Universal Behavior of Atomistic Strain in Self-Assembled Quantum Dots

Abstract

Self-assembled quantum dots (QDs) are highly strained heterostructures. the lattice strain significantly modifies the electronic and optical properties of these devices. A universal behavior is observed in atomistic strain simulations (in terms of both strain magnitude and profile) of QDs with different shapes and materials. In this paper, this universal behavior is investigated by atomistic as well as analytic continuum models. Atomistic strain simulations are very accurate but computationally expensive. On the other hand, analytic continuum solutions are based onassumptions that significantly reduce the accuracy of the strain calculations, but are very fast. Both techniques indicate that the strain depends on the aspect ratio (AR) of the QDs, and not on the individual dimensions. Thus simple closed form equations are introduced which directly provide the atomistic strain values inside the QD as a function of the AR and the material parameters. Moreover, the conduction and valence band edges E C/V and their effective masses m * C/V of the QDs are dictated by the strain and AR consequently. The universal dependence of atomistic strain on the AR is useful in many ways; Not only does it reduce the computational cost of atomistic simulations significantly, but it also provides information about the optical transitions of QDs given the knowledge of E C/V and m * C/V from AR. Finally, these expressions are used to calculate optical transition wavelengths in InAs/GaAs QDs and the results agree well with experimental measurements and atomistic simulations.

Theoretical study of strain-dependent optical absorption in a doped self-assembled InAs/InGaAs/GaAs/AlGaAs quantum dot

“…The magnitude of the biaxial strain increases with increasing diameter and decreases with increasing height, while the magnitude of the hydrostatic strain changes slightly in the direction opposite to the biaxial strain. Increasing the height is equivalent to the decreasing diameter in terms of changing the strain in the quantum dot since it depends almost entirely on the aspect ratio not on the individual dimensions [ 39 ]. Increasing the diameter reduces the energy gap, which further reduces the optical transition energy, while increasing the height increases the energy gap, which works against the reduction in confinement energy.…”

Design of Strain-Engineered GeSn/GeSiSn Quantum Dots for Mid-IR Direct Bandgap Emission on Si Substrate

“…m* is the carrier’s effective mass, ћ is the reduced Planck constant, is the three-dimensional coordinate vector, and V is the carrier’s confinement potential (band discontinuity). To simplify the calculation procedure of the QD electronic structure, we have adopted the constant strain approximation [26, 27] instead of the computationally expensive atomic simulation approach that obviously could give more precision in the strain distribution profile [28, 29]. Indeed, we consider the carriers confining potential in the compressively strained QD to be sufficiently deep to minimize the impact of the strain non-uniformity on the electron confined states [27].…”

Combination of Equilibrium and Nonequilibrium Carrier Statistics Into an Atomistic Quantum Transport Model for Tunneling Heterojunctions

“…Assuming the growth direction is [001], the strain components ii inside the quantum well are given by [33] ε xx = ε yy = a Substrate − a well a well ,…”