Minority charge carriers in extrinsic semiconductors | Class 12 (India) | Physics | Khan Academy

Summary

The script delves into the nuances of semiconductor doping, explaining how the addition of impurities like phosphorus (for n-type) or boron (for p-type) dramatically alters the material's conductive properties. It addresses questions about the band structure changes due to doping and clarifies why the intrinsic band structure remains applicable. The script also explores the math behind doping, showing how even a low concentration of dopants significantly increases free electrons and decreases holes, leading to a million-fold change in carrier concentration and emphasizing the unique properties of semiconductors that enable such manipulation.

Takeaways

• 🌟 Semiconductors can be altered by adding impurities, creating either n-type (with more electrons) or p-type (with more holes) materials.
• 🔬 Phosphorus, a group 15 element, when added to a semiconductor like silicon, donates an extra electron, resulting in an n-type semiconductor.
• 🔬 Boron, a group 13 element, when added, accepts electrons, creating more holes and resulting in a p-type semiconductor.
• 📚 The band structure of a semiconductor is influenced by the material's composition, but the addition of a low concentration of impurities does not significantly change the overall band structure.
• 🔍 Even though phosphorus atoms are added, their atomic orbitals do not overlap significantly due to the low doping concentration, maintaining the discrete energy level.
• 🔢 The doping concentration is typically very low, with about one phosphorus atom for every million silicon atoms, often referred to as 1 ppm (parts per million).
• 📈 The effect of doping is dramatic; a low concentration of impurities can drastically increase the number of charge carriers, such as electrons in n-type semiconductors.
• 🔄 In intrinsic semiconductors, the number of electrons and holes are equal, but in extrinsic semiconductors, the number of electrons can increase significantly while the number of holes decreases.
• 🧩 The recombination rate, which is the product of the number of electrons and holes, must balance the generation rate to maintain thermal equilibrium in semiconductors.
• 📉 The addition of impurities like phosphorus not only increases the number of electrons but also significantly reduces the number of holes, leading to a drastic change in the semiconductor's properties.
• 🚀 The ability to manipulate semiconductor properties through doping is unique to semiconductors and is a key reason for their use in various electronic devices and technologies.

Q & A

What is an intrinsic semiconductor?

An intrinsic semiconductor is a pure semiconductor material that is undoped, meaning it does not have any impurities added to it. It has an equal number of electrons and holes, making it a neutral conductor with limited conductivity that can be manipulated through doping.

What is the role of phosphorus in an n-type semiconductor?

Phosphorus, being a group 15 element with five valence electrons, is added to a semiconductor like silicon to create an n-type semiconductor. It donates its extra electron, increasing the number of negatively charged conduction electrons significantly compared to holes.

How does doping with boron create a p-type semiconductor?

Boron, a group 13 element with three valence electrons, is added to a semiconductor to create a p-type semiconductor. It can accept electrons, leading to an increase in the number of holes, which are positive charge carriers.

Why does the band structure of an extrinsic semiconductor remain similar to the pure material?

The band structure of an extrinsic semiconductor remains similar to the pure material because the doping concentration is kept very low. This means that the impurity atoms are sparsely distributed among the semiconductor atoms, and their effect on the overall band structure is minimal.

Why don't we consider the band structure of the dopant like phosphorus in an n-type semiconductor?

The band structure of the dopant is not considered because the dopant atoms are so far apart that their atomic orbitals hardly overlap. The effect of each dopant atom is discrete and localized, justifying the use of a single donor level rather than a band.

What is the significance of the donor level being close to the conduction band in n-type semiconductors?

The donor level being close to the conduction band allows the extra electrons from the dopant atoms to easily jump into the conduction band, increasing the number of free electrons available for conduction and enhancing the semiconductor's conductivity.

How does the number of electrons change when a semiconductor is doped to become an n-type?

When a semiconductor is doped to become an n-type, the number of electrons increases dramatically due to the addition of dopant atoms like phosphorus, each contributing an extra electron. Even at a low doping concentration, this results in a significant increase in the number of conduction electrons.

What happens to the number of holes in an n-type semiconductor?

In an n-type semiconductor, the number of holes decreases significantly due to the increased number of electrons. The higher electron concentration leads to a higher recombination rate, destroying many electron-hole pairs and reducing the hole concentration.

