Nonparabolic Band Model Research Articles

High magnetic field effects on transport coefficients in heavily doped n-type Mg2Si

In contrast to parabolic band model typically used in understanding electronic properties in general, thermoelectric and magneto-thermoelectric in particular, this study confirms non-parabolic band model results in better understanding of Seebeck coefficient and Nernst coefficient in the presence of magnetic field for Mg2Si. The magneto Seebeck coefficient was found significantly enhanced from its zero-field value for non-parabolic band model compared to parabolic band model for different electron concentrations in the range 0.6 - 12× 1025/m3 and at room temperature due to the high magnetic field slightly beyond |3|T, but not for others. In both cases, the Seebeck coefficient is enhanced as a result of the magnetic field. The result for Nernst coefficient shows increasing trend in high magnetic field in the range |3-9|T for parabolic band model while it is decreasing with magnetic field on average for non-parabolic band model except for few of them slowly increasing.

Magneto-Thermoelectric Coefficients of Heavily Doped N-Type Mg2Si Material

In contrast to parabolic band model typically used in understanding electronic properties in general, thermoelectric and magneto-thermoelectric in particular, this study confirms non-parabolic band model results in better understanding of Seebeck coefficient and Nernst coefficient in the presence of magnetic field for Mg2Si. The magneto Seebeck coefficient was found significantly enhanced from its zero-field value for different electron concentrations in the range 0.6 ‑ 12×1025/m3 and at room temperature due to the magnetic field in the range 0.2 – 1 T for non-parabolic model compared to parabolic band model. The result for Nernst coefficient shows increasing trend as function of magnetic field except for certain electron concentrations for parabolic band model while it is decreasing with magnetic field on average for non-parabolic band model.

LO-Phonons and dielectric polarization effects on the electronic properties of doped GaN/InN spherical core/shell quantum dots in a nonparabolic band model

The electron energy spectrum of a core/shell spherical quantum dot made of zincblende GaN/InN compounds is investigated taking into account the presence of an off-center donor atom and the influence of band nonparabolicity. The interaction of both the charge carrier and the Coulombic core with longitudinal optical phonons is included through Fro hlich and Aldrich-Bajaj theories, respectively. The ground state energy is determined by solving the resulting conduction band effective mass equation via the variational Ritz principle. A detailed analysis of the features of electron and hole spectra as functions of the core and shell sizes is presented, highlighting the possibility of transitioning between type-I and type-II structures. A detailed discussion about the effects of conduction band nonparabolicity, dielectric mismatch and electron-phonon interaction onto the impurity binding energy is provided. It was found that, in general, nonparabolicity of the conduction band leads to larger impurity binding energy, and that LO-phonon and dielectric mismatch effects tend to reduce the value of the latter quantity.

Current-Temperature Scaling for a Schottky Interface with Nonparabolic Energy Dispersion

In this paper, we study the Schottky transport in narrow-gap semiconductor and few-layer graphene in which the energy dispersions are highly non-parabolic. We propose that the contrasting current-temperature scaling relation of $J\propto T^2$ in the conventional Schottky interface and $J\propto T^3$ in graphene-based Schottky interface can be reconciled under Kane's $\mathbf{k} \cdot \mathbf{p}$ non-parabolic band model for narrow-gap semiconductor. Our new model suggests a more general form of $J\propto \left(T^2 + \gamma k_BT^3 \right)$, where the non-parabolicty parameter, $\gamma$, provides a smooth transition from $T^2$ to $T^3$ scaling. For few-layer graphene, it is found that $N$-layers graphene with $ABC$-stacking follows $J\propto T^{2/N+1}$ while $ABA$-stacking follows a universal form of $J\propto T^3$ regardless of the number of layers. Intriguingly, the Richardson constant extracted from the Arrhenius plot using an incorrect scaling relation disagrees with the actual value by two orders of magnitude, suggesting that correct models must be used in order to extract important properties for many novel Schottky devices.

