hwk3.pdf - UCSD Department of Electrical and Computer...

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UCSD Department of Electrical and Computer Engineering ECE 183 Winter 2018 Homework No. 3: Semiconductor Gain Assigned: February 8, 2018. Due: February 22, 2018. 1 Gain spectrum in GaAs We will consider transitions between the conduction band, effective electron mass m c = 0 . 067 m 0 and the heavy-hole valence band, effective hole mass m v = 0 . 50 m 0 . The energy gap is E g Γ = 1.42 eV at temperature T = 300 K. Please use the provided Matlab code to answer the following questions: (a) On the same graph for both the conduction and valence bands, plot E (eV) along the vertical axis and the density of states (per unit energy) ρ ( E ) in units of cm - 3 eV - 1 for the two bands. Use a logarithmic scale for the horizontal axis. (b) On the same graph, also plot the density of filled electron states and empty hole states, for a few different values of N (units of cm - 3 ). You will get a feel for plausible numbers by trying out different values for N ; also try different values of N for the two bands. (c) Assume N c = 1 × 10 18 cm - 3 and N v = 1 × 10 19 cm - 3 . A simple expression for the gain coefficient is γ ( ω ) = λ 2 8 π 2 n 2 τ 2 m r ~ 3 2 ω - E g ~ 1 2 [ f c ( ω ) - f v ( ω )] (1) where τ 3 × 10 - 9 s is the recombination lifetime of an electron in the conduction band with a hole in the valence band, and m r is the reduced effective mass, defined as 1 m r = 1 m c + 1 m v .
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