Kohn Luttinger Research Articles

Design considerations to improve high temperature characteristics of 1.3 μm AlGaInAs-InP uncooled multiple quantum well lasers: Strain in barriers

Uncooled multiple quantum well lasers have great attraction because of their lower power dissipation and smaller size than traditional semiconductor lasers. In this study we will investigate the strain effect in barriers of 1.3 μm AlGaInAs-InP uncooled multiple quantum well lasers. We simulate a laser structure using a band-to-band transition approach. Single effective mass theory has been used for conduction band and Kohn–Luttinger Hamiltonian has been solved for valance band to obtain quantum states and envelope wave functions in the structure. In the case of unstrained barriers, the results have good agreement with a real device fabricated and presented in one of the references. Our main work is proposal of 0.2% compressive strain in the structure Barriers that cause 20% improvement in mode gain–current density characteristic. Significant reduction in leakage current density and Auger current density characteristics is also obtained at 85 °C. Optical gain–photon energy spectrum is increased more than 3% proportional to unstrained barriers.

Pomeranchuk instability in doped graphene

The density of states of graphene has van Hove singularities that can be reached by chemical doping and have already been explored in photoemission experiments. We show that in the presence of Coulomb interactions the system at the van Hove filling is likely to undergo a Pomeranchuk instability breaking the lattice point group symmetry. In the presence of an on-site Hubbard interaction the system is also unstable toward ferromagnetism. We explore the competition of the two instabilities and build the phase diagram. We also suggest that, for doping levels where the trigonal warping is noticeable, the Fermi liquid state in graphene can be stable up to zero temperature avoiding the Kohn–Luttinger mechanism and providing an example of a two-dimensional Fermi liquid at zero temperature.

Phase diagrams of correlated electrons: systematic corrections to the mean fieldtheory

Perturbative corrections to the mean field theory for particle–hole instabilities of interactingelectron systems are computed within a scheme which is equivalent to the recentlydeveloped variational approach to the Kohn–Luttinger superconductivity. This enables anunbiased comparison of particle–particle and particle–hole instabilities within the sameapproximation scheme. A spin-rotation-invariant formulation for the particle–hole instabilitiesin the triplet channel is developed. The method is applied to the phase diagram of thet–t′ Hubbard model on the square lattice. At the Van Hove density, antiferromagnetic andd-wave Pomeranchuk phases are found to be stable close to half filling. However,the latter phase is confined to an extremely narrow interval of densities and,away from the singular filling, d-wave superconducting instability dominates.

Origin of ferromagnetism and nano-scale phase separations in diluted magnetic semiconductors

This paper reviews various origins of ferromagnetic response that has been detected in diluted magnetic semiconductors (DMS). Particular attention is paid to those ferromagnetic DMS in which no precipitation of other crystallographic phases has been observed. It is argued that these materials can be divided into three categories. The first consists of (Ga,Mn)As and related compounds. In these solid solutions the theory built on p–d Zener's model of hole-mediated ferromagnetism and the Kohn–Luttinger kp theory of semiconductors describes quantitatively thermodynamic, micromagnetic, optical, and transport properties. Moreover, the understanding of these materials has provided a basis for the development of novel methods enabling magnetisation manipulation and switching. To the second group belong compounds, in which a competition between long-range ferromagnetic and short-range antiferromagnetic interactions and/or the proximity of the localisation boundary lead to an electronic nano-scale phase separation that results in characteristics similar to colossal magnetoresistance oxides. Finally, in a number of compounds a chemical nano-scale phase separation into the regions with small and large concentrations of the magnetic constituent is present. It has recently been suggested that this spinodal decomposition can be controlled by the charge state of relevant magnetic impurities. This constitutes a new perspective method for 3D self-organised growth of coherent magnetic nanocrystals embedded by the semiconductor matrix.

Controlling the Charge and the Spin Polarization Distributions in (In,Ga,Mn)As-Based Diluted Magnetic Semiconductor Multilayered Structures

A self-consistent Luttinger–Kohn (LK) calculation is used to obtain the electronic structure of Mn-doped semiconductor multilayers. In the particular, case of a (In,Ga)As/GaAs heterostructure, the ternary alloy has a smaller gap than GaAs, and introduces strain due to the differences on the lattice parameters. The aim of this work is to understand how the charge and the spin polarization densities can be controlled by the parameters of the structure in such way that they appear concentrated either on the magnetic or in the non-magnetic region. We show that by changing the In concentration the valence band mismatch competes with the energy splitting due to the magnetic interaction, and we can manipulate the charge and the spin polarization densities in the structure.

