Lecture 3

Question 1

Give the integral for the total electron density in the conduction band

Answer 1

n = total electron density of conduction band
f_e(ε) = electron state probability
g_e(ε) = density of electron state

Question 2

Give the equation for the total number density of electrons in the conduction band of an intrinsic semiconductor

Answer 2

n = number density of electrons
µ = chemical potential
E_g = bandgap energy

Question 3

Give the equation for the total number density of holes in the valence band of an intrinsic semiconductor

Answer 3

p = number density of holes
µ = chemical potential

Question 4

Give the equation for the product of the number density of electrons and the number density of holes in an intrinsic semiconductor

Answer 4

n = number density of electrons
p = number density of holes
E_g = bandgap energy

Question 5

Give the equation for the chemical potential of an intrinsic semiconductor in terms of the number of electrons in the conduction band

Answer 5

µ = chemical potential
E_g = bandgap energy
k_B = Boltzmann’s constant
T = temperature
n = total electron density

Question 6

Give the equation for the chemical potential of an intrinsic semiconductor in terms of the number of holes in the valence band

Answer 6

µ = chemical potential
k_B = Boltzmann’s constant
T = temperature
p = total hole density

Question 7

Describe the relationship between the number density of holes and the number density of electrons in an intrinsic semiconductor

Answer 7

n = p

Question 8

Give the equation for the number density of holes and electrons in an intrinsic semiconductor

Answer 8

n = number density of electrons
p = number density of holes
E_g = bandgap energy

Question 9

Give the equation for the chemical potential of an intrinsic semiconductor in terms of electrons AND holes

Answer 9

µ = chemical potential

Question 10

Why aren’t intrinsic semiconductors used in semiconductor devices?

Answer 10

Because the electron and hole densities are too temperature dependent.

Question 11

How are the number and type of carriers (electrons/holes) controlled in an extrinsic semiconductor?

Answer 11

By introducing impurities (doping)

Question 12

What is an n-type semiconductor?

Answer 12

An extrinsic semiconductor with an excess number of electrons.

Question 13

How is an extrinsic semiconductor with excess electrons produced?

Answer 13

By substituting an element with 5 valence electrons into a material with 4 valence electrons, generating one excess electron per atom. This produces an n-type semiconductor.

Question 14

What is a p-type semiconductor?

Answer 14

An extrinsic semiconductor with an excess number of holes.

Question 15

How is an extrinsic semiconductor with excess holes produced?

Answer 15

By substituting an element with 3 valence electrons into a material with 4 valence electrons, leaving one missing electron per atom. This produces a p-type semiconductor.

Question 16

How are compound semiconductors doped?

Answer 16

An atom with 1 more/less electrons is substituted into one of the two elements, causing there to be an excess/loss of electrons.

Question 17

Give an example of an n-type compound semiconductor

Answer 17

Silicon can be used as a substitute for Gallium to dope Gallium Arsenide (GaAs).

Question 18

Give an example of a p-type compound semiconductor

Answer 18

Carbon can be used as a substitute for Arsenic to dope Gallium Arsenide (GaAs).

Question 19

What is the ‘donor energy level’?

Answer 19

The energy that binds the extra electron to the positively charged donor ion. It sits at this energy level at T = 0 but, at room temperature, most electrons are activated from the donor energy level to the conduction band.

Question 20

What is the ‘acceptor energy level’?

Answer 20

The energy that binds the extra hole to the negatively charged acceptor atom. At room temperature, most acceptor levels are filled by electrons from the valence band.