An Optical Gap Calibration Applied to the Case of Hydrogenated Amorphous Silicon
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D. E. SWEENOR*, S. K. OTLEARY*, and B. E. FOUTZ***
* Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180-3590 Faculty of Engineering, University of Regina, Regina, Saskatchewan, Canada 54S 0A2 School of Electrical Engineering, Cornell University, Ithaca, New York 14853 ABSTRACT There are many different empirical means whereby the optical gap of an amorphous semiconductor may be defined. We analyze some hydrogenated amorphous silicon data with respect to a number of these empirical measures for the optical gap. By plotting these various gap measures as a function of the breadth of the optical absorption tail, we provide a means of relating these disparate measures of the optical gap. The applicability of this calibration to another set of hydrogenated amorphous silicon data is investigated. INTRODUCTION In order to characterize the optical absorption spectrum associated with an amorphous semiconductor it has proven instructive to devise empirical measures for the optical gap. Unfortunately, there is no pronounced feature of this spectrum which can be directly related to such a gap. Instead of terminating abruptly at the fundamental gap, as in the case of a defect-free crystalline semiconductor, the absorption spectrum associated with an amorphous semiconductor exhibits a tail which encroaches into the gap region [1, 2]. While various empirical measures for the optical gap of an amorphous semiconductor have emerged, thus far it has proven difficult to meaningfully compare data which has been interpreted using
disparate measures of this gap. In this paper, we hope to shed light on how these different measures of the optical gap are
related to each other. In particular, we analyze some hydrogenated amorphous silicon data of Cody et al. [1] with respect to a number of empirical measures of the optical gap, the data
of Cody et al. [1] being from a study on how the disorder influences the optical absorption spectrum of hydrogenated amorphous silicon. By plotting these various gap measures as a function of the breadth of the optical absorption tail, we provide a means of relating these disparate measures of the optical gap. The applicability of this calibration to another set of hydrogenated amorphous silicon data is also investigated. Further details of this study will be reported in an upcoming publication of Sweenor et al. [3]. ON DEFINING THE OPTICAL GAP For many years, the Tauc model [4] has served as the standard empirical model whereby the optical gap of an amorphous semiconductor may be defined. Assuming square-root distributions of conduction band and valence band states, assuming that the momentum matrix element is independent of hw, and assuming that the disorder characteristic of amorphous semiconductors relaxes the momentum conservation rules, Tauc et al. [4] suggested that an extrapolation of the essentially linear functional dependence of /a (h1w) b/1, observed in 55 Mat. Res. Soc. Symp. Proc. Vol. 557 © 1999 Materials Research Society
amorphous
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