Mathematical Modeling of Piezoelectric Quantum Dots

Quantum dots (QDs) are nanocrystals that are widely used in electronic devices as semiconductors due to their distinct and unique characteristics. Among them, the nanoscale optoelectronic properties are utilized in fine tuning the electronic band structure to optimize the performance of optoelectronic devices. QD structures are often manufactured as core/shell assembly due to the chemical sensitivity of the core surface which leads to degradation of emission properties. Hence, the shell structures are fabricated to enhance the surface passivation. Since the core and the shell are often made from different materials with different lattice dimensions, the assembled QD core/shell structures can induce misfit strains. The misfit strains have a profound effect on the exciton dynamics and blinking properties which play an important role in determining the light emission performance. The induced strain can alter the theoretical predictions of the optoelectronic properties that are often calculated from the first principle calculations. Hence, in order to better predict the optoelectronic properties, the elastic strains must be included in the Hamiltonian equations in calculating the electronic band structures which are usually calculated by the k∙p method.

The purpose of this work is to provide a linear elasticity solution for a free-standing QD core/shell structure so that the misfit strains can be properly taken into account in quantum mechanical calculations. The obtained solutions are applied to Cadmium Selenide/Cadmium Sulfide (CdSe/CdS) core/shell QD structures which come in the form of zinc-blende (ZB) or wurtzite (WZ) crystals. ZB crystals exhibit cubic material symmetry and show no piezoelectricity, whereas WZ crystals with hexagonal material symmetry show fully coupled piezoelectric effects. Therefore, a piezoelectric analysis is required in studying the electroelastic behavior of wurtzite crystal QDs since both the elastic and piezoelectric fields are equally important in understanding their optoelectonic properties. In this work, the electroelastic fields are obtained for QDs that are modeled as a misfitted inclusion in a finite spherical matrix taking into account the fully-coupled piezoelectric effects.