Total integrated scattering from transparent substrates in the infrared region: validity of scalar theory

Integrated light scattering, from thin, transparent silicon wafers with dif ferent front and backside surface roughness is investigated. The measuremen ts are made at near normal incidence in the IR wavelength region 5 to 20 mu m using an integrating sphere. A method to separate the scattering contrib ution from each interface for measurements on transparent samples is introd uced. Scalar scattering theory is used to calculate the effective root mean square roughness from reflectance and transmittance measurements, and thes e values are compared to profilometer data, correcting for the different ba ndwidth limits. Scattering measurements are performed with both the rough a nd the smooth surface of the wafer oriented toward the light source, which results in additional knowledge. The maximum ratio between the root mean sq uare roughness and the wavelength of the light, to be used in scalar theory , is found to be considerably higher for the transmittance case than for th e reflectance case. In agreement with theory, the calculated root mean squa re roughness is found to be proportional to the refractive index of inciden t medium in reflectance, and to the difference in refractive indices of inc ident and refracting medium for the transmittance case. (C) 2000 society of Photo-Optical instrumentation Engineers. [S0091-3286(00)01902-4].