Impact of shell thickness on exciton and biexciton binding energies of a ZnSe/ZnS core–shell quantum dot

Abstract

Impact of shell structure on the exciton and biexciton binding energies has been studied in a ZnSe/ZnS core–shell quantum dot using Wentzel–Kramers–Brillouin (WKB) approximation. For excitons, the binding is caused by the Coulombic as well as the confinement potentials while biexciton binding energy is determined by taking into account the exchange and correlation effects. The exciton binding energy was found to increase initially with increasing shell thickness which reaches saturation at larger shell thickness. On the other hand, the biexciton binding energy exhibits a crossover from the bonding to antibonding state with increasing shell thickness for smaller core radius of the quantum dot.

Introduction

Semiconductor quantum dots (QDs) have drawn significant attention in the last couple of decades as they play the role of key materials for modern optoelectronic and spintronic nanodevices [1], [2]. In the semiconductor quantum dots, the electrons and holes are confined within the width of a semiconductor layer of lower energy gap which is surrounded by another semiconductor with a higher band gap and is generally lattice matched with the former [3]. The confinements of electrons and holes give rise to novel optical and electronic properties. These nanostructures are popularly known as core–shell quantum dots (CSQDs). It has been experimentally observed that such CSQDs exhibit improved photoluminescence (PL) efficiency over that from the bare quantum dots and the thickness of the shell provides further control on optical and electronic properties of these QDs [4]. Some reported example of CSQD are CdSe/ZnS, ZnS/CdS, CdSe/HgS, CdSe/CdS, ZnSe/ZnS, etc. [5], [6].

Of late, Lad and Mahanuni [5] have observed nearly 42% increase in PL intensity due to the presence of ZnS shell around the ZnSe quantum dot. The electronic and optical properties of ZnSe/ZnS and ZnS/ZnSe CSQDs were theoretically studied by Goswami et al. [6] where they found that a charge transfer from core to shell takes place and the core–shell structure exhibits a red shift in the absorption spectra. Growth and PL study of ZnSe QD was also reported by Chang et al. [7] following a flow controlled method for growing ZnSe QDs embedded in ZnS and observed experimentally that for shorter growth time, the QD size was smaller and the blue shift in the PL spectra was larger. The smaller QD size means smaller core radius which corresponds to larger confinement potential and gives rise to blue shift in absorption spectra.

The stimulus for the present work stems from the report of the red shift in the PL spectra as well as the increase in the PL intensity in CSQD due to the presence of shell [4]. In our earlier work [8], [9], [10], [11], we reported nonlinear and coherent transient optical properties of a single quantum dot. The energy level structure in the bare QD was also reported by our group [12] as well as by other groups [13], [14], [15], [16] taking into account the parabolic, spherical, square well and other types of confinement potential functions. In these models, the spreading of the single particles wavefunctions to the shell was not given due consideration. In our opinion, the inclusion of tunneling property should be incorporated to include the effect of shell on the energy level structures of the core–shell QDs. In the present paper, we have chosen WKB wave functions with due weightage to the boundary conditions at the core/shell interface and calculated the exciton and biexciton binding energies in the CSQDs. The theoretical results exhibit increase in the binding energies of excitons and biexcitons due to the presence of the shell. Consequently, the transition energies also show red shifts as observed by Mahamuni et al. [5] in the PL spectra of CSQD.