Self-consistent energy balance simulations of hole dynamics in SiGe/Si THz quantum cascade structures

Analysis of hole transport in cascaded p-Si/SiGe quantum well structures is performed using self-consistent rate equations simulations. The hole subband structure is calculated using the 6×6 k·p model, and then used to find carrier relaxation rates due to the alloy disorder, acoustic, and optical phonon scattering, as well as hole-hole scattering. The simulation accounts for the in-plane k-space anisotropy of both the hole subband structure and the scattering rates. Results are presented for prototype THz Si/SiGe quantum cascade structures. © 2004 American Institute of Physic

Design and simulation of InGaAs/AlAsSb quantum-cascade lasers for short wavelength emission

The design and simulation of an In-0.53Ga-0.47As/Al-0.56As-0.44Sb quantum-cascade laser emitting in the near infrared is presented. Designed using a self-consistent rate equation solver coupled with an energy balance rate equation, the proposed laser has a calculated population inversion of ~20% at 77 K and sufficient gain to achieve room-temperature laser emission at λ ~2.8 µm. Threshold currents in the range 4–8 kA/cm2 are estimated as the temperature increases from 77 K to 300 K. The output characteristics of the proposed laser are compared to an existing λ ~3.1 µm In-0.53Ga-0.47As/Al-0.56As-0.44Sb quantum-cascade structure presented in the literature

Symmetry of k·p Hamiltonian in pyramidal InAs/GaAs quantum dots: Application to the calculation of electronic structure

A method for the calculation of the electronic structure of pyramidal self-assembled InAs/GaAs quantum dots is presented. The method is based on exploiting the C-4 symmetry of the 8-band k·p Hamiltonian with the strain taken into account via the continuum mechanical model. The operators representing symmetry group elements were represented in the plane wave basis and the group projectors were used to find the symmetry adapted basis in which the corresponding Hamiltonian matrix is block diagonal with four blocks of approximately equal size. The quantum number of total quasiangular momentum is introduced and the states are classified according to its value. Selection rules for interaction with electromagnetic field in the dipole approximation are derived. The method was applied to calculate electron and hole quasibound states in a periodic array of vertically stacked pyramidal self-assembled InAs/GaAs quantum dots for different values of the distance between the dots and external axial magnetic field. As the distance between the dots in an array is varied, an interesting effect of simultaneous change of ground hole state symmetry, type, and the sign of miniband effective mass is predicted. This effect is explained in terms of the change of biaxial strain. It is also found that the magnetic field splitting of Kramer's double degenerate states is most prominent for the first and second excited state in the conduction band and that the magnetic field can both separate otherwise overlapping minibands and concatenate otherwise nonoverlapping minibands

Intersubband carrier scattering in n- and p-Si/SiGe quantum wells with diffuse interfaces

Scattering rate calculations in two-dimensional Si/Si1−xGex systems have typically been restricted to rectangular Ge profiles at interfaces between layers. Real interfaces however, may exhibit diffuse Ge profiles either by design or as a limitation of the growth process. It is shown here that alloy disorder scattering dramatically increases with Ge interdiffusion in (100) and (111) n-type quantum wells, but remains almost constant in (100) p-type heterostructures. It is also shown that smoothing of the confining potential leads to large changes in subband energies and scattering rates and a method is presented for calculating growth process tolerances

Quantum transport in semiconductor quantum dot superlattices: electron-phonon resonances and polaron effects

Electron transport in periodic quantum dot arrays in the presence of interactions with phonons was investigated using the formalism of nonequilibrium Green's functions. The self-consistent Born approximation was used to model the self-energies. Its validity was checked by comparison with the results obtained by direct diagonalization of the Hamiltonian of interacting electrons and longitudinal optical phonons. The nature of charge transport at electron -- phonon resonances was investigated in detail and contributions from scattering and coherent tunnelling to the current were identified. It was found that at larger values of the structure period the main peak in the current -- field characteristics exhibits a doublet structure which was shown to be a transport signature of polaron effects. At smaller values of the period, electron -- phonon resonances cause multiple peaks in the characteristics. A phenomenological model for treatment of nonuniformities of a realistic quantum dot ensemble was also introduced to estimate the influence of nonuniformities on current -- field characteristics

