Influence of Internal Fields on the Electronic Structure in Self-Assembled InAs/GaAs Quantum Dots

Rapid progress in nanofabrication technology has made possible the growth of various nanoscale devices where both the atomicity and quantum-mechanical effects play a critical role in determining the overall device characteristics. This leads to a considerable challenge in modeling these devices. The lack of structural symmetry in the overall geometry of the nanodevices usually requires explicit three-dimensional representation. For example, Stranski-Krastanov growth techniques tend to produce self-assembled InAs/GaAs quantum dots (QDs) [1] [2] with some rotational symmetry, e.g. disks, domes, or pyramids. These structures are generally not perfect geometric objects, since they are subject to interface inter-diffusion and discretization on an atomic lattice. There is no such thing as a round disk on a crystal lattice! Therefore, the underlying crystal/atomistic asymmetry imposes immediate restrictions on the realistic geometry and demands a full atomistic treatment.

Strain originates from the assembly of lattice-mismatched semiconductors and, in the Stranski-Krastanov growth mode, indeed drives the creation of the QDs. In the case of the InAs/GaAs quantum dots, the lattice mismatch is around 7% and leads to a strong long-range strain field within the extended neighborhood of each quantum dot [3]. Strain can be atomistically inhomogeneous, involving not only biaxial components but also non-negligible shear components. Strain in reduced dimensional structures strongly influences the core and barrier material band structures, modifies the energy bandgaps, and further lowers the underlying crystal symmetry. In the nanoscale regime, the classical harmonic linear/continuum elasticity model for strain, which can capture strain only on a mesoscopic scale, is clearly inadequate [4] [5], and device simulations must include the fundamental page 3 quantum character of charge carriers and the long-ranged atomistic strain effects with proper boundary conditions on an equal footing.

A variety of materials such as GaAs, InAs, GaN, are piezoelectric. Any spatial nonsymmetric distortion in nanostructures made of these materials will create piezoelectric fields, which will modify the electrostatic potential landscape. Recent spectroscopic analyses of self-assembled QDs demonstrate polarized transitions between confined hole and electron levels [2]. While the continuum models (effective mass or k•p) can reliably predict aspects of the single-particle energy states, they fail to capture the observed non-degeneracy and optical anisotropy of the excited energy states in the (001) plane. These methods fail because they use a confinement potential which is assumed to have only the structural symmetry of the nanostructure, and they ignore the underlying crystal asymmetry. The experimentally measured symmetry is significantly lower than the assumed continuum/shape symmetry mainly because of underlying crystalline atomicity and interfaces, strain relaxation, and the piezoelectric fields. For example, in the case of pyramidal QDs with square bases, continuum models treat the underlying material in C 4ν symmetry while the atomistic representation lowers the crystal symmetry to C 2ν [2]. QDs with circular bases having structural C ∞ symmetry also exhibit optical polarization anisotropy due to the atomistic asymmetry and the built-in electrostatic fields induced in the underlying lattice.

In this paper, we study the electronic properties of Zincblende InAs quantum dots grown on GaAs substrate. The main objectives are three-fold-(1) to explore the nature and the role of crystal atomicity at the interfaces, strain-field, and piezoelectric polarization in determining the energy spectrum and the wavefunctions, (2) to address shift in the onepage 4 particle energy states, symmetry-lowering and non-degeneracy in the first excited state, and strong band-mixing in the overall conduction band electronic states, a group of inter-related phenomena that has been revealed in recent spectroscopic analyses, and (3) to study the geometry-dependence of the above-mentioned phenomena. Efforts are made to demonstrate the importance of three-dimensional (3-D) atomistic material representation, and the need for using realistically-extended substrate and cap layers in studying the built-in structural and electric fields in these reduced-dimensional QDs. The paper is organized as follows-In Sec. II, we outline the methods for the calculation of strain and piezoelectric fields, and single-particle electronic states. In Sec. III, the internal fields and the electronic structures of InAs/GaAs QDs have been delineated as a function of their geometry.

Conclusions are drawn in Sec. IV.

It is clear that, at nanoscale, modeling approaches based on a continuum representation (such as effective mass [6], and k•p [7]) are clearly invalid. On the other side, various ab initio atomistic materials science methods (fundamental many-electron correlated methods bas

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