Carrier mobility in crystalline germanium at high injection: experimental characterization of carrier-carrier scattering

The decay of the sum of electron and hole mobilities, μ s = μ n + μ p , due to carrier-carrier scattering was experimentally investigated in crystalline germanium (Ge) at high-injection conditions. Contactless measurements of the mobility sum as a function of the excess carrier density (Δ n ) in Ge were obtained using photoconductance decay methods. First, the measurement method was revised and improvements were introduced to ensure that μ s (Δ n ) could be obtained for independent samples with improved accuracy. This method is successfully validated with crystalline silicon and, then, applied to Ge samples of different doping types and resistivity. The analysis of the data suggests that the mobility decay at high injection levels cannot be properly explained with the usual assumption of equal cross section for carrier-carrier and carrier-ion scattering events. Instead, we find the mobility sum due to carrier-carrier scattering to be inversely proportional to Δ n according to the expression 8 × 10 20 ·Δ n −1 cm 2 V −1 s −1 . The limitations and potential error sources of the measurement method are discussed and, finally, the mobility model is used to improve lifetime analysis at high injection, allowing to estimate the ambipolar Auger recombination coefficient at C amb = 7 × 10 −31 cm 6 s −1 .