Reciprocity theorem for charge collection by a surface with finite collection velocity: Application to grain boundaries

Abstract

A proof is given of a reciprocity theorem which applies to charge collection by a semiconductor surface with finite collection velocity. The theorem leads to a boundary-value problem for the charge collection probability φ. This problem is solved by the eigenfunctions expansion method for the normal collector geometry, where the collecting surface corresponds to the edge of a nonideal junction or to a charge-collecting grain boundary. The solution thus obtained is equivalent to that found earlier by the method of images but has a much simpler form. This solution, its asymptotic approximations and low-order moments, as well as the boundary conditions for φ can find use in the determination of the surface collection/recombination velocity and minority-carrier diffusion length in a semiconductor from experimental induced current scans. The new expression for φ is used to calculate the collection efficiency profile of a charge-collecting grain boundary for a generation with finite lateral extent.

Diffusion Characterization Using Electron Beam Induced Current and Time-Resolved Photoluminescence of InAs/InAsSb Type-II Superlattices

“…To extract the minority carrier hole diffusion length, modeling of the recovered signal was carried out using standard EBIC theory [5], supplemented with Monte Carlo simulations to model the distributions of carriers generated by the electron beams at the specified energies [6]. In order to account for the electron hole pairs generated directly in the wide-bandgap barrier layer, we also incorporated a distribution of the energy absorbed in the barrier layers based on beam position.…”

Temperature-Dependent Minority-Carrier Mobility inp-TypeInAs/GaSbType-II-Su

“…Various models have been reported previously to provide an acceptable first-order prediction of EBIC data [34][35][36]. Here, we use the model proposed by Bonard and Ganire [34].…”

“…Here, we use the model proposed by Bonard and Ganire [34]. This model, which will be referred to as Bonard's model in this text, can be considered as the generalized form of an earlier model by Donolato [35]. Bonard's model accounts for the contribution of all three regions of a pn junction, i.e., the n-type region, the depletion region, and the p-type region, in the EBIC signal, while considering the surface recombination at the top surface, for the case of the extended source.…”

Charge Collection From Within a Collecting Junction Well

“…The expression for the case of the U-shaped geometry will similarly be derived using the Green's function. For the latter case, we choose to start the derivation in a slightly different manner, i.e., by applying the reciprocity theorem [22]- [24].…”

“…To derive the EBIC profile for this U-shaped geometry, we will begin by utilizing the reciprocity theorem [22]- [24]. This theorem states that the charge collection current satisfies the homogeneous continuity equation…”