A. D. Andreev

Strain distributions in quantum dots of arbitrary shape

A method based on the Green’s function technique for calculating strain in quantum dot (QD) structures has been developed. An analytical formula in the form of a Fourier series has been obtained for the strain tensor for arrays of QDs of arbitrary shape taking into account the anisotropy of elastic properties. Strain distributions using the anisotropic model for semiconductor QDs are compared to results of a simplified model in which the elastic properties are assumed to be isotropic. It is demonstrated that, in contrast to quantum wells, both anisotropic and isotropic models give similar results if the symmetry of the QD shape is less than or equal to the cubic symmetry of the crystal. The strain distribution for QDs in the shape of a sphere, cube, pyramid, hemisphere, truncated pyramid, and flat cylinder are calculated and analyzed. It is shown that the strain distributions in the major part of the QD structure are very similar for different shapes and that the characteristic value of the hydrostatic st...

A quantitative study of radiative, Auger, and defect related recombination processes in 1.3-/spl mu/m GaInNAs-based quantum-well lasers

By measuring the spontaneous emission (SE) from normally operating /spl sim/1.3-/spl mu/m GaInNAs-GaAs-based lasers we have quantitatively determined the variation of each of the current paths present in the devices as a function of temperature from 130 K to 370 K. From the SE measurements we determine how the current I close to threshold, varies as a function of carrier density n, which enables us to separate out the main current paths corresponding to monomolecular (defect-related), radiative or Auger recombination. We find that defect-related recombination forms /spl sim/55% of the threshold current at room temperature (RT). At RT, radiative recombination accounts for /spl sim/20% of I/sub th/ with the remaining /spl sim/25% being due to nonradiative Auger recombination. Theoretical calculations of the threshold carrier, density as a function of temperature were also performed, using a ten-band k /spl middot/ p Hamiltonian. Together with the experimentally determined defect-related, radiative, and Auger currents we deduce the temperature variation of the respective recombination coefficients (A, B, and C). These are compared with theoretical calculations of the coefficients and good agreement is obtained. Our results suggest that by eliminating the dominant defect-related current path, the threshold current density of these GaInNAs-GaAs-based devices would be approximately halved at RT. Such devices could then have threshold current densities comparable with the best InGaAsP/InP-based lasers with the added advantages provided by the GaAs system that are important for vertical integration.

Theoretical and experimental analysis of 1.3-/spl mu/m InGaAsN/GaAs lasers

We present a comprehensive theoretical and experimental analysis of 1.3-/spl mu/m InGaAsN/GaAs lasers. After introducing the 10-band k /spl middot/ p Hamiltonian which predicts transition energies observed experimentally, we employ it to investigate laser properties of ideal and real InGaAsN/GaAs laser devices. Our calculations show that the addition of N reduces the peak gain and differential gain at fixed carrier density, although the gain saturation value and the peak gain as a function of radiative current density are largely unchanged due to the incorporation of N. The gain characteristics are optimized by including the minimum amount of nitrogen necessary to prevent strain relaxation at the given well thickness. The measured spontaneous emission and gain characteristics of real devices are well described by the theoretical model. Our analysis shows that the threshold current is dominated by nonradiative, defect-related recombination. Elimination of these losses would enable laser characteristics comparable with the best InGaAsP/InP-based lasers with the added advantages provided by the GaAs system that are important for vertical integration.

Calculation of electric field and optical transitions in InGaN∕GaN quantum wells

We present analytical expressions for internal electric field and strain in single and multiple quantum wells, incorporating electromechanical coupling, spontaneous polarization, and periodic boundary conditions. Internal fields are typically 2% lower than the fields calculated using an uncoupled model. We point out two possible interpolation routes to calculate the piezoelectric (PZ) constants eij of an alloy from the PZ constants of the constituent materials and show that, for an In0.2Ga0.8N∕GaN quantum well system, the respective internal electric fields differ by 10%. Using an effective-mass model, we explore the effect of the uncertainty in the elastic and PZ constants of GaN on the internal field and optical transitions of InGaN∕GaN quantum wells, and find that the range of published values of eij produces an uncertainty of more than ±20% in the internal field and of more than ±30% in the blueshift in optical transition energy between zero bias and flatband conditions (when the applied field is equa...

Carrier transport and recombination in p-doped and intrinsic 1.3μm InAs∕GaAs quantum-dot lasers

The radiative and nonradiative components of the threshold current in 1.3μm, p-doped and undoped quantum-dot semiconductor lasers were studied between 20 and 370K. The complex behavior can be explained by simply assuming that the radiative recombination and nonradiative Auger recombination rates are strongly modified by thermal redistribution of carriers between the dots. The large differences between the devices arise due to the trapped holes in the p-doped devices. These both greatly increase Auger recombination involving hole excitation at low temperatures and decrease electron thermal escape due to their Coulombic attraction. The model explains the high T0 values observed near room temperature.

