Full modelling is reported of the capacitance of a long PIN semiconductor diode with a high concentration of generation-recombination (g-r) centres and different concentrations of deep traps. There are considerable differences from the textbook results given for normal lifetime diodes which have low concentrations of g-r centres. For a low density of g-r centres, the capacitance is the usual value. That is it decreases as V-1/2 with increasing reverse bias while it increases rapidly with increasing forward bias. For high density of g-r centres and in reverse bias a departure from this voltage dependence is observed, while in forward bias a negative capacitance appears. This agrees with experiment. From these results we present a physical understanding of the processes involved. There are specific applications of these results to radiation damaged devices, lifetime killed diodes and devices made from high resistance and semi-insulating materials, especially in the interpretation of the C-V curves to evaluate the fixed space charge density. (c) 2006 Elsevier Ltd. All rights reserved.