Twinning and Nonlinear Optics

A comprehensive theory of quasi-phase-matched (QPM) three-wave interactions in twinned plates of q3m semiconductors is developed. The 180* phase change required by QPM is studied by treating the nonlinear polarization as a bilinear form in the applied electric field and decomposing it into invariant and sign changing parts under a 2-fold rotation of an arbitrary crystal lattice. A new 3 X 3 matrix representation of the third rank nonlinear susceptibility tensor. is found for all crystal classes. In the 43m -case the decomposition of this form results in sufficiently compact expressions enabling the evaluation of the nonlinear polarization generated by mixing elliptically polarized waves. The theory shows that use of circularly polarized light is a factor of two more efficient than the conventional linearly polarized light. The predicted 1% second harmonic generation (SHG) efficiency is verified experimentally for a stack of 6 twinned CdTe plates in a Brewster-angle immersion cell using carbon disulphide as index matching medium While SHG was demonstrated in selected twinned material, practical implementation requires either routine optical contacting of large stacks of twinned plates, or the achievement of controlled twinning during crystal growth. The brittleness of CdTe renders the former alternative difficult to implement. The latter alternative, however, is shown to hold significant promise of success. CdTe crystals were grown in a sealed Vertical Bridgman configuration. The systematics of twinning were studied and a special ampoule was designed that allowed some degree of orientational control over twin formation. The experimentally -derived observations, together with information derived from a literature survey led to the proposal of a new model of growth interface anisotropy based on the density of dangling p. 1 bonds gi". The 6-lobe v surface for elemental semiconductors and 12-lobe extension in the polar case both conform to the general form given by Herring in 1951, and represent the first calculation of the Q plots in these crystal systems. The model is found to explain a variety of phenomena related to the interface anisotropy including solitary and lamellar twinning, faceting and etching. In particular, the higher twinning frequency of "A" seeded polar crystals is shown to be the result of the low density of dangling bonds exposed to the melt in t.hat orientation. For elemental semiconductors, a stability map against twinning is explicitly given. Although accidental and two-dimensional nucleation mechanisms are not ruled out, their u'se is not required. It is concluded that growth twinning represents in general a response of the advancing solid-melt interface to a change in the local kinetic undercooling and the orientation of the solidification front relative to the lattice. An alternative model. of growth twinning is also provided for materials characterized by highly-associated melts. Relatively stable 8-atom-clusters are shown to be capable of nucleating the observed oblique twins and predict the existence of a minimal thermal gradient for monocrystalline growth. The dangling bond model provides a framework for further study of anisotropic interfacial phenomena. In particular further quantification of the lamellar mechanism holds the promise of controlled twinning for nonlinear optical applications. Thesis Supervisor: Dr. C. Forbes Dewey, Jr. Title: Professor of Mechanical Engineering