e and h) can be measured, but their mobilities (
e and h) are unknown because the measurement of the Hall coefficient is difficult with the high resistivity CdTe semiconductor.
3. Parameter Analysis Method for Planar Type CdTe Detector with Its Output Pulse
Masahiko Hirasawa and Mikio Yamamoto
Keywords: CdTe, Schottky contact, dead region, mobility, pulse form
It is suggested in terms of spectrum analysis, photon counting, and so on that even planar type totally depleted semiconductor detectors with barrier contact include dead regions. A method is developed to derive the mobilities of electrons and holes, the dead region thickness, and so on by analyzing output pulse from a high resistivity CdTe gamma ray detector with Schottky barrier contact by the Pt cathode. The lifetimes of electrons and holes (e and h) can be measured, but their mobilities (e and h) are unknown because the measurement of the Hall coefficient is difficult with the high resistivity CdTe semiconductor.
For an easier calculation later, the dead region which is defined as the region of zero electric field in the electrically biased state is supposed as concentrated on the side of the anode. The thickness which is obtained by subtracting the total thickness of the dead regions from the real thickness of the CdTe detector us indicated by d. The electric field distribution in d is assumed to be approximately described by the linear expression ax + b where x is the distance from the anode, excluding the dead regions. The point of the photoelectric reaction is also expressed by the distance y from the anode, excluding the dead regions.
The output pulse form from the detector is broken at three points in almost all cases because the ratio of mobilities of electrons and holes is relatively big for semiconductors like CdTe. The V1 (voltage difference between the first and second broken point), V2 (between the first and third), T1 (time difference between the first and second broken point) and T2 (between the first and third) are analytically described by applying the system with energy conservation laws while the charge generated by the photoelectric reaction moves in the detector with the above electric field distribution. This leads to Vr= V2 / V1 and d as functions of only e and h a and b if e and h are known. The values of e h, b and d for a given value of a are relatively easily solved from the values of V1, V2, T1 and T2 for the two pulses using the Newton-Raphson method independently of the initial values.
The pulses caused by the photoelectric reactnon with gamma rays are measured using a 2-mm cube high resistivity CdTe with thin Pt electrode and 140 V of biased voltage. However largely different value sets of e , h, a, b and d are reached by the calculation depending on the selection of a pair of pulses. This is thought to be mainly caused by ununiformuty of e and h based on the inhomogeneous crystal and the impurity distribution in the detector. Accordingly the ratio of mean e and h in the detector is first estimated by the mean times to traverse the detector by electrons and holes which are measured using the pulses caused by the photoelectric reaction in the neighbourhood of the cathode and anode. Any pulse can be tested regarding the ratio of e and h using values of T1 and T2 and the pulse in which the ratio is nearest to the above one is selected and used as the optimum pulse. More pulse measurements provide more precise mean values of the parameters in this method.
Publication:
Hirasawa, M.: Nuclear Instruments and Mathods in Physical Research, submitted.