance or the external applied resistance
will be there from the supply. Then, what is the other equivalent circuit.
This is actually the source point. From then on gm times that voltage Vi that is the equivalent
circuit because input you see from RC resistance and capacitance the output point is generating
a voltage for giving a current source the drain current which is gm times the gate voltage.
So, that is currently by that is iL put it as like that RL we get the output there. Now,
the question is what iL is gm times vi which is actually equal to gm times vg divided by
1 plus jw R Ci. So, that is the iL now what we are telling is the cutoff frequency is
the frequency at which power output becomes half. Power output is I square L into RL when
the power output become half iL becomes root two times at fc P0 is half of the Pm, Pm is
low frequency maximum power that is therefore which is equal to half iL square into so then
iL will be 1 by root 2 times low frequency value.
iL at fc becomes 1 by root 2 times because square root of the low frequency value, so
that becomes 1 by root 2 of low frequency value is gm times vg because this impedance
will be large compared to that entire voltage across that. So, frequency value omega0 value
that is gm times vg. So, it becomes 1 by root 2 of that and then this becomes equal to 1.
At omegac omega R Ci equal to 1 without even growing through this we would have said cutoff
frequencies related RC combination. We just went through that thing to keep the whole
discussion open, now let us just go back here. So, you have got the fc is 1 by 2 pi R Ci.
You can see the whole thing depends upon the RC combination this cut of frequency. But,
the transit time cutoff frequency depends upon gm by Ci. Now, from this circuit point
of view can you tell us what will be the condition for omegat here from this circuit you can
see that, cutoff frequency depends upon R and C here. Now, if you go on reducing R it
looks like as if cutoff frequency becomes infinite. It will not. This is not limited
by this RC combination capacitance input and the resistance of the circuit. But as I keep
on reducing the R what is the ultimate limit for the speed, transit time. Can you see what
happens there what gm by Ci will be that is what I try to illustrate. I want to bring
it down to you to here that is if you call this as I input.
Last thing today is this aspect iL divide by iin how much is
that is iL is gm times vi. I can write vi is iin into, if I have a current coming in
here what will be the vi is i into impedance divided by j omega Ci. So iL is equal to gm
into iin divided by j omega Ci. I am getting at some thing which we usually do not see.
Therefore, iL divided by iin is what magnitude, if it is the gm divided by omega Ci. Now,
you can see when omega is low that is something. Now, iL divided by iin equal to 1. When this
current here is same as the current here, gives when iL divided by iin equal to 1, we
get gm divided by omega Ci equal to 1. Now, what is omega, then, omega equals gm divided
by Ci. That is the key thing I want to tell, so when iL become by iin is equal to 1 the
frequency that happens at the frequency equal to gm by vi. What that actually is omegat,
so you have got now, what we have done now, is the transit frequency omegat is the frequency
at which the current output is equal to the current input. That means it is no longer
working as the way you want to work. We can put the resistors here or as well as here.
You have the current that pumped in; we get certain voltage output I input into RL. Now,
if this current is same as that when we put it here, the output voltage that we get, iL
is equal to iin that also into RL, you would not get benefit of using that amplifier there
and the circuit there.