Homework 3

Due 5pm Friday of third week of class

Photoluminescence spectrum (5pts)

Find the width at half-max of the photoluminescence spectrum from a direct bandgap semiconductor that is “gently” excited (i.e. low density of excess electron-hole pairs).

Give your answer in terms of kT.

Excess Carrier Radiative Recombination Lifetime (10pts)

a) How does τ_R scale with temperature? Assume a direct bandgap semiconductor with no excitonic effects.

b) Would τ_R scale differently for an indirect bandgap material?

Quasi-Fermi Level (10pts)

A 1 mW HeNe laser (632 nm) is focussed to a 50 micron spot size on a thin film of p-doped GaAs (1 micron thickness).

a) Assuming a refractive index of 3.5 at this wavelength, what fraction of light is reflected from the air/GaAs interface?

b) The excess carriers have a 50 ns lifetime. Most of the carriers stay within the 50 micron spot size during their lifetime. Calculate the quasi-Fermi level for electrons in this excited region of the GaAs film.