206 CHAPTER 4. JUNCTIONS IN SEMICONDUCTORS:P-NDIODES
Problem 4.13The diode of problem 4.12 has an area of 1 mm^2 and is operated at a
forward bias of 1.2 V. Assume that 50% of the minority carriers injected recombine with
the majority charge to produce photons. Calculate the rate of the photon generation in the
n-andp-side of the diode.
Problem 4.14Consider a GaAsp-ndiode with a doping profile ofNa=10^16 cm−^3 ,
Nd=10^17 cm−^3 at 300 K. The minority carrier lifetimes areτn=10−^7 s;τp=10−^8 s.
The electron and hole diffusion coefficients are 150 cm^2 /s and 24 cm^2 /s, respectively.
Calculate and plot the minority carrier density in the quasi-neutralnandpregions at a
forward bias of 1.0 V.
Problem 4.15Consider ap-ndiode made from InAs at 300 K. The doping is
Na=10^16 cm−^3 =Nd. Calculate the saturation current density if the electron and hole
density of states masses are 0.02moand 0.4mo, respectively. Compare this value with that
of a siliconp-ndiode doped at the same levels. The diffusion coefficients are
Dn= 800cm^2 /s;Dp=30cm^2 /s. The carrier lifetimes areτn=τp=10−^8 sforInAs.
For the silicon diode use the valuesDn=30cm^2 /s;Dp=10cm^2 /s;τn=τp=10−^7 s.
Problem 4.16Consider ap-ndiode in which the doping is linearly graded. The doping is
given by
Nd−Na=Gx
so that the doping isp-type atx< 0 andn-type atx> 0. Show that the electric field
profile is given by
E(x)=
e
2
G
[
x^2 −
(
W
2
) 2 ]
whereWis the depletion width, given by
W=
[
12 (Vbi−V)
eG
] 1 / 3
Problem 4.17A silicon diode is being used as a thermometer by operating it at a fixed
forward-bias current. The voltage is then a measure of the temperature. At 300 K, the
diode voltage is found to be 0.6 V. How much will the voltage change if the temperature
changes by 1 K?
Problem 4.18Compare the dark currents (i.e., reverse saturation current) inp-ndiodes
fabricated from GaAs, Si, Ge, and In 0. 53 Ga 0. 47 As. Assume that all the diodes are doped at
Nd=Na=10^18 cm−^3. The material parameters are (300 K):
GaAs : τn=τp=10−^8 s;Dn= 100 cm^2 /s;Dp=20cm^2 /s
Si : τn=τp=10−^7 s;Dn=30cm^2 /s;Dp=15cm^2 /s
Ge : τn=τp=10−^7 s;Dn=50cm^2 /s;Dp=30cm^2 /s
Whenp-ndiodes are used as light detectors, the dark current is a noise source.
