302+midterm+_2006_+solutions+2

302+midterm+_2006_+solutions+2 - MATSCI 302: Solar Cells...

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MATSCI 302: Solar Cells Midterm Exam November 2, 2006 1. Recombination The minority carrier lifetime in the bulk (i.e. not near the surface) of a semiconductor grade silicon wafer could in principle be limited by radiative recombination, Auger recombination, or nonradiative recombination via defect states. [5 points for each part] a.) Which recombination mechanism actually limits the carrier lifetime below a doping density of approximately 10 18 cm -3 ? For silicon, non-radiative defect recombination is the dominant mechanism at low doping concentrations. b.) Which mechanism limits the lifetime at higher doping density? Why is recombination by this mechanism so fast at high doping density? At high doping densities, above ~10 18 cm -3 , Auger recombination limits lifetime. The Auger recombination rate is proportional to the square of the dopant density and increases dramatically as dopant density is increased. c.) Why is the third mechanism [the one that you didn’t select for a.) and b.)] not very important in silicon? Radiative recombination is very slow in silicon because silicon is an indirect band gap semiconductor. In an indirect semiconductor, a radiative transition is a second order process involving not only the emission of a photon, but also the simultaneous absorption or emission of multiple phonons, which makes the transition far less probable. 1
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The p region has carrier density of 10 16 cm -3 and the n region has a carrier density of 10 19 cm -3 . The doping profile changes very abruptly at the pi and in interfaces. (i stands for intrinsic) [5 points for each part] a.) Draw the charge density versus position. (Line up all drawings below the sketch shown below. You might want to practice on scratch paper) b.) Draw the electric field versus position. c.) Draw a band diagram with no applied bias. The diagram should include the conduction band, valence band and Fermi level. d.)
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This note was uploaded on 12/01/2011 for the course MS&E 302 taught by Professor Mcghee during the Spring '08 term at Stanford.

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302+midterm+_2006_+solutions+2 - MATSCI 302: Solar Cells...

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