Rocking-Curve Peak Shift in Thin Heterojunction Single Layers
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ROCKING-CURVE PEAK SHIFT IN THIN HETEROJUNCTION SINGLE LAYERS C.R. Wie, Y-W. Choi, H.M. Kim, J.F. Chen, T. Vreeland, Jr.* and C.-J. Tsai* State University of New York at Buffalo, Department of Electrical and Computer Engineering, Bonner Hall, Amherst, NY 14260. * California Institute of Technology, Dept. of Materials Science, Pasadena, CA 91125
ABSTRACT A simple method for determining layer composition and mismatch of semiconductor hetero-epitaxial samples is by measuring the separation of peaks in x-ray rocking curve (XRC). This method fails if the peak separation is affected by other factors. For a small layer thickness, the layer peak position is affected by the x-ray amplitudes of the substrate or other thicker layers through the interference and overlap effects. In this case, a diffraction theory fitting process is necessary for a correct determination of layer parameters. We have used dynamical and kinematical x-ray diffraction theories to calculate the layer peak position as a function of its thickness for various layer/substrate combinations. These two theories yield substantially different results, indicating that the kinematical diffraction theory analysis is no longer valid for these thin layers. When a thick layer is present along with the thin layer, the thick layer is more influential than the substrate to the thin layer peak position, making the dynamical theory fitting necessary even from higher thickness.
INTRODUCTION X-ray rocking curve (XRC) technique is commonly used for measurements of lattice mismatch and alloy composition of hetero-epitaxial semiconductor layers". A simple method is the measurement of separation of peaks, from which the mismatch and composition are calculated by taking into consideration of the unit cell distortion and Vegard's law 5 . A more complicated but accurate method is to fit the experimental XRC with a simulated curve which is calculated with an assumed strain depth-profile using the kinematical 3 or dynamical 4 x-ray diffraction theory. Fewster and Curling 2 reported that the peak separation method (PSM) is invalid when the layer is very thin. They did not, however, notice that there is a minimum layer thickness, down to which the peak separation method is valid, which is greater for a smaller lattice mismatch sample. Below the minimum thickness, the XRC should be analyzed using the x-ray diffraction theory. Since the rocking-curve peak-shifting, which makes the PSM invalid, is a result of the boundary condition at the layer-substrate or Mat. Res. Soc. Symp. Proc. Vol. 145. 01989 Materials Research Society
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layer-layer interface, care must be taken to use a correct boundary condition in the diffraction model. The objective of this paper is to consider the boundary conditions used in the kinematical and dynamical diffraction models and present some calculation results on AlGaAs/GaAs samples. We conclude that the kinematical diffraction model is also invalid when PSM breaks down, and point out that many published papers on the dynamical diffraction theory quot
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