Time delay in thin slabs with self-focusing Kerr-type nonlinearity

Time delays for an intense transverse electric (TE) wave propagating through a Kerr-type nonlinear slab are investigated. The relation between the bidirectional group delay and the dwell time is derived and it is shown that the difference between them can be separated into three terms. The first one is the familiar self interference time, due to the dispersion of the medium surrounding the slab. The other two terms are caused by the nonlinearity and oblique incidence of the TE wave. It is shown that the electric field distribution along the slab may be expressed in terms of Jacobi elliptic functions while the phase difference introduced by the slab is given in terms of incomplete elliptic integrals. The expressions for the field intensity dependent complex reflection and transmission coefficients are derived and the multivalued oscillatory behavior of the delay times for the case of a thin slab is demonstrated

Thermal effects in InGaAs/AlAsSb quantum-cascade lasers

A quantum-cascade laser (QCL) thermal model is presented. On the basis of a finite-difference approach, the model is used in conjunction with a self-consistent carrier transport model to calculate the temperature distribution in a near-infrared InGaAs/AlAsSb QCL. The presented model is used to investigate the effects of driving conditions and device geometries on the active-region temperature, which has a major influence on the device performance. A buried heterostructure combined with epilayer-down mounting is found to offer the best performance compared with alternative structures and has thermal time constants up to eight times smaller. The presented model provides a valuable tool for understanding the thermal dynamics inside a QCL and will help to improve operating temperatures

Self-consistent scattering theory of transport and output characteristics of quantum cascade lasers

Electron transport in GaAs/AlGaAs quantum cascade lasers operating in midinfrared is calculated self-consistently using an intersubband scattering model. Subband populations and carrier transition rates are calculated and all relevant electron-LO phonon and electron-electron scatterings between injector/collector, active region, and continuum resonance levels are included. The calculated carrier lifetimes and subband populations are then used to evaluate scattering current densities, injection efficiencies, and carrier backflow into the active region for a range of operating temperatures. From the calculated modal gain versus total current density dependencies the output characteristics, in particular the gain coefficient and threshold current, are extracted. For the original GaAs/Al0.33Ga0.67As quantum cascade structure [C. Sirtori , Appl. Phys. Lett. 73, 3486 (1998)] these are found to be g=11.3 cm/kA and J(th)=6+/-1 kA/cm(2) (at T=77 K), and g=7.9 cm/kA and J(th)=10+/-1 kA/cm(2) (at T=200 K), in good agreement with the experiment. Calculations shows that threshold cannot be achieved in this structure at T=300 K, due to the small gain coefficient and the gain saturation effect, also in agreement with experimental findings. The model thus promises to be a powerful tool for the prediction and optimization of new, improved quantum cascade structures. © 2002 American Institute of Physics

Electronic structure and optical properties of Sn and SnGe quantum dots

Self-assembled quantum dots in a Si–Ge–Sn system attract research attention as possible direct band gap materials, compatible with Si-based technology, with potential applications in optoelectronics. In this work, the electronic structure near the point and interband optical matrix elements of strained Sn and SnGe quantum dots in a Si or Ge matrix are calculated using the eight-band k·p method, and the competing L-valley conduction band states were found by the effective mass method. The strain distribution in the dots was found with the continuum mechanical model. The parameters required for the k·p or effective mass calculation for Sn were extracted by fitting to the energy band structure calculated by the nonlocal empirical pseudopotential method. The calculations show that the self-assembled Sn/Si dots, sized between 4 and 12 nm, have indirect interband transition energies between 0.8 and 0.4 eV and direct interband transitions between 2.5 and 2.0 eV. In particular, the actually grown, approximately cylindrical Sn dots in Si with a diameter and height of about 5 nm are calculated to have an indirect transition (to the L valley) of about 0.7 eV, which agrees very well with experimental results. Similar good agreement with the experiment was also found for SnGe dots grown on Si. However, neither of these is predicted to be direct band gap materials, in contrast to some earlier expectations

Theory and design of quantum cascade lasers in (111) n-type Si/SiGe

Although most work towards the realization of group IV quantum cascade lasers (QCLs) has focused on valence band transitions, there are many desirable properties associated with the conduction band. We show that the commonly cited shortcomings of n-type Si/SiGe heterostructures can be overcome by moving to the (111) growth direction. Specifically, a large band offset and low effective mass are achievable and subband degeneracy is preserved. We predict net gain up to lattice temperatures of 90 K in a bound-to-continuum QCL with a double-metal waveguide, and show that a Ge interdiffusion length of at least 8 Å across interfaces is tolerable