Optical transitions and radiative lifetime in GaN/AlN self-organized quantum dots

We present a theoretical study of the optical matrix elements and radiative lifetime for the ground state optical transitions in GaN/AlN quantum dots (QD). An efficient plane-wave expansion method is used to calculate the energy levels, wave functions, and optical matrix elements in the framework of a multiband k⋅p model taking account of the three-dimensional strain and built-in electric field distributions for QDs with a hexagonal truncated-pyramid shape. We demonstrate that the built-in electric field determines the energy spectrum of GaN/AlN QDs and leads to a dramatic decrease in the optical matrix element with increasing QD size. As a result, the radiative lifetime for the ground state optical transition increases strongly with QD size. The theoretical results obtained are in good agreement with available experimental data.

Strain distribution in GaN∕AlN quantum-dot superlattices

The two-dimensional strain distribution in a GaN∕AlN quantum-dot (QD) superlattice is measured from high-resolution transmission electron microscopy images using the geometrical phase analysis. The results are compared to elastic theoretical calculations using a combination of Fourier transform and Green’s function techniques. The GaN∕AlN system appears to be a model system for a comparison between theory and experiments as interdiffusion between GaN and AlN is negligible. We verify that for the case of a three-dimensional system, such as a QD, the biaxial strain approximation is not valid. Furthermore, we demonstrate that the presence of QDs induces a modulation in the strain state of the AlN barriers which is the driving force for the vertical alignment of the GaN QDs in the AlN matrix.

The role of Auger recombination in InAs 1.3-/spl mu/m quantum-dot lasers investigated using high hydrostatic pressure

InAs quantum-dot (QD) lasers were investigated in the temperature range 20-300 K and under hydrostatic pressure in the range of 0-12 kbar at room temperature. The results indicate that Auger recombination is very important in 1.3-/spl mu/m QD lasers at room temperature and it is, therefore, the possible cause of the relatively low characteristic temperature observed, of T/sub 0/=41K. In the 980-nm QD lasers where T/sub 0/=110-130 K, radiative recombination dominates. The laser emission photon energy E/sub las/ increases linearly with pressure p at 10.1 and 8.3 meV/kbar for 980 nm and 1.3-/spl mu/m QD lasers, respectively. For the 980-nm QD lasers the threshold current increases with pressure at a rate proportional to the square of the photon energy E/sup 2//sub las/. However, the threshold current of the 1.3-/spl mu/m QD laser decreases by 26% over a 12-kbar pressure range. This demonstrates the presence of a nonradiative recombination contribution to the threshold current, which decreases with increasing pressure. The authors show that this nonradiative contribution is Auger recombination. The results are discussed in the framework of a theoretical model based on the electronic structure and radiative recombination calculations carried out using an 8/spl times/8 k/spl middot/p Hamiltonian.

Optical matrix element in InAs/GaAs quantum dots: Dependence on quantum dot parameters

We present a theoretical analysis of the optical matrix element between the electron and hole ground states in InAs∕GaAs quantum dots (QDs) modeled with a truncated pyramidal shape. We use an eight-band k∙p Hamiltonian to calculate the QD electronic structure, including strain and piezoelectric effects. The ground state optical matrix element is very sensitive to variations in both the QD size and shape. For all shapes, the matrix element initially increases with increasing dot height, as the electron and hole wave functions become more localized in k space. Depending on the QD aspect ratio and on the degree of pyramidal truncation, the matrix element then reaches a maximum for some dot shapes at intermediate size beyond which it decreases abruptly in larger dots, where piezoelectric effects lead to a marked reduction in electron-hole overlap.

Theoretical performance and structure optimization of 3.5–4.5 μm InGaSb/InGaAlSb multiple-quantum-well lasers

We present a comprehensive theoretical investigation to optimize 3.5–4.5 μm InGaSb/InGaAlSb quantum-well (QW) lasers grown on ternary InGaSb substrates. We use an eight-band k⋅P Hamiltonian to calculate the Auger recombination and optical absorption coefficients in the active region, as well as the gain and threshold characteristics. The dominant Auger process involves hole excitation from the QW to unbound valence states. For structure optimization we varied the Ga content in the substrate and QW barrier layers. The optimized structure was obtained by maximizing the strain in the QWs, despite the Auger coefficient also increasing with strain. It is, therefore, demonstrated that the main aim for midinfrared laser optimization can be minimization of the threshold carrier density rather than reduction of the Auger coefficient.