Why is the effect of doping so dramatic even with a low concentration of dopant atoms?

The effect of doping is dramatic even at low concentrations because the intrinsic semiconductor starts with a relatively low number of charge carriers. Adding even a small number of dopant atoms can significantly alter the balance between electrons and holes, leading to a substantial change in the semiconductor's electrical properties.

How does the ratio of electrons to holes change in an extrinsic semiconductor?

In an extrinsic semiconductor, the ratio of electrons to holes changes dramatically due to the addition of dopant atoms. For an n-type semiconductor, the number of electrons increases while the number of holes decreases, resulting in a very high ratio of electrons to holes, which can be in the order of millions or more.

Outlines

00:00

🔬 Understanding Doping in Semiconductors

This paragraph delves into the concept of doping in semiconductors, explaining how the addition of impurities like phosphorus (a group 15 element) creates an n-type semiconductor with an excess of electrons, while boron (a group 13 element) results in a p-type semiconductor with an excess of holes. The paragraph also addresses the band structure of extrinsic semiconductors, noting that the low concentration of dopants means the band structure of the original material (silicon in this case) remains largely unchanged. It emphasizes the subtle but significant impact of doping on the semiconductor's properties, setting the stage for a deeper exploration of these effects.

05:02

📈 Impact of Doping Concentration on Semiconductor Properties

The second paragraph explores the quantitative effects of doping on semiconductors, particularly focusing on the example of phosphorus doping to create an n-type semiconductor. It explains that even at a low doping concentration of about 1 part per million (1 ppm), the number of electrons increases dramatically from the intrinsic level, resulting in a significant excess of electrons compared to holes. The paragraph also discusses the thermal generation and recombination processes that maintain the equilibrium of electrons and holes in semiconductors, and how these processes are affected by the introduction of dopants, leading to a drastic reduction in the number of holes.

10:04

🌐 The Dramatic Effects of Low-Level Doping

The final paragraph highlights the profound impact that even a low level of doping can have on semiconductors. It illustrates how the addition of phosphorus not only increases the number of electrons by a million times but also decreases the number of holes by the same magnitude. This results in an enormous disparity between the number of electrons and holes, demonstrating the sensitivity of semiconductor properties to doping. The paragraph concludes by emphasizing the unique ability to manipulate semiconductor properties through doping, which is not possible with conductors or insulators due to their inherent characteristics.

Keywords

💡Intrinsic Semiconductor

An intrinsic semiconductor is a pure semiconductor material that is not doped with impurities. It is characterized by an equal number of electrons and holes at thermal equilibrium. In the video, the intrinsic semiconductor serves as a baseline to understand the effects of doping, which introduces impurities to alter the material's electrical properties.

💡Extrinsic Semiconductor

An extrinsic semiconductor is a semiconductor material that has been doped with impurities, such as phosphorus or boron, to increase the number of charge carriers and thus enhance its conductivity. The video discusses how doping with group 15 elements like phosphorus creates an n-type semiconductor with more electrons, while doping with group 13 elements like boron results in a p-type semiconductor with more holes.

💡Doping

Doping refers to the process of adding impurity atoms to a semiconductor material to modify its electrical properties. The script explains how low concentrations of dopants, such as phosphorus for n-type or boron for p-type semiconductors, can significantly change the number of charge carriers, making the material more conductive.

💡Valence Electrons

Valence electrons are the electrons located in the outermost shell of an atom and play a key role in chemical bonding. The video script uses the number of valence electrons to explain why certain elements, like phosphorus with five valence electrons, can donate electrons and create n-type semiconductors, while others like boron with three valence electrons can accept electrons and create p-type semiconductors.

💡n-type Semiconductor

An n-type semiconductor is a material doped with donor impurities that have more valence electrons than the semiconductor's base material, resulting in an excess of free electrons as charge carriers. The video describes how adding phosphorus, which has one more valence electron than silicon, creates an n-type semiconductor with a higher concentration of negatively charged conduction electrons.

