Barrier Potential

Summary

This lecture covers the concept of the built-in potential or barrier potential in a PN junction diode without an applied bias. It explains how diffusion leads to the formation of a depletion layer, which acts as a barrier for further charge movement. The lecture introduces the formula for calculating the barrier potential (V_B = V_T * ln(Na * Nd / Ni^2)), where V_T is the thermal voltage, Na and Nd are acceptor and donor concentrations, and Ni is the intrinsic carrier density. The Boltzmann constant, temperature conversion to Kelvin, and the charge of an electron are also discussed. A numerical example calculates the built-in potential for a silicon PN junction at room temperature.

Takeaways

• 🔋 The built-in potential, also known as barrier potential, is the potential difference created at a PN junction with no applied bias.
• 🌀 Diffusion is the process where free charge carriers recombine, leading to the formation of a depletion layer depleted of free charge carriers.
• 💠 The depletion layer consists of fixed immobile ions with positive and negative charges, which create the barrier potential.
• 🚫 The barrier potential acts as a barrier to the further movement of charge, preventing the recombination of holes and electrons.
• 📘 The expression for barrier potential (V_B) is given by V_B = V_T * ln((n_a * n_d) / ni^2), where V_T is the thermal voltage.
• 🔬 Boltzmann's constant (K) is 1.38066 × 10^-23 J/K, used to calculate the thermal voltage (V_T).
• ⚖️ Absolute temperature (T) is in Kelvin, calculated by adding 273 to the temperature in degrees Celsius.
• ⚡ The charge of one electron (e) is 1.6 × 10^-19 coulombs, used in the calculation of V_T.
• 🔢 At room temperature (27°C or 300K), the thermal voltage (V_T) is approximately 0.026 volts.
• 📌 For a silicon PN junction at room temperature, the barrier potential is approximately 0.757 volts.
• 📚 The barrier potential values for silicon and germanium are often used in semiconductor calculations, with silicon typically at 0.7 volts and germanium at 0.3 volts.

Q & A

What is the built-in potential in a PN junction?

The built-in potential, also known as barrier potential, is a potential difference that arises at the junction of a PN junction diode due to the diffusion of charge carriers and the formation of a depletion layer. It acts as a barrier to the further movement of charge carriers.

What causes the formation of a depletion layer in a PN junction?

The depletion layer forms due to the diffusion process where free charge carriers recombine with each other, leading to the creation of immobile ions. This results in a region depleted of mobile charge carriers, leaving behind a layer of fixed immobile ions with opposite charges on the P and N sides.

Why is the depletion layer called so?

The depletion layer is called so because it is depleted of free charge carriers. It contains only fixed, immobile ions, which are the result of recombination between free charge carriers.

What is the role of the barrier potential in a PN junction?

The barrier potential acts as a barrier to the further movement of charge carriers. The positive layer on the N side repels electrons, and the negative layer on the P side repels holes, preventing further diffusion and maintaining the potential difference across the junction.

What is the expression for barrier potential (V_B)?

The expression for barrier potential (V_B) is given by V_B = V_T * ln((n_a * n_d) / ni^2), where V_T is the thermal voltage, n_a is the acceptor concentration, n_d is the donor concentration, and ni is the intrinsic carrier density.

What is the thermal voltage (V_T) and how is it calculated?

Thermal voltage (V_T) is the voltage equivalent of temperature and is calculated using the formula V_T = (K * T) / e, where K is the Boltzmann constant, T is the absolute temperature in Kelvin, and e is the charge of an electron.

What is the Boltzmann constant and its value?

The Boltzmann constant (K) is a physical constant that relates the energy at the particle level to temperature. Its value is 1.380649 × 10^-23 joules per Kelvin.

How do you convert temperature from Celsius to Kelvin?

To convert temperature from Celsius to Kelvin, you add 273 to the Celsius temperature. For example, 27 degrees Celsius is equal to 300 Kelvin.

What is the charge of an electron?

The charge of an electron (e) is -1.6 × 10^-19 coulombs.

How is the built-in potential of a silicon PN junction calculated at room temperature?

At room temperature (27 degrees Celsius or 300 Kelvin), the built-in potential of a silicon PN junction is calculated using the formula V_B = 0.026 * ln((n_a * n_d) / ni^2), with n_a, n_d, and ni being the acceptor concentration, donor concentration, and intrinsic carrier density, respectively.

What is the typical barrier potential for a silicon PN junction at room temperature?

The typical barrier potential for a silicon PN junction at room temperature is approximately 0.7 volts.

