Kane Model Research Articles

Analytical modeling of III-V heterojunction source-all-around vertical tunnel FET and its inverter circuit application

Abstract This paper presents a comprehensive analytical modeling framework for the III-V heterojunction source-all-around vertical tunnel field-effect transistor (SAA V-TFET). Using Kane's model, our approach involves solving Poisson's equations to obtain a continuous surface potential profile, followed by the derivation of drain current. These models demonstrate excellent accuracy across all operating regions, precisely predicting the potential profile, output, and transfer characteristics of SAA V-TFETs. We implemented the models in MATLAB and validated them against Sentaurus TCAD simulations. Furthermore, we present a comprehensive performance analysis of SAA V-TFET-based digital inverters.

Influence of Mixing Valence Band States to the Conduction Band States on Two-Quantum Linear-Circular Dicroism in Semiconductors

A quantitative theory of two-photon linear-circular dichroism caused between the subbands of light and heavy holes of the valence band and conduction band is constructed, which takes into account the admixture of valence band states to the conduction band states and the temperature dependence of the band gap (Eg(T)) in semiconductors of tetrahedral symmetry in the multiband Kane model. It is shown that the type of oscillatory angular dependence or the amplitude values of the probabilities of two-photon optical transitions depend on the state of light polarization. This is due to the fact that, under the influence of linearly polarized light, alignment along the pulse occurs, and under the action of circularly polarized light, the moments of current carriers are oriented. It has been determined that the probability of two-photon optical transitions from the heavy hole subband to the conduction band of semiconductors at a fixed temperature increases with increasing frequency, passes through a maximum, and sharply decreases regardless of the degree of polarization of light, as well as the band gap.

Position operators and interband matrix elements of scalar and vector potentials in the 8-band Kane model

We diagonalize the 8-band Kane Hamiltonian with a proper inclusion of the interband matrix elements of the scalar and vector potentials. This leads, among other results, to a modification of the conventional expression for the spin-orbit coupling (SOC) strength in narrow-gap semiconductors with the zinc blende symmetry. We find that in GaAs, at low temperatures, the correct expression for the SOC strength is actually twice as large as usually considered. In InSb it is 1.761.76 times larger. We also provide a proper treatment of the interband matrix elements of the position operator. We show that the velocity operator in a crystal should be defined as a time-derivative of a fictitious position operator rather than the physical one. We compute the expressions for both these position operators projected to the conduction band of the 8-band Kane model. We also derive an expression for the projected velocity operator and demonstrate that the SOC strength in it differs from the SOC strength in the Hamiltonian. The ratio between them is not equal to 11, as it is often assumed for the Rashba model. It does not equal 22 either. The correct result for this ratio is given by a rational function of the parameters of the model. This function takes values between 4(23+3\sqrt{2})/73≈ 1.494(23+32)/73≈1.49 and 22. Our findings modify a vast number of research results obtained using the Rashba model and provide a path for consistent treatment of the latter in future applications.

Rethinking the consultation paradigm: Validity evidence for a new framework, a multimethods study.

In-hospital consultation is essential for patient care. We previously proposed a framework of seven specific consultation types to classify consult requests to improve communication, workflow, and provider satisfaction. This multimethods study's aim was to evaluate the applicability of the consult classification framework to real internal medicine (IM) consults. We sought validity evidence using Kane's validity model with focus groups and classifying consult requests from five IM specialties. Participants attended five 1 h semi-structured focus groups that were recorded, transcribed, and coded for thematic saturation. For each specialty, three specialists and three hospitalists categorized 100 (total 500) random anonymized consult requests. The primary outcome was concordance in the classification of consult requests, defined as the sum of partial concordance and perfect concordance, where respectively 4-5/6 and 6/6 participants classified a consult in the same category. We used χ2 tests to compare concordance rates across specialties and between specialists and hospitalists. Five major themes were identified in the qualitative analysis of the focus groups: (1) consult question, (2) interpersonal interactions, (3) value, (4) miscommunication, (5) consult framework application, barriers, and iterative development. In the quantitative analysis, the overall concordance rate was 88.8% (95% confidence interval [CI]: 85.7-91.4), and perfect concordance was 46.6% (95% CI: 42.2-51.1). Concordance differed significantly between hospitalists and specialists overall (p = .01),with a higher proportion of hospitalists having perfect concordance compared to specialists (67.2% vs. 57.8%, p = .002). The consult classification framework was found to be applicable to consults from five different IM specialties, and could improve communication and education.

