A geometrical optical model for the image formation of Makyoh (or magic-mirror) topography is presented. General relations are given on the optical settings. The basic equations of the imaging are derived. Fundamental features of the imaging are pointed out, and optimum working conditions are established. Simulations of the image of an isolated defect (hillock or depression) and a periodic (sinusoidal) surface are presented for different optical settings. Supporting experimental images are presented.
Asymmetric strain relaxation and the concomitant misorientation (tilt) of the lattice planes of the epitaxial layer in lattice-mismatched heterostructures is analyzed theoretically. The kinetic relaxation model of Dodson and Tsao [Appl. Phys. Lett. 51, 1325 (1987); 52, 852(E) (1988)] is extended to the growth on vicinal surfaces. We calculate the equilibrium tilt values as well as the evolution of tilt during strain relaxation as a function of material parameters, initial defect densities, and substrate miscut angle. Literature data are interpreted within the framework of the model.
A new method is developed for the measurement of the radii of curvature R of mirror-like semiconductor wafers using the magic-mirror (Makyoh) method. A flat mirror is placed beneath the sample, thus a second, “contour” image of the sample is formed beside the sample image itself. From the size deviation of the two images that results from the curvature of the sample, R can be calculated. Experimental results obtained with mirrors with known curvature show good agreement with the calculations. Implications for the general image formation mechanism are discussed as well.
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