Electron-hole Coulomb Interaction Research Articles

Electron-hole correlations in semiconductor quantum dots with tight-binding wave functions

The electron-hole states of semiconductor quantum dots are investigated within the framework of empirical tight-binding descriptions for Si, as an example of an indirect gap material, and InAs and CdSe as examples of typical III-V and II-VI direct-gap materials. The electron-hole Coulomb interaction is largely insensitive to both the real-space description of the atomic basis orbitals and different ways of optimizing the tight-binding parameters. Tight-binding parameters that are optimized to give the best effective masses significantly improve the energies of the excitonic states due to the better single-particle energies. However, the Coulomb interaction does not vary much between different parameterizations. In addition, the sensitivity of the Coulomb interaction to the choice of atomic or bitals decreases with increasing dot size. Quantitatively, tight-binding treatments of correlation effects are reliable for dots with radii larger than 15--20 angstrom. The calculated excitonic gaps are in good agreement with recent photoluminescence data for Si and CdSe but agree less well for InAs. Further, the effective range of the electron-hole exchange interaction is investigated in detail. In quantum dots of the direct-gap materials InAs and CdSe, the exchange interaction can be long-ranged, extending over the whole dot when there is no local (onsite) orthogonality between the electron and hole wave functions. By contrast, for Si quantum dots the extra phase factor due to the indirect gap effectively limits the range to about 15 angstrom, independent of the dot size.

Vertical coupling and transition energies in multilayerInAs/GaAsquantum-dot structures

Vertically ordered quantum dots in multilayer InAs/GaAs structures have attracted large interest in recent years for device application as light emitters. Contradictory claims on the dependence of the fundamental transition energy on the interlayer separation and number of dot layers have been reported in the literature. We show that either a blueshift or a redshift of the fundamental transition energy can be observed in different coupling conditions and straightforwardly explained by including strain, indium segregation, and electron-hole Coulomb interaction, in good agreement with experimental results.

The Electronic Structure of Semiconductor Nanocrystals

▪ Abstract We review the rapid progress made in our understanding of the crystal properties of semiconductors and nanocrystals focussing on theoretical results obtained within the multiband effective mass approximation. A comparison with experiment shows these results are valid for nanocrystals down 22–26 Å in diameter. The effect of the electron-hole Coulomb interaction on the optical spectra is analyzed. A theory of the quantum–size levels in wide gap (CdSe) and narrow gap semiconductors (InAs) is presented that describes the absorption spectra of these semiconductors well. A great enhancement of the electron-hole exchange interaction leads to the formation of the optically forbidden Dark Exciton in nanocrystals, which strongly affects their photoluminescence. A theory of the band-edge exciton fine structure is presented and applied to the study of the PL in CdSe nanocrystals. The effect of doping on nanocrystal spectra is considered. The enhancement of the short–range spin-spin interaction in Mn-doped nanocrystals leads to a giant splitting of the electron and hole spin sublevels.

Combination of Hartree and Ritz approaches for problem of excitons in semiconductor quantum wells. Additional exciton states

A combination of Hartree and Ritz approaches is applied to the problem of exciton confined in a semiconductor quantum well (QW). The multiplicative representation of exciton wave function is shown to describe satisfactorily the exciton states in the QWs of arbitrary width if electron and hole confinement components are found from the Hartree-like self-consistent equations. The method is illustrated by calculations of ground exciton states in single-band approximation. The validity of other approximations widely applied in the present literature is also discussed. The maximal error of exciton binding energy determination in the model is obtained. The method is applied for the analysis of additional exciton states that are absent without electron–hole Coulomb interaction. Asymmetry of the QW potential can be responsible for the manifestation of optical transitions associated with these additional states with quantum numbers of different parities. The relatively simple procedure developed here can be applied to systems with weak or even absent carrier localization by quantum-well potential (e.g. excitons in type II heterostructures).

