Spectral Sensitivities of X-Ray Diffraction to the Roughness of Si/SiO 2 Interfaces
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K.W. EVANS-LUTTERODTt and MAU-TSU TANG*, tAT&T Bell Laboratories Murray Hill, NJ 07974, and *S.R.R.C, Taiwan R.O.C. ABSTRACT Results from X-ray diffraction studies of the morphology of the growing Si(001)/Si0 2 interface are presented. We show the evolution of the root mean square roughness as a function of the growth variables, and we try to go beyond the root mean square parametrization of the interface by measuring the spectral distribution of interface fluctuations. Within our current experimental sensitivies we cannot resolve any fluctuations with a finite in-plane momentum transfer. INTRODUCTION Understanding the morphology of the Si(001)/Si0 2 interface is important information to help in modeling the physical properties of the interface, such as the electron mobility parallel to the interface, which affects device performance, or the effective barrier height to tunneling, which affects the device reliability. The root mean square (r.m.s.) roughness of a surface is one of the most commonly used parameters that quantifies the surface morphology. A more useful way to parameterize the morphology of an interface is to measure the spectral distribution of fluctuations of the interface. There are two reasons why this may be useful. First, certain physical properties of the interface may be weighted by the roughness spectral distribution, and so only the roughness at particular wavelengths will be important. Secondly, it will allow one to make direct comparisons between the different techniques that measure r.m.s. roughness. All the experimental techniques measure an effective r.m.s. with the range of Fourier components being integrated over limited by the specific technique. To illustrate the first point, let us briefly consider the electron mobility of a two dimensional electron gas, such as is typically found at the Si(001)/Si0 2 interface when a metal-oxide-semiconductor-field-effect-transistor (MOSFET) is in strong inversion. For this system, there are two theoretical approaches 11 to the problem that depend on whether the roughness is due to a slowly varying interface, or rapid atomic-scale fluctuations, where the out-of-plane fluctuation is large compared to the in-plane length distance over which they occur. In the slowly varying interface limit 21, the fluctuations of the interface position are mapped into fluctuations of the potential energy, and this is used in a perturbation calculation of the transport relaxation time. Electrons are strongly scattered by Fourier components of the roughness potential that are within KT of the Fermi wavevector. In the rapidly varying limitt 31 , which describes vacancies quite well, the model for the effect of interface roughness on electron mobility, is based on the graded interface model. The electron wave function is calculated to have some penetration into the oxide, and the reduction in mobility is due to the portion of the electron wavefunction that penetrates into the oxide, and the electron mobility in the oxide. The ability to measure the a
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