Simulating the influence of stoichiometry on the spectral emissivity of Mo$_x$Si$_y$ thin films

Abstract

In this work, we simulate the spectral emissivity of various stoichiometric crystal phases of Mo$_x$Si$_y$ compounds using density functional perturbation theory. The dielectric function, including electronic and ionic contributions, is calculated for each phase. We use the bulk properties obtained to simulate the optical absorption spectrum originating from the compound in thin film ($\sim$20 nm) form. We find that most thin films of Mo$_x$Si$_y$ are metallic, however, our results indicate that their emissivity is not simply correlated with the Mo content. For hot metallic films at around 900 K, we predict a maximal emissivity between 5-10 nm thickness. Our results are in good qualitative agreement with experiments, confirming that the emissivity of hexagonal MoSi$_2$ is much lower than in the tetragonal phase. This is related to the small band gap (hexagonal MoSi$_2$) and low density of states at the Fermi level (tetragonal MoSi$_2$). Furthermore, test calculations on defected MoSi$_2$ demonstrate that the infrared emissivity of MoSi$_2$ thin films can be substantially increased by introducing defects.

Figures (9)

• Figure 1: Flowchart of the simulation and computation setup to calculate the emissivity of thin films starting from first principles. The input is formed by the atomic coordinates $\{\mathbf{R}_{1\ldots N}\}$ and lattice vectors $\{\mathbf{a}_{1,2,3}\}$ of the structures in Figure \ref{['fig:struc']}. The purple dotted line divides the chart, the left hand is on the level of bulk crystal and the right hand side on the level of the thin film.
• Figure 2: Overview of the unit cells considered for the different phases of Mo$_x$Si$_y$: a) hexagonal MoSi$_3$, b) hexagonal MoSi$_2$, c) tetragonal MoSi$_2$, d) hexagonal MoSi , e) tetragonal Mo$_3$Si$_2$, f) hexagonal Mo$_5$Si$_3$, g) tetragonal Mo$_5$Si$_3$, and h) cubic Mo$_3$Si.
• Figure 3: From top to bottom: Band structure, density of states, and dielectric function of a) hexagonal MoSi$_3$, b) hexagonal MoSi$_2$, c) tetragonal MoSi$_2$, d) hexagonal MoSi, e) tetragonal Mo$_3$Si$_2$, f) hexagonal Mo$_5$Si$_3$, g) tetragonal Mo$_5$Si$_3$, and h) cubic Mo$_3$Si. The dielectric function is based on electronic inter-band and ionic contributions only. The black/red line denotes the real/imaginary part in $\varepsilon(\omega)=\varepsilon'(\omega)+i \varepsilon"(\omega)$, respectively.
• Figure 4: The frequency-dependent penetration depth of the eight Mo$_x$Si$_y$ materials based on (top) only the inter+ion dielectric function of Fig. \ref{['fig:bandsdosdiel']}, and the (bottom) full intra+inter+ion dielectric function of Eq. \ref{['eq:epsilon']}) The typical thin film thickness is indicated by the horizontal dashed line.
• Figure 5: Absorption spectra for a 20 nm (top) hexagonal Mo$_5$Si$_3$ and (bottom) tetragonal MoSi$_2$ thin film including different dielectric contributions, and black body radiation spectra at temperatures of 300 K and 900 K. (Black body curves are normalized by peak height.)