High-field Electron Transport Research Articles

TCAD Modeling of High-Field Electron Transport in Bulk Wurtzite GaN: The Full-Band SHE-BTE

Gallium Nitride (GaN) High-Electron Mobility Transistors (HEMTs) actually represent one of the best candidates for medium-high power and radio frequency applications. As they operate at large bias and electric fields, a comprehensive analysis of the high-field transport properties is fundamentals, as hot electrons are expected to play a relevant role for the device reliability. In this perspective, Technology Computer-Aided Design (TCAD) simulations can be a very useful tool for the understanding of the phenomena dominating hot-electron degradation mechanisms. The most-accurate modeling approaches are based on the direct solution of the Boltzmann equation, which is not actually available for the GaN material. In this work, the deterministic solution of the Boltzmann transport equation via the spherical-harmonics expansion (SHE-BTE), as incorporated in a commercial TCAD tool, has been extended to the analysis of GaN electrons. To this purpose, the details of the full-band structure has been derived from DFT calculations as in state-of-art literature works, and the electron density of states, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$g(E)$ </tex-math></inline-formula> , and group velocity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$u_{g}(E)$ </tex-math></inline-formula> , have been calculated for the SHE-BTE for the first time. In addition to this, an accurate calibration of the total scattering rate accounting for nonpolar acoustic and optical carrier-phonon interaction, Coulomb scattering and impact ionization has been carried out against available Monte Carlo data and experiments. The proposed model is also shown to correctly predict the temperature dependence of the electron impact-ionization coefficient and current density up to breakdown.

Full-band Monte Carlo simulation of two-dimensional electron gas in (AlxGa1−x)2O3/Ga2O3 heterostructures

β -Gallium oxide (Ga2O3) is an extensively investigated ultrawide-bandgap semiconductor for potential applications in power electronics and radio frequency switching. The room temperature bulk electron mobility (∼200cm2V−1s−1) is comparatively low and is limited by the 30 phonon modes originating from its 10-atom primitive cell. The theoretically calculated saturation velocity in bulk is 1–2×107cms−1 (comparable to GaN) and is limited by the low field mobility. This work explores the high field electron transport (and hence the velocity saturation) in the 2DEG based on the first principles calculated parameters. A self-consistent calculation on a given heterostructure design gives the confined eigenfunctions and eigenenergies. The intrasubband and the intersubband scattering rates are calculated based on the Fermi’s golden rule considering longitudinal optical (LO) phonon–plasmon screening. The high field characteristics are extracted from the full-band Monte Carlo simulation of heterostructures at 300 K. The overall system is divided into a 2D and a 3D region mimicking the electrons in the 2DEG and the bulk, respectively. The electron transport is treated through an integrated Monte Carlo program which outputs the steady state zone population, transient dynamics, and the velocity–field curves for a few heterostructure designs. The critical field for saturation does not change significantly from bulk values, however, an improved peak velocity is calculated at a higher 2DEG density. The velocity at low 2DEG densities is impacted by the antiscreening of LO phonons which plays an important role in shaping the zone population. A comparison with the experimental measurements is also carried out and possible origins of the discrepancies with experiments is discussed.

Understanding high-field electron transport properties and strain effects of monolayer transition metal dichalcogenides

Monolayer transition metal dichalcogenides (MX2) are promising candidates for future electronics. Although the transport properties (e.g. mobility) at low electric field have been widely studied, there are limited studies on high-field properties, which are important for many applications. Particularly, there is lack of understanding of the physical origins underlying the property differences across different MX2. Here by combining first-principles calculations with Monte Carlo simulations, we study the high-field electron transport in defects-free unstrained and tensilely strained MX2 (M=Mo, W and X=S, Se). We find that WS2 has the highest peak velocity (due to its smallest effective mass) that can be reached at the lowest electric field (owing to its highest mobility). Strain can increase the peak velocity by increasing the scattering energy. After reaching the peak velocity, most MX2 demonstrates negative differential mobility (NDM). WS2 shows the largest NDM among unstrained MX2 due to the strongest effect of electron transfer from the low-energy small-mass valley to the high-energy large-mass valley. The tensile strain increases the valley separation, which on one hand suppresses the electron transfer in WS2, on the other hand allows the electrons to access the non-parabolic band region of the low-energy valley. The latter effect leads to an NDM for electrons in the low-energy valley, which can significantly increase the overall NDM at moderate strain. The valley-separation induced NDM in the low-energy valley is found to be a general phenomenon. Our work unveils the physical factors underlying the differences in high-field transport properties of different MX2, and also identifies the most promising candidate as well as effective approach for further improvement.

