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The use of the Transient Charge Technique (TCT) for the evaluation of high resistivity Mercuric Iodide and Cadmium Selenide nuclear radiation detectors is suggested. It has been shown that the real values of mobilities and trapping times of electrons and holes in HgI2 can be easily obtained from the analysis of the voltage transient response to drift of charge carriers created by alpha particles. This allows to evaluate the bulk transport properties of the material and, additionally, to estimate accurately the surface recombination velocity of the carriers. Preliminary results on the shape of voltage transients in CdSe are also reported, and the limitations of the use of the TCT for characterisation of both materials are discussed.