Homework chapter 12
PROBLEMS
Section 12.1 Optical Absorption
12.1 (a) Calculate the maximum wavelength  of a light source that can generate
electron-hole pairs in Ge, Si, and GaAs. (b) Two sources generate light at
wavelengths of  = 570 nm and  = 700 nm. What are the corresponding photon
energies?
12.2 (a) A sample of GaAs is 0.35 m thick. The sample is illuminated with a light
source with hv = 2 eV. Determine the absorption coefficient and determine the
percentage of light that is absorbed in the sample. (b) Repeat part (a) for silicon.
12.3 A light source with hv = 1.3 eV and at power density of 10-2 W/cm2 is incident
on a thin slab of silicon. The excess minority-carrier lifetime is 10-6 s. Determine
the electron-hole generation rate and the steady-state excess carrier
concentration. Neglect surface effect.
12.4 Consider an n-type GaAs sample with p = 10-7 s. (a) It is desired to generate a
steady-state excess carrier concentration of p = 1015 cm-3 at the surface. The
incident photon energy is hv = 1.9 eV. Determine the incident power density
required. (Neglect surface effects.) (b) At what distance in the semiconductor
does the generation rate drop to 20 percent of that at the surface?
12.5 (a) Consider a GaAs semiconductor illuminated with photons at an energy of hv
= 1.65 eV. Determine the thickness of the material so that 75 percent of the
energy is absorbed. (b) Determine the thickness so that 75 percent of the energy
is transmitted.
12.6 If the thickness of a GaAs semiconductor is 1 m and 50 percent of the incident
monochromic photon energy is absorbed, determine the incident photon energy
and wavelength.
*12.7 Consider monochromatic light at an intensity Iv0 incident on the surface at x = 0
of an n-type semiconductor that extends to x = . Assume the electric field is
zero in the semiconductor and assume a surface recombination velocity, s.
Taking into account the absorption coefficient, determine the steady-state excess
hole concentration as a function of x.
*12.8 Monochromatic light with intensity Iv0 is incident on a p-type semiconductor as
shown in Figure P12.8. Assume the surface recombination velocity at x = 0 is s =
 and assume the surface recombination velocity at x = W is s = s0. Derive the
expression for the steady-state excess electron concentration as a function of x.
Iv0
s=
s = s0
x=0
x=W
Figure P12.8 Figure for Problem 12.8.
Section 12.2 Solar Cells
12.9 Consider an ideal long n+p junction GaAs solar cell at T = 300 K in which
excess carriers are uniformly generated. The parameters of the diode are as
following:
Nd = 1019 cm-3
Na = 3  1016 cm-3
Dp = 6 cm2/s
Dn = 18 cm2/s
p0 = 5  10-7 s
n0 = 5  10-6 s
The generated photocurrent density is JL = 30 mA/cm2. Plot the open-circuit
voltage as a function of the acceptor doping concentration for 1015  Na  1018
cm-3.
12.11 Consider the solar cell in Problem 12.10. If the solar intensity is increased by a
factor of 10, determine the maximum power output of the solar cell. By what
factor has the power increased from that in Problem 12.10?
12.13 The absorption coefficient in amorphous silicon is approximately 10 4 cm-1 at hv
= 1.7 eV and 105 cm-1 at hv = 2.0 eV. Determine the amorphous silicon thickness
for each case so that 90 percent of the photons are absorbed.
Section 12.3 Photodetectors
12.15 Excess arriers are uniformly generated in a GaAs photoconductor at a rate of
GL = 1021 cm-3-s-1. The area is A = 10-4 cm2 and the length is L = 100 m. The
other parameters are
Nd = 5  1016 cm-3
Na = 0
n = 8000 cm2/V-s
p = 250 cm2/V-s
n0 = 10-7 s
p0 = 10-8 s
If a voltage of 5 V is applied, calculate (a) the steady-state excess carrier
concentration, (b) the photoconductivity, (c) the steady-state photocurrent, and (d)
the photoconductor gain.
12.17 Consider a long silicon pn junction photodiode at T = 300 K with the following
parameters:
Nd = 2  1016 cm-3
Nd = 1018 cm-3
Dn = 25 cm2/s
Dp = 10 cm2/s
n0 = 2  10-7 s
p0 = 10-7 s
Assume a reverse-bias voltage of VR = 5 V is applied and assume a uniform
generation rate of GL = 1021 cm-3-s-1 exists throughout the entire photodiode.
Calculate (a) the prompt photocurrent density and (b) the total steady-state
photocurrent density.
12.19 Consider a silicon PIN photodiode at T = 300 K. Consider intrinsic layer
widths of 1, 10, and 100 m. If the incident photon flux is 0 = 1017 cm-2-s-1 and
the absorption coefficient is  = 3  103 cm-1, calculate the prompt photocurrent
density for each diode.
Section 12.4 Light-Emitting Diodes
12.21 Consider a pn junction GaAs LED. Assume that photons are generated
uniformly in all directions in a plane perpendicular to the junction at a distance
of 0.50 m from the surface. (a) Taking into account total internal reflection,
calculate the fraction of photons that have the potential of being emitted from
be semiconductor. (b) Using the results of part (a) and including Fresnel loss,
determine the fraction of generated photons that will be emitted from the
semiconductor into air (neglect absorption losses).
Section 12.5 Laser Diodes
12.23 Consider an optical cavity. If N >> 1, show that the wavelength separation
between two adjacent resonant modes is  = 2/2L.