Comparative study of electron transport mechanisms in epitaxial and polycrystalline zinc nitride films

Zn3N2 has been reported to have high electron mobility even in polycrystalline films. The high mobility in polycrystalline films is a striking feature as compared with group-III nitrides. However, the origins of the high mobility have not been elucidated to date. In this paper, we discuss the reason for high mobility in Zn3N2. We grew epitaxial and polycrystalline films of Zn3N2. Electron effective mass (m*) was determined optically and found to decrease with a decrease in electron density. Using a nonparabolic conduction band model, the m* at the bottom of the conduction band was derived to be (0.08 ± 0.03)m0 (m0 denotes the free electron mass), which is comparable to that in InN. Optically determined intra-grain mobility (μopt) in the polycrystalline films was higher than 110 cm2 V−1 s−1, resulting from the small m*. The Hall mobility (μH) in the polycrystalline films was significantly smaller than μopt, indicating that electron transport is impeded by scattering at the grain boundaries. Nevertheless, μH higher than 70 cm2 V−1 s−1 was achievable owing to the beneficial effect of the high μopt. As for the epitaxial films, we revealed that electron transport is hardly affected by grain boundary scattering and is governed solely by ionized impurity scattering. The findings in this study suggest that Zn3N2 is a high-mobility semiconductor with small effective mass.

Impact of Band Nonparabolicity on Threshold Voltage of Nanoscale SOI MOSFET

This paper reconsiders the mathematical formulation of the conventional nonparabolic band model and proposes a model of the effective mass of conduction band electrons including the nonparabolicity of the conduction band. It is demonstrated that this model produces realistic results for a sub-10-nm-thick Si layer surrounded by an SiO2layer. The major part of the discussion is focused on the low-dimensional electron system confined with insulator barriers. To examine the feasibility of our consideration, the model is applied to the threshold voltage of nanoscale SOI FinFETs and compared to prior experimental results. This paper also addresses a model of the effective mass of valence band holes assuming the nonparabolic condition.

Investigation on the electrical properties of superlattice FETs using a non-parabolic band model

The effect of non-parabolic energy-bands on the electrical properties of an In0.53Ga0.47As/In0.52Al0.48As superlattice FET has been investigated. An energy dependent effective mass was fitted on k·p simulation results and the new band model was implemented into a self-consistent Schrödinger–Poisson solver. This analysis has shown that non-parabolicity effects lead to noticeable changes of the device characteristics with respect the parabolic band model, namely: an increase of the on-state current and a steeper transition from the off- to the on-state sustained across several decades of current, at the expense of an increased off-state leakage. Moreover, the larger density of states in the non-parabolic model causes a 47% growth of the output conductance at low VDS, as well as an increased drain conductance in saturation.

Comparison of High Field Electron Transport in GaAs, InAs and In<sub>0.3</sub>Ga<sub>0.7</sub>As

An ensemble Monte Carlosimulation is used to compare high field electron transport in bulk GaAs, InAs and In0.3Ga0.7As. In particular, velocity overshoot and electron transit times are examined. We find the steady state velocity of the electrons is the most important factor determining transit time over distances longer then 0.2 μm. Over shorter distances velocity overshoot effects in InAs and In0.3Ga0.7 As at high fields are comparable to those in GaAs. We estimate the minimum transit time across a 1 μm InAs sample to be about 4.2 ps. Similar calculations for In0.3Ga0.7As yield 6 ps (for GaAs yield 10 ps). Calculations are made using a nonparabolic effective mass energy band model, Monte Carlo simulation that includes all of the major scattering mechanisms. The band parameters used in the simulation are extracted from optimized pseudopotential band calculations to ensure excellent agreement with experimental information and ab initio band models.

Comparison of hot electron transport properties in wurtzite phase of ZnS, GaN and 6H-SiC

An ensemble Monte Carlo simulation have been carried out to study temperature and doping dependencies of electron drift velocity in ZnS, GaN and 6H-SiC. We study how electrons, initially in thermal equilibrium, drift under the action of an applied electric field within bulk of these materials. Calculations are made using a non-parabolic effective mass energy band model, Monte Carlo simulation that includes all of the major scattering mechanisms. The band parameters used in the simulation are extracted from optimized pseudopotential band calculations to ensure excellent agreement with experimental information and ab-initio band models. For all materials, it is found that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material parameters. Transient velocity overshoot has also been simulated, with the sudden application of fields up to 600 kVm -1 , appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of about 1.5×105 ms -1 within 3 ps, for all crystal structures.

