Charge transport in a-Si:H detectors: comparison of analytical and Monte Carlo simulations

To understand the signal formation in hydrogenated amorphous silicon (a-Si:H) p-i-n detectors, dispersive charge transport due to multiple trapping in a-Si:H tail states is studied both analytically and by Monte Carlo simulations. An analytical solution is found for the free electron and hole distributions n(x,t) and the transient current I(t) due to an initial electron-hole pair generated at an arbitrary depth in the detector for the case of exponential band tails and linear field profiles; integrating over all e-h pairs produced along the particle´s trajectory yields the actual distributions and current; the induced charge Q(t) is obtained by numerically integrating the current. This generalizes previous models used to analyze time-of-flight experiments. The Monte Carlo simulation provides the same information but can be applied to arbitrary field profiles, field dependent mobilities and localized state distributions. A comparison of both calculations is made in a simple case to show that identical results are obtained over a large time domain. A comparison with measured signals confirms that the total induced charge depends on the applied bias voltage. The applicability of the same approach to other semiconductors is discussed