Quantum box energies as a route to the ground state levels of self-assembled InAs pyramidal dots

Abstract

A theoretical investigation of the ground state electronic structure of InAs/GaAs quantum confined structures is presented. Energy levels of cuboids and pyramidal shaped dots are calculated using a single-band, constant-confining-potential model that in former applications has proved to reproduce well both the predictions of very sophisticated treatments and several features of many experimental photoluminescence spectra. A connection rule between their ground state energies is found which allows the calculation of the energy levels of pyramidal dots using those of cuboids of suitably chosen dimensions, whose solution requires considerably less computational effort. The purpose of this work is to provide experimentalists with a versatile and simple method to analyze their spectra. As an example, this rule is then applied to successfully reproduce the position of the ground state transition peaks of some experimental photoluminescence spectra of self-assembled pyramidal dots. Furthermore the rule is used to predict the dimensions of a pyramidal dot, starting from the knowledge of the ground state transition energy and an estimate for the aspect ratio Q

Analytical calculation of eigen-energies for lens-shaped quantum dot with finite barriers

“…The same idea was previously applied in [23] to calculate the electronic states in cylindrical quantum dots of semiconductors. A 2D Fourier expansion has been used in [24] to find the electronic states in InGaAs/InP quantum well-wires structures and in self-assembled InAs pyramidal quantum dots [25].…”

Optical schemes for quantum computation in quantum dot molecules

“…4 and m * p is the effective mass of the particle p. These solutions may be obtained by expanding the Hamiltonian in a set of envelope basis functions of the form Ξ(r) = ξ x (x)ξ y (y)ξ z (z), where the ξ i (i) are the solutions of a one dimensional square well potential with the appropriate effective masses. 73,74 Both bound and unbound states must be used in the expansion in order to obtain convergent solutions: the forms of these are discussed in Appendix A.…”

Investigation of the Electron Energy Spectrum in a Three Dimensional Regimented Tetragonal Quantum Dot Superlattice

“…Thus, a single dot could be thought of as a finite-barrier cubic dot with four additional perturbing potentials [7]. The assumption of cubic dots does not severely limit the generality of our approach since the electronic band structure is much more sensitive to the dot regimentation rather than to the dot shape [6].…”