CALCULATION OF THE GEOMETRICAL CAPACITANCE OF SILICON MICROSTRIP STRUCTURES USING A VARIATIONAL APPROACH

A lower limit to the capacitance of strip-like detectors, for example microstrips, is set by the geometrical capacitance of the electrodes. It is important to estimate this accurately so that proper account can be taken of additional effects such as surface charge layers in the device. We present a method for the calculation of multi-strip structure capacitances based on a variational technique which avoids the need to solve Poisson's equation numerically in two dimensions for the structure in question. Instead, the solution is achieved starting from an approximate charge distribution function. This method is both simple to implement and efficient to run. Experimental results from two types of test device are presented and compared with the calculations. Firstly, microstrip structures were produced, varying both width and pitch. Secondly, 5 mm square diodes with their surfaces divided into connected strips have been produced with a range of different strip pitches.