Driven electron g-factor anisotropy in layered III–V semiconductors: Interfacing, tunnel coupling, and structure inversion asymmetry effects

A key piece for spintronic applications, the so-called electron g-factor engineering is still predominantly based on the semiconductor bulk g factor and its dependence on the bandgap energy. In nanostructures, however, the mesoscopic confinement introduces exclusive anisotropies, transforming scalar g factors into tensors, enabling different renormalization mechanisms as routes for fine-tuning the electron g factor. These questions we address in this comparative theoretical analysis between the obtained electron g-factor (tensor) anisotropies for realistic InAs|AlSb- and In0.53Ga0.47As|InP-based multilayers. The electron g-factor anisotropy, i.e., the difference between g factors for magnetic fields parallel and perpendicular to the interfaces, is analytically calculated via perturbation theory using the envelope-function approach based on the eight-band Kane model. Effects from bulk, interfacing, tunnel coupling, and structure inversion asymmetry are systematically introduced within a transparent comparative view; differences between obtained anisotropies, such as in the magnitude, sign, and other fine details, are analyzed in terms of the heterostructure parameters, mapped over different confining and tunnel-coupling regimes without requiring elaborated numerical computations.

Dimensional quantization in InSb and GaAs in three-zone model

Various cases of size quantization in narrow-gap crystals of cubic or tetrahedral symmetry in the three-band Kane approximation are analyzed. Expressions for the energy spectrum depending on the two-dimensional wave vector are obtained for two different cases, differing in the range of current carrier energy values. The size-quantized energy spectrum of electrons in the conduction band and holes in the subband of light holes in InSb and GaAs semiconductors is analyzed in the three-band Kane model.

To the theory of dimensional quantization in crystals in the Kane approximation

The microscopic mechanism of size quantization of the conduction band and valence band of semiconductors of cubic and tetrahedral symmetry has been theoretically studied in the Kane approximation. It is shown that the matrix Schrödinger equation obtained on the basis of the Kane model cannot be solved analytically for a potential well of an arbitrary profile. Therefore, expressions for the energy spectrum are obtained depending on the two-dimensional wave vector directed along the interface of the heterostructure for various cases that differ in the range of current carrier energy values.

To the Theory of Dimensional Quantization in Narrow-Gap Crystals

This article discusses studies of size quantization phenomena in zero-, one-, and two-dimensional semiconductor structures. The main attention is paid to the mechanisms of photon-kinetic effects in these structures. Despite many studies of the physical properties of low-dimensional systems of current carriers, the size quantization of energy spectra in narrow-gap semiconductors and the associated photonic-kinetic effects are still insufficiently studied. Therefore, this study focuses on the quantum mechanical study of size quantization in certain cases using Kane's multiband model. The insolvability of the 8×8 matrix Schrödinger equation in the Kane model for a potential well of arbitrary shape is analyzed. The dependence of the energy spectrum on the two-dimensional wave vector is studied for various cases. In particular, the energy spectra for InSb and GaAs semiconductors are considered, depending on the band parameters and the size of the potential well. Conclusions are presented on the analysis of various cases of size quantization in narrow-gap crystals with cubic or tetrahedral symmetry in the three-band approximation. It is shown that the energy spectrum corresponds to a set of size-quantized levels that depend on the Rabi parameter, band gap, and well size. The size-quantized energy spectra of electrons and holes in InSb and GaAs semiconductors are analyzed in a multiband model.

A physics-based model of dielectric modulated TFET biosensor considering non-ideal hybridization issue

This article investigates the functionality of Dielectric Modulated-Tunnel Field Effect Transistor (DM-TFET) based biosensor using an analytical model created for the electrostatic potential, electric field and drain current. Channel potential and electric field are determined by solving the 2-D Poisson's equation using the parabolic approximation approach. The drain current is estimated by calculating the generation rate of tunneling using Kane's model. The model illustrates the implications of dielectric constant (k) and charge (NBio) and provides a generic solution that works for both neutral and charged biomolecules. The effect of different biasing conditions and parametric variations on electrical properties of the channel is also studied. Capacitances are modeled for different fill factors of biomolecules entrapped in the cavity region. The model demonstrates its resilience by reacting to different fill factors. The analytical findings are validated using data from SILVACO ATLAS simulations. The comparative sensitivity analysis presented highlights the improvement provided by our proposed work.

