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Type: Report × Subject: piezoelectricity ×

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    Impact of size, shape and composition on piezoelectric effects and the electronic properties of InGaAs/GaAs quantum dots
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Schliwa, Andrei; Winkelnkemper, Momme; Bimberg, Dieter
    The strain fields in and around self-organized In(Ga)As/GaAs quantum dots (QD) sensitively depend on QD geometry, average InGaAs composition and the In/Ga distribution profile. Piezoelectric fields of varying size are one result of these strain fields. We study systematically a large variety of realistic QD geometries and composition profiles, and calculate the linear and quadratic parts of the piezoelectric field. The balance of the two orders depends strongly on the QD shape and composition. For pyramidal InAs QDs with sharp interfaces a strong dominance of the second order fields is found. Upon annealing the first order terms become dominant, resulting in a reordering of the electron p- and d-states and a reorientation of the hole wavefunctions.
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    A mathematical framework for standard generalized materials in the rate-independent case
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Mielke, Alexander
    Standard generalized materials are described by an elastic energy density and a dissipation potential. The latter gives rise to the evolution equation (flow law) for the internal variables. The energetic formulation provides a very weak, derivative-free form of this flow law. It is based on a global stability condition and an energy balance. Using time-incremental minimization problems, which allow for the usage of the rich theory in the direct method of the calculus of variations, it is possible to establish general, abstract existence results as well as convergence for numerical approximations. Applications to shape-memory materials and to magnetostrictive or piezoelectric materials are surveyed.