An experimental setup that employs lock-in detection to measure the optical transmission data on a bulk semiconductor sample is described. A straightforward manipulation of these data yields the semiconductor’s absorption coefficient α in the energy range near its absorption edge (0<α<100 cm−1). The theory of optical transitions in semiconductors required to analyze the resulting absorption spectra is presented. It is shown that a model based on an indirect optical transition involving a single phonon accurately describes data taken on a silicon sample. Based on this analysis, a value of (1.098±0.004) eV for silicon’s indirect band gap and an energy of (51±4) meV for the involved phonon is deduced. Conversely, it is shown that data taken on a gallium–arsenide sample are consistent with a model based on a direct optical transition involving exponential band-tail states. A value for the band-tail’s Urbach slope of E0=(6.7±0.2) meV is found. All of these results accurately agree with published values. This laboratory demonstrates important concepts in solid state physics via universally applicable experimental techniques at a level appropriate for upper-division undergraduates.
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Essick et al. (1993) studied this question.