Signals induced in semiconductor gamma-ray imaging detectors

The signal induced in a readout circuit connected to a pixel electrode in a semiconductor gamma-ray imaging array is calculated by solving the Laplace equation. Two approaches are presented that use Green functions in solving the boundary value problem: decomposition into basis functions, and construction of an infinite series of image charges. Another approach is developed based on the Ramo - Shockley theorem, which makes use of weighting potentials. These potentials may be readily calculated in three dimensions using a Fourier-transform propagation technique. An analytic solution is found for the special two-dimensional case of a strip detector. Experiments on CdZnTe square-pixel test structures using alpha radiation confirm the expected trends in pulse shape as a function of pixel size. Signals observed simultaneously on adjacent pixels also follow the predicted division of currents. Trends with pixel size are also confirmed in the shape of pulse-height spectra taken using a ^99mTc source.