Estimation of the charged defect density from hot-electron transport studies in epitaxial ZnO

High-field electron transport measurements by applying short (few ns) voltage pulses on nominally undoped n-type Zn-polar ZnO epilayers are reported and interpreted in terms of the Boltzmann kinetic equation. The transient measurements do not demonstrate a significant change in the electron density up to 320 kV/cm electric field. This result together with the experimental data on the current allows one to estimate the electron drift velocity from the measured current: the highest value of ~2.9 × 107 cm/s is obtained at the pre-breakdown field of 320 kV/cm for the ZnO layer with the electron density of 1.5 × 1017 cm–3. The densities of double-charged oxygen vacancies (~1.6 × 1017 cm–3) and other charged centres (~1.7 × 1017 cm–3) are assumed for the best fit of the simulated and measured hot-electron effect. A correlation with the epilayer growth conditions is demonstrated: the higher Zn cell temperature favours the formation of a higher density of the oxygen vacancies (1.9 × 1017 cm–3 at 347°C).

Monte Carlo Calculations of Energy and Drift Velocity in ZnS, ZnSe, ZnTe

A Monte Carlo simulation of high field electron transport in ZnS, ZnSe and ZnTe has been presented. The model includes a nonparabolic three valley of the conduction band. The simulation includes scattering mechanisms associated with acoustic, intervalley and polar optical phonons, as well as ionized impurity scattering and impact ionization. The inclusion of the second conduction band is found to have a significant impact on the energy distribution at fields above 100 kV/cm. The second conduction band is also important because of its effect on the impact ionization rate. The results of simulation which are drift velocity and average electron energy are presented and discussed.

Electron transport in the solar-relevant InAlAs

The semiconductor alloy InAlAs is commonly found in many types of heterojunction solar cells, particularly in hot carrier solar cells. Yet, surprisingly little is known about its transport properties. Here, we theoretically determine both its low field and high field electron transport properties, with focus on the alloy In065Al0.35As that is tensilely strained to the InAs lattice constant, a value consistent with its use in many hot carrier solar cells.

Impact of the hot phonon effect on electronic transport in monolayer silicene

The hot phonon effect is a non-equilibrium phenomenon that has an important role in high-field electronic transport in two-dimensional electron gases and in 2D materials like graphene. In this work, the influence of this effect on the electronic transport properties of silicene is investigated by means on an ensemble Monte Carlo simulator that accounts self-consistently for the out-of-equilibrium phonon population and the scattering events under high electric field conditions. In this way, the observed reduction in the carrier drift velocity is analyzed in terms of the microscopic scattering events, wavevector distributions, net phonon emission and phonon temperatures. A comparison with the case of graphene is also carried out, showing that despite the similarities concerning the linear bandstructure near the Dirac points, the hot phonon effect is less dominant in silicene due to the differences in the phonon branches and electron–phonon couplings. Even so, neglecting the role of an out-of-equilibrium phonon population may overestimate the high-field drift velocity in silicene up to 25% at moderate carrier concentrations.

Damping of acoustic flexural phonons in silicene: influence on high-field electronic transport

Silicene is a two-dimensional buckled material with broken horizontal mirror symmetry and Dirac-like dispersion. Under such conditions, flexural acoustic (ZA) phonons play a dominant role. Consequently, it is necessary to consider some suppression mechanism for electron–phonon interactions with long wavelengths in order to reach mobilities useful for electronic applications. In this work, we analyze, by means of an ensemble Monte Carlo simulator, the influence of several possibilities for the description of the effect of ZA phonon damping on electronic transport in silicene. The results show that a hard cutoff situation (total suppression for phonons with a wavelength longer than a critical one), as it has been proposed in the literature, does not yield a realistic picture regarding the electronic distribution function, and it artificially induces a negative differential resistance at moderate and high fields. Sub-parabolic dispersions, on the other hand, may provide a more realistic description in terms of the behavior of the electron distribution in the momentum space, but need extremely short cutoff wavelengths to reach functional mobility and drift velocity values.

Hot LO-phonon limited electron transport in ZnO/MgZnO channels

High-field electron transport in two-dimensional channels at ZnO/MgZnO heterointerfaces has been investigated experimentally. Pulsed current–voltage (I–V) and microwave noise measurements used voltage pulse widths down to 30 ns and electric fields up to 100 kV/cm. The samples investigated featured electron densities in the range of 4.2–6.5 × 1012 cm−2, and room temperature mobilities of 142–185 cm2/V s. The pulsed nature of the applied field ensured negligible, if any, change in the electron density, thereby allowing velocity extraction from current with confidence. The highest extracted electron drift velocity of ∼0.5 × 107 cm/s is somewhat smaller than that estimated for bulk ZnO; this difference is explained in the framework of longitudinal optical phonon accumulation (hot-phonon effect). The microwave noise data allowed us to rule out the effect of excess acoustic phonon temperature caused by Joule heating. Real-space transfer of hot electrons into the wider bandgap MgZnO layer was observed to be a limiting factor in samples with a high Mg content (48%), due to phase segregation and the associated local lowering of the potential barrier.