Unusual Transport and Impact of Nonparabolic Electronic Band Structure on the Thermoelectric Performance in n‐Type In4Se3‐Based Thermoelectric Materials

Unusual thermoelectric (TE) transport in n‐type In4Se3 has been reported in the context of first‐principles electronic structure calculation and Boltzmann transport theory. The density of states (DOS) shows certain peaks due to a nontopological Mexican hat and parabolic capping around the edges of Kane bands. The effect of such hard shifts of bands shows anomalously high Seebeck coefficient (S = 550 μV K−1 at ≈1017 cm−3) at room temperature due to very slow decreasing S and rapidly increasing DOS effective mass with carrier concentration compared to that obtained from Kane and parabolic band model. The best TE performance is predicated in Kane transport region (≈1018 cm−3) over the wide range of temperature, 300–700 K. The calculated values of relaxation time (≈10−14 s at 660 K), electrical conductivity, power factor and figure of merit in iodine‐doped sample and those obtained from the rigid band model of pure sample show excellent agreement with the reported experimental results.

Interband Electron Transitions Energy in Multiple HgCdTe Quantum Wells at Room Temperature

The studies of the interband electron transition energy in multiple Hg1-xCdxTe/Hg1-yCdyTe quantum wells (MQWs) at room temperature were carried out. The MQWs were grown on the (013) GaAs substrate by molecular beam epitaxy, with the layer composition and thickness being measured by the in-situ ellipsometric parameters measurement at the nanometer level. The Hg1-xCdxTe barrier composition and width were x = 0.69 and 30 nm, respectively. The Hg1-yCdyTe well composition was y = 0.06–0.10, and the width varied in the range of 2.7–13 nm. The experimental data of the interband electron transition energy were determined by the absorption spectral analysis. The calculation of the interband electron transition energy was carried out on the basis of the four-band Kane model. A good agreement between the experimental and calculated data was obtained. It was shown that MQWs may be used as a photosensitive material for creating infrared optoelectronic devices operating in different modes in the range of 3–10 μm at room temperature.

Charge transport modelling of perovskite solar cells accounting for non-Boltzmann statistics in organic and highly-doped transport layers

We present a drift–diffusion model of a perovskite solar cell (PSC) in which carrier transport in the charge transport layers (TLs) is not based on the Boltzmann approximation to the Fermi–Dirac (FD) statistical distribution, in contrast to previously studied models. At sufficiently high carrier densities the Boltzmann approximation breaks down and the precise form of the density of states function (often assumed to be parabolic) has a significant influence on carrier transport. In particular, parabolic, Kane and Gaussian models of the density of states are discussed in depth and it is shown that the discrepancies between the Boltzmann approximation and the full FD statistical model are particularly marked for the Gaussian model, which is typically used to describe organic semiconducting TLs. Comparison is made between full device models, using parameter values taken from the literature, in which carrier motion in the TLs is described using (I) the full FD statistical model and (II) the Boltzmann approximation. For a representative TiO2/MAPI/Spiro device the behaviour of the PSC predicted by the Boltzmann-based model shows significant differences compared to that predicted by the FD-based model. This holds both at steady-state, where the Boltzmann treatment overestimates the power conversion efficiency by a factor of 27%, compared to the FD treatment, and in dynamic simulations of current–voltage hysteresis and electrochemical impedance spectroscopy. This suggests that the standard approach, in which carrier transport in the TLs is modelled based on the Boltzmann approximation, is inadequate. Furthermore, we show that the full FD treatment gives a more accurate representation of the steady-state performance, compared to the standard Boltzmann treatment, as measured against experimental data reported in the literature for typical TiO2/MAPI/Spiro devices.

Fourier-transform infrared photoreflectance spectroscopy of the InSb/InAs/In(Ga,Al)As/GaAs metamorphic heterostructures with a superlattice waveguide

Fourier-transform infrared photoreflectance (PR) spectroscopy was used to study the energy spectrum of InSb/InAs/In(Ga,Al)As/GaAs metamorphic heterostructures with a superlattice waveguide at room temperature (RT). Theoretical calculations in the framework of the eight-band Kane model were performed to obtain a reliable knowledge of the actual energies of the most probable optical transitions. The experimental results were analyzed to determine the influence of the design features and stress balance on the energy spectra of the structures. Photoluminescence studies performed at 11 K and RT, as well as the determination of the internal quantum efficiency of luminescence, enabled us to characterize the emission characteristics of the structures, regardless of their waveguide efficiency. The structure with a 5-nm-thick GaAs insertion within the metamorphic buffer layer exhibited the highest probability of the main optical transition observed in the PR spectra as well as the highest luminescence intensity and quantum efficiency.