Outlines

00:00

🔬 PN Junction Diode and Built-in Potential

The paragraph discusses the concept of a PN junction diode without applied bias, explaining the formation of a depletion layer due to the diffusion of free charge carriers. Diffusion is defined as the recombination of free charge carriers, leading to immobile ions with either positive or negative charges. The depletion layer is formed on the P-side with negative immobile ions and on the N-side with positive immobile ions. This layer acts as a barrier to further charge movement, hence called the barrier potential or built-in potential. The paragraph also introduces the formula for calculating the barrier potential, V_B = V_T * ln((n_a * n_d) / ni^2), where V_T is the thermal voltage, n_a is the acceptor concentration, n_d is the donor concentration, and ni is the intrinsic carrier density. The Boltzmann constant (K) and the charge of an electron (e) are also mentioned as essential components in the formula.

05:02

🌡️ Calculating Thermal Voltage (V_T) and Absolute Temperature

This paragraph elaborates on the calculation of thermal voltage (V_T) using the formula V_T = (K * T) / e, where K is the Boltzmann constant, T is the absolute temperature in Kelvin, and e is the charge of an electron. The paragraph explains how to convert temperature from degrees Celsius to Kelvin by adding 273. The values of K and e are provided, and an example calculation for room temperature (27°C or 300K) results in V_T = 0.026 volts. The importance of using the correct temperature for accurate V_T calculations is emphasized, as changing temperature affects the value of V_T.

10:06

📘 Numerical Example of Built-in Potential Calculation

The final paragraph presents a numerical example to calculate the built-in potential (V_B) for a silicon PN junction at room temperature. Given the values for V_T (0.026 volts), acceptor concentration (n_a = 10^16 cm^-3), donor concentration (n_d = 10^16 cm^-3), and intrinsic carrier density (n_i = 1.5 * 10^10 cm^-3), the formula for V_B is applied. The calculation involves taking the natural logarithm of the ratio of the product of acceptor and donor concentrations to the square of the intrinsic carrier density, multiplied by V_T. The result is V_B = 0.757 volts, which represents the barrier potential for a silicon PN junction at room temperature. The paragraph also mentions that similar calculations will be used for other materials like germanium, with different barrier potentials.

Keywords

💡PN Junction

A PN Junction is a boundary or interface between a P-type semiconductor and an N-type semiconductor in a single crystal of semiconductor. It is a fundamental building block of many electronic devices like diodes and transistors. In the script, the PN Junction is discussed in the context of a diode with no applied bias, explaining the formation of a depletion layer due to diffusion of charge carriers.

💡Built-in Potential

Built-in Potential refers to the potential difference created across a PN Junction due to the diffusion of charge carriers and the resulting depletion region. It acts as a barrier to further movement of charge carriers, thus maintaining the diode's characteristics. The script explains that this potential is also known as barrier potential and is crucial for understanding the behavior of diodes.

💡Depletion Layer

The Depletion Layer is the region in a semiconductor where the mobile charge carriers have recombined, leaving behind a region devoid of free charge carriers but filled with immobile ions. In the script, it is described as being formed due to diffusion and is characterized by layers of positively and negatively charged immobile ions on the P and N sides, respectively.

💡Diffusion

Diffusion, in the context of semiconductor physics, is the movement of charge carriers from an area of higher concentration to an area of lower concentration. The script uses the term to describe how free charge carriers (electrons and holes) move and recombine, leading to the formation of the depletion layer and the uncovering of immobile ions.

💡Immobile Ions

Immobile Ions are atoms in a semiconductor lattice that have had their charge altered by the addition or removal of electrons or holes. The script explains that when holes combine with electrons, they become immobile ions with a net negative or positive charge, contributing to the formation of the depletion layer.

💡Barrier Potential

Barrier Potential is the potential energy barrier that forms at the PN Junction due to the separation of charge carriers. It prevents further diffusion of carriers and is crucial for the functioning of diodes. The script discusses how this potential acts as a barrier for the movement of charge carriers and is calculated using a specific formula.

💡Thermal Voltage (V_T)

Thermal Voltage, symbolized as V_T, is the voltage equivalent of the thermal energy in a semiconductor at a given temperature. It is used in the formula to calculate the barrier potential. The script provides the formula to calculate V_T and uses it as a base for calculating the barrier potential at room temperature.

💡Boltzmann Constant (k or K)

The Boltzmann Constant is a fundamental constant in physics that relates the energy at the particle level to temperature. It is used in the formula for calculating thermal voltage. The script mentions its value and its role in determining the thermal voltage at a given temperature.

💡Intrinsic Carrier Density (n_i)

Intrinsic Carrier Density refers to the number of charge carriers per unit volume in an intrinsic (pure, undoped) semiconductor. The script uses this term in the formula for calculating the barrier potential, indicating its importance in determining the potential barrier in a PN Junction.

