Theoretical framework for mapping pulse shapes in semiconductor radiation detectors

An efficient method for calculating of charge pulses produced by semiconductor detectors is presented. The method is based on a quasi-steady-state model for semiconductor detector operation. A complete description of the model and underlying assumptions is given. Mapping of charge pulses is accomplished by solving an adjoint carrier continuity equation. The solution of the adjoint equation yields Greenʹs function, a time- and position-dependent map that contains all possible charge pulses that can be produced by the detector for charge generated at discrete locations (e.g., by gamma-ray interactions). Because the map is generated by solving a single, time-dependent problem, the potential for reduction in computational effort over direct mapping methods is significant, particularly for detectors with complex electrode structures. In this paper, the adjoint equation is presented and the mapping method is validated for a benchmark problem.