We consider the charge collection efficiency (CCE) for semiconductors in which the charge transport parameters, the drift mobility μ, and the carrier lifetime τ have spatial dependence, i.e., μ = μ(x) and τ = τ(x), where x is the distance from the radiation receiving top electrode toward the rear electrode. The small signal carrier packet drift analysis (CPDA) is re-examined, and the CCE efficiency for electrons and holes is formulated in terms of μ(x)τ(x)F(x), where F is the field. We use two model mobility and lifetime variations that are linear and exponential and then calculate and compare CCE determined from the CPDA equation, numerical solution of the continuity equation and Monte Carlo simulations as a function of the parameters characterizing the linear and exponential changes. The use of standard CCE equations for nonuniform samples is extensively examined, and errors are quantified by introducing a spatial average (SA) ⟨τ(x)⟩, average inverse (AI) ⟨1/τ(x)⟩, a new effective lifetime, and a kth order average. The SA lifetime works best when τ(x) monotonically decreases with x and AI works best when τ(x) monotonically increases with x. Stabilized a-Se x-ray photoconductors were considered as a practical application of this work. Both hole and electron lifetimes decrease in a-Se upon x-ray irradiation. Using the empirical equations derived recently for τh(x) and τe(x) as a function of dose D(x) in the sample, the CCE for two a-Se samples corresponding to a low-end device quality and the “best” was determined as a function of applied field.

Hecht collection efficiency η0 and its formulations for exponential absorption have been widely used in modeling charge collection efficiency in photoconductive detectors. The basic assumption of the Hecht formulation is that the electric field in the device is uniform, i.e., the photoinjected carriers do not perturb the field. Here, we have used Monte Carlo simulations to model the initial injection of electron and hole pairs and their subsequent transport and trapping in the presence of an electric field, which is calculated from the Poisson equation. Each injected carrier is tracked as it moves in the semiconductor until it is either trapped or reaches the collection electrode. Trapped carriers do not contribute to the photocurrent but continue to contribute to the field through the Poisson equation. The instantaneous photocurrent iph(t) is calculated from the drift of the free carriers through the Shockley–Ramo theorem. iph(t) is integrated over the duration of the photocurrent to calculate the total collected charge and hence the collection efficiency ηr. ηr has been calculated as a function of the charge injection ratio r, the electron and hole ranges (drift mobility and lifetime products, μτ), mean photoinjection depth δ, and drift mobility ratio b. The deviation of the collection efficiency ηr from the uniform field case η0 can be as much as 30% smaller than the small signal model prediction. However, for a wide range of electron and hole schubwegs and photoinjection ratios, typical errors remained less than 10% at full injection, the worst case. The present study provides partial justification to the wide-spread use of the uniform-field collection efficiency η0 formula in various applications, even under high injection conditions.

The Hecht collection efficiency η 0 , and its modified expressions for exponential absorption, have been widely used in time-of-flight type transient photoconductivity experiments as well as in the assessment of the sensitivity of integrating-type radiation detectors. However, the equations apply under small signals in which the internal field remains uniform (unperturbed). We have used Monte Carlo simulation and the numerical solution of the continuity, trapping rate and Poisson equations to calculate the collection efficiency η r (CE) for various levels of charge injection and deep trapping. The carriers are injected instantaneously very near the radiation receiving electrode and then drift under space charge perturbed conditions. The CE deviation from the ideal Hecht value has been quantified in terms of the injection ratio r and the normalized trapping time τ with respect to the transit time under small signals. The results can be represented by a scaled, compressed exponential with coefficients that depend on τ. A plot is provided for these coefficients. The CE drops significantly below the Hecht value as r increases and the deviation is more pronounced for smaller τ values. The errors in extracting τ from the application of the Hecht equation has been also calculated and mapped as a function of different r and τ values.

Microbeam radiation therapy (MRT) utilizes highly collimated synchrotron generated x-rays to create narrow planes of high dose radiation for the treatment of tumors. Individual microbeams have a typical width of 30–50 µm and are separated by a distance of 200–500 µm. The dose delivered at the center of the beam is lethal to cells in the microbeam path, on the order of hundreds of Grays (Gy). The tissue between each microbeam is spared and helps aid in the repair of adjacent damaged tissue. Radiation interactions within the peak of the microbeam, such as the photoelectric effect and incoherent (atomic Compton) scattering, cause some dose to be delivered to the valley areas adjacent to the microbeams. As the incident x-ray energy is modified, radiation interactions within a material change and affect the probability of interactions, as well as the directionality and energy of ionizing particles (electrons) that deposit energy in the valley regions surrounding the microbeam peaks. It is crucial that the valley dose between microbeams be minimal to maintain the effectiveness of MRT. Using a monochromatic x-ray source with x-ray energies ranging from 30 to 150 keV, a detailed investigation into the effect of incident x-ray energy on the dose profiles of microbeams was performed using samarium doped fluoroaluminate (FA) glass as the medium. All dosimetric measurements were carried out using a purpose-built fluorescence confocal microscope dosimetric technique that used Sm-doped FA glass plates as the irradiated medium. Dose profiles are measured over a very a wide range of x-ray energies at micrometer resolution and dose distribution in the microbeam are mapped. The measured microbeam profiles at different energies are compared with the MCNP6 radiation transport code, a general transport code which can calculate the energy deposition of electrons as they pass through a given material. The experimentally measured distributions can be used to validate the results for electron energy deposition in fluoroaluminate glass. Code validation is necessary for using transport codes in future treatment planning for MRT and other radiation therapies. It is shown that simulated and measured micro beam-profiles are in good agreement, and micrometer level changes can be observed using this high-resolution dosimetry technique. Full width at 10% of the maximum peak (FW@10%) was used to quantify the microbeam width. Experimental measurements on FA glasses and simulations on the dependence of the FW@10% at various energies are in good agreement. Simulations on energy deposited in water indicate that FW@10% reaches a local minimum around energies 140 keV. In addition, variable slit width experiments were carried out at an incident x-ray energy of 100 keV in order to determine the effect of the narrowing slit width on the delivered peak dose. The microbeam width affects the peak dose, which decreases with the width of the microbeam. Experiments suggest that a typical microbeam width for MRT is likely to be between 20–50 µm based on ...

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