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Bhattacharya, P.

doi:10.1023/a:1007065203823

Cited by 8 publications

(2 citation statements)

References 24 publications

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“…Thus there is a linear relation between wave vector and frequency in classical elasticity, i.e., there is no dispersion and hence no nonlocal effects. When dispersion or nonlocal effects are incorporated, this relation gets modified: 4 . ͑20͒…”

Section: ͑12͒mentioning

confidence: 99%

“…Quantum dots ͑QDs͒ have been the focus of several experimental and theoretical researchers due to the promise of improved optoelectronic properties and are considered crucial building blocks for several nanoelectronic applications, e.g., next generation lighting, 1,2 lasers, 3,4 quantum computing, information storage and quantum cryptography, [5][6][7] biological labels, 8 sensors, 9 and many others. [10][11][12][13][14][15] QDs are typically embedded in another semiconductor material with differing lattice parameter.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Size dependency of strain in arbitrary shaped anisotropic embedded quantum dots due to nonlocal dispersive effects

Zhang

Sharma

2005

Phys. Rev. B

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Both quantitative and qualitative knowledge of strain and strain distributions in quantum dots are essential for the determination and tailoring of their optoelectronic properties. Typically strain is estimated using classical elasticity and then coupled to a suitable band structure calculation approach. However, classical elasticity is intrinsically size independent. This is in contradiction to the physical fact that at the size scale of a few nanometers, the elastic relaxation is size dependent and a departure from classical mechanics is expected. First, in the isotropic case, based on the physical mechanisms of nonlocal interactions, we herein derive ͑closed-form͒ scaling formulas for strain in embedded lattice-mismatched spherical quantum dots. In addition to a size dependency, we find marked differences in both spatial distribution of strain as well as in quantitative estimates especially in cases of extremely small quantum dots. Fully recognizing that typical quantum dots are neither of idealized spherical shape nor isotropic, we finally extend our results to cubic anisotropy and arbitrary shape. In particular, an exceptionally simple expression is derived for the dilation in an arbitrary shaped quantum dot. For the more general case ͑incorporating anisotropy͒, closed-form results are derived in the Fourier space while numerical results are provided to illustrate the various physical insights. Apart from qualitative and quantitative differences in strain states due to nonlocal effects, an aesthetic by-product for the technologically important polyhedral shaped quantum dots is that strain singularities at corners and vertices ͑which plague the classical elasticity formulation͒ are absent. Choosing GaAs as an example material, our results indicate that errors as large as hundreds of meV may be incurred upon neglect of nonlocal effects in sub-10-nm quantum dots.

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Section: ͑12͒mentioning

confidence: 99%