Kane Model Research Articles

The role of exchange interaction in nonradiative energy transfer between semiconductor quantum dots

The contribution of exchange interaction to the probability of nonradiative energy transfer between two (donor and acceptor) semiconductor quantum dots based on A3B5 compounds has been analyzed using the Kane model of energy-band structure. It is established that the dependence of the exchange contribution on the distance between donor and acceptor centers has a power character for nearly contact distances and acquires an exponential character when the distance increases. Numerical calculations showed that the exchange contribution is comparable with that of the dipole-quadrupole interaction of quantum dots and is one to two orders of magnitude lower than the contribution of the dipole-dipole interaction at shorter distances.

Modeling of a space flexible probe–cone docking system based on the Kane method

Recent developments in micro- and nano-satellites have attracted the interest of the research community worldwide. Many colleges and corporations have launched their satellites in space. Meanwhile, the space flexible probe–cone docking system for micro- and nano-satellites has become an attractive topic. In this paper, a dynamic model of a space flexible probe–cone docking system, in which the flexible beam technology is applied, is built based on the Kane method. The curves of impact force versus time are obtained by the Lagrange model, the Kane model, and the experimental method. The Lagrange model was presented in the reference and verified by both finite element simulation and experiment. The results of the three methods show good agreements on the condition that the beam flexibility and the initial relative velocity change. It is worth mentioning that the introduction of vectorial mechanics and analytical mechanics in the Kane method leads to a large reduction of differential operations and makes the modeling process much easier than that of the Lagrange method. Moreover, the influences of the beam flexibility and the initial relative velocity are discussed. It is concluded that the initial relative velocity of space docking operation should be controlled to a certain value in order to protect the docking system.

Plasmons due to the Interplay of Dirac and Schrödinger Fermions

We study the interplay between Dirac and Schrödinger fermions in the polarization properties of a two-dimensional electron gas (2DEG). Specifically, we analyze the low-energy sector of narrow-gap semiconductors described by a two-band Kane model. In the context of quantum spin Hall insulators, particularly, in Hg(Cd)Te quantum wells, this model is named the Bernevig-Hughes-Zhang model. Interestingly, it describes electrons with intermediate properties between Dirac and Schrödinger fermions. We calculate the dynamical dielectric function of such a model at zero temperature within random phase approximation. Surprisingly, plasmon resonances are found in the intrinsic (undoped) limit, whereas they are absent-in that limit-in graphene as well as ordinary 2DEGs. Additionally, we demonstrate that the optical conductivity offers a quantitative way to identify the topological phase of Hg(Cd)Te quantum wells from a bulk measurement.

A TCAD and Spectroscopy Study of Dark Count Mechanisms in Single-Photon Avalanche Diodes

It is shown through dark count rate spectroscopy (DCRS) and TCAD-simulations that in single-photon avalanche diodes (SPADs), the majority of low dark count rate (DCR) devices in modern CMOS arrays are free of deep-level traps and that DCR can therefore be explained by saturation current and band-to-band tunneling (BTBT). The DCRS performed on the Megaframe 32 × 32 show that the activation energies for the high DCR devices are consistent with a single type of defect at ≈ 0.44 eV, thought to be the E-center, in differing electric fields. Calibrated TCAD-simulated reverse bias leakage currents are orders of magnitude lower than those measured due to the lack of parasitic leakage paths but give theoretical DCRS that are close to the measured values for four different SPAD designs and predict the voltage dependence at high fields. The coefficients for Kane's indirect tunneling model in the [100] direction are determined as A ≈ 2×1015 cm-3/s and B ≈ 2.39×107 V/cm through TCAD calibration, DCR measurement, and theory. It is found that indirect BTBT dominates the DCR of SPADs with low breakdown voltages.

