A theoretical study of the charge collection properties of coaxial Ge(Li) detectors is presented. Normalized relationships are derived, which can easily be handled for a great number of practical cases. A geometrical factor g = ri/w (ri - internal radius of the coaxial counter, w - depletion layer width) has been introduced. The case of planar detectors can be derived if great values are given to g. Calculations have been performed assuming a 1/r r field variation, and a punctual single event gamma ray energy loss (electron-hole pair created in a point). Concerning the variation of the charge carrier drift velocity vs the electric field, two kinds of approximation have been used in the calculations : variable velocity (VVA) and constant velocity approximation (CVA). Trapping has also been taken into account by assuming an uniform distribution of trapping centers throughout the detector sensitive volume. For different interaction points, geometrical factors and trapping parameters, the relationships for the charge carrier collection efficiency (peak position of monoenergetic spectra in the case of a collimated radiation beam), as well as the shapes of current and charge pulses have been established and plotted. The prompt coincidence curves (using the charge pulse leading edge timing) are calculated by evaluating the probability distribution of the time at which the charge signal crosses a discriminating level. The influence on these curves of the geometrical factor, the discriminator tevet, the noise and the trapping parameters is taken into account and discussed.

Collection Efficiency and Charge Carrier Losses in Coaxial and Planar Ge(Li) Detectors. Influence on the Time Resolution

Amplitude and rise time compensated timing optimized for large semiconductor detectors

A timing system for Ge(Li) detectors

A model is presented for the prompt time-response from leading-edge triggering, where calculations are rendered simpler for uniform gamma -irradiation of a coaxial Ge(Li) detector. Pulse shapes are formed at the timing filter amplifier output, from direct detector pulses. The average pulse-shape method is found responsible for some sort of walk compensation, and by displaying time-resolution vs. triggering fraction, one can predict the best FWHM with detection of an RC-filtered signal. It also shows the effect of the mixed filter time-constant on RMS noise. Taking account of both statistical and noise effects of FWHM, the statistical contribution increases to 7% at a 3 MeV detected energy. >

Average pulse shape model for leading edge timing with Ge(Li) coaxial detector

An experimental examination of the effect of several filters and two discriminator techniques on the time measurement of the signals from coaxial Ge(Li) detectors is presented in this paper. The signal to the filters and discriminators was obtained from the output of the charge-sensitive preamplifier in order not to degrade the energy resolution of the system. The discriminators used were a level discriminator for leading-edge discrimination and a fast zero-crossing discriminator. The filters examined for leading-edge discrimination were four RC time-invariant and four RC time-variant filters, and the filters for zero-crossing discrimination were three time-invariant RC filters. A comparison of time-invariant and time-variant filters reveals two advantages of the time-variant filter. These advantages are smaller timing errors and lower discrimination levels. The lower discrimination levels allow the reduction of energy dependent timing errors. Likewise, zero-crossing discrimination provides several improvements over leading-edge discrimination. By a compensation method, timing errors due to charge collection variations are reduced; and, due to the invariancy of the zero-crossing point as a function of amplitude, energy-dependent timing errors are also reduced.

T. D. Douglass

Papers

A Comparison of Various Filter and Discriminator Techniques on Timing with Ge(Li) Detectors