Determination of the optical constants of fine grained diamond layers on silicon substrates using curve-fitting procedures

Abstract

The optical constants of fine-grained diamond layers have been investigated by spectrophotometric means in the near-IR and visible spectral ranges. The layers were deposited by a microwave chemical vapour deposition technique on 〈100〉 and 〈111〉 oriented silicon substrates. For determining the optical parameters, measurements of the directed and diffuse reflectance and transmittance of the layer-on-substrate system have been carried out. The calculation of the optical constants has been accomplished by a curve-fitting procedure. For that purpose, a quadratic error function has been minimized by the method of conjugated gradients. To reduce the multiplicity of solutions, the refractive index has been assumed to increase with increasing wavenumber following a quadratic dispersion law, while the loss coefficient is assumed to increase exponentially with increasing wavenumber. The investigation of experimental spectra has shown that the method works successfully in application to layers with a surface r.m.s. roughness less than approximately 100 nm. For such layers, refractive index values have been obtained which are slightly lower than those of natural diamond, while the loss coefficients are much higher because of surface and bulk scattering.