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240b_ps3 - Physics 240B Problem Set#3(20 1 M L Cohen Spring...

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Physics 240B M. L. Cohen Spring 2008 Problem Set #3 Due: 03/18/08 ( 20) 1. "Ultimate efficiency" of a single-gap solar cell. The goal of this problem is to derive an upper bound on the power conversion efficiency—defined here as the ratio of output electrical power to input radiative power—of a photovoltaic (PV) device with a single band gap, E g . Consider an idealized solar cell, a pn junction with surface area 1 m 2 , held at T = 0K. Assume the sun is a blackbody with T = 6000K. (a) Compute the incident power (energy/sec) due to the blackbody radiation, assuming for simplicity, all the black body radiation is focused on the 1m 2 area. (b) On an average sunny day around lunchtime, incident sunlight has an intensity of about 1000 W/m 2 . Why does the number in (a) differ? (c) Assuming each incident photon with energy greater than E g produces a single electron-hole pair ("detailed balance"), each charge producing a voltage of magnitude h ν g /e, derive an expression for the output electrical power in terms of the band gap E g . (Hint: If each of the number of absorbable photons resulted in
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