💡Acceptor Concentration (n_a)

Acceptor Concentration is the number of acceptor atoms per unit volume in a P-type semiconductor. In the script, it is used in the numerical example to calculate the built-in potential of a silicon PN Junction, showing its role in determining the barrier potential.

💡Donor Concentration (n_d)

Donor Concentration is the number of donor atoms per unit volume in an N-type semiconductor. The script includes this term in the formula for calculating the barrier potential, highlighting its importance in the doping process and the resulting potential barrier.

Highlights

Explanation of PN Junction diode without applied bias

Introduction to built-in potential due to diffusion

Definition of diffusion and its role in PN Junction

Process of recombination of free charge carriers

Explanation of immobile ions acquiring charge

Formation of depletion layer and its characteristics

Role of depletion layer in impeding charge movement

Derivation of the term 'barrier potential'

Expression for barrier potential and its significance

Formula for barrier potential V_B and its components

Explanation of thermal voltage (V_T) and its calculation

Value of Boltzmann constant and its role

Conversion of Celsius temperature to Kelvin

Calculation of absolute temperature from Celsius

Charge of one electron and its significance in V_T

Detailed calculation of V_T at room temperature

General formula for V_T at any temperature

Numerical problem-solving approach for barrier potential

Practical example calculation for silicon PN Junction

Final calculation result for barrier potential at room temperature

Comparison of barrier potentials for silicon and germanium

Conclusion and预告 of next lecture topic

Transcripts

in the last lecture we completed PN

Junction diode with no applied bias I

explained by air potential in the same

lecture and it is also called as

built-in potential built-in potential in

case of no applied bias we do not apply

any external voltage source across these

two terminals and because of diffusion

we have depletion layer because of

diffusion we have depletion layer now

what is diffusion diffusion is the

process in which free charge carriers or

mobile charge carriers recombine with

each other for example for example if we

have immobile ion with hole and if this

hole combines with electron then we have

immobile ion with negative charge on the

other hand if we have immobile ion with

electron and if this electron combines

with hole we have immobile ion with

positive charge now why this immobile

ion is having negative charge on it

whereas this immobile ion is having

positive charge on it because hole this

hole is positively charged and this

immobile ion is losing one hole so it

will have one negative charge on it on

the other hand electron is negatively

charged and this immobile ion is losing

one electron so it will have positive

charge on it and if you see this if you

see the depletion layer you will find on

P side on P side we have layer of

negative immobile ions because whole

combined with electrons and on the N

side we have layer of positively charged

immobile ions because electrons combine

with holes so this is how we get the

depletion layer and it is called as

depletion layer because it is depleted

of free charge carriers we do not have

mobile charge carriers in this reason we

only have fixed immobile ions this whole

process is also called as uncovering of

immobile ions because when we have

immobile ion and hole the charge

neutrality is maintained when we have

mobile ion and electron then also

charged neutrality is maintained but

when whole combines with electron or

electron combines with whole the

uncovering of charge carriers takes

place and we have negatively charged

immobile ion and positively charged a

mobile ion and you can see the layer of

negative immobilize and layer of

positive immobilize act as the potential

difference and this potential difference

is called as barrier potential now why

we are calling it barrier potential

because it is acting as the barrier for

the further movement of charge this

positive layer here will repel the holes

and this negative layer here will repel

the electrons and because of this there

is no further movement of charge

therefore we call it barrier potential

it is also called as built-in potential

and in this lecture we will see the

expression for building potential and we

will also solve one numerical problem on

it so if I draw the built-in potential

or barrier potential then initially it

is zero initially it is zero then it

increases like this and the value the

value is given by V subscript B V

subscript B is barrier potential and we

have to find out the expression for

barrier potential V subscript B and it

is equal to KT by E natural log in

bracket we have na and D upon ni square

so this is the expression for barrier

potential and the derivation is not

important in this course you only have

to remember this formula we will use

this formula to find out barrier

potential this term this term KT by E is

VT VT is the thermal voltage this is

thermal voltage or you can call it

voltage world

age equivalent of temperature and V T is

equal to K T by E we can easily

calculate the value of VT and in

numerical problems we will use the value

of VT directly now what is K K is

Boltzmann constant Boltzmann's constant

and it is equal to one point one point

three eight zero double six multiplied

by 10 raised to power minus 23 joules

per Kelvin so this is the value of

Boltzmann constant and capital T here

capital T here is absolute temperature

absolute temperature and it is in Kelvin

the unit for absolute temperature is

Kelvin and if you have temperature in

degree Celsius if you have temperature

in degree Celsius and you want to

calculate the absolute temperature then

