J. Adamowski

LO-phonon-induced screening of electron–electron interaction in D− centres and quantum dots

Ap roblem of screening of electron–electron interaction by LO phonons is investigated for bound two-electron systems in bulk semiconductors and semiconductor quantum dots. We consider a D − centre and a two-electron quantum dot and obtain the effective LO-phonon-induced interaction between the electrons, i.e., Veff (r12) ∼ e 2 /[eeff(r12)r12], where r12 is the interelectron distance and eeff(r12) is th ee ffective phonon dielectric function. The calculated phonon dielectric function rapidly increases for small r12 starting from the high-frequency dielectric constant, e∞ ,a nd reaches some constant value, ¯ e ,a t relatively small interelectron distances. We have found that—in most cases— ¯ is less than the static dielectric constant, es .O nly i nt he weakly ionic compounds, like GaAs, ¯ e � es .W ea rgue that—in the bound few-electron systems—¯ e better approximates the average LO-phonon-induced screening than the commonly used es .W e have also shown that the coupling with LO phonons leads to the increase of the binding energy of the two-electron system confined in the quantum dot.

Modelling of confinement potentials in quantum dots

Abstract The problem of confinement potential profile in quantum dots has been studied. We have proposed a new class of the confinement potentials, called the power-exponential potentials, which are sufficiently flexible to approximate the realistic confinement potentials in the quantum dots. The one-electron energy spectra for the power-exponential potentials of the cylindrical symmetry have been calculated by the high-order finite-difference method. We have discussed the properties of the spectra and the applicability of the power-exponential potentials to the quantum dots.

Ground and excited states of few-electron systems in spherical quantum dots

Abstract Energy spectra of two- and three-electron systems confined in semiconductor quantum dots, i.e., artificial helium and lithium atoms, are studied by the variational method under the assumption of the spherically symmetric confinement potential of finite depth. It is shown that the electron pairs and triples can form bound states if the quantum ‘capacity’, V 0 R 2 , of the quantum dot, is sufficiently large ( V 0 is the potential-well depth and R is the quantum-dot radius). The conditions of binding have been determined for the ground and excited states. The binding energy and dipole transition energy have been calculated for several QDs. It is found that the dipole transition energy for the one-, two-, and three-electron artificial atoms is nearly independent of the number of electrons.

Electron–electron correlation in quantum dots

Abstract The problem of correlation has been studied for two-electron systems in semiconductor quantum dots with harmonic-oscillator confinement potentials of both the spherical and cylindrical symmetry. The eigenvalue problems have been solved by the iterative extraction-orthogonalization method, which provides the exact results for the harmonic-oscillator potential with arbitrary frequency. It is shown that — on the contrary to the previous results — in the absence of external magnetic field, the ground state is the spin singlet for quantum dots of arbitrary size, i.e., a singlet–triplet spontaneous “phase transition” does not occur. We have performed the comparative calculations using the Hartree–Fock method and shown that the previously predicted singlet–triplet “phase transition” results from the neglect of the electron–electron correlation. We have found that for sufficiently large quantum dots the singlet ground state becomes degenerate with the first excited triplet state and pair-correlation functions for these states are almost identical.

Binding energy of the biexcitons

Abstract The binding energy of the biexciton is shown to vary monotonically with the electron-to-hole effective mass ratio.

Electrostatic quantum dots with designed shape of confinement potential

Abstract In electrostatic (gated) quantum dots, the potential confining the electrons is generated by the electrostatic field, which is created by the external voltages applied to the leads. Changing the geometry of the nanodevice we can obtain a diverse class of confinement potentials. We discuss the choice of the nanodevice parameters, which allows us to get the confinement potentials with the designed shape: from the rectangular potential well to the potential well with smooth edges. In particular, we find the conditions, under which the confinement potential possesses the Gaussian shape or is parabolic in a large region of the quantum dot.

Energy spectrum of centres in spherical quantum dots

The properties of negatively charged donor centres have been studied for semiconductor quantum dots with the finite spherically symmetric confinement potential. The energy levels of the ground state and the excited states of both the spin-singlet and spin-triplet configurations have been calculated by variational means. It has been shown that the excited states of the centre in quantum dots are bound for sufficiently strong confinement potential. The conditions of binding for the excited states have been determined as functions of the potential-well depth and quantum-dot radius. The formation of the bound excited states of the centre is a new property, which results from the confinement of electrons in the quantum dot. A possible application of the present results to the ion trapped in a microcavity is discussed.

Binding energy of the biexcitons in isotropic semiconductors

Abstract The dependence of the binding energy W of the biexciton on the electronhole mass ratio σ is discussed. The bounds from above and from below on the possible curves y = W (σ) have been obtained. In particular, the upper bound implies a positive binding of the biexcitons in the whole interval of the parameter σ. The bounds on W (σ) have been compared with experimental results on biexcitons in semiconductors.

Effective Hamiltonian for few-particle systems in polar semiconductors

Abstract The interaction between carriers in semiconductors is considered, including the coupling with LO-phonon field. The effective Hamiltonian, derived by the variational method, is valid for any values of the electron-phonon coupling constant. Applying it to the problem of exciton in Cu2O, CuBr and CuCl, we obtain the energies which agree well with the experimental spectra. Owing to its simple form this Hamiltonian may be useful for few-particle systems.

Effect of the repulsive core on the exciton spectrum in a quantum ring

A theoretical study of an exciton confined in a quantum ring is presented. The quantum ring is described as a two-dimensional circular quantum dot with a repulsive core, which is modelled with the help of two Gaussian functions. We have applied the variational method and investigated the evolution of the low-energy exciton spectrum with the change of the confinement potential. The calculations have been performed for the recently produced self-assembled ring-shaped InGaAs quantum dots. We have shown that the repulsive core strongly increases the radiative transition probability from the exciton ground state at the expense of the decreasing probability of the transitions from the excited states. This effect results from the orthogonality properties of the exciton wavefunctions, which are specific to the quantum-ring confinement potential. We have studied the characteristic features of the exciton spectrum, which can be used as a signature of the presence of the repulsive core in the quantum-dot potential.