# Correlation versus mean-field contributions to excitons, multiexcitons, and charging energies in semiconductor quantum dots

## Abstract

Single-dot spectroscopy is now able to resolve the energies of excitons, multiexcitons, and charging of semiconductor quantum dots with {approx}<1 meV resolution. We discuss the physical content of these energies and show how they can be calculated via quantum Monte Carlo (QMC) and configuration interaction (CI) methods. The spectroscopic energies have three pieces: (i) a ''perturbative part'' reflecting carrier-carrier direct and exchange Coulomb energies obtained from fixed single-particle orbitals, (ii) a ''self-consistency correction'' when the single particle orbitals are allowed to adjust to the presence of carrier-carrier interaction, and (iii) a ''correlation correction.'' We first apply the QMC and CI methods to a model single-particle Hamiltonian: a spherical dot with a finite barrier and single-band effective mass. This allows us to test the convergence of the CI and to establish the relative importance of the three terms (i)--(iii) above. Next, we apply the CI method to a realistic single-particle Hamiltonian for a CdSe dot, including via a pseudopotential description the atomistic features, multiband coupling, spin-orbit effects, and surface passivation. We include all bound states (up to 40000 Slater determinants) in the CI expansion. Our study shows that (1) typical exciton transition energies, which are {approx}1 eV, can be calculated tomore »

- Authors:

- Publication Date:

- Sponsoring Org.:
- (US)

- OSTI Identifier:
- 40205480

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 63; Journal Issue: 15; Other Information: DOI: 10.1103/PhysRevB.63.155316; Othernumber: PRBMDO000063000015155316000001; 036108PRB; PBD: 15 Apr 2001; Journal ID: ISSN 0163-1829

- Publisher:
- The American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUND STATE; CONFIGURATION INTERACTION; EFFECTIVE MASS; ELECTRON CORRELATION; ELECTRONIC STRUCTURE; EXCITED STATES; EXCITONS; PERTURBATION THEORY; SLATER METHOD

### Citation Formats

```
Shumway, J, Franceschetti, A, and Zunger, Alex.
```*Correlation versus mean-field contributions to excitons, multiexcitons, and charging energies in semiconductor quantum dots*. United States: N. p., 2001.
Web. doi:10.1103/PhysRevB.63.155316.

```
Shumway, J, Franceschetti, A, & Zunger, Alex.
```*Correlation versus mean-field contributions to excitons, multiexcitons, and charging energies in semiconductor quantum dots*. United States. doi:10.1103/PhysRevB.63.155316.

```
Shumway, J, Franceschetti, A, and Zunger, Alex. Sun .
"Correlation versus mean-field contributions to excitons, multiexcitons, and charging energies in semiconductor quantum dots". United States. doi:10.1103/PhysRevB.63.155316.
```

```
@article{osti_40205480,
```

title = {Correlation versus mean-field contributions to excitons, multiexcitons, and charging energies in semiconductor quantum dots},

author = {Shumway, J and Franceschetti, A and Zunger, Alex},

abstractNote = {Single-dot spectroscopy is now able to resolve the energies of excitons, multiexcitons, and charging of semiconductor quantum dots with {approx}<1 meV resolution. We discuss the physical content of these energies and show how they can be calculated via quantum Monte Carlo (QMC) and configuration interaction (CI) methods. The spectroscopic energies have three pieces: (i) a ''perturbative part'' reflecting carrier-carrier direct and exchange Coulomb energies obtained from fixed single-particle orbitals, (ii) a ''self-consistency correction'' when the single particle orbitals are allowed to adjust to the presence of carrier-carrier interaction, and (iii) a ''correlation correction.'' We first apply the QMC and CI methods to a model single-particle Hamiltonian: a spherical dot with a finite barrier and single-band effective mass. This allows us to test the convergence of the CI and to establish the relative importance of the three terms (i)--(iii) above. Next, we apply the CI method to a realistic single-particle Hamiltonian for a CdSe dot, including via a pseudopotential description the atomistic features, multiband coupling, spin-orbit effects, and surface passivation. We include all bound states (up to 40000 Slater determinants) in the CI expansion. Our study shows that (1) typical exciton transition energies, which are {approx}1 eV, can be calculated to better than 95% by perturbation theory, with only a {approx}2 meV correlation correction; (2) typical electron addition energies are {approx}40 meV, of which correlation contributes very little ({approx}1 meV); (3) typical biexciton binding energies are positive and {approx}10 meV and almost entirely due to correlation energy, and exciton addition energies are {approx}30 meV with nearly all contribution due to correlation; (4) while QMC is currently limited to a single-band effective-mass Hamiltonian, CI may be used with much more realistic models, which capture the correct symmetries and electronic structure of the dots, leading to qualitatively different predictions from effective-mass models; and (5) CI gives excited state energies necessary to identify some of the peaks that appear in single-dot photoluminescence spectra.},

doi = {10.1103/PhysRevB.63.155316},

journal = {Physical Review B},

issn = {0163-1829},

number = 15,

volume = 63,

place = {United States},

year = {2001},

month = {4}

}