Examples on Drift Current and Drift Velocity in Electronics Devices & Circuits by Engineering Funda

Hello friends, welcome to Engineering Fund of Emily, in this video I am going to solve

4 very interesting coefficients based on drift current and drift velocity.

Before I start with solution, I would like to show you all those equations and what I want

is you just try out all those equations by your own first.

Later you can check for the solution.

So, let me show you the equations one by one.

This is first one.

You can freeze the video in between.

This is second question.

This is third question.

This third question is having two equations.

So, it consists 4 marks in gate examination.

Then I will be explaining you this course question.

So, I hope you have freeze the video in between and you have tried solution by your own.

Now, let me explain all those equations one by one.

So, let us see the first question over here.

So, first question is based on drift current.

So, drift current in semiconductor depends upon option A is only the electric field

only the carrier concentration gradient both electric field and carrier concentration

and option D is both the electric field and carrier concentration gradient.

So, first of all you should know what is the basic formula for drift current.

Let me explain you that see drift current that is depending on drift current density.

So, drift current that is N mu N plus P mu P into charge into electric field.

Now, if I consider that with respect to direction then electric field will be having direction like this.

And if you wanted to have drift current then that will be drift current density dot area.

So, see this drift current is depending on drift current density.

And if you observe this drift current so that is depending on electric field as well as it is depending on carrier concentration.

Carrier concentration gradient that comes into the picture when you calculate diffusion current.

I have explained diffusion current even.

So, if you see my video based on drift current and diffusion current in that diffusion current density

or N type and P type I have explained.

Or N type it is Q into D N into D N by D x.

So, this D N by D x that is gradient of carrier concentration right.

So, here we are talking about drift current this is about diffusion current.

So, this drift current that depends on the electric field as well as carrier concentration.

And it does not depend on carrier concentration gradient.

So, here option C that will be correct choice over here.

Let us move on to second question over here.

This second question that is quite interesting let me read the question first.

Question is a DC voltage of 10 volt is applied across N type silicon bar having a rectangular cross section and length of 1 centimeter as shown in figure.

So, we are having N type silicon bar and we are applying 10 voltage across it.

The donor doping concentration N D and mobility of electrons mu N that is given over here.

The average time taken by electrons to move from one end of bar to other end is.

So, we need to identify how much time that electrons takes to have woman from one end to another end.

So, here we need to find drift velocity first.

Based on drift velocity we can calculate how much time that it takes from woman from one end to another end.

Now, first of all you need to understand what is drift velocity.

See drift velocity drift velocity that even I have explained in theory video that is mu N into electric field.

So, now question is what is electric field over here.

So, electric field that we can calculate based on length of bar and potential applied across it.

And electric field will be uniform throughout the bar remember this why the reason is that is based on planar electric field.

So, when we talk about planar electric field that will be constant throughout this bar.

Now, how to have electric field over here.

So, electric field over here that will be simply potential divided by distance.

So, potential over here that is 10 voltage divided by distance over here that is 1 centimeter.

So, you can say 10 volt per centimeter that is electric field that is happening through this bar.

Now, mu N mu N that is given to us see mobility of electrons mu N that is 1000 centimeter square per volt second.

Right. And based on that we can have drift velocity.

So, let us calculate drift velocity first see drift velocity that is mu N that is 1000.

So, 10 to the power 3 into E. So, E that we have calculated 10.

So, drift velocity over here that is 10 to the power 4.

And this is there in terms of centimeter per second you see we are considering units in terms of centimeter

remembrance. Right. Now, we need to find what we need to find how much time that it takes to reach from one end to another end.

So, that we can simply calculate by having simple relation of velocity as per distance by time.

Now, here see what is distance distance that is given to us that is 1 centimeter.

And we can have time over here based on it. So, time will be distance by drift velocity.

Now, here see this distance that is 1 centimeter and velocity that is 10 to the power 4.

So, time will be 10 to the power minus 4 and that is there in terms of second.

But we need to see what is the question over here. If you observe the question we need to find

to find average time in microsecond. Question is there in terms of microsecond. So, we need to

convert this 10 to the power minus 4 into microsecond. So, microsecond is 10 to the power minus 6.

If you make it to 10 to the power minus 6, then you will be having 100 into 10 to the power minus 6.

