Determining sample alignment in x-ray reflectometry using thickness and density from GaAs/AlAs multilayer certified reference materials

Abstract

X-ray reflectometry (XRR) provides researchers and manufacturers with a non-destructive way to determine thickness, roughness and density of thin films deposited on smooth substrates. Due to the nested nature of equations modeling this phenomenon, the inter-relation between instrument alignment and parameter estimation accuracy is somewhat opaque. In this study, we intentionally shift incident angle information from a high-quality XRR data set and refine a series of shifted data sets using an identical structural model to assess the effect this angle misalignment has on parameter estimation. We develop a series of calibration curves relating angle misalignment to variation in layer thickness and density for a multilayer GaAs/AlAs Certified Reference Material on a GaAs substrate. We then test the validity and robustness of several approaches of using known thickness and density parameters from this structure to calibrate instrument alignment. We find the highest sensitivity to and linearity with, measurement misalignment from buried AlAs and GaAs layers, in contrast to the surface layers, which show the most variability. This is a fortuitous result, as buried AlAs and GaAs exhibit the highest long-term stability in thickness. Therefore, it is indeed possible to use reference thickness estimates to validate XRR angle alignment accuracy. Buried layer mass density information also shows promise as a robust calibration approach. This is surprising, as electron density of buried layers is both a highly-correlated phenomenon and a subtle component within the XRR model.