D.V.Roshchupkin
X-RAY DIFFRACTION BY SURFACE ACOUSTIC WAVES
Institute of Microelectronics Technology RAS
Russia, 142432 Chernogolovka, Moscow district
Tel: (095) 962-8074; Fax: (095) 962-8047;
E-mail: [email protected]
Process of X-ray diffraction on the crystals modulated by surface acoustic waves was investigated
under the total external conditions and in the Bragg diffraction conditions. It is shown that X-ray
diffraction is determined by wavelength and amplitude of the surface acoustic waves. The systems
of space-time control of X-ray radiation by ultrasonic superlattices are demonstrated.
1. Introduction
X-Ray diffraction has been used to study the characteristics of surface acoustic waves (SAW)
propagation in the crystals [1-7]. At the same time, SAW have directly provided an interesting tool for
the modulation and control of special and temporal structure of an X-ray beam. SAW have been used in
X-ray optics for generating dynamical gratings at the surface of the crystals [5-7]. In this article, the
process of X-ray diffraction by SAW was investigated under the total external reflection condition and
at the Bragg diffraction on the crystal lattice modulated by SAW.
2. The X-ray/SAW interaction
Coherent X-ray scattering on the lateral acoustic superlattice leads to the formation of
diffraction satellites on the both sides of the reflected beam. These satellites appear in specific directions
along which constructive interferences induced by the modulated crystal occur. The angular directions
can be deduced from the grating equation:
cosΘm=cosΘ0+m(λ/Λ),
(1)
where λ the X-ray wavelength, Λ the acoustic wavelength, Θ0 the incident angle of X-ray radiation, m
the diffraction order number and Θm the angle of the emergence of the m-th order satellite with respect
to the crystal surface.
3. X-ray diffraction by surface acoustic waves in the total external reflection conditions
Under the total external reflection conditions X-ray diffraction by SAW is characterized by the
small incident angle of X-ray radiation. The value of the critical angle of the LiNbO3 is 0.32o at X-ray
wavelength λ=0.154 nm. At grazing incidence the coefficient of X-ray reflection from the crystal
surface is 95% of the intensity of the incident X-ray radiation. Fig. 1 shows the dependencies of the
diffracted X-ray intensity. It is possible to observe the diffraction satellite around the intense zero
diffraction satellite. The differences in the intensities and angular positions of the diffraction satellites
are determined by the small incident angle of X-ray radiation. Diffraction of X-ray radiation by SAW in
the total external reflection conditions is characterized by the large angular divergence between
diffraction satellites which is very useful for realisation of different X-ray optical scheme for space
scanning of the diffracted X-ray radiation by the change of the SAW wavelength (X-ray scanning
microscopy) [8].
The Kirkpatrick-Baez experimental scheme was used for two-dimensional scanning of the
diffracted X-ray radiation (fig. 2). In this case the incident X-ray radiation diffracts on the first
ultrasonic superlattice, and after the diffraction satellites diffract on the second ultrasonic superlattice.
The resulting diffraction satellites have index (m, m). The change of the SAW excitation frequency on
the first and second crystals leads to the two-dimensional scanning of the diffracted X-ray satellites.
Fig. 3 shows the experimental X-ray topograph of two-dimensional X-ray scanning obtained at the
distance of 70 cm from the second crystal. The (+1, +1) rectangle defines the scanned area by
corresponding beam in the case of available frequency bandpasses of 107-137 MHz on the two SAW
devices The size of this area is 400*500 µm 2. The efficiency of the system (in terms of intensity) is of
the order of 2%. The large spot size are due to the divergence of the beam (defined by the source side
and the pinhole). Thus, the ultrasonic superlattices can be used for X-ray space scanning.
Fig. 1. Dependencies of diffracted X-ray intensity vs. the detector scanning angle ∆Θ obtained
at the incident angle of X-ray radiation Θ0=0.22o (SAW: ƒ=87.2 MHz, Λ=40 µm,
SAW amplitude h=1.5 nm, YZ-cut of a LiNbO3 crystal).
4. X-ray Bragg diffraction in the crystal excited by the surface acoustic waves
At the Bragg diffraction conditions X-ray radiation diffracts on the crystal lattices. Modulation
of the crystal lattice by surface acoustic waves leads to the formation of diffraction satellites on both
sides of the Bragg diffraction peak. Fig. 4 shows the rocking curves of the YZ-cut of a LiNbO3 crystal
recorded with and without SAW excitation. It is seen, that excitation of SAW with wavelength of Λ=4
µm and amplitude of h=1.5 nm leads to the formation of 6 diffraction satellites on the both sides of the
zero Bragg peak.
Bragg diffraction of X-ray radiation on the crystal is very interesting for fast time modulation
of the diffracted X-ray radiation [9]. Time modulation of X-ray radiation can be realized by SAW pulse
modulation. In this case X-ray radiation diffracts into diffraction satellites only during the time of the
interaction between the incident X-ray radiation and SAW pulse propagation across illuminated region.
Fig. 5 presents the result of time modulation of X-ray radiation from synchrotron radiation source
ESRF. The intensity was recorded in the +1 satellite directions as a function of time for 16-bunch mode
(16 equally spaced bunches around the ring, full time of rotation in the ring 2.8 µs, the distance between
two bunches 0.185 µs). Synchronization of SAW pulses (width of 0.185 µs) with temporal structure of
synchrotron was used to select the X-ray pulses (fig. 5: (a) - temporal structure of synchrotron
radiation, (b) - one bunch from 3 bunches; (c) - one bunch from 16 bunches).
Fig. 2. Experimental scheme of two-dimensional X-ray scanning (Kirkpatrick-Baez scheme).
Fig. 3. Experimental topograph of two-dimensional X-ray scanning.
Fig. 4. Rocking curves of the YZ-cut of a LiNbO3 crystal modulated by SAW (X-ray: reflection
(030), X-ray wavelength λ=0.1 nm, ΘBragg=20.2o; SAW: ƒ=872 MHz, SAW
wavelength Λ=4 µm, SAW amplitude h=1.5 nm).
Fig. 5. Time modulation of the diffracted X-ray radiation.
5. Conclusion
X-ray diffraction method is useful for investigation of SAW propagation in solids. Interaction
of X-ray radiation with ultrasonic superlattices can be used for design the different X-ray optical
systems for space-time modulation of the diffracted X-ray radiation.
REFERENCES
[1] H. Cerva and W. Graeff, Phys.Stat.Sol.(a) 82, 35 (1984).
[2] I.R. Entin, J.Appl.Cryst. 23, 355 (1990).
[3] E. Zolotoyabki and B. Sander, Act.Cryst. A51, 163 (1995)
[4] K.D. Liss, A. magerl, A. Remhof, and R. Hock, Act.Cryst. A53, 181 (1997)
[5] D.V. Roshchupkin, M. Brunel, F. de Bergevin, and A.I. Erko, Nucl. Instr. and Meth. B72, 471(1992).
[6] D.V. Roshchupkin, I.A. Schelokov, R. Tucoulou, M. Brunel, Nucl. Instr. and Meth. B129, 414 (1997).
[7] D.V. Roshchupkin, R. Tucoulou, A. Masclet, M. Brunel, I.A. Schelokov, and A.S. Kondakov, Nucl. Instr.
and Meth. B142, 432 (1998).
[8] R. Tucoulou, M. Brunel, D.V. Roshchupkin, and I.A. Schelokov, Rev.Sci.Instrum. 69, 2704 (1998).
[9] D.V. Roshchupkin and M. Brunel, Rev.Sci.Instrum. 64, 379 (1993).