Intrinsic carrier effects in $HfO2$–Ge metal–insulator–semiconductor capacitors

Germanium metal–insulator–semiconductor capacitors with $HfO2$ or other high-$κ$ gate dielectrics show unusual low frequency behavior of the high frequency (1 kHz or higher) capacitance-voltage characteristics when biased in inversion. Here, we provide evidence that this effect is partly due to the high intrinsic carrier concentration $ni$ in Ge. We show in particular that the ac conductance in inversion is thermally activated and it is governed either by generation-recombination processes in depletion, varying proportional to $ni$ or by diffusion-limited processes varying as $ni2$⁠, depending on whether the temperature is below or above 45 °C, respectively. From these measurements, we also show that the minority carrier response time in Ge is very short, in the microsecond range (much shorter than in Si), depending inversely proportional to $ni$ at room temperature. This means that due to high $ni$⁠, the inversion charge is built fast in response to high frequency signals at the gate, inducing the observed low frequency behavior.