On the Accurate Determination of Absorption Coefficient From Reflectanceand Transmittance Measurements

Document Type

Article

Publication Date

7-1-2016

Identifier/URL

40890693 (Pure)

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Abstract

For light impinging normally on the surface of a double-side-polished sample of thickness d, the sample's absorption coefficient α can be determined from the well-known formula for fractional transmittance: Tmeas = (1 − R)2exp(−αd)/[1 − R2exp(−2αd)]. Here, R is a fundamental property of the air/sample interface and is known as the “reflectance coefficient.” Often R in this equation is equated to the measured top-surface reflectance Rmeas, but such an approximation can lead to serious error. In fact, the authors explicitly show that Rmeas = R + R(1 − R)2exp(−2αd)/[1 − R2exp(−2αd)] and then further develop an easily solvable transcendental equation that determines both R and α from Tmeas and Rmeas. In strongly absorptive regions (αd ≫ 1), it turns out that R ≈ Rmeas, but in the opposite limit (αd ≪ 1), R ≈ Rmeas/(2 − Rmeas). Formulation by the authors enables accurate determinations of: (1) ε∞, the high-frequency dielectric constant; and (2) relatively weak absorbances, such as those related to defects or impurities with energy levels in the bandgap. The authors also compare the exact calculations of α in semi-insulating GaN:Fe with those obtained from commonly used approximations.

DOI

10.1116/1.4954211

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