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Week7HW Solutions

Ece 606 18 spring 2013 mark lundstrom

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Unformatted text preview: in the bulk, there are no excess carriers so Fn = Fp = E F . The electron QFL 9) must get closer to the conduction band near the surface, because the excess electron concentration is larger there. The variation is linear with position because Δn ( x ) varies exponentially with position. 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. Assume that the semiconductor is only 5 μm long. You may also assume that there is an “ideal ohmic contact” at x = L = 5 μm, which enforces equilibrium conditions at all times. Make reasonable approximations, and approach the problem as follows. HINT: treat the thin layer at the surface as a boundary condition – do not try to resolve Δn ( x ) inside this thin layer. 9a) Simplify the Minority Carrier Diffusion Equation for this problem. Solution: ∂ Δn d 2 Δn Δn Begin with: = Dn − + GL ∂t dx 2 τn d 2 Δn Δn Simplify for steady- state: 0 = Dn − + GL dx 2 τn Let’s treat the generation in a thin surface layer as a boundary condition, so GL = 0 ; the simplified MDE equation is: ECE- 606 15 Spring 2013 Mark Lundstrom Dn d 2 Δn Δn d 2 Δn Δn − = 0 2 − = 0 dx 2 τn dx Dnτ n 2/24/2013 d 2 Δn Δn − 2 = 0 dx 2 Ln Ln = Dnτ n Since the sample is much thinner than a diffusion length, we can ignore recombination, so d 2 Δn = 0 . dx 2 9b) Specify the initial and boundary conditions, as appropriate for t...
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