Electronic structure in narrow-gap quantum dots

Abstract

In this work we calculated the electronic structure of spherical quantum dots based on zincblend semiconductor compounds. The strong conduction-valence band coupling in this class of semiconductors induces a strong mixing of the electronic states which requires a theoretical model to properly take i n to acount these e ects. We h a ve used a full 88 Kane Hamiltonian in order to include the strong admixture and study the set of symetries associated with these electronic states and their angular momentum in this central force problem. As an application, we h a ve calculated the electronic structure in narrow-gap HgCdTe, InSb and CdTe quantum dots. I IntroductionThe synthesis and characterization of new structural materials showing potential application as optical devices has been the subject of a large number of investigations in recent y ears. Almost all of them have studied semiconductor structures such as quantum wellsQW, quantum well wiresQWW and quantum dotsQD, presenting quantum con nement in one, two and three dimensions, respectively. The main interest in this work will be the electronic structure of QD which show a completely discrete energy spectrum for all carriers and, for this reason, they are frequently referred to as arti cial atoms ". Synthesis on colloids and on vitreous matrices are techniques which h a ve shown high degree of reproducibility and control. The crystallites have uniform spherical shapes where the diameter size can be tuned during the synthesis or by thermal treatment of the vitreous matrices producing narrow distribution of QD sizes within 5 rms 1 .In these nanocrystallite structures the number of carriers in the dots can be controlled externally 2 and the full spatial con nement, besides producing sharp energy levels, also has strong in uence on their linear 3 and nonlinear 4 optical properties.In this short work we show some results for the electronic structure of quantum dots with spherical symmetry within the envelope-function approximation where we solve analytically the full k:p Hamiltonian. II The k:p representationA large number of band structure calculation has been used in solids however the k:p, rst introduced by Kane 5 and Luttinger 6 has proved to be the most general e ective mass approach for heterostructures where the states are expanded in a nite set of Bloch states close to an extremum, k 0 , of the bulk band structure inside the Brillouin zone of the crystal.The basic k:p Hamiltonian procedure used by u s i s well described by W eiler 7 and used in a modi ed version by 8 in QD's. We are going to use the standard k.p version, with only a special ordering of states in two sets with spin up and down, as c

Optical transitions in geometrical quantum islands

“…[18,19] it is possible to treat analytically quantum islands having different ratios b/a for the case in which the potential barrier height is infinite. However, the difficulties increase drastically when the barriers are limited and therefore the eigenstates are non-separable.…”