Response of silicon diodes for synchrotron radiation Igor E. Anokhin, M. Lerch, Member, IEEE, M. Petasecca, Member, IEEE A. Rosenfeld, Senior Member, IEEE, O. Zinets Abstract– Because of very high intensity and pulsed nature of synchrotron radiation the nonlinear effects in recombination- generation kinetics must be taken into account in the response of silicon diodes under irradiation. Dependences of the charge carrier lifetime and the ambipolar diffusion coefficient on the excess carrier density generated by the synchrotron radiation have been considered. Response of silicon diodes on photons from synchrotron sources with energy 20-100 keV has been calculated using the Shockley-Reed recombination statistics. Diffusion equation with time-dependent generation functions has been solved numerically for various intensity of the photon beam and parameters of diodes (diodes design and characteristics of impurity centers). Optimal choice of parameters of diodes for the short-cut current and the photovoltaic operation mode are discussed. Dependencies of responses on the generation rate can be converted into the dose rate responses of diodes by calculating the energy deposition in silicon. At very high beam intensity (the excess minority carrier density is much larger than the density of the majority charge carriers), the Shockley-Reed recombination model would be invalid and the Auger recombination becomes dominant. To explain experimental data on the dose rate response it is needed to use a correct function of the excess carrier lifetime versus the carrier density. Results can be used for dosimetry of intensive synchrotron therapeutic X-ray beams. I. INTRODUCTION any synchrotron radiation sources of X-ray and gamma photons are used both for physical investigations and medical application [ESRF, DESY, Stanford, BNL]. Silicon diodes are widely used for diagnostics and dosimetry of X-ray from synchrotron sources [1-5]. Synchrotron radiation have pulsed nature and requires studying the time dependence of the diode response. Transient effects in semiconductor diodes were considered in a number of papers (see review [6]). Because of very high intensity (10 14 photon/(s·cm 2 )) of the synchrotron radiation the nonlinear effects in recombination- generation kinetics of excess carriers and its effect on the response of silicon diodes must be taken into account. This peculiarities lead to the dose rate dependence of response of radiation diode detectors. The dose rate response of the Si diode was studied in a paper [7] in a framework of simplified analytical model. In papers [7] the lifetime of excess electron- hole pairs in a diode base under irradiation was suggested to be close to constant. Manuscript received November 15, 2012. Igor E. Anokhin is with the Institute for Nuclear Research, Kiev, UKRAINE (e-mail: anokhin@kinr.kiev.ua). O. Zinets is with the Institute for Nuclear Research, Kiev, UKRAINE. M. Lerch, M. Petasecca and A. Rosenfeld are with the Centre for Medical Radiation Physics, University of Wollongong, NSW 2522, AUSTRALIA. In the present report the response of n-Si diodes to photons with the energy 20-100 keV has been calculated using the Shockley-Reed recombination statistics and possible effect of the Auger recombination have been discussed. Diffusion equations with time-dependent generation functions have been solved numerically for various intensities of photon beams and parameters of diodes (diodes design and characteristics of impurity centers). The aim of the work is to explain some results on dose rate dependencies obtained in the [8]. II. X-RAY RADIATION CHARACTERISTICS FOR RADIATION THERAPY AND PROPERTIES OF THE SI DIODE SENSOR The X-ray flux and absorbed doses on medical LINACs and synchrotrons in radiation therapy can be measured using silicon diodes as a radiation detector as mentioned above. Temporary pattern and dose rate characteristics of synchrotron therapeutic sources and medical LINAC MV bremsstrahlung are different. The dose rate for patient treatments on medical LINAC is about 100 Gy/s while on synchrotron Microbeam Radiation Therapy (MRT) is about 10 5 Gy/s. A. Characteristics of synchrotron radiation Characteristics of synchrotron sources vary for different facilities and depend on the storage ring energy and used bending magnets, wriggler or undulator. But all sources give bunches of very short pulses of high intensity10 14 photon/(s·cm 2 ) X-ray. For instance, the pulse durations are in the range from 0.1 to 2 ns, the pitch is of order 200 ns. The x- ray in a wide energy range can be obtained. For example, X- ray energies of the white beam on the medical beamline ID17 of ESRF for MRT application is in the range of 15-600 keV with the average energy about 100 keV for 6.0 GeV electrons storage ring and presented in a Fig.1 [4]. B. The characteristic of medical LINAC source The typical medical LINACs X-Ray bremsstrahlung radiation is in a range of 6-18 MV with average photon energies 2-5 MeV respectively. The radiation is delivered by acceleration of electrons using LINAC with RF frequency about 200 MHz providing radiation pulses 1-2 microseconds with pitch 2-5 milliseconds. Microseconds duration LINAC pulses have temporal microstructure corresponding to RF frequency of the klystron, i.e. 5-10 ns pulses filling uniformly 1-2 microseconds radiation pulses. Temporal pattern of LINAC radiation corresponds to actual average dose rate in a single pulse about 100 Gy/s (while average is 4Gy/min) which should be considered in modeling of the detector response M