A perfect lens for ballistic electrons: An electron-light wave analogy

The analogy between electromagnetic waves and ballistic electrons within the Kane's model is developed and subsequently applied to a theoretical description of a quantum version of a metamaterial planar lens. Restrictions imposed on the perfect lens and the poor man's lens by available semiconductor band structures are discussed. A realistic implementation is proposed for the quantum poor man's lens, which uses specific properties of the HgTe compound. The properties of the lens are presented on the basis of a calculated transmission of oblique electrons through the lens structure.

Electronic-spin generation in multi-photon processes: Cubic anisotropy of pumping

We study the spin generation in multi-photon absorption processes in a bulk semiconductor, pumped it by a circularly polarized intense light by varying the angle of incidence. The generated spin polarization is calculated using the eight-band Kane model in the limit of large spin–orbit splitting and on the basis of the multi-photon photo-generation rate of the conduction electron spin density. It is found that the spin polarization strongly depends on the pumping photon energy outside the band edge. Cubic anisotropy in crystal pumping is also calculated. The results show that due to this anisotropy the spin generation differs by ∼8%, in consistence with earlier results obtained by others.

Optical band gap and the Burstein–Moss effect in iodine doped PbTe using diffuse reflectance infrared Fourier transform spectroscopy

Optical absorption edge measurements are performed on I doped PbTe using diffuse reflectance infrared Fourier transform spectroscopy. The Burstein–Moss shift, an increase in the absorption edge (optical band gap) with increasing doping level, is explored. The optical gap increases on the order of 0.1 eV for doping levels ranging from 3 × 1018 to 2 × 1020 cm−3, relevant doping levels for good thermoelectric materials. Chemical potential is estimated from transport measurements—specifically, Hall effect and Seebeck coefficient—using a single band Kane model. In heavily doped semiconductors, it is well-known that the band gap shrinks with increasing doping level. This effect, known as band gap renormalization, is fit here using an n1/3 scaling law which reflects an electron–electron exchange interaction. The renormalization effect in these samples is shown to be more than 0.1 eV, on the same order of magnitude as the band gap itself. Existing models do not explain such large relative changes in band gap and are not entirely self-consistent. An improved theory for the renormalization in narrow gap semiconductors is required.

Interband electrooptical transitions in InSb quantum well

On the example of the quantized film InSb in the frame of two-band Kane model, the influence of an external uniform electric field on the interband optical absorption in a narrow-gap semiconductor quantum well is theoretically studied. Absorption coefficients of interband electrooptical transitions in the well for different intervals of values of the external field are analytically calculated. We also consider the effect of nonparabolicity law of the dispersion of light charge carriers in the narrow-band film on the threshold frequency of the interband transitions and the frequency dependence of the electroabsorption coefficient.

SiGe Band-to-Band Tunneling Calibration based on p-i-n Diodes: Fabrication, Measurement and Simulation

For the purpose of calibrating the nonlocal Kane band-to-band tunneling model for Si1-xGex based on TCAD simulations, SiGe p-i-n tunnel diodes are fabricated by epitaxial growth. The quality of the tunnel junction is examined by the ideality factors of the diodes and the band-to-band tunneling regime is determined based on activation energy extractions. By comparing experimental data to simulations with theoretically calculated prefactors of Kane's model, we conclude that the TCAD simulator overestimates the tunneling current in strained Si1-xGex diodes.

Renormalization of spin-rotation coupling

We predict the enhancement of the spin-rotation coupling due to the interband mixing. The Bloch wavefunctions in the presence of mechanical rotation are constructed with the generalized crystal momentum which includes a gauge potential arising from the rotation. Using the eight- band Kane model, the renormalized spin-rotation coupling is explicitly obtained. As a result of the renormalization, the rotational Doppler shift in electron spin resonance and the mechanical torque on an electron spin will be strongly modulated.

