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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 Fall '08
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