Exercise 4.1
GaAs, at T = 300 K, is uniformly doped with acceptor impurity atoms to a concentra- tion of Na = 2 × 1016 cm−3. Assume an excess carrier lifetime of 5 × 10−7 s.
Determine the electron-hole recombination rate if the excess electron concentration is δn=5×1014 cm−3.
Exercise 4.2
Consider an infinitely large, homogeneous n-type semiconductor with a zero applied electric field. Assume that, for t < 0, the semiconductor is in thermal equilibrium and that, for t ≥ 0, a uniform generation rate exists in the crystal.
(a) Calculate the excess carrier concentration as a function of time assuming the condition of low injection.
(b) Consider n-type silicon at T = 300 K doped to Nd = 5 × 1016 cm−3. Assume that g′ =5×1021 cm−3 s−1 andletτp0 =10−7 s.
Determineδp(t)at(i)t=0,(ii)t=10−7 s,(iii)t=5×10−7 s,and(iv)t→∞.
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Exercise 4.3
Consider a silicon sample at T = 300 K that is uniformly doped with acceptor impurity atoms at a concentration of Na = 1016 cm−3. At t = 0, a light source is turned on gener- ating excess carriers uniformly throughout the sample at a rate of g′ = 8× 1020 cm−3 s−1. Assume the minority carrier lifetime is τn0 = 5 × 10−7 s, and assume mobility values of μn =900cm2/V·sandμp =380cm2/V·s.
(a) Determine the conductivity of the silicon as a function of time for t ≥ 0. (b) What is the value of conductivity at (i)t = 0 and (ii) t = ∞ ?
Exercise 4.4
A p-type gallium arsenide semiconductor at T = 300 K is doped at Na = 1016 cm−3. The excess carrier concentration varies linearly from 1014 cm−3 to zero over a distance of 50μm. Plot the position of the quasi-Fermi levels with respect to the intrinsic Fermi level versus distance.
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Exercise 4.5
In a GaAs material at T = 300 K, the doping concentrations are Nd = 8×1015 cm−3 and Na = 2×1015 cm−3. The thermal equilibrium recombination rate is Ro = 4× 104 cm−3 s−1.
1. A uniform generation rate for excess carriers results in an excess carrier recombination rate of R′ = 2× 1021 cm−3 s−1. What is the steady-state excess carrier concentration?
2. What in the excess carrier lifetime?
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Exercise 4.6
Consider a bar of n-type silicon that is uniformly doped to a value of Nd = 2 × 1016 cm−3 atT =300K.
The applied electric field is zero.
A light source is incident on the end of the semiconductor (x = 0).
The steady-state concentration of excess carriers generated at x = 0 is ∆n(0) =
∆p(0)=3×1014 cm−3.
Assume the following parameters: μn = 1100 cm2/Vs, μp = 500 cm2/Vs, τn0 = 2 ×
10−6 s,andτp0 =8×10−7 s. Neglecting surface effects
(a) Determine the steady-state excess electron and hole concentrations as a function of distance into the semiconductor from the surface (x = 0).
(b) Calculate the steady-state hole diffusion current density as a function of distance into the surface from the surface (x = 0).
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Reference
1. Neamen, Donald A. Semiconductor physics and devices: basic principles. McGraw- hill, 2003.