Magnetospectroscopy of two-dimensional HgTe-based topological insulators around the critical thickness

Recently, a new class of materials, so-called topological insulators, has emerged. These are systems characterized by the inversion of the electronic band structure and also by a certain strength of the spin-orbit interaction. HgTe/Cd${}_{x}$Hg${}_{1\ensuremath{-}x}$Te quantum wells represent a prominent example. They can change to the topological insulator phase from the conventional insulator phase when the thickness of the quantum well is increased over the critical thickness ${d}_{c}$ = 6.3 nm. Here, we report on a far-infrared magnetospectroscopy study of a set of HgTe/Cd${}_{x}$Hg${}_{1\ensuremath{-}x}$Te quantum wells with different thicknesses from below to above the critical value ${d}_{c}$. In quantizing magnetic fields up to 16 T, both intraband and interband transitions have been clearly observed. In the widest quantum well with inverted band structure, we confirm the avoided crossing of the zero-mode Landau levels observed earlier in similar structures. In both noninverted quantum wells close to the critical thickness, we report unambiguously on the square root dependence of the transition energy on the magnetic field, as expected in the single-particle model of massless Dirac fermions. The obtained results are compared with the allowed transition energies between Landau levels in the valence and conduction bands calculated using the 8 \ifmmode\times\else\texttimes\fi{} 8 Kane model.

Cyclotron resonance in HgTe/CdTe(013) narrowband heterostructures in quantized magnetic fields

Electron cyclotron resonance in HgTe/CdTe(013)-based narrowband heterostructures with a noninverted band structure in quantized magnetic fields has been investigated at different electron concentrations. Cyclotron transitions from the lower Landau levels of the conduction band have been discovered. The Landau levels have been calculated in the Kane model with the inclusion of strain. Comparison with the experimental data indicates that the energies of the observed cyclotron resonances are systematically higher than the calculated ones.

Optical transitions in Cd x Hg1 − x Te-based quantum wells and their analysis with account for the actual band structure of the material

Quantum-confinement levels in a CdxHg1 − xTe-based rectangular quantum well are calculated in the framework of the four-band Kane model taking into account mixing between the states of electrons and three types of holes (heavy, light, and spin-split holes). Comparison of the calculation results with experimental data on the photoluminescence of CdxHg1 − xTe-based quantum wells suggests that optical transitions involving the conduction and light-hole bands are possibly observed in the spectra.

Optoelectronic properties of InAs/GaSb superlattices with asymmetric interfaces

In this work the optoelectronic properties of InAs/GaSb superlattices are investigated. The k∙p method and four-band Kane model were used to calculate the electronic states in the structure at 0K. Superlattices with different period thickness and two types of interfaces were considered. In the calculations strain and nonparabolicity effects were taken into account. Transition energies and the corresponding cut-off wavelengths were determined.

Steady state and transient electron transport properties of bulk dilute GaNxAs1−x

Two valley ensemble Monte Carlo simulations have been performed to investigate the electronic transport properties of bulk GaNxAs1−x alloys where the nitrogen concentration x ≤ 0.02 (2%). We have investigated these properties using two separate approaches, 1) through simulation of GaAs using the standard Kane model with the addition of isolated and pair state nitrogen scattering mechanisms and 2) approximating the lower “mixed state” band that arises from the use of band-anticrossing model with an analytic function that implements the inflection point (for concentrations >1%). From the steady-state properties, we find that the nitrogen scattering model produces a better fit with other results, both theoretical and experimental. We also comment on the transient properties of GaNxAs1−x, noting that the velocity overshoot peaks are of a much lower velocity than is found in GaAs at comparable field strengths, and through the use of model 2, that negative effective mass states have a significant role in the transient behavior. We find that the system takes much longer to reach equilibrium when compared to bulk GaAs in both models, and through the use of model 2, there is a significant population of negative effective mass states when the system is subjected to higher fields.

Radiative recombination of hot carriers in narrow-gap semiconductors

The mechanism of the radiative recombination of hot carriers in narrow-gap semiconductors is analyzed using the example of indium antimonide. It is shown that the CHCC Auger recombination process may lead to pronounced carrier heating at high excitation levels. The distribution functions and concentrations of hot carriers are determined. The radiative recombination rate of hot carriers and the radiation gain coefficient are calculated in terms of the Kane model. It is demonstrated that the radiative recombination of hot carriers will make a substantial contribution to the total radiative recombination rate at high carrier concentrations.

