New method to characterize mesoscopic range and very small strain with using multi-wave X-ray diffraction

A new technique to observe mesoscopic-range strain fields (up to several hundreds of nm) is proposed, using modulation of the crystal-truncation-rod (CTR) scattering caused by Bragg reflection. This technique is particularly sensitive to small, long-range strain fields near crystal surfaces and interfaces, which are usually difficult to be discriminated by using Bragg reflection. A simple interpretation can be made for the modulation profile: the technique is physically simple with a few parameters fitted to the data and, independently of any model, is able to determine the total displacement due to mesoscopic strain field for depths up to several hundreds of nanometers. We applied this method to a Si(0 0 1) wafer whose surface is covered with a thermal oxide layer 3 nm thick. On the basis of the expressions we obtained for the modulation profile a least-squares fitting was carried out to give a result that under the oxide layer there exists a total displacement of −0.16 Å. It was also revealed from the visibility of the modulation profile that the total displacement has a static fluctuation of at least ±0.13 Å in the lateral direction. The new method can be used for the correction of the errors of the X-ray standing wave (XSW) method produced by strained layers near crystal surfaces.