Si and Ge hemispherical concave wafers can be prepared by plastic deformation using Si and Ge single- and polycrystal wafers. Deformation regions in which such Si and Ge hemispherical wafers can be obtained by high-temperature plastic deformation were systematically studied. The deformation regions in which well-shaped Si concave wafers can be obtained were studied for (1 0 0), (1 1 1), and polycrystal Si. It was found that Si (1 1 1) crystal wafers can be more easily deformed to a perfect hemispherical shape than (1 0 0) wafers because of the crystallographic symmetry. Si hemispherical wafers with a small radius of 25 mm can be perfectly deformed when 0.5-mm-thick Si (1 1 1) crystal wafers are used. Ge hemispherical wafers with a radius of 100 mm can be perfectly deformed when 0.5-mm-thick Ge crystal wafers are used. Ge hemispherical concave wafers with a perfect shape can be more easily obtained using Ge (1 1 1) wafers than (1 0 0) wafers. According to these results, the deformation behavior of Ge wafers is very similar to that of Si wafers at a normalized pressing temperature. As both the radius and the load on Si and Ge hemispherical wafers increase, thicker Si and Ge wafers can be used to obtain hemispherical wafers with a perfect shape. The dislocation density in the shaped wafers markedly decreases as the pressing temperature and hemisphere radius increase. Thus, it is suggested that Si and Ge shaped wafers are of sufficient quality and have the high potential for use as several types of lens such as those in Si and Ge X-ray monochromators.
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