An application of extensions of the Ramo-Shockley theorem to signals in silicon sensors

We discuss an extension of the Ramo–Shockley theorem that allows the calculation of signals in detectors that contain non-linear materials of arbitrary permittivity and finite conductivity (volume resistivity) as well as a static space-charge. The readout-electrodes can be connected by an arbitrary impedance network. This formulation is useful for the treatment of semiconductor sensors where the finite volume resistivity in the sensitive detector volume cannot be neglected. The signals are calculated by means of time dependent weighting fields and weighting vectors. These are calculated by adding voltage or current signals to the electrodes in question, which has a very practical application when using semiconductor device simulation programs. An analytic example for an un-depleted silicon sensor is given.