Corrections to the Hecht collection efficiency in photoconductive detectors under large signals: non-uniform electric field due to drifting and trapped unipolar carriers

Abstract

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.

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

“…This MC simulation is assumed to be valid because the η 0 values it generates are consistent with the analytical expression for CE η 0 , which is well known (see section 1). This agreement between the MC simulation and analytical solutions gives support to the σ 2 0 solution in equation ( 16) Further, the MC method for the Hecht case (δ ≪ L) was confirmed by numerical solutions of the continuity and rate equations and the Poisson equation in [17].…”

“…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:…”

“…The initial decrease in variance as s e /L increases from very small values, is due to the existence of significant quantity of trapped carriers. Carriers are more readily trapped with large signals [17,18], reducing the CE. However, these trapped carriers will perturb the field so much that the field E τ acting on drifting free carriers is more than E 0 , which reduces the amount of time these free carriers spend in the detector and thus reducing the variance in the signal they produce as illustrated in figure 7.…”

“…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.…”