That will be microsecond. So, here time will be 100 microseconds. So, your answer over here is

100 microsecond. Right? I hope you have understood this. Let us move on to next interesting

intuition over here. This question is quite interesting. Let us read the question first.

See in third question, the silicon sample with unit cross-sectional area shown below is in thermal

equilibrium. So, here we are given with silicon bar and that is having donor impurities means

small n is equals to nd and that is 10 to the power 16 per centimeter.

Following informations are given. temperature is given charge value is given thermal voltage is given

and electron mobility is given. And here there are two questions. So, in gate or 4 marks this question

is there. Let us see how first question is there. The magnitude of electric field at x is equals to 0.5

micrometer is. So, we need to find electric field through this silicon bar. And you should

know see across this enter silicon bar. Electric field will be uniform. So, even if question is there

at x is equals to at x is equals to 0.5 micrometer. You need to understand it will be constant through

this entire bar. Right. So, here there is no there is no importance of x is equals to 0.5.

Electric field will be constant and in my last example also I have explained how to calculate electric

field voltage by distance. Right. So, same thing that we will be doing over here. See electric field

over here. Electric field over here that is voltage by distance. Voltage is 1 volt and distance

over here that is from 0 to 1 micrometer means 1 micrometer. So, you can say 10 to the power 6

volt per meter that is electric field. But, if you observe answer is there in terms of kilo volt per centimeter.

So, we need to convert this in terms of kilo volt per centimeter. Let me show you how to do that.

See if you wanted to have kilo volt then 10 to the power 3 should be over here per centimeter means

10 to the power minus 2 should be over here and you need to make it to 10 to the power 6.

So, 10 to the power 1 into 10 to the power 3 that will be 4 divided by minus 2 means 10 to the power 6.

Right. Volt per meter. So, now you can say 10 kilo volt per centimeter. This is how you can convert this.

So, every time you need to see in which unit answer is there based on that you should be calculated

So, our correct choice over here that is option C right. Now, let us see how second

question is available over here. The magnitude of electric drift current density at x is equals to 0.5

micrometer is. So, at x is equal to 0.5 micrometer we need to find current density. So, current density

current density that is j n and we need to find drift current density right. So, that is n mu n into

q into electric field. This is what we have already derived in my theory video right and you need to

remember this formula. Here issue is there in terms of conversion in units,

formulas are very simple. Let us substitute the values. So, n is electron concentration. So, here

doping is given and that is donor impurities means electron concentration is 10 to the power 16

per centimeter cube. So, let me write that 10 to the power 16, 10 to the power 16, 10 to the power 16

per centimeter cube. Now, you see what I am doing is I am showing you units over here. So, that you can

understand things in calculation right. So, n is 10 to the power 16 per centimeter cube mu n is

electron mobility that is also given. So, electron mobility is 1, 3, 5, 0 and that is

there in terms of centimeter square per volt second right. Then charge is given, charge is 1.6 into 10 to

the power minus 19 coulom right. So, unit is there in terms of coulom and then electric field is there

which we have calculated that is 10, that is 10 kilo volt per centimeter. Let me multiply

10 to the power 3 over here. So, that I can make it to volt per centimeter. Now, if you observe here

see this centimeter, this centimeter, this centimeter, this centimeter square and this centimeter

will get cancelled. And here 1 centimeter will remain and divided by centimeter square will be

there right. Now, it will be centimeter square and coulom per second that will be ampere right.

coulom per second that will be ampere. So, here unit will be here unit will be ampere per centimeter square

centimeter square right, ampere per centimeter square. Now, here see what is this value

10 to the power 16 into 10 to the power minus 19 into 10 to the power 3. So, that will get cancelled

right. And if you calculate this 1 35 0 into 1.6 into 10 then your answer that should be let me see my

answer that is 2 1 6 0 0. So, here you can say this is this answer is there in terms of

ampere per centimeter square only, but you see 2.16 2.16 into 10 to the power 4

ampere per centimeter square that you can say. So, your correct option is a over here right.

So, here whenever you solve question at it and you should be precise about how units are there.

Usually what I recommend is you will have to convert things in terms of centimeter over here when you

apply the things and later you will be observing your correct answers will be there in options right.

