Interfacial Elasticity Corrections to Size-Dependent Strain-State of Embedded Quantum Dots

Abstract

PACS: 85.35.Be; 68.35.Gy; 62.25.+g; 62.20.Dc Introduction Quantum Dots (QDs) have recently been the focus of several experimental and theoretical researchers due to the promise of improved and new opto-electronic properties [1]. Frequently, embedded QD structures (e.g. InAs/GaAs system), to preserve coherency, must accommodate large lattice mismatch. The ensuing elastic relaxation and the hydrostatic strain state within the QD structure are well known to impact its opto-electronic properties [2,3]. Several works, of varying sophistication (both analytical and numerical), have focused on the "accurate" calculation of the strain state in buried quantum dots [4][5][6][7][8]. Recently, two papers have caught the present authors attention. Pan and Young [4] indicated significant difference in strain calculation when anisotropic elastic behavior is assumed compared to simplified isotropic elasticity. Further, a recent article by Ellaway and Faux [8] indicated (via atomistic simulations) that the elastic properties of QD are staindependent and such a consideration on strain calculation can result in a significant correction (of 16%) to the hydrostatic strain (in their article, for a buried spherical InAs/GaAs QD). In this communication, we show that the so-far unconsidered interfacial elastic properties can also significantly alter the strain calculations; the exact correction sensitively being dependent upon the size of the QD structure and the interfacial elastic constants. We find that the correction resulting from interfacial elasticity is comparable to that due to either anisotropic or strain-dependency effects.Classical elasticity (on which most of the previous works are based) does not admit intrinsic size dependence in the elastic solutions of embedded inhomogeneities. For structures with sizes > 50 nm, typically, the surface-to-volume ratio is negligible and the deformation behavior is governed by classical bulk strain energy. Currently, no formulation exists which combines interface elasticity with bulk elasticity to analyze embedded inclusions. Eshelby's [9] celebrated formalism, often used in QD literature, is based entirely on classical bulk elasticity. In this communication (using a variational approach) we derive a general expression for the correction in hydrostatic strain due to interfacial elasticity (for an embedded spherical quantum dot). Despite the lack of precise data, we are able to show (using InAs/GaAs as an example system) that inclusion of interfacial elasticity effects can result in minimum corrections between 1.8% and 12% in the typical size range of QD structures (2-20 nm).

Energy release or absorption due to simultaneous rotation of two nano voids in plane elastic materials as influenced by both surface effect and interacting effect

“…(13,14,15) that: (a) A does NOT concerned with surface parameters; (b) the impact from surface effect on the L-integral is represented by B. Therefore, the curves in Fig.…”

“…Surface effect at the nano scale on the stress field and the effective moduli has been well explored in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The commonly recognized viewpoint is that this effect influences the phenomenological physical quantities such as stress distributions and macro effective moduli significantly.…”

Energy release or absorption due to simultaneous expansion of many interacting nanoholes in elastic materials

“…Besides, Gurtin and Murdoch [4] and Gurtin et al [5] presented the continuum mechanics theory to account for the surface or interface energy. After the twentieth century, much attention is focused on the investigations of material properties at nanoscale by using the elastic continuum theory (see e.g., Sharma and Ganti [6,7], Sharma et al [8], Duan et al [9][10][11][12]16], Miller and Shenoy [13], Cui and Lieber [14], Shenoy [15], Marian et al [17], Lim et al [18], Dingreville et al [19], Tian and Rajapakse [20], Park and Klein [21], Mogilevsaya et al [22,23] among many others).…”

Energy release or absorption due to simultaneous expansion of many interacting nano-holes in elastic materials

“…Besides, Gurtin and Murdoch [4] and Gurtin et al [5] presented the continuum mechanics theory to account for the surface or interface energy. After the twentieth century, much attention is focused on the investigations of material properties at nanoscale by using the elastic continuum theory (see, e.g., Sharma and Ganti [6,7]; Sharma et al [8]; Duan et al [9][10][11][12]16]; Miller and Shenoy [13]; Cui and Lieber [14]; Shenoy [15]; Marian, et al [17];; Lim et al [18]; Dingreville, et al [19]; Tian and Rajapakse [20]; Park and Klein [21] and Mogilevsaya et al [22,23] among many others).…”