Simulation of|carrier profiles

For a better understanding of lifetime measurements and to achieve a better comparability between different measuring methods, it is necessary to perform simulations.

The numerical tool is based on a generalized rate equation system, which is solved for all possible transitions between the defect levels in the forbidden gap and the bands of a semiconductor. The only approximation is that no interactions between defect levels are included. This is a valid approximation, since the defect concentrations in silicon are typically low.

The applied rate equation system describes the time dependent change of carrier concentrations in the conduction and valence band, as well as in defect levels. In this equation system the optical and thermal generation rates, the band to band and Auger recombination rates and the carrier capture and emission rates from all defects (Cj, Dj, Ej, Fj) are included. The transition rates are described without any approximations.

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The measurement of thick samples as bricks leads to new questions and problems. One of these questions is how the carrier profiles that develop in a sample effect the lifetime measurements. To solve this problem, we developed a simulation tool for the simulation of carrier profiles. This tool consists of a partial differential equation system of the transport equations for electrons and holes and the Poisson equation.

The simulations for measurements with a long (typical MDP condition) or a very short light pulse (typical µ-PCD conditions) at thick unpassivated samples are shown in figure 1 and 2. It becomes clear, that the carrier profile of a long light pulse expands through a large volume of the sample, where as the carrier profile of the only 200 ns long light pulse is very surface near. This has a direct effect on the measured lifetime, since the surface recombination has a much stronger effect on the µ-PCD measurements.

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