On the differential gain in coupled quantum wells

We have analyzed the combined self-consistent and well coupling effects on differential gain in quantum wells within the self-consistent solution of the Poisson, Schrödinger, and 4×4 Luttinger–Kohn (LK) equations. The many-body effects of band-gap renormalization, Coulombic scattering interactions, and a non-Markovian distribution are also included. The analysis has been performed for a 1.55 μm InGaAsP/InP lattice-matched system grown in the [001] direction. The analysis shows that self-consistent effects significantly affect the differential gain.

Temperature dependence of the conductance in diluted magnetic semiconductors

Abstract The effect that the ferromagnetic order has on the electrical properties of the diluted magnetic semiconductors is investigated by analyzing the temperature dependence of the dielectric constant and the resistivity. We use a six band Kohn–Luttinger Hamiltonian, thermal fluctuations are treated in the mean-field approximation, carrier–carrier interaction in the random phase approximation, and transport properties using the relaxation time approximation. Resistivity changes near 20% when going from zero to Curie temperature are obtained in good agreement with experiment. We explain this change in the resistivity in terms of the variation of the Fermi surface and the transport scattering time when going from the ferromagnetic phase to the paramagnetic phase.

A theoretical study of atomistic effects on the quantum hydrodynamics of carriers in decanano semiconductor devices using non-self-averaged Green functions

Recent developments in silicon MOSFET nanoelectronics point the way to devices having channel dimensions in the range down to a few nm. At these atomistic scales only a finite number of impurities occur in the device volume and it is demonstrated that the Kohn–Luttinger self-averaging ansatz and consequently standard Green function perturbation theory must fail. A non-self-averaged T-matrix approach is instead proposed for a model system of randomly distributed hard sphere potentials which utilises the interference between the non-asymptotic exact partial-wave scattering from each impurity using the method of images to build in the effects of confinement by the device boundaries. The quantum hydrodynamic representation is used to discuss the resulting current flows through the model device.

Valence band states in boron delta-doped diamond systems

Valence band ( hh and lh) states in B δ-doped diamond quantum wells are calculated within the effective mass approximation using a local density Thomas-Fermi approximation for the description of the band bending profile. Many-body Hartree, exchange and correlation terms are included in the potential energy well function. The diagonalization of the Kohn–Luttinger Hamiltonian is performed using different sets of Luttinger parameters for diamond reported in the literature. The results could be useful in identifying the actual valence band structure of diamond.

Doping-induced bandgap narrowing in Si rich n- and p-typeSi1−xGex

The shifts of the fundamental and optical bandgap energies as functions ofdopant concentration in heavily n-type and p-type doped Si1−xGex (x ≤ 0.3)have been investigated theoretically. The band structure ofthe intrinsic crystal was described by the k · p-perturbationmethod, where the Kohn–Luttinger parameters were determined froma first-principles and full-potential band-structure calculation. Thedoping-induced effects on the bandgap were thereafter calculated using azero-temperature Green function formalism within the random phaseapproximation and with a local field correction of Hubbard. We found onlysmall effects on the bandgap energies due to variation of compositionx. Thecalculated bandgap narrowing of Si and of Si0.82Ge0.18 were found to be in goodagreement with photoluminescence measurements.

Mean-field theory of magnetic properties of Mn xIII 1− xV semiconductors

We present a mean-field theory of carrier-induced ferromagnetism in Mn x III 1− x V diluted magnetic semiconductors with a special emphasis placed on the magnetic anisotropy. The valence band holes are described using the six band Kohn–Luttinger model. We find that the magnetic anisotropy is a complicated function of sample parameters such as hole density or strain. Results of our numerical simulations are in agreement with magnetic anisotropy measurements on samples with both compressive and tensile strains.

Valence-band structure of undoped and p-doped cubic GaN/InGaN multiple quantum wells

Valence band structure calculations of cubic GaN/In x Ga 1− x N quantum wells and superlattices are presented, in which coupling between the heavy-, light-, and spin–orbit-split-hole bands, strain effects due to lattice mismatch, and the difference in the parameters due to the materials forming the heterostructures are considered. The calculations are performed within a self-consistent approach to the k· p theory by means of a full six-band Luttinger–Kohn (LK) Hamiltonian. The effects of different materials are taken into account explicitly through the inclusion of different sets of Luttinger parameters and by considering the corresponding additional LK matrix elements, not present in the one-material based heterostructures. Our results show that strain effects and the inclusion of the split-off band play a fundamental role in a realistic description of the valence band structure in these systems. Due to the large difference in hole effective masses, for p-doped systems we find that only heavy-hole bands are occupied in the well.

