Temperature dependent empirical pseudopotential theory for self-assembled quantum dots

Abstract

We develop a temperature dependent empirical pseudopotential theory to study the electronic and optical properties of self-assembled quantum dots (QDs) at finite temperature. The theory takes the effects of both lattice expansion and lattice vibration into account. We apply the theory to InAs/GaAs QDs. For the unstrained InAs/GaAs heterostructure, the conduction band offset increases whereas the valence band offset decreases with increasing temperature, and there is a type-I to type-II transition at approximately 135 K. Yet, for InAs/GaAs QDs, the holes are still localized in the QDs even at room temperature, because the large lattice mismatch between InAs and GaAs greatly enhances the valence band offset. The single-particle energy levels in the QDs show a strong temperature dependence due to the change of confinement potentials. Because of the changes of the band offsets, the electron wavefunctions confined in QDs increase by about 1-5%, whereas the hole wavefunctions decrease by about 30-40% when the temperature increases from 0 to 300 K. The calculated recombination energies of excitons, biexcitons and charged excitons show red shifts with increasing temperature which are in excellent agreement with available experimental data.

Temperature-Dependent Energy-Level Shifts of Spin Defects in Hexagonal Boron Nitride

“…In Figure b, the ZFS parameter D has a nonlinear dependence on temperature from 5 to 600 K, and we fit it with the Varshni empirical equation: where D 0 is the value of D at T = 0 K; α and β are fitting parameter characteristics of the given material, which should be positive to ensure the monotonicity of D as a function of temperature: α is an empirical constant and β is commonly supposed to be related and comparable to the Debye temperature Θ D . While this equation is regrettably very weak in its theoretical foundation and inconsistent with the Debye model in the low-temperature limit, it is still one of the most widely quoted models due to the irreplaceable simplicity and monotonicity and has had great success in describing the temperature dependence of energy gaps in many semiconductor bulk and nanopowdered materials. − In our experiment, the fitting based on the Varshni function showed outstanding agreement over the entire measured temperature range. As an example, the fit of the Varshni equation with parameters D 0 = 3584 ± 1 MHz, α = 1.06 ± 0.05 MHz/K, and β = 559 ± 51 K in Figure b describes the D shifts extremely well, with errors less than 12 MHz in the 5–600 K range.…”

Strained band edge characteristics from hybrid density functional theory and empirical pseudopotentials: GaAs, GaSb, InAs and InSb

“…Afterwards, ab initio theoretical studies abounded [18][19][20][21][22][23][24][25]. As these ab initio calculations suffer from well-known bandgap errors and require high computational cost [26], semi-empirical methods were preferred [27][28][29][30][31][32][33][34]. In particular, O'Reilly using a tight-binding method took into account the crystals under biaxial compression and tension to study the [0 0 1] axial deformation potential b in group-III-V semiconductors [35].…”

Strained band edge characteristics from hybrid density functional theory and empirical pseudopotentials: GaAs, GaSb, InAs and InSb

“…Afterwards, ab initio theoretical studies soared [18,19,20,21,22,23,24,25]. As these ab initio calculations suffer from well-known bandgap errors and require high computational cost [26], semiempirical methods have also been preferred [27,28,29,30,31,32,33,34]. Particularly, O'Reilly using tightbinding method has taken into account the crystals under biaxial compression and tension to study [001] axial deformation potential b in group-III-V semiconductors [35].…”