Dark excitons due to direct Coulomb interactions in silicon quantum dots

Electron-hole exchange interactions can lead to spin-forbidden ''dark'' excitons in direct-gap quantum dots. Here, we explore an alternative mechanism for creating optically forbidden excitons. In a large spherical quantum dot made of a diamond-structure semiconductor, the symmetry of the valence band maximum (VBM) is t{sub 2}. The symmetry of the conduction band minimum (CBM) in direct-gap material is a{sub 1}, but for indirect-gap systems the symmetry could be (depending on size) a{sub 1}, e, or t{sub 2}. In the latter cases, the resulting manifold of excitonic states contains several symmetries derived from the symmetries of the VBM and CBM (e.g., t{sub 2}xt{sub 2}=A{sub 1}+E+T{sub 1}+T{sub 2} or t{sub 2}xe=T{sub 1}+T{sub 2}). Only the T{sub 2} exciton is optically active or ''bright,'' while the others A{sub 1}, E, and T{sub 1} are ''dark.'' The question is which is lower in energy, the dark or bright. Using pseudopotential calculations of the single-particle states of Si quantum dots and a direct evaluation of the screened electron-hole Coulomb interaction, we find that, when the CBM symmetry is t{sub 2}, the direct electron-hole Coulomb interaction lowers the energy of the dark excitons relative to the bright T{sub 2} exciton. Thus, the lowest energy exciton ismore » forbidden, even without an electron-hole exchange interaction. We find that our dark-bright excitonic splitting agrees well with experimental data of Calcott et al., Kovalev et al., and Brongersma et al. Our excitonic transition energies agree well with the recent experiment of Wolkin et al. In addition, and contradicting simplified models, we find that Coulomb correlations are more important for small dots than for intermediate sized ones. We describe the full excitonic spectrum of Si quantum dots by using a many-body expansion that includes both Coulomb and exchange electron hole terms. We present the predicted excitonic spectra. (c) 2000 The American Physical Society.« less

Pseudopotential study of electron-hole excitations in colloidal free-standing InAs quantum dots

Excitonic spectra are calculated for free-standing, surface passivated InAs quantum dots using atomic pseudopotentials for the single-particle states and screened Coulomb interactions for the two-body terms. We present an analysis of the single particle states involved in each excitation in terms of their angular momenta and Bloch-wave parentage. We find that (i) in agreement with other pseudopotential studies of CdSe and InP quantum dots, but in contrast to k.p calculations, dot states wavefunction exhibit strong odd-even angular momentum envelope function mixing (e.g. $s$ with $p$) and large valence-conduction coupling. (ii) While the pseudopotential approach produced very good agreement with experiment for free-standing, colloidal CdSe and InP dots, and for self-assembled (GaAs-embedded) InAs dots, here the predicted spectrum does {\em not} agree well with the measured (ensemble average over dot sizes) spectra. (1) Our calculated excitonic gap is larger than the PL measure one, and (2) while the spacing between the lowest excitons is reproduced, the spacings between higher excitons is not fit well. Discrepancy (1) could result from surface states emission. As for (2), agreement is improved when account is taken of the finite size distribution in the experimental data. (iii) We find that the single particle gap scales as $R^{-1.01}$ (not $R^{-2}$), that the screened (unscreened) electron-hole Coulomb interaction scales as $R^{-1.79}$ ($R^{-0.7}$), and that the eccitonic gap sclaes as $R^{-0.9}$. These scaling laws are different from those expected from simple models.

Circularly polarized dynamic Franz-Keldysh effect

We consider the optical properties associated with the photoexcitation and radiative recombination of free electron-hole pairs and excitons in an intrinsic quantum well in a strong THz-frequency electric field, namely the cw optical transmission and reflection through the quantum well for linearly and circularly in-plane polarized THz fields. We first neglect the electron-hole Coulomb interaction, which is associated with the Sommerfeld factor and the formation of excitons. For the linear case, the optical spectra exhibit a series of THz sidebands whose spacing is given by twice the THz frequency; for the circular case, no sidebands occur. Next, the electron-hole Coulomb interaction is included in the limit of strong driving fields; the THz sidebands for circularly polarized fields are strongly suppressed. These features are explained by the classical and quantum dynamics of driven free particles, and are reproduced by detailed numerical solution of the semiconductor Bloch equations.

Excitonic transitions and exchange splitting in Si quantum dots

In a quantum dot made of an indirect gap material such as Si, the electron–hole Coulomb interaction alone can give rise to “dark” excitons even in the absence of exchange interaction. We present the predicted excitonic spectra for hydrogen-passivated Si dots and find very good agreement with the recent experiment of Wolkin, Jorne, Fauchet, Allan, and Delerue [Phys. Rev. Lett. 82, 197 (1999)]. The calculated splitting between dark and bright excitons, arising from Coulomb and exchange interactions, agrees very well with the optical data of Calcott, Nash, Canham, Kane, and Brumhead [J. Phys Condens. Matter 5, L91 (1993)].

Theory of excitonic confinement in semiconductor quantum wires

We review our theoretical approach to the optical response of low-dimensional semiconductor structures. The method is based on the density-matrix formalism and can treat low-density (excitonic) and high-density (gain) regimes on the same footing while retaining the full complexity of realistic nanostructures. We discuss in particular its generalization for studying the combined effects of dielectric and quantum confinement, as well as novel developments aimed at the analysis of local absorption spectra. We examine the main effects of electron-hole Coulomb correlation on the optical spectra of semiconductor quantum wires, where it determines the suppression of band-edge singularities and the peculiar scaling properties of excitonic binding and non-linearities. On the basis of our recent results on different types of nanostructure, we present a critical discussion of possible strategies for tailoring electron-hole Coulomb interaction, and predicting its influence on near-field spectra.

