Keung L. Luke

Quantification of the effects of generation volume, surface recombination velocity, and diffusion length on the electron‐beam‐induced current and its derivative: Determination of diffusion lengths in the low micron and submicron ranges

A systematic and quantitative analysis is carried out to investigate the effects of the shape (point, cube, Gaussian) and size of the generation volume, the surface recombination velocity, and the diffusion length on the electron‐beam‐induced current (EBIC) and its derivative (DEBIC). Thick homogeneously doped samples exhibiting diffusion lengths in the low micron and submicron range are considered. The results are presented in computed EBIC curves as a function of scanning distance and of the ratio true diffusion length/effective diffusion length. Using these curves, we show (1) a simple and yet rigorous method for the determination of the true diffusion length, taking into consideration all of the factors cited above, (2) a method for the rapid determination of the surface recombination velocity, (3) the condition under which the source shape becomes insignificant, and (4) a new value for the lower limit of the diffusion length which can be determined by the EBIC technique.

Quantitative interpretation of electron-beam-induced current grain boundary contrast profiles with application to silicon

An improved method is described for extracting material parameters from an experimental electron-beam-induced current (EBIC) contrast profile across a vertical grain boundary by directly fitting an analytical expression. This allows the least-squares values of the grain boundary recombination velocity and the diffusion length in each grain to be determined without the need for the reduction of the experimental profile to a few integral parameters, as is required in a previously reported method. Greater accuracy of the extracted values is expected since none of the information contained in the experimental contrast data is discarded and a less extensive spatial range of measured data is required than in the commonly used method. Different models of the carrier generation volume are used in the fitting and the effect of the choice of generation model on extracted values is investigated. In common with other EBIC approaches, this method is insensitive to changes in the diffusion length when the collection ef...

Analysis of the interaction of an electron beam with back surface field solar cells

In this paper the short circuit current ISC induced by the electron beam of a scanning electron microscope in a back surface field solar cell will be determined theoretically. It will be shown that, in a configuration used previously for solar cells with an ohmic back surface, the ISC gives a convenient means for estimating the back surface recombination velocities and thus the quality of back surface field cells. Numerical data will be presented applicable to a point source model for the electron–hole pair generation.

An EBIC equation for solar cells

Abstract When an electron beam of a scanning electron microscope (SEM) impinges on an N-P junction, the generation of electron-hole pairs by impact ionization causes a characteristic short circuit current I SC to flow. The I SC , i.e. EBIC (electron beam induced current) depends strongly on the configuration used to investigate the cells response. In this paper we consider the case where the plane of the junction is perpendicular to the surface. An EBIC equation amenable to numerical computations is derived as a function of cell thickness, source depth, surface recombination velocity, diffusion length, and distance of the junction to the beam-cell interaction point for a cell with an ohmic contact at its back surface. It is shown that the EBIC equation presented here is more general and easier to use than those previously reported. The effects of source depth, ohmic contact, and diffusion length on the normalized EBIC characteristic are discussed.

EVALUATION OF DIFFUSION LENGTH FROM A PLANAR-COLLECTOR-GEOMETRY ELECTRON-BEAM-INDUCED CURRENT PROFILE

The subject of this article is the determination of the minority carrier diffusion length L from a planar‐collector‐geometry electron‐beam‐induced current (EBIC) profile. Among extant techniques based on the analysis of a ln[IEBIC(x1)xα1] vs x1 plot, (x1 is beam‐to‐collector distance, and α is a constant), we find two major problems that demand immediate attention. First, the most widely used technique is found to be based on an invalid assumption, which results in the intrusion of large systematic errors into the values of L and surface recombination velocity sT. Therefore, this technique in its present form is no longer usable. Second, all these techniques are asymptotic (x1≳2L), a matter of great concern to experimentalists because large x1 means small signal‐to‐noise ratio and the proximity of adjacent active regions. We devise a nonasymptotic technique, based also on the analysis of a ln [IEBIC(x1)xα1] vs x1 plot, to evaluate L from a region close to the collector, as close as one‐half, but no farthe...