NONLINEAR ABSORPTION OF POLARIZED RADIATION IN CRYSTALS WITH A COMPLEX BAND

The matrix elements of one- and two-photon optical transitions from the subbands of the valence band and the spin-orbital splitting band to the conduction band are calculated, expressions are obtained for them depending on the polarization vector and light frequency, as well as on the band parameters of the crystal. Expressions are obtained for the spectral-polarization and spectral-temperature dependences of the coefficients of interband two-photon absorption of light and linear-circular dichroism in semiconductors of tetrahedral symmetry in the three-band Kane model. It is shown that in the spectral-polarization dependence of the total coefficient of two-photon absorption of linearly and circularly polarized light in InSb: firstly, all spectral-polarization dependences have an oscillatory character; secondly, as the light frequency increases, the oscillation amplitude increases; thirdly, for circularly polarized light, the oscillation becomes aperiodic. KEYWORDS: spectral, temperature and polarization dependence, optical transitions, linear-circular dichroism, two-photon absorption of linearly and circularly polarized light.

Ultralow Lattice Thermal Conductivity and Improved Thermoelectric Performance in Cl-Doped Bi2Te3-xSex Alloys.

Bi2Te3-based alloys are the main materials for the construction of low- and medium-temperature thermoelectric modules. In this work, the microstructure and thermoelectric properties of Cl-doped Bi2Te3–xSex alloys were systematically investigated considering the high anisotropy inherent in these materials. The prepared samples have a highly oriented microstructure morphology, which results in very different thermal transport properties in two pressing directions. To accurately separate the lattice, electronic, and bipolar components of the thermal conductivity over the entire temperature range, we employed a two-band Kane model to the Cl-doped Bi2Te3–xSex alloys. It was established that Cl atoms act as electron donors, which tune the carrier concentration and effectively suppress the minority carrier transport in Bi2Te3–xSex alloys. The estimated value of the lattice thermal conductivity was found to be as low as 0.15 Wm–1 K–1 for Bi2Te3–x–ySexCly with x = 0.6 and y = 0.015 at 673 K in parallel to the pressing direction, which is among the lowest values reported for crystalline materials. The large reduction of the lattice thermal conductivity in both pressing directions for the investigated Bi2Te3–xSex alloys is connected with the different polarities of the Bi-(Te/Se)1 and Bi-(Te/Se)2 bonds, while the lone-pair (Te/Se) interactions are mainly responsible for the extremely low lattice thermal conductivity in the parallel direction. As a result of the enhanced power factor, suppressed bipolar conduction, and ultralow lattice thermal conductivity, a maximum ZT of 1.0 at 473 K has been received in the Bi2Te2.385Se0.6Cl0.015 sample.

Engineering topological phases in triple HgTe/CdTe quantum wells

Quantum wells formed by layers of HgTe between Hg_{1-x}Cd_xTe barriers lead to two-dimensional (2D) topological insulators, as predicted by the BHZ model. Here, we theoretically and experimentally investigate the characteristics of triple HgTe quantum wells. We describe such heterostructure with a three dimensional 8times 8 Kane model, and use its eigenstates to derive an effective 2D Hamiltonian for the system. From these we obtain a phase diagram as a function of the well and barrier widths and we identify the different topological phases composed by zero, one, two, and three sets of edge states hybridized along the quantum wells. The phase transitions are characterized by a change of the spin Chern numbers and their corresponding band inversions. Complementary, transport measurements are experimentally investigated on a sample close to the transition line between the phases with one and two sets of edges states. Accordingly, for this sample we predict a gapless spectrum with low energy bulk conduction subbands given by one parabolic and one Dirac subband, and with edge states immersed in the bulk valence subbands. Consequently, we show that under these conditions, local and non-local transport measurements are inconclusive to characterize a sole edge state conductivity due to bulk conductivity. On the other hand, Shubnikov-de Haas (SdH) oscillations show an excellent agreement with our theory. Particularly, we show that the measured SdH oscillation frequencies agrees with our model and show clear signatures of the coexistence of a parabolic and Dirac subbands.