But here for understanding purpose I have shown you all those units otherwise you can directly

place things as I have explained over here and things should be there in terms of centimeter then your

answer will come automatically. I hope you have understood this let us move on to last interesting

question over here. Last question is quite interesting and there are few basic things that you need to know

let me read the question first. The dependence of drift velocity of electrons on electric field

in a semiconductor shown below. So, here drift velocity and electric field that is depending on each other

with respect to graph that is given. The semiconductor has uniform electron concentration

of n is equals to this charge is equals to this if bias of five voltage is applied across one

meter region of the semiconductor. The resulting current density in this region in

below MPR per centimeter square is how much. So, we need to find current density over here. So,

first of all let me write the formula what is current density and then we will try to analyze like how to

solve this question. So, drift current density drift current density that is n mu n into

q into E and mu n into q into E that is how drift current density is there. Now here if you observe

we do not we are not having electric field and mu n in this data and one more thing that you can say

mu n into E mu n into E that is drift velocity. So, q into n into drift velocity that is drift

current density. So, if you if you calculate drift velocity then you can have drift drift current

density but drift drift velocity is also not given. So, here what we need to do is from this graph

we need to understand how to have drift velocity. Now electric field that we can calculate you see

voltage and distance that is given to us. So, based on that we can have electric field and by

placing electric field in this graph we can have drift velocity over here. Let me show you how see here we can

have electric field how electric field that is voltage by distance what is voltage 5 what is distance

1 micrometer. So, electric field here that will be 5 into 10 to the power 6 volt per meter.

But if you observe here units then it should be there in volt per centimeter. So, to have this

in volt per centimeter what we need to do per centimeter that we need to have. So, 5 into

10 to the power 4 divided by 10 to the power minus 2 that I can do. So, that will be volt per centimeter

right. So, electric field over here that is 5 into 10 to the power 4 volt per centimeter. Now this electric

field in this graph will give you drift velocity and that drift velocity that we can place it over here

and q and n that is available over here. So, we can have drift current density. So, you see this electric

field 5 into 10 to the power 4. So, 5 into 10 to the power 4 that will be somewhere over here.

So, over here what is drift velocity that we need to check right. Now, how to have this by

simply applying basic rule of mathematics of slope you see how drift velocity that we wanted to have

divided by electric field that we have calculated that is equals to this divided by this right.

So, here 10 to the power 7 divided by 5 into 10 to the power 5. Now based on this we can have drift

velocity. So, 10 to the power 7 into electric field that is 5 into 5 into 10 to the power 4

divided by 5 into 10 to the power 5. So, if you solve this then you will be having 10 to the power 6

over here right. So, 10 to the power 6 and unit will be there in terms of centimeter per second.

Now, we are having drift velocity. So, we can place that in this drift current density. So, drift current

density now drift current density j that will be q that is 1.6 into 10 to the power minus 19 into n

n is 10 to the power 16 into mu n e. But, mu n is drift velocity that we have calculated that is 10 to

the power 6 that is 10 to the power 6 and this n is 16 right 10 to the power 16. So, if you solve this

you will be having 1.6 into 10 to the power 3 and this will be there in terms of

this will be there in terms of m p r per centimeter right square m p r per centimeter square.

So, you can say this is 1.6 into 10 to the power 3 m p r per centimeter square. But, you need to have

this in terms of kilo m p r per centimeter square. So, here it will be 1.6 kilo m p r per centimeter square

right 10 to the power 3 m p r means kilo m p r. So, 1.6 that will be a answer over here.

Right 1.6 that will be a answer over here. So, this is how you can have solution. So, first of all

you need to understand what is basic formula and how to utilize it. See here there are few basic things

that I am again repeating when you talk about bar then across bar always electric will be uniform.

So, even if they try to give more data at that time you need to understand like extra data is given

you do not need to focus about x is equals to 0.5. Uniform electric will be voltage by distance directly

you can calculate that and then you will have to substitute that in formulas which we have remembered.

Right. So, I hope you have understood this sometimes this type of graph may be given to you.

At that time you want to be thinking like this question is humongous. But, if you understand how slope is

there then from slope we can have drift velocity and then we can substitute it at in basic formula

and we can have answers. I hope you have understood this clearly. If anything that you like to share,

please note it down in the instruction. I will be happy to help you. Thank you so much for watching this.