Excitons in quantum boxes: Correlation effects and quantum confinement

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Abstract
Ultrasmall, quasi-zero-dimensional, quantum-box structures can now be made which exhibit quantum carrier confinement in all three dimensions. We present calculations of the properties of excitons confined in quantum boxes. The boxes are modeled as square (side L), flat plates (width w). Infinite barriers are used to confine the electron and hole. The effective-mass Schrödinger equation is solved to determine exciton properties. A variational wave function is used to calculate the exciton ground-state energy and optical properties. The exciton wave function is also expanded in terms of electron-hole configurations made from electron and hole single-particle box states. This wave function is used to study the onset of correlation effects. Exciton ground-state total energies, interaction energies, Coulomb energies, kinetic energies, electron-hole separations, and oscillator strengths are determined. The results illustrate the competing effects of quantum confinement and Coulomb-induced electron-hole correlations. For large boxes (L≳100 nm) excitons in quantum boxes are strongly correlated and confinement effects are negligible. In small boxes (L≲10 nm) excitons are weakly correlated. Confinement effects are dominant and the electron and hole occupy the lowest-energy pair of single-particle levels. Confinement enhances the exciton kinetic and direct Coulomb energies, reduces the electron-hole separation, and increases the oscillator strength. Even in the transition regime (10 nm ≲L≲100 nm), the enhancement of exciton oscillator strengths could enhance optoelectronic properties.