Emission of Qd in Electrostatic Fields

The paper presents the wave functions ψ, probability functions ψψ* and the ground states energy of a nanostructure consisting of a Si QD embedded in SiO2 dielectric medium, which is under bias of varying electrostatic field. Abrupt displacement of the peak of ψψ* at a certain field value is elucidated as the QD emission. The field distribution and the characteristics of the nanostructure quantum states are obtained with help of Comsol Multiphysics Poisson-Schrödinger 2D (PSM) model, developed by the authors. Introduction Quantum dots (QDs) are advanced semiconductor nanodevices, consisting of hundreds to hundreds of thousands atoms, produced by temporary top experimental techniques (molecular beam epitaxy, chemical vapor deposition). They are fabricated in many different shapes (cubes, spheres, discs, pyramids, cones and their combinations). The semiconductor nucleus or nanocrystal is usually embedded in a larger-bandgap semiconductor or a dielectric. Colloidal QD can be supplied in liquid suspensions or dispersed in a glass or plastic composites. The QD application have been reported in many fields: as memory elements – in quantum informatics and computers, as efficient lasers, light-emitting diodes, solar cells – in modern electronics, as biological sensors and optical tags – in biology, detectors of explosive – in criminalistics. Promising results have been obtained in medicine with tumor targeting and others [1]. 1 Quantum states of nanostructures The behavior of QD is described by Quantum mechanics. Energy levels are discrete, strongly determined by the QD size and shape and probability of electron location is proportional to the square of the wave function amplitude. The QDs can be viewed as tunable artificial atoms. Properties of QDs are under permanent study of researchers for several years. Numerical analysis of GaAs-InAs nanostructure with conical QD was performed by Melnik and Wilatzen in 2004 [2]. They applied FEM method available in COMSOL program. Deleruyelle et al. used COMSOL in 2007 and obtained 1D band diagram with probability function of the ground state at several biasing fields. They did not attempt to estimate the emission field value – the significant QD characteristic parameter [3]. The authors of the present paper performed numerical analysis of electron traps in paper [4]. The present paper is devoted to the numerical analysis of a circular Si QD. A 2D Poisson-Schrödinger COMSOL Multiphysics model was developed and solved. The results, including the emission bias value are presented and discussed. 1.1 Nanostructure The nanostructure under investigation is sketched in Fig. 1. The rectangular nanostructure in xy plane is 12 nm long and 4 nm wide. The radius R of the circular Si QD is 1 nm, the centre is at 7/12 of the nanostructure length. Relative permittivity of Si is 11.9. The QD is surrounded by insulating medium SiO2 with relative permittivity of 3.9. The potential barrier between the QD and its surroundings is 3.2 eV. It is result of different electron affinities of Si and SiO2. Effective electron mass is meff = 0.9. 1.2 Electrostatic field Electrostatic field is applied to the nanostructure between edges a, b. It points from edge a (grounded) to edge b. The bias of the field is Vab = Va – Vb. The field distribution obeys the Poisson Equation (PEq)