Noise Analysis for a Silicon Particle Detector with Internal Multiplication

Internal carrier multiplication in a particle detector makes possible a reduction in the noise contribution of the following amplifier. The carrier multiplication, however, introduces additional noise from two sources. First, the statistical nature of the multiplication process gives rise to variations in the magnitude of the carrier multiplications. Second, as pointed out by Shockley, l the inherent statistical spatial fluctuations of impurity density within the space charge layer of a p-n junction lead to corresponding local fluctuations of the avalanche breakdown voltage Vb. At a bias below Vb this corresponds to local fluctuations of the multiplication factor M. The significance of both noise sources is evaluated. It is found that in general multiplication will improve the energy resolution only for the detection of low energy particles and for moderate values of M. The findings are illustrated by detailed calculations for a silicon junction having a breakdown voltage of 30 volts with a corresponding space charge layer thickness of 1.3 microns, appropriate for low energy particle detection.