On the ballistic deficit and the signal-to-noise ratio of semiconductor spectrometers for energy and position spectroscopy

Abstract

The ballistic deficit and the signal-to-noise ratio of one dimensional position sensitive detectors are investigated by means of a simple model describing the detector as a line of a continuously distributed junction capacitance C and resistance R of the back layer. R has an upper limit, if the variation of the ballistic deficit for particles incident on different positions has been given a fixed value. On the other hand low values of the resistance of the back layer cannot be tolerated because of serious noise problems. Thus a compromise was found between these two conflicting aspects allowing a sufficiently small variation of the ballistic deficit and a resonable resolution of the position and energy signal. In a typical case, e.g. C = 150 pF, R = 7.8 kΩ , equivalent noise resistance of the preamplifier R eq = 250 ohm and using RC-integration and single delay line differentiation of 0.7 μsec, the variation of the ballistic deficit is less than 1%, the energy resolution 26 keV fwhm Si and the position resolution 44 keV fwhm Si. For a 50 mm long detector and 5.5 MeV particles the position resolution corresponds to 0.4 mm fwhm Si.