ANALYTICAL EXPRESSIONS FOR THE CALCULATION OF PIXEL DETECTOR CAPACITANCES

In this paper, analytical expressions for calculating the capacitance of an isolated pixel diode as well as a pixel diode in an array are pr esented. These expressions fit the three-dimensional numerical solutio n of the Laplace equation better than 10% as previously calculated for these diodes, covering most practical cases. The total pixel capacita nce C-P is Obtained by a simple substitution of parameters in the anal ytical expressions. In addition, a simple method to obtain the real di ode capacitance, the parasitic capacitance, and the substrate concentr ation is proposed on the basis of the analytical equation for the capa citance for an isolated diode. The coincidence of measured and calcula ted data for the capacitance is shown. The procedures presented permit a very precise description of the real C-V curve for an isolated diod e as web as for diodes in a pixel array, allowing the design of the be st coupling between each pixel and its corresponding readout preamplif ier with a minimum calculation effort.