A simple solution to systematic errors in density determination by X-ray reflectivity: The XRR-density evaluation (XRR-DE) method

Abstract X-ray reflectivity (XRR) is a non-destructive, accurate and fast technique for evaluating film density. Indeed, sample-goniometer alignment is a critical experimental factor and the overriding error source in XRR density determination. With commercial single-wavelength X-ray reflectometers, alignment is difficult to control and strongly depends on the operator. In the present work, the contribution of misalignment on density evaluation error is discussed, and a novel procedure (named XRR-density evaluation or XRR-DE method) to minimize the problem will be presented. The method allows to overcome the alignment step through the extrapolation of the correct density value from appropriate non-specular XRR data sets. This procedure is operator independent and suitable for commercial single-wavelength X-ray reflectometers. To test the XRR-DE method, single crystals of TiO 2 and SrTiO 3 were used. In both cases the determined densities differed from the nominal ones less than 5.5%. Thus, the XRR-DE method can be successfully applied to evaluate the density of thin films for which only optical reflectivity is today used. The advantage is that this method can be considered thickness independent.