Analytical Model for the Optical Functions of Indium Gallium Nitride with Application to Thin Film Solar Photovoltaic Cells
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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). open access
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.
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 with a thin GaN buffer layer 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.
The InxGa1-xN films were characterized via spectroscopic ellipsometry using the lab's 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. In order to produce a real physical shape for dispersion over the entire energy range (absorbing regions now included), the Cauchy layer was converted into a general oscillator layer using 2-3 Gaussian oscillators to enforce Kramers-Kronig consistency.
Top-down and cross-sectional SEM images were taken using a field-emission scanning electron microscope (SEM) in the Queen's Physics Department.
For this paper, four InxGa1−xN thin films with estimated indium contents of x=0.38,0.54,0.64 and 0.68 were characterized. The top-down SEM images of these films are shown below:
The InxGa1−xN films display a clear relationship of larger grain or nanocolumn diameters with increasing indium content, which has been reported previously. Additionally, the two highest indium content films show not only thicker much better defined and isolated platelets/nanocolumns.
The following image shows the cross-sectional view of the In0.68Ga0.32N thin film:
This image reveals the partially coalesced nanocolumnar microstructure of the high indium content films and verifies the accuracy of the film thickness (221 nm) determined from the ellipsometric model.
The Kramers-Kronig consistent parametric dispersion model described earlier was found to fit the experimental data (Ψ and Δ) very well with mean-squared errors (MSE) under 16. This, in addition to film thicknesses confirmed by SEM imaging, allowed the conclusion that the model developed is both accurate and physically meaningful. Using these models for the InxGa1−xN films, film thicknesses and optical properties were obtained. The following graphs show the real and imaginary parts of the dielectric function, ε1 and ε2, as a function of photon energy for the analyzed InxGa1−xN films:
The InxGa1−xN films show similar trends for the real and imaginary parts of the dielectric function. As expected, the ε2 curves indicate strong absorption at the higher photon energies above the band gaps. However, there is also evidence of non-zero absorption at the low energy end which could indicate sub-gap absorption due to a high density of absorbing free electrons, dislocations and defects. The rather broad curves of the dielectric functions and index of refraction curves can an be largely attributed to the large lattice mismatch the In-rich InxGa1−xN films presented here suffer from which tend to cause structural disorder and slight fluctuations in composition. Absorption coefficients extracted from the model were found to be on the order of 105 cm-1 at the absorption edges and this strong absorption, despite imperfect crystallinity, illustrates the potential of the InxGa1−xN for photovoltaic applications.
The paper also presents the parameters of the Gaussian oscillators used to fit the ellipsometric data. The parameters presented can be used to help describe the optical functions and absorption of similar wurtzite In-rich InxGa1−xN films. This is particularly important for the complex nature of proposed multi-junction solar photovoltaic devices, which rely on multiple layers of InxGa1−xN films with varying indium content.
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.
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