Problem # 1:
For a non-degenerate semiconductor, the peak in the electron distribution versus energy inside the
conduction band occurs at Ec + kbT/2. Expressed as a fraction of the electron population at the peak
energy, what is the electron population in a non-degenerate semiconductor at E = Ec + 5kbT? Consider
GaAs, what is the maximum donor and acceptor concentration at room temperature?
Problem # 2:
At room temperature, an unknown indirect band gap, intrinsic, cubic semiconductor has the following
band structure: There are 6 X minima along the <100> directions. If mn*(Γ) = 0.065 m0, mn*(X) = 0.30
m0 for each X minimum, mp* = 0.47m0, the band gap is 1.7 eV and the energy separation between Γ and
X is 0.35 eV. At what temperature is the electron concentration in Γ the same as at X?
Problem # 3:
A 2 cm long doped Si bar with Nd = 1016 cm-3 has a cross-sectional area of 0.05 cm2, what is the current if
we apply 2V across it? Now shine a laser on the system which generates 1020 cm-3 EHP per second
uniformly in the bar and the electron and hole lifetimes are both 10-4 s what is the new current? Assume
that α does not change for high-level injection. If the voltage is increased to 100,000 V, what is the new
current? Assume the hole mobility is 500 cm2/V*s but you must choose the proper value for electrons.
Problem # 4:
I want you to design a photodetector using 5 μm thick CdS assuming that the electron and hole lifetimes
are 1 μs and Nd = 1014 cm-3. The dark resistance should be 10 MΩ and must fit in a square 0.5 cm on a
side. What is the resistance change when 1021 EHP/cm3*s are generated when the photodetector is
illuminated?
Problem # 5:
A 100-mW laser beam with wavelength λ = 632.8 nm laser is focused on a 100 μm thick piece of GaAs.
The absorption coefficient is 3 x 104 cm-1. Find the number of photons emitted per second by radiative
recombination in the GaAs assuming perfect efficiency. What is the power delivered to the sample as
heat?