Determination of charge carrier trapping times in Si(Li) X-ray detectors

Complete text of publication follows. In high quality Si(Li) X-ray detectors the influence of charge trapping is usually negligible. Recently, however, in order to thoroughly characterize two liquid nitrogen cooled Si(Li) detectors a sensitive measurement of charge carrier trapping times have been performed. The determination was based on the the bias dependence of the charge collection efficiency for a wide energy range of photons incident on one side, whereby the fractional contribution of the charge carriers in the collection process is varied, enabling to determine trapping data for both carriers simultaneously [1]. On the basis of the high degree of Li+- compensation as checked by C-V measurents, nearly uniform electric fields in the applied 100-1000 V bias range for both detectors were assumed. At the same time the low temperature and the ∼ 5 mm detector thicknesses provide transit times much shorter (30-100 ns) than the peaking times applied (40-50 μs), therefore the influence of ballistic deficit was neglected, and so was the detrapping due to the intense cooling, independent of the long shaping. Despite the constancy of detector capacitances, nonnegligible bias dependent gain changes were corrected for by a reference pulser. With the above assumptions and for low charge collection loss, which was the case here, the collection efficiency η can be written in the following linear approximation η(Ud,Ex) ∼ 1 - w [F'0(Ex)/τe+ve(Ud) + L'0(Ex)/τh+vh(Ud)], where w is the depleted region thickness, τe+ and τh+ are the trapping times sought, ve and vh are the charge collection velocities, Ud is the applied bias voltage, Ex the energy of the photon detected, F'0 and L'0 are first order series expansion terms for electrons and holes, respectively, characterizing their contribution to the total charge carrier collection efficiency. The positions of 9 major peaks in the 6-60 keV region were determined by spectrum fitting, using the MEWA interactive spectrum evaluation code [2]. Fortuitously, in the particular temperature and electric field strength region ve ∼ 2.3vh, so the originally 2D fitting problem of Eq. can be reduced to 1D, as can be seen in the figure. Charge carrier velocities at the estimated ∼90 K temperature were taken from [3]. Note that for the better quality detector (nr.2) at 1000 V the mean free pathlengths before trapping τi+ vi are in the order of 1 m for electrons and holes alike, while the charge losses are 0.12 % and 0.06 % in the low (Ex → 0) and high (Ex→ ∞) energy limits, respectively. For 60 keV this translates to 36 eV deficit, or corresponds to 1 channel at the 1700th one in a MCA spectrum. The advantage of the method applied is that it comes as a spin-off of a 'simple' bias dependent energy calibration procedure of X-ray detectors [4]. (author)