Comparison of hot electron transport properties in wurtzite phase of ZnS, GaN and 6H-SiC

An ensemble Monte Carlo simulation have been carried out to study temperature and doping dependencies of electron drift velocity in ZnS, GaN and 6H-SiC. We study how electrons, initially in thermal equilibrium, drift under the action of an applied electric field within bulk of these materials. Calculations are made using a non-parabolic effective mass energy band model, Monte Carlo simulation that includes all of the major scattering mechanisms. The band parameters used in the simulation are extracted from optimized pseudopotential band calculations to ensure excellent agreement with experimental information and ab-initio band models. For all materials, it is found that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material parameters. Transient velocity overshoot has also been simulated, with the sudden application of fields up to 600 kVm-1, appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of about 1.5×105 ms-1 within 3 ps, for all crystal structures. Keywords: Ensemble Monte Carlo, drift velocity, transient velocity, pseudopotential.

Calculated electron steady-state drift velocity in lattice matched Ga0.5In0.5P and Al0.26Ga0.26In0.48P using a threevalley Monte Carlo simulation

We present calculations based on an ensemble Monte Carlo program of the steady-state electron drift velocity in bulk Ga0.5In0.5P and Al0.26Ga0.26In0.48P as well as present a list of material parameters for these substances which are of use in the modeling of semiconductor devices made from these material types. Calculations are made using a non-parabolic effective mass energy band model, Monte Carlo simulation that includes all of the major scattering mechanisms. The band parameters used in the simulation are extracted from optimized pseudopotential band calculations to ensure excellent agreement with experimental information and ab-initio band models. The effects of alloy scattering on the electron transport physics are examined. For two materials, it is found that electron velocity overshoot only occurs when the electric field is increased to a value above a certain critical field, unique to each material. This critical field is strongly dependent on the material parameters. Key words: Steady-state, pseudopotential, alloy scattering, velocity overshoot, critical field.

Analytical Model for Conduction Band Nonparabolicity to Transport Analysis of Nano-Scale SOI MOSFET

This paper reconsiders the mathematical formulation for the conventional nonparabolic band model, and discusses how the nonparabolicity of the conduction band impacts the effective masses of electrons that are confined within the barriers. To support this consideration, this paper proposes an analytical expression for the conduction-band effective mass of electrons including the term of band nonparabolicity.

Extension of analytical model for conduction band nonparabolicity to transport analysis of nanoscale metal-oxide-semiconductor field-effect transistor

This paper reconsiders the mathematical formulation for the conventional nonparabolic band model and discusses how the nonparabolicity of the conduction band impacts the effective masses of electrons that are confined within the barriers. Since the conventional simplified model for band nonparabolicity does not include the external potential effect as a perturbation, it is examined whether this perturbation can be implemented into the conventional model for usefulness. When the perturbation energy is smaller than the unperturbed energy, the insertion of the perturbation energy term into the conventional expression for the nonparabolic band model is reasonably valid. It is demonstrated that this approximation is actually accurate given a sub-10-nm-thick Si layer surrounded by an SiO2 layer. A major part of this discussion is focused on the low-dimensionality electron system confined with insulator barriers so this study contributes to the analysis of future electron devices. To support this consideration, this paper proposes an analytical expression for the conduction-band effective mass of electrons including the term of band nonparabolicity.

COMPARISON OF HIGH AND LOW FIELD ELECTRON TRANSPORT IN Al0.2Ga0.8N, AlN AND GaN

We present a comprehensive study of the transport dynamics of electrons in the binary and ternary compounds AlN , GaN and Al 0.2 Ga 0.8 N . Calculations are made using a non-parabolic effective mass energy band model, Monte Carlo simulation that includes all of the major scattering mechanisms. The band parameters used in the simulation are extracted from optimized pseudopotential band calculations to ensure excellent agreement with experimental information and ab initio band models. The effects of alloy scattering on the electron transport physics are examined. The steady-state velocity field curves and low field mobilities are calculated at room temperature. The results are in fair agreement with other recent calculations.