High field electron transport in indium gallium nitride and indium aluminium nitride

In this paper, we study theoretically the hot electron transport in two nitride semiconductor solid solutions, InxGa1−xN and InxAl1−xN, in the electric fields up to 30 kV/cm. We calculate the electron drift velocity field dependence at 77 and 300 K for the bulk samples with the electron concentration of 1 × 1018 and 1 × 1019 cm−3 and alloy composition x = 0, 0.25, 0.5, 0.75, and 1.

High-field electron transport in doped ZnO

Current–voltage characteristics have been measured for ZnO:Ga and Zn:Sb epitaxial layers with electron densities ranging from cm−3 to cm−3. Two-terminal samples with coplanar electrodes demonstrate virtually ohmic behavior until thermal effects come into play. Soft damage of the samples takes place at high currents. The threshold power (per electron) for the damage is nearly inversely proportional to the electron density over a wide range of electron densities. Pulsed voltage is applied in order to minimize the thermal effects, and thus an average electric field of 150 kV cm−1 is reached in some samples subjected to 2 ns voltage pulses. The results are treated in terms of electron drift velocity estimated from the data on current and electron density under the assumption of uniform electric field. The highest velocity of ∼ cm s−1 is found at an electric field of ∼100 kV cm−1 for the sample with an electron density of cm−3. The non-ohmic behavior due to hot-electron effects is weak, and the dependence of the electron drift velocity on the doping resembles the variation of mobility.

Magneto transport in crossed electric and magnetic fields in compensated bulk GaN

Low-temperature high-field electron transport is studied for compensated bulk GaN subjected to crossed electric and magnetic fields. The electron kinetics, distribution function, and field dependencies of the magneto transport characteristics are analyzed by using the Monte-Carlo method. At zero magnetic field, for an ionized impurity concentration of 1016 cm−3 and an electron concentration of 1015 cm−3, it is shown that dissipative streaming transport with a strong anisotropic electron distribution in the momentum space is realized at electric fields in the range 3−10 kV/cm and for a lattice temperature of 30 K. The magnetic field destroys the dissipative streaming transport. Indeed, for a magnetic field greater than 4 T, the electrons are predominantly confined in a region of the momentum space where their energy is smaller than the optical phonon energy and the strong inelastic scattering by optical phonons is practically eliminated. A quasi-ballistic electron transport occurs in the form of a vortex-like motion in the momentum space. The axis of rotation of this vortex coincides with the average electron momentum. A general analysis of the distribution function suitable for any configuration of the Hall circuit is presented. The main magneto transport characteristics (dissipative current, Hall current, and Hall electric field) are studied for the short and open Hall circuits. We show that the magneto transport measurements can provide valuable information on the main features of the electron distribution function and electron dynamics in GaN. Finally, we suggest that the strong dependency of the dissipative current on the parameters of the Hall circuit can be used for current modulation and current switching.

Monte Carlo Investigation of High-Field Electron Transport Characteristics in ZnMgO/ZnO Heterostructures

The high-field electron transport properties of ZnMgO/ZnO heterostructures considering multisubband conduction were systematically investigated with an ensemble Monte Carlo program developed by us. Electronic band structures were obtained by first-principles calculations using density functional theory, which provides more accurate parameters to calculate the electronic states and transport characteristics of 2-D electron gas. Wave functions and energy levels describing the subband structure were achieved to determine the 2-D scattering rates by solving the Schrodinger and Poisson equations self-consistently. The highest electron mobility gained at room temperature was approximately $4.23\times 10^{\mathrm {2}}$ cm2/Vs. The negative differential mobility was observed with a threshold electric field of approximately 80 kV/cm. The peak drift velocity of the Zn0.694Mg0.306O/ZnO heterostructure at 200 KV was about $2.011\times 10^{8}$ cm/s. This paper benefits the development of high-performance ZnMgO/ZnO heterostructure devices.

High-field electron transport in GaN under crossed electric and magnetic fields

High-field electron transport studied in crossed electric and magnetic fields in bulk GaN with doping of 1016 cm-3, compensation around 90% at the low lattice temperature (30 K). It was found the range of the magnetic and electric fields where the non-equilibrium electron distribution function has a complicated topological structure in the momentum space with a tendency to the formation of the inversion population. Field dependences of dissipative and Hall components of the drift velocity were calculated for the samples with short- and open- circuited Hall contacts in wide ranges of applied electric (0 — 20 kV/cm) and magnetic (1 — 10 T) fields. For former sample, field dependences of dissipative and Hall components of the drift velocity have a non-monotonic behavior. The dissipative component has the inflection point which corresponds to the maximum point of the Hall component. For latter sample, the drift velocity demonstrate a usual sub-linear growth without any critical points. We found that GaN samples with controlled resistance of the Hall circuit can be utilized as a electronic high-power switch.

