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MSE+302+Problem+Set+2_solutions

# MSE+302+Problem+Set+2_solutions - MSE 302 Problem Set 2...

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MSE 302 Problem Set 2 Solutions (32 Points) 1. (6 Points) a. d o Aug o r d Aug r p p τ α α τ τ τ τ τ + + = 1 1 1 1 1 1 2 + + = b. The Auger and defect rates will be equal when 3 16 2 10 6 . 8 ... 1 × = = cm p p o o Aug d α τ ( **note , this rate coefficient is ~100x too high, so a more realistic p o for the point when the Auger rate dominates would be ~10 18 cm -3) At this dopant concentration, the radiative decay rate is slower than the Auger or defect rates. c. Using the Einstein relation and mobility data for electrons q kT L n n τ μ = At p o =10 15 cm -3 , the defect rate dominates m q s kT Vs m L n μ 420 10 5 . 4 15 . 0 5 2 = × = At p o =10 19 cm -3 , the Auger process dominates and s 9 10 3 . 3 × τ m q s kT Vs m L n μ 93 . 0 10 3 . 3 01 . 0 9 2 = × = 2. (12 Points) a. Remember that EQE is the number of electrons out of your device divided by the number of photons that strike your device. In part a) we have assumed no reflection or recombination losses and complete absorption so the EQE should be perfect starting from wavelengths equal to the bandgap energy. I have included this EQE curve below.

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