Low temperature thermal, thermoelectric, and thermomagnetic transport in indium rich Pb1−xSnxTe alloys

Galvanomagnetic and thermomagnetic data of single crystal indium rich Pb1−xSnxTe are analyzed, and electronic band parameters are calculated using nonparabolic band model. Transport properties at 80K are presented as a function of Sn (x=0–0.3) and In concentrations. Our results indicate pinning of Fermi level by indium impurity levels in these alloys. Effects of interaction of band with impurity level are investigated in terms of change in effective mass and energy scattering exponent. Indium doping slightly improves the thermoelectric properties of PbSnTe alloys.

Diamagnetic susceptibility of a hydrogenic donor in low lying excited states in a Quantum Well

Abstract We present the χ dia of a hydrogenic donor in low lying excited states like 2s, 2p± and 2p0 in a GaAs/ AlxGa1−xAs Quantum Well for various Al compositions x both in the parabolic and non-parabolic conduction band model using the variational method. To our knowledge there has been no such reports both theoretically and experimentally in the literature. It was observed that χ dia increases with increase of x for both the parabolic and non-parabolic cases. The effect of non-parabolicity on χ dia is larger for the lower well width region for 2s and 2p± states. Interestingly, we observe a “turn over” in the variation of χ dia against well widths in the lower well width region, a trend which is similar to the one observed in the variation of binding energy of donors in low lying excited states.

Diamagnetic susceptibility of hydrogenic donor impurity in low-dimensional semiconducting systems

The binding energies of a hydrogenic donor both in the parabolic and non-parabolic conduction band model within the effective mass approximation have been computed for the low-dimensional semiconducting systems (LDSS) like quantum well, quantum well wire and quantum dot taking GaAs/Al x Ga 1− x As systems as an example. It is observed that the effect of non-parabolicity is not effective when the system goes to lower dimensionality. The diamagnetic susceptibility of a hydrogenic donor impurity has also been computed in these LDSS in the infinite barrier model. Since no theoretical or experimental works on the diamagnetic susceptibility of LDSS are available in the literature, as a realistic case the diamagnetic susceptibility has been computed in the finite barrier model ( x=0.3) for a quantum well and the results are discussed in the light of semiconductor–metal transition.

Effects of nonparabolic bands in quantum wires

A nonparabolic band model has been implemented for a one-dimensional electron gas, using a modified Schrödinger equation which takes into account size quantization in the transverse cross section of a silicon quantum wire. The quantized states and the corresponding one-dimensional density of states have been analyzed when the nonparabolicity is present, to quantify the importance of the effect of realistic bands at higher energies.

Transverse magnetoresistance of single crystals of bismuth doped with gallium and indium

Transverse magnetoresistance in single crystals of bismuth doped with gallium and indium has been measured as functions of magnetic field up to 0.75 T and as functions of temperature between 80 and 300 K. Magnetoresistance does not obey the quadratic dependence on magnetic field strength in the low temperature limit and an approximately quadratic field dependence has been found nearly at room temperature. An attempt has been made here to explain the observed facts in these alloys of bismuth on the basis of an ellipsoidal non-parabolic band model.

Monte Carlo simulation of electron transport in the III-nitride wurtzite phase materials system: binaries and ternaries

We present a comprehensive study of the transport dynamics of electrons in the ternary compounds, Al/sub x/Ga/sub 1-x/N and In/sub x/Ga/sub 1-x/N. Calculations are made using a nonparabolic effective mass energy band model. Monte Carlo simulation that includes all of the major scattering mechanisms. The band parameters used in the simulation are extracted from optimized pseudopotential band calculations to ensure excellent agreement with experimental information and ab initio band models. The effects of alloy scattering on the electron transport physics are examined. The steady state velocity field curves and low field mobilities are calculated for representative compositions of these alloys at different temperatures and ionized impurity concentrations. A field dependent mobility model is provided for both ternary compounds AlGaN and InGaN. The parameters for the low and high field mobility models for these ternary compounds are extracted and presented. The mobility models can be employed in simulations of devices that incorporate the ternary III-nitrides.