💡p-type Semiconductor

A p-type semiconductor is one that is doped with acceptor impurities, which have fewer valence electrons than the base semiconductor material, leading to an abundance of 'holes' or positive charge carriers. The script illustrates this concept by explaining how boron, with three valence electrons, can accept electrons and create a p-type semiconductor.

💡Donor Level

The donor level refers to the energy level in a semiconductor that is close to the conduction band and is associated with donor impurities. In the video, it is mentioned that the donor level being close to the conduction band allows electrons from the donor atoms to easily jump into the conduction band, increasing the number of free electrons in an n-type semiconductor.

💡Acceptor Level

The acceptor level is the energy level near the valence band in a semiconductor, associated with acceptor impurities. The script explains that the acceptor level's proximity to the valence band allows acceptor atoms to easily accept electrons, creating more holes in a p-type semiconductor.

💡Band Structure

Band structure refers to the arrangement of energy levels that electrons can occupy in a material. The video discusses how the band structure of a semiconductor changes when doped with impurities, but also explains that the band structure of the doped material can be approximated as that of the base semiconductor due to the low concentration of dopants.

💡Thermal Generation

Thermal generation is the process by which electron-hole pairs are created due to thermal energy. The video script explains that this process is temperature-dependent and is one of the key factors that determine the equilibrium number of electrons and holes in both intrinsic and extrinsic semiconductors.

💡Recombination

Recombination is the process where an electron and a hole meet and annihilate each other, reducing the number of free charge carriers in a semiconductor. The video describes how the recombination rate is affected by the number of electrons and holes, and how it leads to a decrease in the number of holes in an n-type semiconductor due to the increased number of electrons from doping.

Highlights

Introduction to the concept of doping semiconductors with impurities to create n-type and p-type semiconductors.

Explanation of how adding phosphorus, a group 15 element, creates n-type semiconductors by donating electrons.

Description of boron, a group 13 element, creating p-type semiconductors by accepting electrons and increasing hole concentration.

Discussion on the subtle questions related to the band structure changes due to doping.

Clarification on why the band structure of the doped material is considered similar to the pure semiconductor.

Insight into the low doping concentration and its impact on the overall band structure.

Explanation of how the atomic orbitals of phosphorus atoms do not significantly overlap due to their sparse distribution.

Analysis of the dramatic increase in the number of electrons in an n-type semiconductor due to doping.

Mathematical illustration of the ratio between silicon atoms and phosphorus atoms in a doped semiconductor.

Comparison of the number of electrons and holes in an intrinsic semiconductor at room temperature.

Calculation of the number of phosphorus atoms in a one-centimeter cube of n-type semiconductor.

Highlighting the significant increase in the number of conduction electrons due to doping.

Discussion on the decrease in the number of holes in an n-type semiconductor and its impact on the material's properties.

Explanation of the generation and recombination processes in semiconductors and their equilibrium state.

Analysis of how the recombination rate changes in an extrinsic semiconductor and its effect on hole concentration.

Conclusion on the drastic change in electron to hole ratio due to low-level doping and its practical implications.

Reflection on the unique properties of semiconductors that allow for such significant changes with minimal doping.

