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Consider a p-type silicon bar of length L which is homogeneously doped with an acceptor concentration NA >> ni. Light is incident on both ends of the bar such that NA/1000 excess electrons are generated at = 0 and at x = L. No light penetrates inside the bar (0 < x < L). Assume steady-state conditions and T = 300 K. Electron recombination lifetime is ™ and electron diffusion coefficient is Dr in the semiconductor. Δη (0) = NA 1000 An(L) = NA 1000 light ->> p-type Si (NA) (no light inside bar) - light X L (a) Derive an analytical expression for the excess electron concentration, An(x), as a function of distance in the silicon bar. (b) Derive an analytical expression for the electron diffusion current density at r = 0, i.e. Jn,diff(0). (c) Draw the energy band diagrams (with Fermi or quasi-Fermi levels) of the semiconductor (i) at equilibrium before light illumination and (ii) under steady-state light illumination as described above.

Consider a p-type silicon bar of length L which is homogeneously doped with an acceptor concentration NA >> ni. Light is incident on both ends of the bar such that NA/1000 excess electrons are generated at = 0 and at x = L. No light penetrates inside the bar (0 < x < L). Assume steady-state conditions and T = 300 K. Electron recombination lifetime is ™ and electron diffusion coefficient is Dr in the semiconductor. Δη (0) = NA 1000 An(L) = NA 1000 light ->> p-type Si (NA) (no light inside bar) - light X L (a) Derive an analytical expression for the excess electron concentration, An(x), as a function of distance in the silicon bar. (b) Derive an analytical expression for the electron diffusion current density at r = 0, i.e. Jn,diff(0). (c) Draw the energy band diagrams (with Fermi or quasi-Fermi levels) of the semiconductor (i) at equilibrium before light illumination and (ii) under steady-state light illumination as described above.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Consider a p-type silicon bar of length L which is homogeneously doped with an acceptor concentration NA >> ni. Light is incident on both ends of the bar such that NA/1000 excess electrons are generated at = 0 and at x = L. No light penetrates inside the bar (0 < x < L). Assume steady-state conditions and T = 300 K. Electron recombination lifetime is ™ and electron diffusion coefficient is Dr in the semiconductor. Δη (0) = NA 1000 An(L) = NA 1000 light ->> p-type Si (NA) (no light inside bar) - light X L (a) Derive an analytical expression for the excess electron concentration, An(x), as a function of distance in the silicon bar. (b) Derive an analytical expression for the electron diffusion current density at r = 0, i.e. Jn,diff(0). (c) Draw the energy band diagrams (with Fermi or quasi-Fermi levels) of the semiconductor (i) at equilibrium before light illumination and (ii) under steady-state light illumination as described above.
Transcribed Image Text:Consider a p-type silicon bar of length L which is homogeneously doped with an acceptor concentration NA >> ni. Light is incident on both ends of the bar such that NA/1000 excess electrons are generated at = 0 and at x = L. No light penetrates inside the bar (0 < x < L). Assume steady-state conditions and T = 300 K. Electron recombination lifetime is ™ and electron diffusion coefficient is Dr in the semiconductor. Δη (0) = NA 1000 An(L) = NA 1000 light ->> p-type Si (NA) (no light inside bar) - light X L (a) Derive an analytical expression for the excess electron concentration, An(x), as a function of distance in the silicon bar. (b) Derive an analytical expression for the electron diffusion current density at r = 0, i.e. Jn,diff(0). (c) Draw the energy band diagrams (with Fermi or quasi-Fermi levels) of the semiconductor (i) at equilibrium before light illumination and (ii) under steady-state light illumination as described above.
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