Analysis of quantum-dot systems under thermal loads based on gradient elasticity

Since quantum-dot (QD) nanostructures in many applications are subjected to cyclic electrical and thermal loads, it is very important to analyze such nanostructures under transient thermal loads that affect the induced strains which in turn affects the response of the QD system. When the dimensions of the QDs are of the same order of magnitude as the material length scale, gradient elasticity theory should be used to account for the size-dependent behavior of such nano-sized QDs. In this work, a new finite element formulation for gradient-based thermo-electro-mechanical three-dimensional model of strained QDs in piezoelectric matrix under both static and dynamic thermal loads is developed. The proposed formulation requires only C0 shape functions since the original fourth order partial differential equation (PDE) is split into two PDEs of lower order. A unit cell of Indium Arsenide QD in a finite sized Gallium Arsenide (GaAs) substrate is analyzed. Results under dynamic loads demonstrate that the magnitude of the strain component in the thermal loading direction increases significantly with the thermal shock time. On the other hand, at a fixed time, the magnitude of the induced field quantities, such as the strain, decreases remarkably with increasing the size effect parameter. Given that large lattice mismatch induced strain fields are located in or near the QD regions, these newly observed features need to be carefully considered when designing such QD nanostructures.