Quantum Electronic Stress: Density-Functional-Theory Formulation and Physical Manifestation

Abstract

The concept of "quantum stress (QS)" is introduced and formulated within density functional theory (DFT), to elucidate extrinsic electronic effects on the stress state of solids and thin films in the absence of lattice strain. A formal expression of QS (σ Q ) is derived in relation to deformation potential of electronic states (Ξ) and variation of electron density (∆n), σ Q = Ξ∆n, as a quantum analog of classical Hook's law. Two distinct QS manifestations are demonstrated quantitatively by DFT calculations: (1) in the form of bulk stress induced by charge carriers; and (2) in the form of surface stress induced by quantum confinement. Implications of QS in some physical phenomena are discussed to underlie its importance. 68.35.Md A fundamental property of solid materials is their stress state. At the equilibrium lattice constant, the bulk of a crystalline solid is stress free, but the surface of a solid has intrinsic non-zero stress and stress is commonly induced by any form of lattice distortion [1]. The stress (strain) state of a solid or thin-film material has profound effects on its thermodynamic stability and physical and chemical properties [1][2][3], and has been employed in a wide range of applications such as electromechnical devices [4], mechanochemcial sensors [5] and flexible electronics [6], and even to make new nanotructures [7,8]. Here, we introduce the concept of "quantum stress (QS)", which adds an interesting quantum mechanical aspect to our conventional view of "classical stress (CS)" based on classical mechanics. We mathematically formulate the expression of QS within density function theory (DFT), and use DFT calculations to demonstrate quantitatively two distinct physical manifestations of QS, in the form of bulk stress induced by charge carriers in a homogeneous system of crystalline solids and in the form of surface stress induced by quantum confinement in a heterogeneous system of nanoscale thin films. We will then apply the concept of QS to elucidate a few examples of physical phenomena that underlie the importance and usefulness of QS. Concept of QS.We first introduce the concept of QS in contrast with the CS. Figure 1 illustrates the fundamental difference between the QS and CS using a simple model of a one-dimensional (1D) lattice. Consider a lattice is under compressive (Fig. 1a) or tensile lattice strain (ε), such as in an epitaxial film due to lattice mismatch between the film and substrate [9,10]. The "atomic" lattice deformation energy can be expressed as E = (1/2)Y ε 2 V , where Y is Young's modulus and V is the volume of lattice. By definition, the lattice formation induced lattice stress, which we refer to here as CS, is expressed as σ C = (1/V )(dE/dε) = Y ε , the Hook's law. Now, consider an equilibrium lattice in the absence of strain (ε = 0), but electronically perturbed or excited, such as an electron is kicked out by a photon leaving behind a hole, as shown in Fig. 1b, which redistributes the electron density. The "electronic deformation" energy can be expressed as E...

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