Charge collection in X-ray pixel detectors based on SI-GaAs doped with Cr G.I.Ayzenshtat a, M.V.Bimatov b, O.P.Tolbanov c, A.P.Vorobiev d a Science & Production Enterprise “Semicond. Dev. Research Inst”, Tomsk, Russia b Tomsk State University, Tomsk, Russia c Siberian Physical Technical Institute, Tomsk, Russia d State Science Center “High-Energy Physics Institute”, Protvino, Russia

Introduction The charge collection in a pixel detector and output current shape were investigated for LEC SI-GaAs in the works by P.J.Sellin, M.G.Bisogni and others. The purpose of our work is to simulate a current and charge signal in the pixel detector after X-ray absorption at various positions in the detector for GaAs compensated by Cr. This material distinctive features are: an uniform electric field distribution through the detector; much longer lifetime of an electron than of a hole (τ e >> τ h ). The material characteristics: The mobility and lifetime values of charge carriers are: µ h = 200 cm 2 /Vs, µ e = 1500 cm 2 /Vs τ h  0.2 ns, τ e  10 ns, The electron velocity depends nonlinearly on the electric field strength: v e = µ e E when E 5 kV/cm

A Formula for the pixel current The following formula was obtained for calculation of the current induced on a pixel by a moving charge: where R=D/2 is half pixel size, x and y are the horizontal coordinates, q and v are the charge value and the charge velocity respectively; function f is:, k=0,±1,±2,… where z is the perpendicular coordinate, h is the detector thickness. (1) (2) D=100µm thickness=500µm z x y x

The currents induced on irradiated and neighbouring pixels (the capture was neglected) µ e = 1500 cm 2 /Vs, µ h = 200 cm 2 /Vs The conclusion: The negative current pulse arises in the neighbouring pixel thickness=500µm D=100µm The side view of the detector: the irradiated pixel the neighbouring pixel z

Pixel contacts should be anodes (for SI – GaAs:Cr) lifetimes of the charge carriers: τ h  0.2 ns τ e  10 ns The current induced on the pixel tacking into account the capture

Dependences of CCE on the photon absorption depth for events occurring under the pixel center Pixel contacts should be anodes (for SI – GaAs:Cr) z 0 500µm

Signal induced on the next nearest pixel is negligible. The dependences of CCE on the photon absorption depth for events occurring at various distances from the pixel center the examined pixel z x=50µm x 0 the examined pixel z x=100µm x 0

There is an optimal detector thickness for the mean collected charge. Its value is determined by the photon energy and the drift length of charge carriers. Mean charge collected on the pixel as a function of the detector thickness The charge averaged over all photons incident on the detector cell

Conclusions The formula for the current induced on the square pixel by a moving charge was obtained. The negative current pulse arises in the neighbouring pixel. The pixel contacts should be anodes in the detector based on SI-GaAs compensated by Cr. There is an optimal detector thickness for the mean collected charge. Its value is determined by the photon energy and the drift length of charge carriers.