5.5.1 Direct Recombination

Direct recombination is an important transition in semiconductors with a direct band gap like lead telluride. Recombination goes hand in hand with radiative emission, while carrier generation is used within photodetectors for selective frequencies matching the band gap. For lead telluride, the sensitive frequency region is the infrared range. Due to the strong band gap dependence on material composition in lead tin telluride, the corresponding wavelength can be adjusted. The according generation/recombination rate depends on the carrier concentration and is modeled as

$$R^{\ensuremath{\mathrm{RAD}}} = C^{\ensuremath{\mathrm{RAD}}} \left( \ensuremath{n}\ensuremath{p}- \ensuremath{n_\mathrm{i}}^2 \right) \,,$$ (5.46)

where $C^{\ensuremath{\mathrm{RAD}}}$ denotes a proportionality factor. Calculated radiative carrier lifetimes of $0.6 \,\ensuremath{\mathrm{\mu s}}$ are reported in [291] for lead telluride comparable to $0.8 \,\ensuremath{\mathrm{\mu s}}$ in [292].

M. Wagner: Simulation of Thermoelectric Devices