Impact ionisation thresholds in silicon and germanium under hydrostatic pressure and strain

Abstract

We have studied experimentally and theoretically impact ionisation thresholds in the indirect band-gap semiconductors, silicon and germanium. The threshold energies for electron- and hole-initiated ionisation processes were calculated numerically using an empirical pseudopotential band-structure which includes spin-orbit interactions. In silicon, the threshold energy for holes is significantly greater than that for electrons, whereas in germanium the thresholds are almost equal. We point out the band-structure features responsible for this behaviour, and its influence on the multiplication noise of avalanche photodiodes fabricated in these materials. We have measured the breakdown voltage in silicon and germanium avalanche photodiodes while varying the band-structure using hydrostatic pressure. For silicon, the results are consistent with impact ionisation dominated by electron-initiated umklapp processes associated with the Δ minima, in agreement with the calculations. The results for germanium show experimental evidence for impact ionisation above the threshold energy (‘soft’ threshold), and for multiple ionisation processes contributing to the carrier multiplication. We have also calculated the thresholds for impact ionisation in strained silicon grown on (100) germanium, and for strained germanium grown on (100) silicon. The results show that strained layers fabricated in indirect band-gap semiconductors are potentially attractive for use in low-noise avalanche photodiodes.