Unformatted text preview: n ( x ) → GLτ n ⎡1 − e− x / Ln ⎤
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⎦ which behaves as expected. ECE 606 11 Spring 2013 Mark Lundstrom 2/24/2013 7d) Provide a sketch of the solution, and explain it in words. Solution: Concentration is GLτ n in the bulk, but less at the surface, because of surface recombination. The transition from the surface to the bulk takes place over a distance that is roughly the diffusion length. The hole QFL is constant and almost exactly where the equilibrium Fermi level was, because we are in low level injection (the hole concentration is very, very near its equilibrium value). But the electron QFL is much closer to the conduction band edge. It moves away from EC near the surface, because surface recombination reduces Δn ( x ) near the surface. The variation with position is linear, because Δn ( x ) varies exponentially with position. ECE 606 12 Spring 2013 Mark Lundstrom 8) 2/24/2013 The sample is uniformly illuminated with light, resulting in an optical generation rate GL = 1024 cm 3 sec 1, but all of the photons are absorbed in a thin layer (10 nm wide near x = 0). Find the steady state excess minority carrier concentration and QFL’s vs. position. You may assume that the sample extends to x = +∞ . HINT: treat the thin layer at the surface as a boundary condition – do not try to resolve Δn ( x ) inside this thin layer. Approach the problem as follows. 8a) Simplify the Minority Carrier Diffusion Equation for this problem. Solution: ∂ Δn
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