Measurements of spontaneous bending attributed to surface stresses in thin crystals in aluminium nitride

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Abstract
The phenomenon of spontaneous biaxial bending in thin crystals of aluminium nitride has been studied quantitatively by transmission electron microscopy. The crystals were grown from the vapour with large surfaces parallel to the basal planes, and they were free from dislocations or other visible defects. Measurements of radii of curvature R and thicknesses t, over a wide range of these variables, have shown that R∝t 2; this is in accord with the equation which is expected if bending is due to the difference in surface stresses (σB–σA) at the polar B and A surfaces. The present data give (σB–σA)=(3°63±0·15) × 103 dynes/cm for AIN. Other evidence, from experiments on the temperature dependence of the bending and on reflection electron diffraction, is given to support the belief that the elastic bending phenomenon in AIN is due to the net surface stress. The bending is clearly revealed by six-fold symmetrical patterns of intersecting bend contours; these exhibit many fringes which are attributed to the simultaneous excitation of many Bragg reflections. Precise values of thickness were derived from measurements of the positions of subsidiary maxima of bend contours, by using equations of the dynamical theory for two beams in an ideally bent crystal. For this measurement, crystals were tilted away from the many-beam position to a two-beam position. The sensitivity of the best measurements of thickness was about 2% of the extinction distance, i.e. about 30 Å.