X-ray Single-mode Difiraction from Si-nanowires on Silicon

TLDR: In this paper, a single-mode operation in x-ray difiraction from crystalline materials is realized by using singly-polarized x-rays wide angle incidence and grazing emergence DIFIRACT from Si-nanowires and bare Si substrate.

Abstract: Single-mode operation in x-ray difiraction from crystalline materials is very di-- cult to reach because many modes of wave propagation are simultaneously excited in crystals, thus hinders the application of single-mode x-ray difiraction in coherent x-ray optics and ma- terials characterization. We report here a method of realizing single-mode difiraction by using singly-polarized x-rays wide angle incidence and grazing emergence difiraction from Si-nanowires and bare Si substrate. For a bare Si substrate, the surface difiracted and specular re∞ected beam of single-mode excitation are separated by difierent angular settings due to the extremely asym- metric difiraction at grazing emergence. For Si-wires on Si, single-mode difiraction is achieved by tuning the x-ray energy so as to have nearly grazing emergent re∞ection, or by decreasing the incident angle to both the Si-wires and Si substrate to satisfy the condition of total re- ∞ection. Dynamical theory of x-ray difiraction is employed to calculate the dispersion relation, linear absorption coe-cient, excitation of mode of wave propagation, and intensity distribution. Single-mode operation can be understood from these dynamical calculations. An equation which determines the vertical component of the difiracted wavevector, Kz, as a function of photon en- ergy and azimuth angle of rotation is derived from the difiraction geometry. It is proved that the difiraction from the Si-wires on Si is of single-mode, when the corresponding Kz is smaller or equal to zero. Synchrotron difiraction experiments also conflrm this Kz relationship. This development opens up new opportunities of using crystal difiraction, in addition to optical re- ∞ection/refraction, for the design of coherent x-ray optics.