A simple model of charge collection in silicon detectors

The charge collection and the resulting currents of electrons and holes in silicon detectors are described well by a simple model derived from the basics of semiconductor theory. Depending on various parameters like resistivity, bias voltage and thickness, we calculate the currents resulting from charge movement across the detector. In heavily irradiated silicon detectors, the bulk converts from n- to p-type and the pn-junction moves from the readout side to the backplane side. Nevertheless, neglecting trapping due to radiation damage, it can be shown that the overall currents before and after this inversion are the same although the single-carrier contributions are quite different. Furthermore the detector currents are applied to a model of the APV amplifier with CR-RC shaping and deconvolution. The amplifier output is shown for several parameter settings.