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

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.