Chapter 5 established that a visible photon's wavevector is tiny compared with the…

PHYSICS · Subjective · Fermi University Physics · Optics & Photonics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure

Condensed Matter Physics, Ch The junction: diodes, transistors, lamps and solar cells

Problem

Chapter 5 established that a visible photon's wavevector is tiny compared with the width of the Brillouin zone. Take a red photon of

\lambda=700\,\mathrm{nm}

and silicon's zone boundary at

k_{\rm max}=\pi/a

with

a=5.43\,\mathrm{\mathring{A}}

. Find the ratio

k_{\rm max}/k_{\rm photon}

, and use Chapter 9's sharp-versus-gradual absorption edges together with this ratio to explain why an indirect-gap crystal like germanium absorbs and emits far less readily than a direct-gap one of a similar gap.

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