Ece 606 18 spring 2013 mark lundstrom

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 01/15/2014 for the course ECE 606 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

Ask a homework question - tutors are online