Tunability of High-Dielectric-Constant Materials from First Principles
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Tunability of High-Dielectric-Constant Materials from First Principles K. M. Rabe Department of Physics and Astronomy, Rutgers University Piscataway, New Jersey 08854-8019 ABSTRACT A first-principles method, based on density functional perturbation theory, is presented for computing the leading order tunability of high-dielectric-constant materials. INTRODUCTION High-dielectric-constant materials are of great interest for high-performance electronic devices. Besides the high dielectric constants themselves, which could in principle allow miniaturization of devices beyond that possible with silicon dioxide, tunability of the dielectric response by a dc electrical bias opens up a wide range of additional applications. Understanding the fundamental physics of high-dielectric-constant insulators does, however, pose some significant challenges. In particular, the effects of homogeneous electric fields on the electronic and crystal structure of insulators, and on their dielectric and piezoelectric properties, involves subtleties that have only recently begun to be systematically addressed. Key advances include the correct formulation of the electric field perturbation within density-functional perturbation theory (DFPT) [1, 2], and the expression of polarization as a well-defined bulk property through the Berry-phase formalism [3]. Subsequently, the effects of finite fields have been formulated using Taylor expansions around zero field [4]. Using a closely related approach, a formalism in which polarization is the independent variable has been developed [5] which includes a method for computing the nonlinear dielectric susceptibility. In this paper, we present a first-principles method for the efficient direct computation of the tunability of high-dielectric-constant materials to leading order in the electric field. This method is designed for implementation into existing density functional pertubation theory packages, such as ABINIT [6] and PWSCF/PHONON [7], which typically calculate second derivatives of the energy and can be extended to compute third derivatives without significant additional computational effort. If third derivatives are available, the collinear susceptibility of a ferroelectric material can be computed with the sole approximation that the electric-field derivative of the electronic susceptibility be fixed at the value at zero field with corresponding equilibrium structural parameters. For noncollinear tunability or tunability of paraelectrics, or if the DFPT packages are to be used for collinear susceptibility of ferroelectrics without extension to computation of third derivatives, nearly all of the necessary higher derivatives can be obtained from finite differences with a calculation at a single additional structure. However, to complete the calculation in these cases, it is necessary to estimate the highest derivatives of the electronic susceptibility with respect to the structural parameters, as their complete specification would require additional finite-difference calcu-
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