K. B. Hong

Two-step strain analysis of self-assembled InAs/GaAs quantum dots

Strain effects on optical properties of self-assembled InAs/GaAs quantum dots grown by epitaxy are investigated. Since a capping layer is added after the self-assembly process of the quantum dots, it might be reasonable to assume that the capping layer neither experiences nor affects the induced deformation of quantum dots during the self-assembly process. A new two-step model is proposed to analyse the three-dimensional induced strain fields of quantum dots. The model is based on the theory of linear elasticity and takes into account the sequence of the fabrication process of quantum dots. In the first step, the heterostructure system of quantum dots without the capping layer is considered. The mismatch of lattice constants between the wetting layer and the substrate is the driving source for the induced elastic strain. The strain field obtained in the first step is then treated as an initial strain for the whole heterostructure system, with the capping layer, in the second step. The strain from the two-step analysis is then incorporated into a steady-state effective-mass Schrodinger equation. The energy levels as well as the wavefunctions of both the electron and the hole are calculated. The numerical results show that the strain field from this new two-step model is significantly different from models where the sequence of the fabrication process is completely omitted. The calculated optical wavelength from this new model agrees well with previous experimental photoluminescence data from other studies. It seems reasonable to conclude that the proposed two-step strain analysis is crucial for future optical analysis and applications.

Influences of template layer thickness on strain fields and transition energies in self-assembled SiGe∕Si quantum dots

This paper investigates the influence of thickness of template layer on strain fields and transition energies in lens-shaped self-assembled SiGe∕Si quantum dots. This study analyzes strain fields in and around quantum dots on the basis of the theory of linear elasticity. Strain fields are then incorporated into the steady-state effective-mass Schrodinger equation. Energy levels and wavefunctions of both electrons and holes are calculated. The calculated results of strain-induced phonon frequency are consistent with previous results obtained by Raman spectroscopy. Moreover, the calculated transition energy agrees well with previous experimental photoluminescence data. Numerical results also suggest that transition energy decreases as the template layer thickness increases.

Fully coupled and semi-coupled piezoelectric models on the optical properties of InGaN quantum dots

This paper investigates the differences between the fully coupled and the semi-coupled piezoelectric models for determining strain fields, piezoelectric potentials and optical properties of wurtzite InGaN quantum dots (QDs) in three different shapes. Through the calculations, we show that the relative difference of the x-component strain inside the dot remains almost unchanged regardless of the shapes and the sizes of the dot. On the other hand, a large relative difference for the z-component strain is obtained with the use of the semi-coupled model. We also find that the semi-coupled model clearly overestimates the piezoelectric potential, and the transition energy difference increased with increases in the dot size and indium composition. Consequently, the semi-coupled model causes a great amount of distortion in predicting the optical properties of InGaN QDs. It is thus evident that the fully coupled model for calculating the electromechanical fields and optical properties of InGaN QDs may be more appropriate according to our numerical examples.

Effect of piezoelectric constants in electronic structures of InGaN quantum dots

This study theoretically investigates the effect of the sign of the shear piezoelectric constant on the optical properties of wurtzite InGaN quantum dots (QDs) that are grown on polar, semipolar and nonpolar GaN substrates. The strain fields, electric potentials and single- particle state energies are analyzed using the theory of piezoelectricity and the strained k p Hamiltonian. Calculations reveal that the sign of e15 greatly affects the electric potentials and optical properties, especially of larger QDs. The change in electron energy is particularly sensitive to the height of QDs for either sign of e15. A positive e15 causes a greater decrease (increase) in electron (hole) energies than a negative e15. Furthermore, the exciton binding energy of polar QDs is sensitive to dot height, unlike semipolar and nonpolar QDs, which have weak binding energies. The transition energies of InGaN QDs in semipolar or nonpolar substrates are greatly increased. However, the overlap of the electron–hole wavefunctions is clearly greater when the indium content is lower. Based on the results herein, QDs grown on (1 1 0 1) planes should be preferred to those grown on polar and nonpolar planes for optical applications.

Influence of wetting layers on the electric potentials and optical properties of InGaN quantum dots

This study investigates the influence of wetting layers (WLs) on the electric potentials and electronic structures of InGaN quantum dots (QDs). The single particle electron and hole energies of QDs with different thicknesses and indium compositions of the WLs are calculated using the four-band k ⋅ p Hamiltonian. Numerical results show that there is an average of 60 mV increase in the maximum electric potential drop per every 0.2 nm increment in the thickness of the WL or per every 0.05 increase in indium composition α of the WL. Consequently, the transition energy decreases significantly with increasing thickness and/or indium composition of the WL. We find that the strained bandgap shifts down by 125 meV leading to a 128 meV decrease in the transition energy per every 0.4 nm increment in the thickness of the WL, which corresponds to 5.6% and 4.8% of the strained bandgap and the transition energy, respectively, for the cases without the WL. Furthermore, there is also a 32.5 meV transition energy decrease per every 0.025 increase in indium composition α of the WL. Hence, it is important to consider the thickness and indium composition of the WL in the analysis of InGaN QDs.

Fully coupled piezoelectric models on the optical properties of InGaN quantum dots

This paper investigates the fully coupled piezoelectric models for determining strain fields, piezoelectric potentials, and optical properties of wurtzite InGaN quantum dots (QDs). Through the calculations, we find that the semi-coupled model clearly overestimates the piezoelectric potential, and the transition energy difference increased with increases in the dot size and indium composition. Consequently, the semi-coupled model causes a great amount of distortion in predicting the optical properties of InGaN QDs, compared to the fully coupled piezoelectric models.

Strain Fields and Transition Energies in Multilayer InAs/GaAs Quantum Dots

Strain fields and transition energies of vertically stacked semiconductor quantum dots are investigated. Strain fields, induced by lattice mismatches in heterostructures, in and around quantum dots are analyzed on the basis of the linear elasticity. The three-dimensional steady-state strained-effective-mass Schrodinger equation is then modified by incorporating the effects of strain fields into the carrier confinement potential and is analyzed by finite element methods numerically. The results include the energy levels and wavefunction spectra of InAs/GaAs quantum dots. The calculated optoelectronic transition energies agree well with the previous experimental photoluminescence data. Numerical results also suggest that transition energy decreases as the spacer thickness increases.Copyright

Size and Piezoelectric Effects on Optical Properties of Self-Assembled InGaAs/GaAs Quantum Dots

Size effects on optical properties of self-assembled quantum dots are analyzed based on the theories of linear elasticity and of strain-dependent k-p with the aid of finite element analysis. The quantum dot is made of InGaAs with truncated pyramidal shape on GaAs substrate. The three-dimensional steady-state effective-mass Schrodinger equation is adopted to find confined energy levels as well as wave functions both for electrons and holes of the quantum-dot nanostructures. Strain-induced as well as piezoelectric effects are taken into account in the carrier confinement potential of Schrodinger equation. The optical transition energies of quantum dots, computed from confined energy levels for electrons and holes, are significantly different for several quantum dots with distinct sizes. It is found that for QDs with the the larger the volume of QD is, the smaller the values of the optical transition energy. Piezoelectric effect, on the other hand, splits the p-like degeneracy for the electron first excited state about 1~7 meV, and leads to anisotropy on the wave function.Copyright