Composition and Strain Dependence of the Piezoelectric Coefficients in Semiconductor Alloys
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1017-DD04-11
Composition and Strain Dependence of the Piezoelectric Coefficients in Semiconductor Alloys T. Hammerschmidt1, M. A. Migliorato2, D. Powell2, A. G. Cullis2, and G. P. Srivastava3 1 University of Oxford, Oxford, United Kingdom 2 University of Sheffield, Sheffield, United Kingdom 3 University of Exeter, Exeter, United Kingdom
ABSTRACT We propose a tight-binding model for the polarization that considers direct and dipole contributions and employs microscopic quantities that can be calculated by first-principles methods, e.g. by employing Density Functional Theory (DFT). Applying our model to InxGa1-xAs alloys allows us to settle discrepancies between the values of e14 as obtained from experiments and from linear interpolations between the values of InAs and GaAs. Our calculated piezoelectric coefficient is in very good agreement with photo current measurements of InAs/GaAs(111) quantum well samples. INTRODUCTION Piezoelectric fields in semiconductor heterostructures have attracted a substantial amount of interest in recent years [1-3], and were identified as the source of experimentally observable optical anisotropies [4-6]. These anisotropies are due to the dipole charge distribution that arises at deformed anion-cation bonds: the well-known piezoelectric effect [7,8]. In zinc blend crystals, a deformation of this bond corresponds to shear strain, i.e. non-vanishing strain tensor components in the [111] direction. Therefore, the piezoelectric effect is pronounced in quantum wells that are epitaxially grown on (111) substrates. However, this effect can also be observed in epitaxially grown quantum wires and quantum dots. In previous works, the piezoelectric effect in InxGa1-xAs heterostructures was treated in first order with respect to the shear strain. The value of the piezoelectric coefficient was determined from either the experimentally deduced piezoelectric coefficients of bulk InAs and bulk GaAs or from linear interpolations of them. Recently, Bester and co workers [9] pointed out the limited applicability of this approximation: The second order terms are in fact of the same order of magnitude as the first order terms and tend to cancel the latter. Based upon the results of self-consistent density functional theory (DFT) calculations combined with a linear response technique, the authors manifested doubts in the bulk experimental values of the piezoelectric coefficient reported in the literature [10]. In this paper we present an alternative approach to obtain the first- and second-order piezoelectric coefficients that provides significantly improved agreement with experimental data for InAs/GaAs quantum wells.
THEORY The piezoelectric effect [7,8] in III-V semiconductors with zinc blend or wurtzite crystal structure is due to the lack of inversion symmetry [11]. The polarization Pi = eijk ε jk generated by a strain tensor εjk is described by the piezoelectric coefficients eijk. The crystal symmetry reduces the piezoelectric tensor to a scalar, commonly called e14, and simplifies the expression f
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