you can easily do it so this is how you

can find the absolute temperature T dash

is the temperature in degree Celsius and

you have to add 273 to it and you will

have your temperature in Kelvin this is

a very basic thing to know for example

for example if temperature is 27 degree

Celsius it means T prime or T dash is

equal to 27 degree Celsius to find out

absolute temperature to find out

absolute temperature

it means capital T it is equal to 273

plus 27 and this will give us 300 Kelvin

so in this way you can find out absolute

temperature the next thing is small e

small a small e is the charge of one

electron charge of electron and it is

equal to it is equal to 1.6

into 10 raised to power minus 19 coulomb

so we are done with the terms involved

in the volts equivalent of temperature

or thermal voltage now we will see what

we have inside this bracket and a and a

is the exception acceptor concentration

and D is donor donor concentration and

Ni and I is intrinsic intrinsic carrier

density so if we have all these things

we can easily calculate the value for VB

that is the barrier potential we will

first calculate the value of V T the

thermal voltage because we will use it

directly in numerical problems it will

save our time so first we will calculate

V T so let's do it quickly VT is equal

to KT by E and let's say the temperature

T - it means the temperature in degree

Celsius is equal to 27 degree Celsius

this is the room temperature this is the

room temperature and as we are

performing the calculations at room

temperature the value of VT is also

valid for room temperature only K is

equal to one point three eight zero

double 6 multiplied by 10 raised to

power minus 23

absolute temperature capital T is equal

to 273 plus 27 and it is equal to 300

Kelvin so we have 300 here and the

charge on one electron is 1.6 into 10

raised to power minus 19 and when you

solve this you will get zero point zero

two six volts so the value of VT is zero

point zero two six and we will use this

directly in numerical problem but there

is one important thing this value of VT

is valid for room temperature only this

is valid

room temperature only because when you

change the temperature when you change

the temperature this number here will

change and the value of VT will also

change but generally you will get

questions in which the temperature is 27

degree Celsius or in question it will be

given calculate the barrier potential at

room temperature in that case we will

take VT equals to zero point zero two

six volts

I will generalize this I will generalize

this for any temperature T dash we will

generalize this T is equal to 273 plus T

dash and this is in Kelvin

VT is equal to K KT by E T is equal to

273 plus T dash so we have 273 plus T

dash I can write this as e by K 273 plus

T dash e by K is 1 point 6 into 10

raised to power minus 19 divided by one

point three eight zero six six

multiplied by 10 raise to power minus 23

and when you solve this when you solve

this you will get 273 plus T dash

divided by one one six double zero so

this is the generalized form of VT and

if it is not the room temperature you

can easily put the value of temperature

here in degree Celsius and you will have

the value of VT so I will modify the

expression I will modify the expression

this expression and V B is equal to VT

natural log in bracket we have n a and D

upon ni square so this is the formula we

will use while solving the numerical

problems let's move to

the numerical problem and this problem

we have to consider a silicon PN

Junction a silicon PN Junction at room

temperature now we have room temperature

so we can say that value of VT is equal

to zero point zero two six volts and it

is doped at na equals to 10 raised to

power 16 per centimeter cube value of n

is equal to 10 raised to power 16 per

centimeter cube and value of nd the

donor concentration is equal to 10

raised to power 17 per centimeter cube

an intrinsic carrier density

it means ni is equal to 1.5 this is 1

point 5 into 10 raised to power 10 per

centimeter cube so n I is equal to 1

point 5 into 10 raised to power 10 per

centimeter cube and we have to calculate

the built-in potential it means we have

to calculate we beam this is very easy

problem we only have to put the values

in the formula so we'll do it quickly VB

is equal to VT natural log in bracket we

have n a nd by ni square VT is equal to

zero point zero two six natural log n a

is equal to 10 raised to power 16 so we

have 10 raised to power 16 multiplied by

10 raised to power 17 and is equal to 10

raised to power 17 and I is 1 point 5

into 10 raised to power 10 so we have 1

point 5 into 10 raised to power 10 whole

square 0.026 natural log 10 raised to

power 16 multiplied by 10 raised to

power 17 is 10 raised to power 33 1

point 5 square

is to point to 5 into 10 raised to power

20 right or we can write it as we can

write it as 0.026 natural log 10 raised

to power 13 10 raise to power 33 divided

by 10 raised to power 20 is equal to 10

raised to power 13 2.25 0.026

when you solve this when you solve this

you will get twenty nine point one two

three after multiplication we have zero

point seven five seven volts and this is

our answer so the barrier potential or

built-in potential is equal to is equal

to zero point seven five seven and this

is for silicon PN Junction at room

temperature and in coming presentations

also I will use barrier potential for

silicon equal to 0.7 volts and barrier

potential for germanium equals to zero

point three volts this is very important

because we will use this a lot this is

important and this is calculated at room

temperature so this is all for this

lecture

in the next lecture we will discuss

width of depletion region we will solve

one numerical problem on width of

depletion region so this is also in the

next one