Impact of Band Anticrossing on Band-to-Band Tunneling in Highly Mismatched Semiconductor Alloys

We theoretically analyze band-to-band tunneling (BTBT) in highly mismatched, narrow-gap dilute nitride and bismide alloys, and quantify the impact of the $\mathrm{N}$- or $\mathrm{Bi}$-induced perturbation of the band structure---due to band anticrossing (BAC) with localized impurity states---on the electric-field-dependent BTBT generation rate. For this class of semiconductors, the assumptions underpinning the widely employed Kane model of BTBT break down, due to strong band-edge nonparabolicity resulting from BAC interactions. Via numerical calculations based on the Wentzel-Kramers-Brillouin approximation we demonstrate that BAC leads, at fixed band gap, to reduced (increased) BTBT current at low (high) applied electric field compared to that in a conventional ${\mathrm{In}\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$ alloy. Our analysis reveals that BTBT in ${\mathrm{In}\mathrm{N}}_{x}{\mathrm{As}}_{1\ensuremath{-}x}$ and ${\mathrm{In}\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{Bi}}_{x}$ is governed by a field-dependent competition between the impact of $\mathrm{N}$ ($\mathrm{Bi}$) incorporation on (i) the dispersion of the evanescent Bloch band linking the valence and conduction band edges, which dominates at low field strengths, and (ii) the conduction- (valence-) band-edge density of states, which dominates at high field strengths. The implications of our results for applications in long-wavelength avalanche photodiodes (APDs) and tunneling field-effect transistors (TFETs) are discussed. For APDs, we describe that leakage currents in ideal dilute nitride and bismide devices are likely comparable to those in devices based on conventional III-V materials, but that the expected reduction of the hole impact ionization rate in ${\mathrm{In}\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{Bi}}_{x}$ is promising from the perspective of obtaining low excess noise factor. For TFETs, we describe that $\mathrm{Bi}$ incorporation provides the potential to obtain both reduced subthreshold swing and increased on-state current, making ${\mathrm{In}\mathrm{As}}_{1\ensuremath{-}x}{\mathrm{Bi}}_{x}$ of interest for the development of low-power, high-speed devices.

Electrostatic characteristics of a high-k stacked gate-all-around heterojunction tunnel field-effect transistor using the superposition principle

We use the superposition method to model the electrostatic characteristics of a high-k stacked gate-all-around heterojunction tunneling field-effect transistor (TFET). The heterojunction is formed from Ge/Si material in the source/channel, respectively. The modeling is accomplished by considering the space-charge regions at the source–channel and drain–channel junctions and in the channel region. The surface potential in the channel region is obtained by applying the superposition principle derived in the source/drain region by solving the two-dimensional (2D) or one-dimensional (1D) Poisson’s equation, respectively. Furthermore, the electric field and the drain current are modeled by using the surface potential and the Kane model, respectively. The results are confirmed using ATLAS technology computer-aided design (TCAD) simulations.

Polarization-spectral dependences of three-photon interband absorption of light and linear-circular dichroism in semiconductors with cubic symmetry

The polarization and frequency-polarization dependences of the linear-circular dichroism and light absorption coefficients in semiconductors of cubic symmetry, caused by vertical three-photon optical transitions between the states of the spin-orbit splitting and conduction bands, are calculated in narrow-gap semiconductors in the Kane model. Keywords: initial, virtual and final states, interband three--photon absorption of light, Kane's approximation.

Межзонный двухфотонный линейно-циркулярный дихроизм в полупроводниках в приближении Кейна

Interband two-photon optical transitions are classified and expressions are obtained for the matrix elements in a narrow-gap semiconductor depending on the band parameters, degree of polarization, and light frequency. It is shown that the main contribution to two-photon linear-circular dichroism in narrow-gap semiconductors is made by optical transitions proceeding from the subband of light holes to the conduction band. The dependences of the partial coefficients of interband two-photon absorption of light, which differ from each other by the types of optical transitions, are analyzed depending on the degree of polarization of the light, and a quantitative analysis of the coefficient of linear-circular dichroism of two-photon absorption of light is carried out. Expressions are obtained for the spectral dependence of the coefficient of interband two-photon absorption of light in narrow-gap semiconductors in the Kane model.