Theory of high-field electron transport in the heterostructures AlxGa1-xAs/GaAs/AlxGa1-x with delta-doped barriers. Effect of real-space transfer

Steady-state electric characteristics of quantum heterostructures AlxGa1–xAs/GaAs/AlxGa1–xAs with  -doped barriers have been analyzed in this work. It has been shown that at high doping the additional low-conductive channels are formed in the barrier layers. Current-voltage characteristics of the structure were obtained in the wide interval of applied electric fields up to several kV/cm being based on the solution of Boltzmann transport equation. It has been found that in the electric fields higher than 1 kV/cm the effect of exchange of the carriers between the high-conductive channel of the GaAs quantum well and the channels in the AlGaAs barriers becomes essential. This effect gives rise to the appearance of the strongly nonlinear current-voltage characteristics with a portion of negative differential conductivity. The developed model of heterostructure is adequate to those recently fabricated and studied by Prof. Sarbey’s group. The obtained results explain some observation of this paper. It has been found that the effect of electron real-space transfer takes place at both low temperatures and room temperatures, which opens perspectives to design novel type nanostructured current controlled devices.

First-principles study of high-field-related electronic behavior of group-III nitrides

Based on accurate band structures of AlN, GaN, and InN, we report physical quantities related to high-field electron transport, including effective masses, energies of inflection points, and satellite valleys in the conduction band. The band structures are obtained from density functional theory with a hybrid functional, as well as many-body perturbation theory based on the ${G}_{0}{W}_{0}$ approach. We also calculate the electron-energy relaxation time due to the electron-longitudinal-optical-phonon interaction within the Fr\ohlich model. Our results provide insights into the physical origin of negative differential resistance and the high-frequency characteristics of group-III nitrides and their alloys under high-field operation.

Steady-State and Transient Electron Transport within Bulk InAs, InP and GaAs: An Updated Semiclassical Three-Valley Monte Carlo Simulation Analysis

An ensemble Monte Carlosimulation is used to compare high field electron transport in bulk InAs, InP and GaAs. In particular, velocity overshoot and electron transit times are examined. For all materials, we find 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, about 3 kV/cm for InAs, 10 kV/cm for InP and 5 kV/cm for the case of GaAs, We find that InAs exhibits the highest peak overshoot velocity and that this velocity overshoot lasts over the longest distances when compared with GaAs and InP. Finally, we estimate the minimum transit time across a 1 μm InAs sample to be about 2 ps. Similar calculations for InP and GaAs yield 6.6 and 5.4 ps, respectively. We find that the optimal cutoff frequency for an ideal InAs based device ranges from around 79 GHz when the device thickness is set to 1 μm. We thus suggest that indium arsenide offers great promise for future high-speed device applications. The steady-state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.

Comparison of High Field Electron Transport in GaAs, InAs and In&amp;lt;sub&amp;gt;0.3&amp;lt;/sub&amp;gt;Ga&amp;lt;sub&amp;gt;0.7&amp;lt;/sub&amp;gt;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.

High-field transport in a graphene nanolayer

High-field electron transport properties in a two-dimensional nanolayer are studied by an application of the anisotropic nonequilibrium distribution function, a natural extension of the Fermi-Dirac distribution by inclusion of energy gained/absorbed in a mean free path (mfp). The drift velocity for conical band structure of graphene is shown to rise linearly with the electric field in a low electric field that is below the critical electric field. The critical electric field, equal to thermal voltage divided by the mfp, marks the transition from ohmic linear transport to saturated behavior in a high electric field. As field rises beyond its critical value, the drift velocity is sublinear resulting in ultimate saturation; the ultimate saturation velocity is comparable to the Fermi velocity in graphene. The quantum emission is found not to affect the mobility, but is efficient in lowering the saturation velocity. Excellent agreement is obtained with the experimental data for graphene on silicon dioxide substrate.

Nonequilibrium optical phonon effect on high-field electron transport in InN

The effect of nonequilibrium longitudinal optical (LO) phonons on electron transport in wurtzite InN in high electric fields is studied by Monte Carlo simulations. The novel and efficient single-particle Monte Carlo method for a self-consistent simulation of nonequilibrium electron and phonon systems is developed. The effect of nonequilibrium LO phonons on electron drift velocity, valley population, and small-signal ac mobility in InN is investigated. It is found that the effect of nonequilibrium LO phonons on electron transport characteristics in InN becomes pronounced when electron density exceeds 1017 cm−3.