We analyze the carrier energy band structure in a three-dimensional regimented array of semiconductor quantum dots using an envelope function approximation. The coupling among quantum dots leads to a splitting of the quantized carrier energy levels of single dots and formation of three-dimensional minibands. By changing the size of quantum dots, interdot distances, barrier height, and regimentation, one can control the electronic band structure of this artificial quantum dot crystal. Results of simulations carried out for simple cubic and tetragonal quantum dot crystal show that the carrier density of states, effective mass tensor and other properties are different from those of bulk and quantum well superlattices. It has also been established that the properties of artificial crystal are more sensitive to the dot regimentation rather then to the dot shape. The proposed engineering of three-dimensional mini bands in quantum dot crystals allows one to fine-tune electronic and optical properties of such nanostructures.

We propose a mechanism for enhancement of the thermoelectric figure-of-merit in regimented quantum dot superlattices. A proof-of-concept calculation has been carried out for p-type regimented superlattice of Ge dots on Si. It is shown that when conditions for miniband formations are satisfied, carrier transport in such structures can be tuned in a favorable way leading to large carrier mobility, Seebeck coefficient, and, as a result, to the thermoelectric figure-of-merit enhancement. To maximize the improvement, one has to tune the parameters of quantum dot superlattice in such a way that electrical current is mostly through the well-separated minibands of relatively large width ͑at least several k B T, where k B is Boltzmann's constant and T is temperature͒.

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Anharmonicity of the interatomic potential is taken into account for the quantitative simulation of the conduction and valence band offsets for strained semiconductor heterostructures. The anharmonicity leads to a weaker compressive hydrostatic strain than that obtained with the commonly used quasiharmonic approximation of the Keating model. Compared to experiment, inclusion of the anharmonicity in the simulation of strained InAs/ GaAs nanostructures results in an improvement of the electron band offset computed on an atomistic level by up to 100 meV. The accurate simulation of the electronic structure is of utmost importance for the design of nanoelectronic and optoelectronic device structures. It has been shown both theoretically 1,2 and experimentally, 1,3-5 that the energy spectrum in semiconductor nanostructures is extremely sensitive to the built-in strain. The continuum elasticity method fails to adequately describe the strain profile in InAs/ GaAs heterostructures with a 7% lattice mismatch between the constituent materials. 2 The two-parameter valence-force-field (VFF) Keating model 6,7 is a commonly used approximation for atomistic-level calculations of the equilibrium atomic positions in realistic-size nanostructures. 8 In this letter the quasiharmonic Keating model is shown to be insufficient to describe highly strained InAs/ GaAs nanostructures due to the anharmonicity of the strain energy.The Keating model treats atoms as spring-connected points in a crystal lattice. The strain energy depends only on nearest-neighbor interactions 6,7The coefficient ␣ corresponds to the spring constant for the bond length distortion, while ␤ corresponds to the change of the angle between the bonds ("bond-bending"). The summation is over all atoms m of the crystal and their nearest neighbors n and k. r mn and d mn are the vectors connecting the mth atom with its nth neighbor in the strained and unstrained material, respectively. The Keating potential in Fig. 1 (dashed line) fails to reproduce the weakening of the realistic interatomic interaction (solid line with circles) with increasing distance between atoms and it underestimates the repulsive forces at close atomic separation. Therefore Eq. (1) can adequately describe the strain energy only at small deformations. In InAs/ GaAs heterostructures, the lattice mismatch is as large as 7% and anharmonicity of the interatomic potential is expected to become important.The anharmonicity is included directly into the VFF constants ␣ and ␤ of the Keating model ͑3͒with ␤ 0 nmk ϵ ͱ ␤ 0 mn ␤ 0 mk , B nmk ϵ ͱ B mn B mk , and C nmk ϵ ͱ C mn C mk .nmk and 0 nmk are the actual and the unstrained angles between mn and mk bonds, respectively. In homogeneous materials all bonds are the same and the indexes m, n, and k can be dropped. ␣ 0 and ␤ 0 are the VFF constants in the unstrained crystal. The anharmonicity corrections A and C describe the dependence of ␣ and ␤ on hydrostatic strain, while B is responsible for the change of the bond-bending term with the angle between bonds. The d...

The effect of wetting layers on the strain and electronic structure of InAs self-assembled quantum dots grown on GaAs is investigated with an atomistic valence-force-field model and an empirical tight-binding model. By comparing a dot with and without a wetting layer, we find that the inclusion of the wetting layer weakens the strain inside the dot by only 1% relative change, while it reduces the energy gap between a confined electron and hole level by as much as 10%. The small change in the strain distribution indicates that strain relaxes only little through the thin wetting layer. The large reduction of the energy gap is attributed to the increase of the confining-potential width rather than the change of the potential height. First-order perturbation calculations or, alternatively, the addition of an InAs disk below the quantum dot confirm this conclusion. The effect of the wetting layer on the wave function is qualitatively different for the weakly confined electron state and the strongly confined hole state. The electron wave function shifts from the buffer to the wetting layer, while the hole shifts from the dot to the wetting layer.