Optical properties of Mo and amorphous MoOx, and application to antireflection coatings for metals

Abstract

To form antireflection (AR) coatings to hide metal architecture in display technologies, we deposited thin films of metal Mo and oxide MoOx by sputtering targets of various compositions using pure Ar sputter gas. The optical constants [n,k] of these samples were measured by the direct numerical solution of reflectance and transmittance at each wavelength point measured. We find that 50 nm films are uniform in the growth direction, but for thicker 100 nm samples, evidence exists for nonuniform growth, where the top 20 nm appears to be metal rich. From these [n,k], negative Tauc bandgap energies show these oxides are semi-metals. We then identified the specific composition (x) that optimizes the AR response for a host of metals (Al, Cu, Ag, Au). Finally, two methods were used to understand why these MoOx materials function well as AR media, including (i) using phasor rays and (ii) developing a universal expression for the AR condition that applies to both dielectric and metal substrates. In (i), we find two characteristics for AR of metals: (a) its optical thickness should be roughly π3, not the π2 for dielectrics, since for MoOx, their [r^ij,t^ij] Fresnel phases differ from the usual [180°, 0°] of dielectrics; and (b) the medium incorporates a k-dominant strategy whose function is to absorb the energy that is reflected at the AR/metal interface. In (ii), the universal AR condition is found to be r^01+r^12z^=0. For dielectrics, this reduces to the well-known nAR=nairnsub condition. However, for metals, a concise analytic expression is lacking since this expression is highly nonlinear but is easily solved by numerical methods.