VE320 Homework 4 -Solved

 Exercise 4.1
GaAs, at T = 300 K, is uniformly doped with acceptor impurity atoms to a concentration 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 conditionof 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 and let τp0 = 10−7 s.

Determine δp(t) at (i) t = 0, (ii) t = 10−7 s, (iii) t = 5 × 10−7 s, and (iv) t → ∞.

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 generating 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 = 900 cm2/V · s and µp = 380 cm2/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.

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 recombinationrate of R′ = 2× 1021 cm−3 s−1. What is the steady-state excess carrier concentration?

2.    What in the excess carrier lifetime?


Exercise 4.6
Consider a bar of n-type silicon that is uniformly doped to a value of Nd = 2 × 1016 cm−3 at T = 300 K.

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, and τp0 = 8 × 10−7 s.

Neglecting surface effects

(a)     Determine the steady-state excess electron and hole concentrations as a function ofdistance into the semiconductor from the surface (x = 0).

(b)    Calculate the steady-state hole diffusion current density as a function of distance intothe surface from the surface (x = 0).
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