Lecture 2 Flashcards
Describe the basic structure of a direct bandgap semiconductor
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*.
For a direct bandgap semiconductor, the top of the valence band and the bottom of the conduction band are at ___ _____ k-vector.
The same
For an indirect bandgap semiconductor, the top of the valence band and the bottom of the conduction band are at ___________ k-vectors.
Different
Describe the basic structure of an indirect bandgap semiconductor
What happens to a direct semiconductor when a photon (of energy equal to/greater than the bandgap) is fired at it?
The photon is absorbed and an electron crosses the bandgap from the valence band to the conduction band. This creates an electron-hole pair.
How can semiconductor bandgaps be measured?
By measuring the optical absorption of photons by the semiconductor as a function of photon energy.
What is the difference in k from the top of the valence band to the bottom of the conduction band in an indirect semiconductor?
~ π/a (where a = lattice constant)
What must be conserved when electrons move from the valence band to the conduction band?
- Energy
- Wavevector, k
Is photon absorption alone possible in an indirect semiconductor?
No
Conservation of the wavevector, k, can be thought of the conservation of ‘________ ________’.
Effective momentum
Give the equation for the ‘effective momentum’ (i.e. the wavevector) of an electron
k = wavevector
m* = effective mass
v = velocity
ℏk = p = momentum
Give the equation for the energy of a photon
E = hf = hc/λ
E = energy
f = frequency
c = speed of light
λ = wavelength
Give the equation for the wavevector of a photon
k = photon wavevector
ε = photon energy
c = speed of light
What is a phonon?
A quantum of lattice vibrational energy.
Why are phonons supplied to/emitted from indirect semiconductors?
To supply the additional k-vector needed for an indirect transition of an electron from the valence band to the conduction band.
Give the equation for the energy of a phonon
ε = phonon energy
k_B = Boltzmann’s constant
T = temperature
Give the equation for the wavevector of a phonon
k = phonon wavevector
ε = phonon energy
v_s = velocity of sound
The energy of a phonon is _____ _______ than the energy of the bandgap.
Much smaller
The energy of a photon is ____________ _______ to the energy of the bandgap.
Approximately equal
The wavevector of a phonon is ____________ _______ to the change in the wavevector of the bandgap.
Approximately equal
The energy of a photon is _____ _______ than the change in the wavevector of the bandgap.
Much smaller
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
E_g = bandgap energy
ε = energy
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
∆k = change in wavevector
k = wavevector
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
E_g = bandgap energy
ε = energy
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
∆k = change in wavevector
k = wavevector
Describe the transition of an electron across an indirect band gap when both a photon and a phonon are absorbed
Describe the transition of an electron across an indirect band gap when both a photon is absorbed and a phonon is emitted
________ gap semiconductors like _____ are required for efficient optoelectronics.
Direct
GaAs
What is the other name for conduction electron density?
Electron carrier density
Describe the relationship between the electron carrier density and temperature
Electron number density depends approximately exponentially on temperature.
Give the equation for the electron density in intrinsic (pure) semiconductors
n = electron density
E_g = bandgap energy
k_B = Boltzmann’s constant
T = temperature
For intrinsic semiconductors, the number of electrons in the __________ band is ______ __ the number of holes in the _______ band.
Conduction
Equal to
Valence
Give the equation for the energy of an electron state in the conduction band
ε = energy of electron state
E_g = bandgap energy
k = wavevector
m_e* = effective mass of an electron
Give the equation for the energy of a hole state in the valence band
ε = energy of hole state
k = wavevector
m_h* = effective mass of a hole
Give the equation for the number density of electron states in the conduction band
g_e(ε) = number density
m_e* = effective mass of an electron
ε = energy of electron state
E_g = bandgap energy
Give the equation for the number density of hole states in the valence band
g_h(ε) = number density
m_h* = effective mass of a hole
ε = energy of electron state
What does the Fermi-Diract distribution describe?
The probability that a conduction band electron state is occupied.
Give the equation for the probability that a conduction band electron state is occupied
f_e(ε) = electron probability function
ε = energy of electron state
µ = chemical potential
k_B = Boltzmann’s constant
T = temperature
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)
f_h(ε) = hole probability function
f_e(ε) = electron probability function
Give the equation for the number density of occupied electron states in the conduction band
n(ε) = number density of occupied states
f_e(ε) = electron probability function
g_e(ε) = electron number density
Give the equation for the number density of occupied hole states in the valence band
p(ε) = number density of occupied states
f_h(ε) = hole probability function
g_h(ε) = hole number density
What is chemical potential?
The chemical potential, µ(T), is the energy for which f(µ) = 1/2.
Where is the chemical potential when the hole effective mass equals the electron effective mass
In the middle of the bandgap
What is the Fermi energy?
The chemical potential at T = 0K (i.e. µ(0))
What is the Fermi level?
The chemical potential at any temperature (i.e. µ(T))
