Real-Time Reciprocal Space Mapping of Nano-Islands Induced by Quantum Confinement
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diffraction is essentially a two-dimensional (2-D) scattering process. The scattering can be defined by two angles. At a given sample orientation, the Ewald sphere in reciprocal space determines the 2-D shell one can observe in diffraction. In principle, with area detectors, one can capture a 2-D area of scattering information in reciprocal space at once. In the case of large single crystal samples, the chance to see any Bragg diffraction is slim unless the crystal is oriented for the diffraction condition. However, as the objects becomes smaller in dimension, the chance increases to observe appreciable scattering at a given sample orientation in a 2-D area of reciprocal space. Good examples of objects with such small dimensions are surfaces, interfaces, and thin films. Although X-rays do not interact with atoms strongly, the synchrotron radiation from undulator beamlines is bright enough for the 2-D scattering intensity distribution from them to be recorded. As increasingly sensitive area detectors become available, we can observe surface phenomena in the time scale of 1 second in two dimensions. Similarly, nanoscale crystalline subjects will give an abundance of structural and morphological information through 2-D scattering with a fixed orientation. This finding is a result of the spread of scattering in momentum space, which is inversely proportional to the lateral sizes. By rotating the sample around a chosen angle, the Ewald sphere can be made to sweep through a large volume of the momentum space. HAWOONG HONG, Physicist, is with Argonne National Laboratory, Argonne, IL 60439. Contact e-mail: [email protected] AARON GRAY, Graduate Student, is with the Department of Physics, University of Illinois, Urbana-Champaign, IL 60801. T.-C. CHIANG, Professor, is with the Department of Physics and the Frederick Seitz Materials Laboratory, University of Illinois. Manuscript submitted February 22, 2010. Article published online June 12, 2010 32—VOLUME 42A, JANUARY 2011
By coordinating the rotary motion and the 2-D scattering measurements, one can achieve rapid acquisition of three dimensional (3-D) reciprocal space maps. Concomitantly, it has been observed that electron confinement within quantum wells made of metals has very interesting consequences in nanoscales.[1] The new quantum states from the confinement even dictate the structure and morphology of metal films and islands. Pb in particular shows pronounced quantum size effects, such as magic islands heights, bilayer oscillation in the lattice spacing, and ordering between islands.[2–5] In this regimen, the Pb island heights are on the order of 1 nm. The scale of the lateral dimension of the island is on the order of 10 nm to 100 nm. The 2-D or 3-D reciprocal space mapping (RSM) has been playing significant roles in investigating the structural and morphological phenomena of these nano-islands.
II.
2-D RSM
X-ray diffraction from surfaces has a rod-like distribution in reciprocal space instead of points. An Ewaldsphere resulting from high-energy X-rays intersects with many of th
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