Rashba and Dresselhaus spin-orbit interaction strength in GaAs/GaAlAs heterojunctions

Abstract Using a recently developed variational theory for the spin split subbands, we investigate the relative strength of the Rashba and Dresselhaus spin orbit terms in GaAs/GaAlAs heterojunctions. The envelope function formalism is employed using the 8-band k · p Kane model for the bulk, and the Rashba split subbands are obtained with spin-dependent trial functions. The total spin splitting is then calculated analytically by including also the bulk Dresselhaus contribution via quasi-degenerate first order perturbation theory. The total spin-orbit splitting at the Fermi energy of the two dimensional electron gas (2DEG) is calculated as a function of the direction of the Fermi wave-vector. The obtained total spin-orbit splittings along [11] and [1 o 1] in-plane directions are shown to be in good agreement with recent experiments. The well known ratio α/β between the Rashba and Dresselhaus contributions is a fundamental parameter in dierent proposals for new semiconductor spintronic devices. Due to barrier penetration and the corresponding spin dependent boundary conditions, the total spin-orbit anisotropy calculated here is shown to be in general determined by more then one parameter, and thus the above ratio should not be estimated using the common α and β = k 2 > z expressions.

Cyclotron resonance and interband optical transitions in HgTe/CdTe(0 1 3) quantum well heterostructures

Cyclotron resonance spectra of 2D electrons in HgTe/CdxHg1−xTe (0 1 3) quantum well (QW) heterostructures with inverted band structure have been thoroughly studied in quasiclassical magnetic fields versus the electron concentration varied using the persistent photoconductivity effect. The cyclotron mass is shown to increase with QW width in contrast to QWs with normal band structure. The measured values of cyclotron mass are shown to be systematically less than those calculated using the 8 × 8 Kane model with conventional set of HgTe and CdTe material parameters. In quantizing pulsed magnetic fields (Landau level filling factor less than unity) up to 45 T, both intraband (CR) and interband magnetoabsorption have been studied at radiation wavelengths 14.8 and 11.4 µm for the first time. The results obtained are compared with the allowed transition energies between Landau levels in the valence and conduction bands calculated within the same model, the calculated energies being again systematically less (by 3–14%) than the observed optical transition energies.

Band-mixing-mediated Andreev reflection of semiconductor holes

We have investigated Andreev-reflection processes occurring at a clean interface between a $p$-type semiconductor and a conventional superconductor. Our calculations are performed within a generalized Bogoliubov-de Gennes formalism where the details of the semiconductor band structure are described by a $6\times 6$ Kane model. It is found that Andreev reflection of light-hole and heavy-hole valence-band carriers is generally possible and that the two valence-band hole types can be converted into each other in the process. The normal-reflection and Andreev-reflection amplitudes depend strongly on the semiconductor's carrier concentration and on the angle of injection. In the special case of perpendicular incidence, Andreev reflection of heavy holes does not occur. Moreover, we find conversion-less Andreev reflection to be impossible above some critical angle, and another critical angle exists above which the conversion of a heavy hole into a light hole cannot occur.

Metamaterial-inspired perfect tunnelling in semiconductor heterostructures

In this paper, we use a formal analogy of the electromagnetic wave equation and the Schrödinger equation in order to study the phenomenon of perfect tunnelling (tunnelling with unitary transmittance) in a one-dimensional semiconductor heterostructure. Using the Kane model of a semiconductor, we show that this phenomenon can indeed exist, resembling all the interesting features of the corresponding phenomenon in classical electromagnetism in which metamaterials (substances with negative material parameters) are involved. We believe that these results can pave the way toward interesting applications in which metamaterial ideas are transferred into the semiconductor domain.