Spring 2016
EE 529 Homework #1 (due on 4/14/2016)
1. (25%) An In1− x Gax As y P1− y quaternary compound that is lattice matched to InP at 300K has a
1.3 µm. It is not intentionally doped, so that its
bandgap optical wavelength of λ g =
equilibrium electron and hole concentrations are n0 ≈ p0 ≈ ni = 1.7 × 1022 m −3 . The
recombination coefficients A, B, and C can be determined experimentally by measuring the
carrier lifetime τs as a function of the injected excess carrier concentration N. (Assume
C=
C=
C / 2 ) This experiment can be carried out by measuring the decay time of the
e
h
photoluminescence when the sample is injected with excess electron and hole pairs either
optically or electrically. Such an experiment yields the following data: τs =30, 17.1, 3.13,
and 1.25 ns for N = 5 × 1023 m −3 , 1 × 1024 m −3 , 5 × 1024 m −3 , and 1 × 1025 m −3 , respectively.
(a) What is the composition of this quaternary compound?
(b) Find coefficients A, B, and C from these experimental data.
(c) What is the carrier lifetime at an excess carrier concentration of N = 2 × 1025 m −3 ?
2. (25%) Consider a p-type GaAs that is doped with N a− − N d+ =×
2 1022 m −3 . The intrinsic
carrier concentration for GaAs at 300 K=
ni 2.33 × 1012 m −3 . The recombination coefficients
are A= 5 × 105 s −1 , B= 8 × 10−17 m3 s −1 , and C =Ce + Ch =5 × 10−42 m 6 s −1 . Assume that
C=
C=
C / 2 . (a) Find the ranges of the excess carrier concentration N where each of the
e
h
three different recombination processes dominates. (b) Assume both the Shockley-Read and
the Auger recombination processes in this semiconductor are nonradiative while the
bimolecular process is purely radiative. Find and plot the spontaneous carrier recombination
lifetime, the radiative carrier lifetime, and the internal quantum efficiency as a function of
excess carrier concentration N for N in the range between 1018 and 1026 m-3. (c) In what range
of carrier densities is high radiative efficiency ( ηi > 50% ) found? What is the peak internal
quantum efficiency?
3. (25%) An n-type sample of GaAs has 1014 cm-3 electrons in the conduction band in thermal
equilibrium at room temperature. It has the following parameters: Eg = 1.42 eV, ni = 2.33×
N C 4.35 × 1017 cm-3, and N
=
9.41 × 1018 cm-3. Photo-excitation is used to create
106 cm-3, =
V
1020 cm-3s-1 electron-hole pairs in the sample. Assume bimolecular recombination process
dominates and the coefficient for bimolecular recombination B= 8 × 10−11 cm3 s −1 .
(a) Determine the electron and hole concentration, and the recombination lifetime.
(b) Find the energy position of the hole and electron quasi-Fermi levels in the energy
bandgap under the photo-excitation condition.
4. (25%) A GaAs p-n junction diode has a cross-sectional area A = 1 mm2. The thickness of the
p- and n-regions is 1.0 mm each. It is symmetrically doped with N=
N=
1017 cm −3 . At
a
d
300 K the electron and hole mobility in GaAs=
is m e 8500 cm 2 /V ⋅ s
and
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Spring 2016
=
m h 400 cm 2 /V ⋅ s . The intrinsic carrier concentration is ni = 2.33 × 106 cm −3 . Assume the
minority carrier lifetime is 10 ns in both n- and p-regions.
(a) Neglect recombination in the depletion layer, calculate the saturation current density J s .
(b) Calculate the forward bias across the depletion layer necessary to drive 1 mA and 10 mA
through the diode.
(c) Taking into consideration the voltage drop across the bulk p- and n-regions, what should
be the overall external bias for these forward currents?
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