Many-body pseudopotential theory of excitons in InP and CdSe quantum dots

We present a pseudopotential approach to the calculation of the excitonic spectrum of semiconductor quantum dots. Starting from a many-body expansion of the exciton wave functions in terms of single-substitution Slater determinants constructed from pseudopotential single-particle wave functions, our method permits an accurate and detailed treatment of the intraconfiguration electron-hole Coulomb and exchange interactions, while correlation effects can be included in a controlled fashion by allowing interconfiguration coupling. We calculate the exciton fine structure of InP and CdSe nanocrystals in the strong-confinement regime. We find a different size dependence for the electron-hole exchange interaction than previously assumed (i.e., ${R}^{\ensuremath{-}2}$ instead of ${R}^{\ensuremath{-}3})$. Our calculated exciton fine structure is compared with recent experimental results obtained by size-selective optical spectroscopies.

Direct resonant interband tunneling into exciton states in multiquantum well structures

Resonant Zener tunneling is investigated in a multiquantum-well p-i-n diode at cryogenic temperatures. Current-voltage characterization in presence of high magnetic fields demonstrates the dominant role of the electron–hole Coulomb interaction in driving this process. After a theoretical modelization in a variational scheme we conclude that tunneling electrons are directly injected into exciton states. We also suggest that similar transport experiments can be an alternative exciton spectroscopic technique with respect to the more conventional optical ones.

Electron-hole Coulomb interaction in InGaN quantum dots

In contrast to group-III arsenide-based quantum dots, group-III nitride-based quantum dots are much smaller in size and have less conduction band offset. For this reason, it is important to take into account the electron-hole Coulomb interaction in which the spherical quantum dot is substituted for the cube-shaped quantrum dot, which in this paper is treated within the Hartree approximation. In addition to making the electron binding energy several times larger, this strong Coulomb interaction between carriers in quantum dots makes conventional distribution functions invalid, requiring their recalculation. Such calculations reveal that while the one-particle distribution functions are donor-like, the electron-hole function is quite different from its predecessors.

Optical gain in (Zn,Cd)SeZn(S,Se) quantum wells as a function of temperature

We have investigated the mechanism of stimulated emission in ZnCdSeZnSSe quantum wells through measurements of the optical gain spectrum between 77 and 270 K. We also calculated the optical gain using a model which included many-body effects and found excellent agreement with our measurements. Our results are inconsistent with an excitonic gain mechanism and we conclude that the stimulated emission arises from an electron—hole plasma in our samples. However, we find that the electron-hole Coulomb interaction is still significant at room temperature in II–VI heterostructures.

Stimulated emission, gain, and coherent oscillations in II-VI semiconductor microcavities

The large oscillator strength for excitons in ZnSe-based quantum wells (QW's) is reflected in a normal-mode (Rabi) splitting which exceeds 10 meV per QW at low temperatures when measured by conventional linear optical probes or by four-wave mixing technique. The dominating impact of the electron-hole Coulomb interaction extends to high pair densities, including the regime of vertical cavity laser operation. Measurement of gain spectra shows how the composite photon-exciton oscillator supplies the optical gain for a laser operating beyond the perturbative regime.

Excitonic quantum confinement effects and exciton electroabsorption in semiconductor thin quantum boxes

We investigate the excitonic optical properties in thin quantum boxes in the intermediate regime between the two-dimensional (2D) and zero-dimensional (0D) with a theoretical analysis that rigorously treats excitonic confinement effects. It is found that the exciton binding energy is substantially enhanced and that the oscillator strength concentrates to the lowest excitonic transition, even in a thin box whose lateral width is considerably (about five times) larger than the Bohr radius. Novel optical properties experimentally observed in semiconductor quantum disks, which are the intense photoluminescence spectrum and ultranarrow photoluminescence excitation spectrum, are explained well by the theoretical results. We also calculate exciton absorption in a thin box in which an electric field is applied in the lateral direction. The present theory can simulate how the electroabsorption evolves from the quantum confined Stark effect in the 0D to the quantum confined Franz–Keldysh effect in the 2D with an increase in the lateral size of the box. In the intermediate regime between 2D and 0D, a strong excitonic electric-field effect, distinct from the well-known electroabsorption effects at 0D and 2D, is found. These theoretical results demonstrate that even though the lateral confinement is weak, it considerably enhances the electron–hole Coulomb interaction and alters excitonic optical features markedly in the thin quantum box.

