5.5.3 Auger Recombination

Auger recombination is a process with three particles involved. In this mechanism, the energy set free by the recombination of an electron-hole pair is absorbed by a third carrier which is thus raised to a higher energy. In a second step, this carrier falls back to its initial state and thus transfers its excess energy to the lattice. Auger recombination becomes important for high carrier concentrations. It is modeled as the triple concentration product [268]

$$R^{\ensuremath{\mathrm{AU}}} = \left( C_{\ensuremath{n}}^{\ensure... ...right) \left( \ensuremath{n}\ensuremath{p}- \ensuremath{n_\mathrm{i}}^2 \right)$$ (5.57)

introducing the Auger coefficients $C_{\ensuremath{n}}^{\ensuremath{\mathrm{AU}}}$ and $C_{\ensuremath{p}}^{\ensuremath{\mathrm{AU}}}$ . In [293], the importance of Auger recombination in highly excited lead telluride has been discussed for thin films. Furthermore, the coefficients were determined by photo-conductivity measurements as $5 \times 10^{-28} \,\ensuremath{\mathrm{cm}}^6 \ensuremath{\mathrm{s}}^{-1}$ . In contrast to temperature dependent values as suggested for several semiconductors in [73] constant values over a wide temperature range have been observed in [294]. The coefficients for $\ensuremath{\mathrm{Pb_{1-x} Sn_x Te}}$ have been determined both theoretically and by measurement in [290]. For pure lead telluride, the theoretical value of $4.5 \times 10^{-28} \,\ensuremath{\mathrm{cm}}^6/\ensuremath{\mathrm{s}}$ corresponds quite well with the measured value of $3.8 \times 10^{-28} \,\ensuremath{\mathrm{cm}}^6/\ensuremath{\mathrm{s}}$ at $300\,\ensuremath{\mathrm{K}}$ . With a tin telluride content of $x=0.17$ , the according values for room temperature shift to $4.3 \times 10^{-27} \,\ensuremath{\mathrm{cm}}^6/\ensuremath{\mathrm{s}}$ and $4.5 \times 10^{-27}\,\ensuremath{\mathrm{cm}}^6/\ensuremath{\mathrm{s}}$ .

M. Wagner: Simulation of Thermoelectric Devices