Transcripts

we've seen in previous videos that if

you take an intrinsic or a pure

semiconductor and you add some

impurities like say phosphorus which is

group 15 it has five valence electrons

one more than silicon and as a result it

will end up donating its electrons and

so now you will have a lot more

electrons a lot more negatively charged

conduction electrons compared to holes

and so we call that as an n-type

semiconductor and similarly if you were

to dope with if you had to add a group

13 element like boron which has only

three valence electrons then it can

accept electrons now and as a result you

will have a lot of holes so more

positive type charge carriers so we call

it as p-type semiconductor and we also

saw their band structure and we

understood that the whole thing is

possible because of the donor level

being very close to conduction band the

energy level of that extra electron

being very close as the result electrons

can easily jump and over here the

acceptor level being very close to the

valency band and so we spoke all about

this in previous videos so if you need a

refresher it would be a great idea to go

back and watch those videos and come

back over here

in this video we're not going to learn

more but we'll go deeper into these

impure extrinsic conductors we'll

explore some fantastic and very subtle

questions and eventually we'll also see

the numbers over here i mean we know

over here like there are more electrons

and and less holes but how much more how

much more are these is it 10 times more

100 times more the answer is going to be

mind-boggling all right so let's do it

here's one very subtle question we can

ask remember that the band structure

really depends on which material we're

dealing with silicon has one band

structure and germanium has another band

structure well notice this extrinsic

semiconductor is no longer silicon it's

silicon and phosphorus together so

wouldn't the band structure of that

material change why did we still use the

same band structure as that of silicons

and another question we could ask is now

that we have so many phosphorous atoms

uh aren't the ato or orbitals of the

phosphorus atoms overlapping and

shouldn't we also consider the band

structure for phosphorus i mean look

over here we said the donor level i mean

same question we can ask here let's just

concentrate on one the donor level over

here we just took one single discrete

level shouldn't that also be a band how

do we justify these

and the reason we can do all of this we

can justify all of this is because of

one simple reason we keep our doping

concentration very very low the doping

is so low that the impurities that we

add is so low that it turns out that

about usually about one phosphorus atom

for example is surrounded by about a

million silicon atoms so if you could

actually see that

then usually we would draw something

like this but if you were to zoom out

then you would see that one phosphorous

atom is surrounded by lots and lots of

silicon atoms something like this and so

you really have to travel a lot a lot of

atoms to actually find the next

phosphorus atom it's all silicon it

might be somewhere over here here's

another one here's another one

so this should answer the question if

you look at this crystal this is pretty

much silicon

and that's why we can justify and say

that hardly anything has changed by

adding these phosphorous atoms and so we

could say yeah the band structure is

going to remain the same this also helps

us understand why we don't have to

consider the band structure or

phosphorus for example the reason is two

phosphorous atoms are so far apart that

atomic orbitals are hardly going to

overlap and as a result

we can totally justify that we are using

a single discrete energy level and not

the band structure of phosphorus because

they're so far apart it wouldn't matter

and the same thing can be exp same thing

will happen over here as well

the immediate follow-up question we

could ask is since each phosphorous atom

is contributing to one under conduction

electron so one extra electron per

phosphorous atom and since the number of

phosphorous atoms is so low that's just

that's what we saw right now then is is

the number of electrons here

considerably increasing i mean what how

much is it more than the holes is it a

lot does it really matter

and the answer is yes it turns out that

even if you are using a very low amount

of impurity atoms their effect is

dramatically high incredibly high and to

understand why that works out to be that

way we have to look into the math behind

it and don't worry we're going to keep

the math very simple

now the first thing we'll do is write

down the doping concentration

doping level we just saw that

if you take phosphorus we'll take

phosphorus as an example um one

phosphorus atom is pretty much

surrounded by about a million silicon

atoms so let's write that down one

phosphorous atom

is surrounded by

surrounded by about 10 to the power 6 a

million silicon atoms and usually people

call that as one ppm one part per

million but that's what it means okay

and if we go back to our intrinsic

semiconductor intrinsic semiconductor a

pure semiconductor without any doping

then we have seen some numbers before

and let me just write that down one more

time we've seen that if you go to say

room temperature

if you look at room temperature and if

you take a tiny box of silicon

let's say one centimeter cube box of

silicon and if you look inside that

okay this is one centimeter cube let's

say then you will find roughly these

numbers can be worked out we don't have

to worry too much about them the numbers

can be the numbers will be roughly about

number of electrons

and the number of holes are equal and

they're about 10 to the power 10.

and the number of silicon atoms

themselves

the total number of silicon atoms is

roughly about

roughly about 10 to the 20 10 to the 22.

i just happen to remember these numbers

you don't have to remember this okay

it's definitely not needed we're just

going to work out some things with this

okay now having said this given this

we want to figure out how many

phosphorus atoms will be there in the

n-type

semiconductor all right

given this if you look at an n-type

semiconductor again take one centimeter

cube box

how many phosphorous atoms will you find

and this is math okay so i want you to

try and pause the video and and see if

you can figure this out look at this

number

look at this number and see if you can

do it

all right so we saw that 10

one phosphorous atom uh is surrounded by

a million silicon atoms so we could just

ask if you take 10 to the 22 silicon

atoms how many phosphorous atoms will be

there so let's just do it let's do that

we saw that 10 to the power 6 silicon

atoms

you will find one phosphorous atom

so if you have about 10 to the 22

because that's what you find in one

centimeter cube if there are 10 to the

22 silicon atoms

how many phosphorous atoms will you find

well if you do cross multiplication you

get 10 to the 22 divided by 10 to the 6

that is if you do that 10 to the 16

phosphorous atoms

and now get this we we saw that one

phosphorus atoms one phosphorous atom

donates one extra electron which means

that by adding this impurity the number

of electrons that we are getting

is we already had this much

plus 10 to the 16

plus 10 to the 16.

