E. Assaid

On the anomalous Stark effect in a thin disc-shaped quantum dot

The effect of a lateral external electric field F on an exciton ground state in an InAs disc-shaped quantum dot has been studied using a variational method within the effective mass approximation. We consider that the radial dimension of the disc is very large compared to its height. This situation leads to separating the excitonic Hamiltonian into two independent parts: the lateral confinement which corresponds to a two-dimensional harmonic oscillator and an infinite square well in the growth direction. Our calculations show that the complete description of the lateral Stark shift requires both the linear and quadratic terms in F which explains that the exciton possess nonzero lateral dipolar moment and polarizability. The fit of the calculated Stark shift permits us to estimate the lateral permanent dipole moment and the polarizability according to the disc size. Our results are compared to those existing in the literature. In addition the behavior of the optical integral shows that the exciton lifetime is greater than that under zero field which is due to the field-induced polarization.

Binding energy of excitons in inhomogeneous quantum dots under uniform electric field

Abstract Excitons in inhomogenous quantum nanospheres have been theoretically studied within the effective mass approximation. An infinite deep potential has been used to describe the effects of quantum confinement. The binding energy with or without an applied electric field is determined by the Ritz variational method taking into account the correlation between the electron and the hole in the trial wave function. It appears that the binding energy strongly depends on the core and shell radii. The existence of a radius ratio critical value has been shown: it may be used to distinguish between tridimensional and spherical surface confinement. The influence of a uniform electric field is analyzed. It has been found that the Stark effect appears even for very small sizes and that the energy shift is more significant when the exciton is near the spherical surface.

Size dependence of the polarizability and Haynes rule for an exciton bound to an ionized donor in a single spherical quantum dot

We study the effect of an external electric field on an exciton bound to an ionized donor (D+, X) confined in a spherical quantum dot using a perturbative-variational method where the wave function and energy are developed in series of powers of the electric field strength. After testing this new approach in the determination of the band gap for some semiconductor materials, we generalize it to the case of (D+, X) in the presence of the electric field and for several materials ZnO, PbSe, and InAs, with significant values of the mass ratio. Three interesting results can be deduced: First, we show that the present method allows to determine the ground state energy in the presence of a weak electric field in a simple way (E = E0 − αf2) using the energy without electric field E0 and the polarizability α. The second point is that our theoretical predictions show that the polarizability of (D+, X) varies proportionally to R3.5 and follows an ordering αD0

Lateral induced dipole moment and polarizability of excitons in a ZnO single quantum disk

The lateral Stark shift of an exciton confined in a single ZnO quantum thin disk of radius R was calculated using a variational approach within the two bands effective mass approximation. It is shown that the exciton has a non negligible induced dipole moment when an external electric field is applied mainly for electron-hole separation below to the 3D excitonic Bohr radius. The behavior of the exciton lateral Stark shift proves the existence of an important correlation between the polarizability and the induced dipole moment.

Excitons in InP/InAs inhomogeneous quantum dots

Wannier excitons confined in an InP/InAs inhomogeneous quantum dot (IQD) have been studied theoretically in the framework of the effective mass approximation. A finite-depth potential well has been used to describe the effect of the quantum confinement in the InAs layer. The exciton binding energy has been determined using the Ritz variational method. The spatial correlation between the electron and the hole has been taken into account in the expression for the wavefunction. It has been shown that for a fixed size b of the IQD, the exciton binding energy depends strongly on the core radius a. Moreover, it became apparent that there are two critical values of the core radius, acrit and a2D, for which important changes of the exciton binding occur. The former critical value, acrit, corresponds to a minimum of the exciton binding energy and may be used to distinguish between tridimensional confinement and bidimensional confinement. The latter critical value, a2D, corresponds to a maximum of the exciton binding energy and to the most pronounced bidimensional character of the exciton.

Deep-level traps and recombination centers effects on photovoltaic conversion efficiency of GaAs based crystalline solar cell

In this work, we proceed to analytical and numerical resolutions, using finite difference method, of semiconductor four equations system governing the variations of electrostatic potential, electrons and holes densities, density profile of occupied levels associated to deep-level traps as well as concentration profile of occupied levels related to recombination centers, in one-dimensional thin-film crystalline solar cell based on Gallium Arsenide (GaAs). In addition to physical quantities mentioned above, the problem resolution, achieved using Maple computer algebra software, enables us to retrieve electrostatic field, electrons and holes current densities as well as energy band diagram throughout the device. Ultimately, particular attention is devoted to specific phenomena related to semiconductors such as the presence of deep-level traps or recombination centers whose levels are in the middle of the gap. In this way, we show that the presence of deep-level traps or recombination centers leads, via Shockley-Read-Hall mechanisms, to a decrease of solar cell photovoltaic conversion efficiency. We also show that these effects are dependent on energy levels of traps and defects, on traps and defects concentrations as well as their electron and hole capture cross sections.

Finite difference numerical solution of Poisson equation in a Schottky barrier diode using maple

In the present study, we determine using Maple software the exact numerical solution of Poissons equation in a Schottky barrier junction according to three different approaches. First, we consider the simple case where the space charge zone is depleted and the doping impurities are fully ionized. Then we treat the case where the space charge zone is non-depleted and the doping impurities are fully ionized. Finally, we solve rigorously the more general case where the space charge zone is non-depleted and the doping impurities are partially ionized. We use two different methods to solve the problem. In the former one, the distance of each point to the junction is calculated as a function of its potential. In the second one, we use a finite difference scheme to solve the Poissons equation. The calculations may be integrated into a course on semiconductor devices to show the use of Maple capabilities in the resolution of the second order non-linear differential equation governing the potential in electronic devices.