Generalized demonstration of Ramoʹs theorem with space charge and polarization effects

Ramoʹs theorem provides a convenient way of simulating the currents induced through the electrodes of a radiation detector by the movement of charge carriers. The concept of weighting potential or of weighting field is the key ingredient in the calculation of the induced currents. A new demonstration of the theorem, based on energy balance, is provided that explicitly takes into account the effect of material polarization. It is shown that Ramoʹs theorem is valid in an arbitrary linear material and that polarization charges at interfaces between different materials or in the bulk of inhomogeneous materials must be included in calculating the weighting potentials. The use of our definition of weighting potential is also demonstrated for non-linear materials. The present proof is thus more generally valid than previous ones.