Luttinger Revisited—The Renormalization Group Approach

Luttinger's contributions abound in different parts of many-body physics. Here I review the ones that appear when one uses the Renormalization Group (RG) to study the subject: the Luttinger Liquid, Luttinger's Theorem (on the volume of the Fermi surface) and the Kohn–Luttinger Theorem on the superconducting instability of all metals as one approaches absolute zero.

Critical temperature and phase diagram for a 2D superfluid Fermi gas with repulsion

In the framework of a 2D Fermi gas with short-range repulsive interaction we find the critical temperature of the superfluid phase transition based on Kohn–Luttinger effect, and analyze its dependence on magnetic field. We calculate strong coupling corrections to the Ginzburg–Landau free energy functional and analyze the stability of 2D superfluid phases. Possible applications of the results to real systems are discussed.

Well-coupling and band-mixing effects on differential gain of coupled quantum wells

The structural effect of coupling between quantum wells on differential gain is analyzed. Band-mixing effects within the Luttinger–Kohn (LK) effective mass equation are rigorously included. The analysis is performed for a GaAs/Al0.3Ga0.7As system. It shows that well coupling enhances the differential gain for narrow quantum wells (30 Å) for barriers within the range of 20–50 Å depending on carrier concentration. For wide wells (100 Å), the increase of differential gain is observed only for barriers thinner than 10 Å. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 21: 282–286, 1999.

Magneto-optical investigations on cubic GaN in high magnetic fields

We report on direct IR–cyclotron resonance (CR) spectra of p-type cubic GaN (c-GaN) using semidestructive single-turn coil megagauss field generation. Two strong temperature dependent CR transitions were detected using measurement techniques with optimized signal to noise ratio resolving transmission changes smaller then 2%. On the basis of group theoretical relations between the valence-band energy-parameters of the effective Rashba–Sheka–Pikus Hamiltonian for the wurtzite and the effective Kohn–Luttinger Hamiltonian for the zincblende structure the Landau level scheme was calculated for c-GaN and compared with the observed transitions.

Channel effective mass and interfacial effects in Si and SiGe metal-oxide-semiconductor field effect transistor: A charge control model study

We present results of a numerical formalism developed to address the band structure and charge control problem in n- and p-type silicon and silicon-germanium metal-oxide-semiconductor field effect transistors. We focus on the following issues: (i) the dependence of the in-plane carrier effective mass on sheet charge density and germanium content; (ii) the fraction of charge near the interface and the evaluation of the interface roughness matrix element. Results are compared to existing models. For n-type structure, the effective mass approximation and deformation potential theory is used to describe the electron states. However, for p-type structure, a six-band k⋅p Kohn–Luttinger formulation is used to describe the hole states due to the strong coupling of heavy-hole, light-hole, and split-off bands. This allows us to examine the influence of the coupling of the heavy-hole, light-hole, and the split-off bands.

Band alignment in Si1−yCy/Si(001) heterostructures

Photoluminescence peak energy shifts under applied [110] and [100] uniaxial stress are interpreted within the framework of a multi-band Kohn–Luttinger model which takes into account the mixing of heavy, light, and spin-orbit split-off holes within the valence band. Experimental data are presented for 0.5%, 1%, and 1.7% Si1−yCy/Si samples which are best fitted with a conduction band offset of approximately 70%. At this value of the conduction band offset, we show that small amounts of space charge induced band bending are required to explain the experimentally observed results.

Valence subband structure of 〈011〉-oriented quantum wells

We present semianalytical calculations of the valence subband structure for 〈011〉-oriented quantum wells of cubic semiconductors. Working in the Kohn–Luttinger formalism [Phys. Rev. 97, 869 (1955)], we present analytic expressions for the effective mass tensor and show the full subband dispersion for GaAs and InAs. In addition to the usual extremum at k∥=0, 〈011〉-oriented wells support saddle point spectra. In this case, the effective mass changes sign as a function of in-plane crystallographic direction.

Thermal averaging in quantum many-body systems: a non-perturbative thermal cluster cumulant approach

We present here a non-perturbative cluster cumulant approach for effecting thermal averaging in quantum-mechanical observables. We introduce a new representation of thermo field dynamics (TFD), with the associated thermal normal order and Wick expansion, and replace the thermal averaging by a quantum mechanical one involving a thermal “base state” |0 β〉. Unlike the traditional TFD, only the physical variables appear in our formulation. The imaginary time evolution of the statistical operator is treated by our recently developed time-dependent coupled cluster theory. The partition function Z is evaluated as a completely contracted quantity involving |0 β〉. We have computed Z for an anharmonic oscillator with quartic perturbation as an illustrative application. We also demonstrate numerically the validity of the Kohn—Luttinger theorem.