Self-Referenced Method for Estimating Refractive Index and Absolute Absorption of Loose Semiconductor Powders

The absolute absorption coefficient, α(E), is a critical design parameter for devices using semiconductors for light harvesting associated with renewable energy production, both for classic technologies such as photovoltaics and for emerging technologies such as direct solar fuel production. While α(E) is well-known for many classic simple semiconductors used in photovoltaic applications, the absolute values of α(E) are typically unknown for the complex semiconductors being explored for solar fuel production due to the absence of single crystals or crystalline epitaxial films that are needed for conventional methods of determining α(E). In this work, a simple self-referenced method for estimating both the refractive indices, n(E), and absolute absorption coefficients, α(E), for loose powder samples using diffuse reflectance data is demonstrated. In this method, the sample refractive index can be deduced by refining n to maximize the agreement between the relative absorption spectrum calculated from bidirectional reflectance data (calculated through a Hapke transform which depends on n) and integrating sphere diffuse reflectance data (calculated through a Kubleka-Munk transform which does not depend on n). This new method can be quickly used to screen the suitability of emerging semiconductor systems for light-harvesting applications. The effectiveness of this approach is tested using the simple classic semiconductors Ge and Fe₂O₃ as well as the complex semiconductors La₂MoO₅ and La₄Mo₂O₁₁. The method is shown to work well for powders with a narrow size distribution (exemplified by Fe₂O₃) and to be ineffective for semiconductors with a broad size distribution (exemplified by Ge). As such, it provides a means for rapidly estimating the absolute optical properties of complex solids which are only available as loose powders.