Choice of a range‐energy relationship for the analysis of electron‐beam‐induced‐current line scans

The electron range in a material is an important parameter in the analysis of electron‐beam‐induced‐current (EBIC) line scans. Both the Kanaya–Okayama (KO) and Everhart–Hoff (EH) range‐energy relationships have been widely used by investigators for this purpose. Although the KO range is significantly larger than the EH range, no study has been done to examine the effect of choosing one range over the other on the values of the surface recombination velocity sT and minority‐carrier diffusion length L evaluated from EBIC line scans. Such a study has been carried out, focusing on two major questions: (1) When the KO range is used in different reported methods to evaluate either or both sT and L from EBIC line scans, how different are their values thus determined in comparison to those using the EH range?; (2) from EBIC line scans of a given material, is there a way to discriminate between the KO and the EH ranges which should be used to analyze these scans? Answers to these questions are presented to assist ...

Determination of diffusion length in samples of diffusion-length size or smaller and with arbitrary top and back surface recombination velocities

Higher-quality semiconductor materials and smaller devices present new challenges to the electron-beam-induced current technique as device sizes become less than or approximately equal to diffusion length. Oftentimes the regions of interest are bounded by surfaces with arbitrary surface recombination velocities. How can the diffusion length in such a region be determined? The aim of this article is to lay the theoretical foundation showing how this determination can be carried out and to provide useful results to guide the experimentalist in both making the measurements and extracting the diffusion length from the data. Practical device conditions considered are top surface recombination velocity of 1×103 and 1×104 cm/s; back surface recombination velocity of 1×104 and 1×106 cm/s; and diffusion length/sample thickness ratios of 0.5, 1.0, and 2.0, respectively.

THE EVALUATION OF SURFACE RECOMBINATION VELOCITY FROM NORMAL-COLLECTOR GEOMETRY ELECTRON-BEAM-INDUCED CURRENT LINE SCANS

There are two well‐known point source‐based methods for the evaluation of the surface recombination velocity s from normal‐collector geometry electron‐beam‐induced current (EBIC) line scans. The first was proposed by Jastrzebski, Lagowski, and Gatos [Appl. Phys. Lett. 27, 537 (1975)], the second was by Watanabe, Actor, and Gatos (WAG) [IEEE Trans. Electron Dev. ED‐24, 1172 (1977)]. Scheer, Wilhelm, and Lewerenz [J. Appl. Phys. 66, 5412 (1989)] were unsuccessful in using the first method to extract s from their EBIC data. Hakimzadeh, Moller, and Bailey [J. Appl. Phys. 72, 2919 (1992)] applied the second method to evaluate s from their EBIC data without accounting for the mismatch between the theoretical requirement and the experimental condition relating to source size and electron penetration depth at which the WAG expression is to be evaluated. In this article these two methods are evaluated and their applicability to both point and extended‐source data is examined quantitatively. Their limitations and s...

Analysis of the electron-beam-induced current of a polycrystalline p-n junction when the diffusion lengths of the material on either side of a grain boundary differ

The short circuit current generated by the electron beam of a scanning electron microscope in p‐n junctions is reduced by enhanced recombination at grain boundaries in polycrystalline material. Frequently, grain boundaries separate the semiconductor into regions possessing different minority carrier life times. This markedly affects the short circuit current ISC as a function of scanning distance from the grain boundary. It will be shown theoretically that (a) the minimum of the ISC in crossing the grain boundary with the scanning electron beam is shifted away from the grain boundary toward the region with smaller life time (shorter diffusion length), (b) the magnitude of the minimum differs markedly from those calculated under the assumption of equal diffusion lengths on either side of the grain boundary, and (c) the minimum disappears altogether for small surface recombination velocities (s<104 cm/s). These effects become however negligible for large recombination velocities s at grain boundaries. For p...

The effect of beamwidth on the analysis of electron‐beam‐induced current line scans

A real electron beam has finite width, which has been almost universally ignored in electron‐beam‐induced current (EBIC) theories. Obvious examples are point‐source‐based EBIC analyses, which neglect both the finite volume of electron–hole carriers generated by an energetic electron beam of negligible width and the beamwidth when it is no longer negligible. Gaussian source‐based analyses are more realistic but the beamwidth has not been included, partly because the generation volume is much larger than the beamwidth, but this is not always the case. In this article Donolato’s Gaussian source‐based EBIC equation is generalized to include the beamwidth of a Gaussian beam. This generalized equation is then used to study three problems: (1) the effect of beamwidth on EBIC line scans and on effective diffusion lengths and the results are applied to the analysis of the EBIC data of Dixon, Williams, Das, and Webb; (2) unresolved questions raised by others concerning the applicability of the Watanabe–Actor–Gatos ...