GATE EC 2022 Set 1 — Question 56
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Question
A -type semiconductor with zero electric field is under illumination (low level injection) in steady state condition. Excess minority carrier density is zero at , where cm is the diffusion length of electrons. Assume electronic charge, C. The profiles of photo-generation rate of carriers and the recombination rate of excess minority carriers () are shown. Under these conditions, the magnitude of the current density due to the photo-generated electrons at is _________ mA/cm (rounded off to two decimal places).
📷 Figure: Profiles vs x: photo-generation rate 10^20 cm^-3/s for -l_n<x<l_n (zero elsewhere), and recombination rate R = 10^20 exp(-|x|/l_n) for -l_n<x<l_n (zero elsewhere), with x marked from -2l_n to 2l_n
Correct answer
0.57 to 0.61
Solution
With zero electric field the electron current is pure diffusion, and in steady state the continuity equation givesNet generation inside the sample (both and are non-zero only for ):The profiles are symmetric about and the excess density vanishes at both ends , so half of these electrons flow out through :Answer: 0.59
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