I need an answer with solution. Thanks in advance. 4. A piece of intrinsic silic

Question

I need an answer with solution. Thanks in advance.

4. A piece of intrinsic silicon is illuminated with light (photon energy Eg) such that carriers are created uniformly everywhere in the sample at the rate of 4 X 18 cm 3s 1. If the lifetime of the carriers is 106 sec, what is the change in conductivity due to the exposure to light. Assume a steady state condition, i e. carrier concentrations are constant in time. Take the mobility values from the appropriate figures in the course reader. Mobilities for intrinsic silicon: ni 1420 cm2vis 1 Alpi 500 cm2 V-is

Explanation / Answer

When illuminated with light for one incident photon, we get a pair electron-hole, so that the number of excess electrons and holes are the same. The semiconductor will remain intrinsic (the Fermi level will still lie at the middle of the gap). Thus the given values of the mobilities will not change.

delta(n) = delta(p) = G-R

G=4*10^18 1/(cm^3*s) is the generation rate

R =1/(V*t) is the recombination rate
V =1 cm^3
t = 10^-6 sec
R =10^6 1/(cm^3*s)

delta(n) = G   since G>>R

Change in conductivity is
delta(sigma) = e*delta(n)*mu_n +e*delta(p)*mu_p = e*delta(n)*(mu_n+mu_p) =
=1.6*10^-19*4*10^18*(1420+500)=1228.8 1/(ohm*cm)

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