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.

Voltage filling pulse measurements taken on a-Si:H/c-Si heterostructure Schottky diode samples are used to examine the capture of electrons from the c-Si substrate into a-Si:H defect states. These measurements, along with the capacitance versus temperature spectra of these diodes, indicate a nearly zero conduction-band offset (50±50 meV). In addition, we have observed trapping of holes at the valence-band discontinuity ΔEv. A clear threshold for the subsequent optical release of these holes yields a value of ΔEv =0.58±0.02 eV. Our measurements also provide the energy and spatial distribution of deep defects within the a-Si:H layer and indicate a region of anomalously large defect density (1018 cm−3) within roughly 350 Å of the a-Si:H/c-Si interface.

We describe an experiment that implements capacitance-voltage profiling on a reverse-biased Schottky barrier diode to determine the density of impurity dopants in its semiconductor layer as well as its built-in electric potential. Our sample is a commercially produced Schottky diode. Three different experimental setups, one using research-grade instrumentation, the other two using low-cost alternatives, are given and their results compared. In each of the low-cost setups, phase-sensitive detection required to measure the sample's capacitance is carried out using an inexpensive data acquisition (DAQ) device and a software program that implements a lock-in detection algorithm. The limitations of the DAQ device being used (e.g., restricted analog-to-digital conversion speed, inadequate waveform generation capabilities, lack of hardware triggering) are taken into account in each setup. Excellent agreement for the value of the doping density obtained by the all three setups is found and this value is shown to be consistent with the result of an independent method (secondary ion mass spectroscopy). V

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