and if you add them that's not 10 to the

26 because it's an exponent but just

think about one and ten zeros one and

sixteen zeros

this number is so huge you can totally

neglect this and you could say that the

number of electrons

in the n type is roughly 10 to the 16.

look at that that is an incredible

amount of increase

and if you think about it that's a

million times higher than what we had

before but that's not it now it's time

for the climax

what do you think

happens to the number of holes

pause the video and think about this

okay now if we didn't think too much

here here's the way we could we could

answer this we could say that you see

but since we're adding phosphorus and

phosphorus only giving us electrons only

electrons would be affected and the

holes shouldn't be affected so we could

say that the number of holes should

remain 10 to the power 10

right

guess what that's wrong not just wrong

it's very wrong to understand why we

need to recall two important processes

that happen in semiconductors one

process is generation remember remember

thermal generation uh that's a process

by which electron hole pairs are

continuously being created due to

thermal energy that's happening all the

time and we've seen in previous videos

that that rate rate at which thermal

generation happens that is a function of

temperature it's only some function we

don't care what that is but some

function of temperature and we saw

another process called the recombination

where electron whole pairs meet up and

destroy each other and we saw that that

number depends on the product it's even

proportional to the product of the

number of electrons and holes and so

that number would be we could say some

constant k times this product and the

product would be about 10 to the 20.

and at thermal equilibrium these two

must be exactly the same otherwise the

total number of electrons and the holes

will keep on changing it'll keep on

increasing or decreasing arbitrarily

this is what we saw for intrinsic

now what can we write for extrinsic this

these two process are continuously

happening even in extrinsic

semiconductor even in the n-type

semiconductor so if you go up a little

bit

all right so if we write down the

generation rate over here well the

generation rate must be exactly the same

as before because the generation rate

only depends on the temperature we are

using the same temperature so the

generation rate over here for the n-type

must still be the same number it should

still be k times

k times 10 to the 20.

but what about the recombination rate

the recombination rate is the product of

these two right so if the number of

holes was 10 to the 10

look what happens to the recombination

rate this number would be a whopping 10

to the

26

and that's not equal to each other you

now see that the recombination rate

would be much higher than the generation

rate and that's not thermal equilibrium

so because the recombination rate has

skyrocketed what's going to happen now

is that a lot of electron holes will

recombine with each other and as a

reason a lot of holes will be destroyed

i mean of course electrons will also be

destroyed but the electron number is so

huge we can neglect that and so now we

can ask the question how many holes are

left well to do that

we know that the recombination rate is

the num product of number of electrons

and the number of holes

we have to make sure that the rate is

exactly the same as 10 to the 20. so to

do that let's say we don't know what

that is

it has to be equal to k times 10 to the

20.

and so now if you look carefully you see

that the number of holes

is not 10 to the 10 but it is 10 to the

20 divided by 10 to the 16 that is 10 to

the power 4.

that is 10 to the power 4 that means it

has decreased a million times

whoa so can you see the subtle effect

by adding phosphorus not only have you

increased the electrons a million times

more

but if you look carefully you've also

decreased the number of holes a million

times smaller

and that

is incredible and now if you look at the

ratio of the number of electrons and the

number of holes that's a million million

what is that i don't even know what to

call it anymore but the fascinating

thing is that we have just

done such a low level of doping and yet

the effect is so high and that is all

possible because in intrinsic in the

pure semiconductor we had this much

amount of charge carriers so guess what

this is only possible in semiconductors

and that's the main reason why we can we

can change the properties of

semiconductors and we can't do that for

conductor it's too high nothing will

work and for insulator is too low so it

only works for semiconductors isn't this

just awesome