Monte Carlo calculation of X-ray depth profiles in Si substrate coated with films

Using Monte Carlo methods, we have calculated depth profiles of X-ray production, Phi ( rho z) curves, for Si K alpha in a Si substrate coated with Cu, Ag and Au films of varying film thickness and electron beam voltages from 10 to 30 kV, as well as the characteristic radiation from films for comparison with August and Wernisch's (1991) analytical approach. Calculation results shows that, for radiation from the film, general agreement is found with August and Wernisch's formula, while it is not found for radiation from the substrate. We demonstrate that the Monte Carlo simulated Phi ( rho z) curves from Si substrate can be well described by the modified Gaussian profile of Packwood and Brown (1981), and the calculated profiles may be parameter-fitted into the analytical formula Phi ( rho z)= Theta ( rho z- rho Delta z)( gamma -(( gamma - Phi (0))exp(- beta rho z)))exp($ - alpha 2 ( rho z) 2 ).