High-depth-resolution Rutherford backscattering data and error analysis of SiGe systems using the simulated annealing and Markov chain Monte Carlo algorithms

The thickness and composition of SiGe/Si quantum wells has been studied by high-depth-resolution Rutherford backscattering (RBS) analysis. While a depth resolution at the surface of 8 nm is achieved, the degradation of resolution with depth must be taken into account for a correct analysis of the data. Fully automated analysis incorporating the depth resolution as a function of depth was performed using the simulated annealing algorithm. Bayesian inference using the Markov chain Monte Carlo method was also employed, and confidence limits on the SiGe depth profiles obtained from the RBS data are established. The results obtained are used to show that the interface sharpness in SiGe/Si multilayers depends on the temperature of growth. Finally, it is shown that standard RBS using a normal angle of incidence is sufficient to obtain narrow limits of confidence in the thickness and stoichiometry of single quantum wells, but not of multiple quantum wells, for which high-depth-resolution experiments are necessary.