Effects of Dimensionality on Radiative Recombination Lifetime of Excitons in Thin Quantum Boxes of Intermediate Regime between Zero and Two Dimensions

We report on effects of dimensionality on radiative recombination lifetime in thin quantum boxes of intermediate regime between 0D and 2D. The temperature dependence of the recombination lifetime is calculated using a theoretical analysis that rigorously treats the electron-hole Coulomb interaction. We show how the dependence evolves from 2D to 0D with a decrease in the lateral width of the box. We also examine the effects of exciton localization, which arises from structural defects in the boxes, on the radiative recombination lifetime. These theoretical results are compared with experimental data obtained from InGaAs quantum disks on a (311)B GaAs substrate. Good agreement between theoretical results and the experimental data is obtained.

Exciton magnetic polaron in semimagnetic semiconductor nanocrystals

We present a theoretical study of the magnetic polaron associated with an electron-hole pair in a diluted magnetic semiconductor quantum dot. It is based on the effective-mass approximation in the strong confinement regime, which incorporates the coupling between the light- and heavy-hole bands. The magnetic polaron, arising from the sp-d exchange interaction between the confined carriers and the magnetic ions, is treated in a self-consistent mean-field approach that leads to coupled nonlinear Schr\"odinger equations for the electron and the hole. The local response to the effective field is modeled by the experimental high-field magnetization curve in the bulk. The electron-hole Coulomb interaction is taken into account. An exact numerical solution of the three coupled equations is used to calculate the equilibrium polaron size, binding energy (${\mathrm{E}}_{\mathrm{p}}$), and spin (${\mathrm{S}}_{\mathrm{p}}$). Results are first presented for ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Te nanocrystals with x=0.11. ${\mathrm{E}}_{\mathrm{p}}$ decreases and the orbital contraction increases with an increasing quantum dot radius (a). In small dots, approaching saturation in the core region, ${\mathrm{E}}_{\mathrm{p}}$ decreases slowly as the temperature (T) increases. In large dots ${\mathrm{E}}_{\mathrm{p}}$(T) decreases rapidly towards the fluctuation regime, where ${\mathrm{E}}_{\mathrm{p}}$\ensuremath{\propto}${\mathrm{a}}^{\mathrm{\ensuremath{-}}3}$. A similar temperature dependence is obtained for ${\mathrm{S}}_{\mathrm{p}}$; the fluctuation-regime value is, however, size independent. The light-induced magnetization enhancement due to polaron formation is considered and an optimal quantum dot radius is predicted to be \ensuremath{\sim}30 \AA{}. We have also calculated ${\mathrm{E}}_{\mathrm{p}}$ as a function of an applied magnetic field, which shows a decreasing behavior that depends on a and T. Theoretical results for ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Mn}}_{\mathrm{x}}$Se nanocrystals show a good agreement with recently reported experimental data on the photoluminescence Stokes shift versus magnetic field.

Radiative recombination lifetime of excitons in thin quantum boxes

Exciton radiative recombination lifetime in a thin quantum box in the intermediate spatial dimension between the two-dimension and the zero-dimension is investigated by a theoretical analysis which rigorously treats the electron-hole Coulomb interaction. The higher exciton states as well as the ground exciton state are explicitly taken into account to estimate the temperature dependence of exciton recombination lifetime. We clarify how the temperature dependence of the recombination lifetime varies with a change in the quantum confinement dimension which can be controlled by the lateral width of a thin quantum box. We also discuss the effect of the exciton localization due to structural imperfection on the radiative recombination lifetime.

Two-particle calculation of excitonic effects in semiconductor nanocrystals

Abstract We present a novel method for calculating the excitonic properties of nanometer-sized semiconductor structures. The method uses a time-dependent checkerboard propagation technique within the light-binding approximation, and includes the electron-hole Coulomb interaction in the zeroth order Hamiltonian. We illustrate the method with two-particle calculations of exciton energies in CdSe and Si nanocrystals. The results of the two-particle calculations are compared with calculations which treat the Coulomb interaction perturbatively, and with measured absorption energies.

Type-II interface exciton in ZnSe/(Zn,Mn)Se heterostructures.

Two emission bands are observed in the photoluminescence spectrum of ZnSe/(Zn,Mn)Se heterostructures. These bands emerge in a magnetic field and are associated with interface excitons formed as a result of a magnetic-field-induced type-I\char21{}type-II transition of the band alignment. Time-resolved measurements yield lifetimes in the ns range signifying a relatively large spatial separation of electrons and holes and hence low optical oscillator strength. These features are confirmed by a theoretical analysis of the interface exciton state revealing a reduced importance of the electron-hole Coulomb interaction in comparison with type-II excitons in quantum wells. \textcopyright{} 1996 The American Physical Society.