The purpose of this study is to review and compare simulation methods for describing the transport of charge clouds in silicon based semiconductor detectors and investigate the effects on energy spectrum for silicon based photon counting strip detectors. Charge clouds and detailed carrier transport are sim ulated and compared using two different approaches including analytical and Monte Carlo schema. The results of the simulations are evaluated using pulse height spectra (PHS) for a silicon strip detector with edge on geometry at two energies (25 and 75 keV) at various x-ray absorption locations relative to the pixel boundary and detector depth. The findings confirm carrier diffusion plays a large role in the charge sharing effect in photon counting detectors, in particular when the photon is absorbed near the pixel boundary far away from the pixel electrode. The results are further compared in terms of the doublecounting probability for x-ray photons absorbed near the pixel boundary as a function of the threshold energy. Monte Carlo and analytical models show reasonable agreement (2% relative error in swank factor) for charge sharing effects for a silicon strip detector with edge-on geometry. For 25 keV mono-energetic photons absorbed at 5 µm from the pixel boundary, the theoretical threshold energy at 10% double-counting probability based on charge sharing is 5.5, 8.5 and 9.2 keV for absorption depths of 50, 250 and 450 µm from the electrode, respectively. The transport of charge clouds affects the spectral characteristics of photon counting detectors and the double-counting probability results show the theoretical threshold energy to avoid double-counting as a function of x23 ray energy and x-ray interaction locations for silicon and can be considered for future studies of charge sharing effects.

Introduction

Photon-counting detectors with energy discrimination capabilities have been recently developed for many medical x-ray imaging applications[1, 2] promising several advances including the ability to estimate the energy of transmitted photons at each pixel location. This technological development could enable improved material decomposition, higher spatial resolution, and implementa tion of beam hardening corrections.In most cases, photon counting detectors with energy discrimination can achieve higher signal-to-noise ratio[3] leading to improvements in existing modalities or allowing novel applications.[1, 4–۸] In addition, photon-counting detectors can be used in spectral CT applications.[9– ۱۵] One major challenge for photon-counting detectors is a phenomenon gen erally known as charge sharing. Under an externally applied bias, a cloud of charge carriers created by the energy imparted by an absorbed x-ray photon travels within the semiconductor and reaches the detector electrode. Near a pixel boundary, the cloud may be divided and detected simultaneously by multiple pixels recording energies lower than the energy carried by the x-ray quantum. The distribution of energy causes distortions in the spectral response. The significance of this effect depend on the detection material, charge carrier mobil ity, pixel size, absorption location with respect to the pixel boundary, depth of interaction within the active detector layer, temperature, applied bias (including non-uniform electric field affects due to Frisch grid structures).