Prediction of an Excitonic Ground State inInAs/InSbQuantum Dots

Abstract

Using atomistic pseudopotential and configuration-interaction many-body calculations, we predict a metal-nonmetal transition and an excitonic ground state in the InAs/InSb quantum dot (QD) system. For large dots, the conduction band minimum of the InAs dot lies below the valence band maximum of the InSb matrix. Due to quantum confinement, at a critical size calculated here for various shapes, the single-particle gap Eg becomes very small. Strong electron-hole correlation effects are induced by the spatial proximity of the electron and hole wavefunctions, and by the lack of strong (exciton unbinding) screening, afforded by the existence of fully discrete 0D confined energy levels. These correlation effects overcome Eg, leading to the formation of a bi-excitonic ground state (two electrons in InAs and two holes in InSb) being energetically more favorable (by ∼ 15 meV) than the state without excitons. We discuss the excitonic phase transition on QD arrays in the low dot density limit. The formation of excitons in semiconductors and insulators usually requires energy, e.g. photons, for one has to excite carriers across the single-particle band-gap E g . There is a special interest, however, in the possibility of forming excitons exothermically, i.e. an "excitonic ground state" as envisioned by Mott [1] and Keldysh et al. [2]. Indeed, the electron-hole system exhibits a rich range of phases [3,4] as a function of the carrier density and effective-mass ratio m e /m h , including various excitonic insulating states such as molecular solid, exciton liquid, Mott insulator, and also various metallic phases. The excitonic ground state is of fundamental interest in itself because excitons can be a better alternative to atoms for studying Bose-Einstein condensation [5,6] on account of the lighter excitonic mass, thus higher condensation temperature. It is natural to search for excitonic ground states in systems where E g is small, yet the screening is weak enough so as to prevent unbinding of the exciton. The search in bulk solids [7] has thus focused on indirect gap semiconductors and semimetals to reduce screening, but excitonic ground states have not been conclusively observed so far in such systems. Ground state excitons were also searched in nanostructures, specifically in spatially indirect quantum-wells [8,9], where electrons and holes are confined in different spatial regions. In "type II" systems such as GaInAs/InP or CdTe/CdSe, electrons are localized in the well, whereas holes are localized on the barrier, so screening is weak, but E g is finite. In contrast, in "type III" heterostructures such as [10] InAs/GaSb, the conduction band minium (CBM) of the InAs well is lower than the valence band maximum (VBM) of the GaSb barrier, so at certain a well thickness one can have E g →0 [10], as well as separation of electrons from holes. Thus, at this thickness, one could expect an excitonic ground state if the electron-hole correlation energy will be large enough to stabilize the complex. Recent experiments [11] show evid...

Hole levels in InAs self-assembled quantum dots

“…Previously, high field energy spectra of electron4,6 and exciton6,17,21 systems were ana lyzed within the Fock-Darwin (FD) model,22,23 i.e., a 2D harmonic oscillator in a perpendicular magnetic field. Using this description, recent C -V experiments on p -type InAs QDs have suggested an incomplete shell filling, which means that the d shell starts filling before the p shell is full.8,24 A differ ent, yet similar, anomalous filling due to hole correlation effects was found theoretically by He et al10,11 using an atomistic pseudopotential approach. An alternative explana tion was given by Climente et al12 in terms of the single particle hole levels.…”

Statistics of excitons in quantum dots and their effect on the optical emission spectra of microcavities

“…In bulk, the two oppositely charged particles can be strongly correlated by the Coulomb interaction and bound as hydrogenic states (Wannier-Mott exciton). Although finding binding energies and wavefunctions for the single exciton case is a difficult problem in various geometries, 14,15,16 as far as the vacuum coupling limit is concerned, the exciton field operator which links the two manifolds H 1 and vacuum always assumes the simple form σ + regardless of the details of the exciton. As a particle constituted of two fermions, the exciton is commonly regarded as a boson, from consideration of the angular momentum addition rules and the spin-statistics theorem.…”

Multiple charging ofInAs∕GaAsquantum dots by electrons or holes: Addition energies and ground-state configurations

“…11,13 An atomistic pseudopotential description of electronic structure effects can be used instead of 2D-EMA to calculate charging energies. 18,19,20,21,22 Here, we show that such an atomistic theory correctly reproduces the many-particle configurations as well as addition spectra for carriers in self-assembled quantum dots. We study systematically the electronic structure of self-assembled InGaAs/GaAs quantum dots, provide detailed information on the electron and hole single-particle spectrum, many-particle charging and addition spectrum, as well as ground state configurations using single-particle pseudo-potential and many-particle configuration inter-action (CI) methods.…”

“…As a consequence, the p 2 levels are energetically very close to the d 1 levels, leading, as we will see below, to a nontrivial charging pattern that breaks Hund's rule and the Afubau principle. 18 (c) Wave function characters: An analysis of the wave function show that these levels have somewhat mixed S, P or D characters. For example, for a lens-shaped InAs/GaAs QD of height=3.5 nm and base=25 nm, the "s level" has 92% S character, and the two "p levels", p 1 and p 2 , have 86% P character respectively (see Table II of Ref.…”

“…In contrast to electrons, the hole charging patterns show complicated behaviors that defy the Hund's rule and the Aufbau's principle for most of the cases of N =5, 6 holes. 18 To understand the differences between the groundstate configurations of electrons and holes and the driving forces for these differences, we developed a general phase-diagram approach 18 that classifies the manyparticle configurations for electrons and holes in quantum dots in terms of simple electronic and geometric parameters. To do so, we calculate for each particle number N , the configuration which minimizes the total-energy under the single-configuration approximation at different p 1 -p 2 splitting (δ p1,p2 = ǫ p2 − ǫ p1 ) and p 2 -d 1 energy spacing (δ p2,d1 = ǫ d1 − ǫ p2 ) using Coulomb integrals J and K in units of J ss .…”