Lecture 2

Question 1

Describe the basic structure of a direct bandgap semiconductor

Answer 1

Electron states in the conduction band behave like free electrons but with an effective mass of m_e*.

Holes in the valence band have a single effective mass of m_h*.

Question 2

For a direct bandgap semiconductor, the top of the valence band and the bottom of the conduction band are at ___ _____ k-vector.

Answer 2

The same

Question 3

For an indirect bandgap semiconductor, the top of the valence band and the bottom of the conduction band are at ___________ k-vectors.

Answer 3

Different

Question 4

Describe the basic structure of an indirect bandgap semiconductor

Answer 4

Question 5

What happens to a direct semiconductor when a photon (of energy equal to/greater than the bandgap) is fired at it?

Answer 5

The photon is absorbed and an electron crosses the bandgap from the valence band to the conduction band. This creates an electron-hole pair.

Question 6

How can semiconductor bandgaps be measured?

Answer 6

By measuring the optical absorption of photons by the semiconductor as a function of photon energy.

Question 7

What is the difference in k from the top of the valence band to the bottom of the conduction band in an indirect semiconductor?

Answer 7

~ π/a (where a = lattice constant)

Question 8

What must be conserved when electrons move from the valence band to the conduction band?

Answer 8

• Energy
• Wavevector, k

Question 9

Is photon absorption alone possible in an indirect semiconductor?

Answer 9

No

Question 10

Conservation of the wavevector, k, can be thought of the conservation of ‘________ ________’.

Answer 10

Effective momentum

Question 11

Give the equation for the ‘effective momentum’ (i.e. the wavevector) of an electron

Answer 11

k = wavevector
m* = effective mass
v = velocity

ℏk = p = momentum

Question 12

Give the equation for the energy of a photon

Answer 12

E = hf = hc/λ

E = energy
f = frequency
c = speed of light
λ = wavelength

Question 13

Give the equation for the wavevector of a photon

Answer 13

k = photon wavevector
ε = photon energy
c = speed of light

Question 14

What is a phonon?

Answer 14

A quantum of lattice vibrational energy.

Question 15

Why are phonons supplied to/emitted from indirect semiconductors?

Answer 15

To supply the additional k-vector needed for an indirect transition of an electron from the valence band to the conduction band.

Question 16

Give the equation for the energy of a phonon

Answer 16

ε = phonon energy
k_B = Boltzmann’s constant
T = temperature

Question 17

Give the equation for the wavevector of a phonon

Answer 17

k = phonon wavevector
ε = phonon energy
v_s = velocity of sound

Question 18

The energy of a phonon is _____ _______ than the energy of the bandgap.

Answer 18

Much smaller

Question 19

The energy of a photon is ____________ _______ to the energy of the bandgap.

Answer 19

Approximately equal

Question 20

The wavevector of a phonon is ____________ _______ to the change in the wavevector of the bandgap.

Answer 20

Approximately equal

Question 21

The energy of a photon is _____ _______ than the change in the wavevector of the bandgap.

Answer 21

Much smaller

Question 22

Give the equation for the bandgap energy when an electron in the valence band absorbs a photon and also absorbs a phonon to move to the conduction band

Answer 22

E_g = bandgap energy
ε = energy

Question 23

Give the equation for the change in the wavevector when an electron in the valence band absorbs a photon and also absorbs a phonon to move to the conduction band

Answer 23

∆k = change in wavevector
k = wavevector

Question 24

Give the equation for the bandgap energy when an electron in the valence band absorbs a photon and emits a phonon to move to the conduction band

Answer 24

E_g = bandgap energy
ε = energy

Question 25

Give the equation for the change in the wavevector when an electron in the valence band absorbs a photon and emits a phonon to move to the conduction band

Answer 25

∆k = change in wavevector k = wavevector

Question 26

Describe the transition of an electron across an indirect band gap when both a photon and a phonon are absorbed

Answer 26

Question 27

Describe the transition of an electron across an indirect band gap when both a photon is absorbed and a phonon is emitted

Answer 27

Question 28

________ gap semiconductors like _____ are required for efficient optoelectronics.

Answer 28

Direct GaAs

Question 29

What is the other name for conduction electron density?

Answer 29

Electron carrier density

Question 30

Describe the relationship between the electron carrier density and temperature

Answer 30

Electron number density depends approximately exponentially on temperature.

Question 31

Give the equation for the electron density in intrinsic (pure) semiconductors

Answer 31

n = electron density E_g = bandgap energy k_B = Boltzmann's constant T = temperature

Question 32

For intrinsic semiconductors, the number of electrons in the __________ band is ______ __ the number of holes in the _______ band.

Answer 32

Conduction Equal to Valence

Question 33

Give the equation for the energy of an electron state in the conduction band

Answer 33

ε = energy of electron state E_g = bandgap energy k = wavevector m_e* = effective mass of an electron

Question 34

Give the equation for the energy of a hole state in the valence band

Answer 34

ε = energy of hole state k = wavevector m_h* = effective mass of a hole

Question 35

Give the equation for the number density of electron states in the conduction band

Answer 35

g_e(ε) = number density m_e* = effective mass of an electron ε = energy of electron state E_g = bandgap energy

Question 36

Give the equation for the number density of hole states in the valence band

Answer 36

g_h(ε) = number density m_h* = effective mass of a hole ε = energy of electron state

Question 37

What does the Fermi-Diract distribution describe?

Answer 37

The probability that a conduction band electron state is occupied.

Question 38

Give the equation for the probability that a conduction band electron state is occupied

Answer 38

f_e(ε) = electron probability function ε = energy of electron state µ = chemical potential k_B = Boltzmann's constant T = temperature

Question 39

Give the equation that a valence band state is 'occupied by a hole' (i.e. the probability that the state is not occupied by an electron)

Answer 39

f_h(ε) = hole probability function f_e(ε) = electron probability function

Question 40

Give the equation for the number density of occupied electron states in the conduction band

Answer 40

n(ε) = number density of occupied states f_e(ε) = electron probability function g_e(ε) = electron number density

Question 41

Give the equation for the number density of occupied hole states in the valence band

Answer 41

p(ε) = number density of occupied states f_h(ε) = hole probability function g_h(ε) = hole number density

Question 42

What is chemical potential?

Answer 42

The chemical potential, µ(T), is the energy for which f(µ) = 1/2.

Question 43

Where is the chemical potential when the hole effective mass equals the electron effective mass

Answer 43

In the middle of the bandgap

Question 44

What is the Fermi energy?

Answer 44

The chemical potential at T = 0K (i.e. µ(0))

Question 45

What is the Fermi level?

Answer 45

The chemical potential at any temperature (i.e. µ(T))