Charge collection efficiency in photoconductive detectors under small to large signals

Abstract

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.

Fluctuations in the collected charge in integrating photoconductive detectors under small and large signals: the variance problem

“…The CE under arbitrary injection is represented by η r . The dependence of η r and its deviation from the small signal case on the injection ratio r was reported in our previous paper [18]. This work examines the deviation of the variance of the CE, σ 2 r on r and evaluates the errors involved in using the analytical expression based on the small signal case (the unperturbed field).…”

“…The most expedient procedure to obtain the variance σ 2 r is by using MC simulation. The CE efficiency has been studied with MC simulations in two previous works as a function of the injection ratio r under Hecht conditions [17] and exponential photogeneration [18]; the latter has the details of the MC simulation that was used in the present case inasmuch as we have used an exponential electron-hole pair (EHP) photogeneration profile. In summary, the MC simulations are carried out as follows:…”

“…If one continues to use σ 2 0 , what are the errors? The purpose of this paper is two fold: first to present corrections to previous derivations [4,12,14,16] and, second, to quantify the answer to the latter question through MC simulations carried out as previously reported [17,18].…”

“…Evaluation of η r involves N-body interactions necessitating the use of simulation methods. Monte Carlo (MC) simulations have clearly shown that the errors in the CE can become significant as the charge injection ratio increases [17,18]. Therefore, small signal-based DQE models need to be revised for large signals conditions.…”

The Effect of Fractionation during the Vacuum Deposition of Stabilized Amorphous Selenium Alloy Photoconductors on the Overall Charge Collection Efficiency

“…It should be emphasized that the usefulness of Equation (4) is not limited to small signals. It can still be used under high radiation intensities with errors quantified in [ 22 ]. Equation (4) can also be used for a semiconductor in which the carrier range varies monotonically (either simply increasing or decreasing along x ) if one defines appropriately averaged carrier ranges [ 6 ].…”