Citation

Dirk V. P. McLaughlin and J.M. Pearce, “Analytical Model for the Optical Functions of Indium Gallium Nitride with Application to Thin Film Solar Photovoltaic Cells”, Materials Science and Engineering: B, 177, 239-244 (2012).

Abstract

This paper presents the preliminary results of optical characterization using spectroscopic ellipsometry of wurtzite indium gallium nitride (InxGa1−xN) thin films with medium indium content (0.38 < x < 0.68) that were deposited on silicon dioxide using plasma-enhanced evaporation. A Kramers–Kronig consistent parametric analytical model using Gaussian oscillators to describe the absorption spectra has been developed to extract the real and imaginary components of the dielectric function (ɛ1, ɛ2) of InxGa1−xN films. Scanning electron microscope (SEM) images are presented to examine film microstructure and verify film thicknesses determined from ellipsometry modeling. This fitting procedure, model, and parameters can be employed in the future to extract physical parameters from ellipsometric data from other InxGa1−xN films.

Background

InxGa1−xN is a III-V semiconductor alloy with optoelectronic properties that are well-suited for application in solar photovoltaic (PV) cells. By altering the indium content in the alloy, the band gap of InxGa1−xN can be tuned from 0.7 eV to 3.4 eV spanning nearly the entire solar spectrum. However, due to a variety of factors such as atomic lattice mismatch between InN and GaN, it is difficult to grow high-quality InxGa1−xN films with a medium-high indium content using conventional deposition techniques. The InxGa1−xN thin films characterized in this paper could be deposited on an inexpensive silicon dioxide (SiO2) substrate using a novel plasma-enhanced evaporation deposition system. This paper presents the results of optical characterization using spectroscopic ellipsometry of wurtzite InxGa1−xN thin films with medium indium content (0.38<x<0.68) and proposes a Kramers-Kronig consistent parametric model for the optical functions of InxGa1−xN.

Experimental

The InxGa1-xN films were characterized via spectroscopic ellipsometry using a J.A. Woollam Co. vertical-variable angle spectroscopic ellipsometer (V-VASE) with a photon range of 0.8 eV to 4.5 eV.


In order to extract useful information about the thin films using ellipsometry, a Kramers-Kronig consistent parametric model was developed to fit the raw ellipsometric through a regression-based data analysis. In building the parametric model, each unique layer of material in the sample must be represented: Si wafer, SiO2 substrate (grown on the Si wafer), InxGa1-xN layer and a surface roughness layer (treated as a Bruggeman Effective Medium Approximation consisting of a 50/50 mixture of InxGa1-xN film and void space. In order to represent the unique absorbing InxGa1-xN layer, parametric dispersion relationships were used. A Cauchy layer with Urbach absorption was first used over the non-absorbing (transparent) regions of the ellipsometric data output before being converted to a real physical relationship using Gaussian oscillators.


Top-down and cross-sectional SEM images were taken using a field-emission scanning electron microscope (SEM)

Results

Dirk Ellips Paper Figure 1.jpeg
Dirk Ellips Paper Figure 2.jpeg
Dirk Ellips Paper Figure 3.jpeg

Conclusions

A Kramers-Kronig consistent parametric model has been developed for the optical functions of wurtzite InxGa1-xN alloy films of medium indium contents (0.38<x<0.68) deposited by a novel plasma-enhanced evaporation deposition system. This model employing simple Gaussian oscillators was used to fit spectroscopic ellipsometric data over the 0.8 eV to 4.5 eV range to obtain film thicknesses, dielectric functions and absorption coefficients. Using analytical expressions to accurately describe the optical functions of InxGa1-xN films is an extremely important step in understanding the semiconductor and its utilization in high-efficiency solar photovoltaic cells. The optical characterization methods employed and the model developed can be used as a basis for the optical characterization of similar InxGa1-xN thin films.

Citation List

The list of sources used in the paper can be found here

Contact

The author can be contacted at pvdirk@gmail.com

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