High-field Electron Transport Research Articles

Ab initioimpact ionization rate in GaAs, GaN, and ZnS

We have performed extensive ab initio band structure calculations within density functional theory using an exact exchange formalism with a local density approximation for correlations. The wave-vector-dependent impact ionization rate is determined for GaAs, GaN, and ZnS. A strong asymmetry of the microscopic scattering rate as well as a pronounced influence of the band structure is found. We present also energy-averaged impact ionization rates which can be used in ensemble Monte Carlo simulations of high-field electron transport in these materials.

Hot-electron transport in AlGaN∕GaN two-dimensional conducting channels

We report on experimental studies of high-field electron transport in AlGaN∕GaN two-dimensional electron gas. The velocity–electric field characteristics are extracted from 10to30ns pulsed current–voltage measurements for 4.2 and 300K. An electron drift velocity as high as 1.7×107cm∕s was obtained in the fields 150kV∕cm. Estimates of thermal budget of the system show that overheating of the electrons exceeds 1700K at highest electric fields achieved in the experiment.

Phase-plane analysis and classification of transient regimes for high-field electron transport in nitride semiconductors

We present a detailed theoretical analysis of steady-state, transient time-dependent, and spatially dependent electron transport in the group-III nitrides at high and ultrahigh electric fields. To develop an analytical model, we derive time-dependent differential equations describing the hot-electron rates of momentum and energy relaxation in electron–polar-optical-phonon scattering and analyze them by employing phase-plane analysis. From the structure of the phase-plane partitioning based on the phase trajectories, the transient regimes are investigated and classified depending on various initial conditions. We have studied different subpicosecond regimes and found a considerable velocity overshoot effect. One of our findings is that when the velocity reaches the maximum, the electron temperature is of a moderate magnitude but increases considerably in the subsequent stage. Dynamic regimes with high electron temperature overshoot have been revealed. For the dominant electron–polar-optical-phonon scattering, the observed overshoot can be treated as a rudiment of the runaway effect typical for that mechanism. In nanoscale nitride diodes with space-charge limited transport, the transient processes are extended to sufficiently larger distances, the overshoot is weaker and the electron heating in the region of the peak velocity is greater than that found for time-dependent problem with a constant electric field throughout a homogeneous sample.

The applicability of analytical-band Monte Carlo for modelling high field electron transport in GaAs

An analytical-band Monte Carlo model incorporating four non-parabolic spherical valleys to represent the first two conduction bands has been developed to model hot electron transport and impact ionization in GaAs. We have tested the performance of this simple model against full-band Monte Carlo simulations for calculating the probability distribution function of impact ionization path length, time and energy; and transient velocity overshoot at high fields. This simpler model is found capable of reproducing the full-band model results satisfactorily but at much lower computational cost.

Choice of wavefunction phases in the equations for electric-field-induced interband transitions

A set of equations for calculating the probability for electric-field-induced interband transitions in periodic crystals (Krieger and Iafrate 1986 Phys. Rev. B 33 5494) can be used in combination with the full band Monte Carlo method to study high-field electronic transport properties in semiconductors. However, when the equations are applied to realistic cases in which the underlying band structure is obtained from numerical band structure programmes, the equations are not directly solvable because of the indeterminacy of the phases of the band structure Bloch wavefunctions. Here we discuss this problem and present a method for choosing the phases of the Bloch functions in such a way that the equations yield physically correct interband transition probabilities.

The effect of hot phonons on the drift velocity in GaN/AlGaN two dimensional electron gas

We present the effect of hot-phonon production on the high-field drift velocity in the steady state in GaN/AlGaN heterostructures . The results are compared with a model taking into account the effect of hot phonon production on the high-field transport of electrons. Experimental results show that the drift velocity saturates at around v d ≈3.8×10 5 cm / s at an electric field of F≈8.9×10 2 V / cm at 3.8 K . The theoretical calculations show that the enhancement of the momentum relaxation rate due to the production of non-drifting hot phonons reduces the drift velocity at high field. The reduction in the drift velocity increases with increasing population of non-drifting non-equilibrium phonons (LO phonons).

Terahertz emission due to interminiband resonant Zener tunneling in wide-miniband GaAs/Al0.3Ga0.7As superlattices

We have investigated terahertz (THz) emission induced by high-field electron transport in biased wide-miniband GaAs/Al0.3Ga0.7As superlattices. With increasing bias electric fields, two distinct regimes are observed in the bias-field dependence of the emitted THz intensity. These two regimes are attributed to the intraminiband transport and interminiband Zener tunneling regimes, respectively. In the Zener tunneling regime, quasiperiodic structures are observed in the bias field dependence of the emitted THz intensity and are identified to be due to the resonant Zener tunneling between the Wannier–Stark ladders associated with the ground and excited minibands.

The effect of hot phonons on the drift velocity in GaN/AlGaN two dimensional electron gas

We present the effect of hot-phonon production on the high-field drift velocity in the steady state in GaN/AlGaN heterostructures. The results are compared with a model taking into account the effect of hot phonon production on the high-field transport of electrons. Experimental results show that the drift velocity saturates at around v d ≈3.8×10 5 cm/ s at an electric field of F≈8.9×10 2 V/ cm at 3.8 K . The theoretical calculations show that the enhancement of the momentum relaxation rate due to the production of non-drifting hot phonons reduces the drift velocity at high field. The reduction in the drift velocity increases with increasing population of non-drifting non-equilibrium phonons (LO phonons).

Nonparabolic multivalley balance-equation approach to high-field electron transport and impact ionization in ZnS: Comparison with full-band Monte Carlo simulations

Extended nonparabolic multivalley balance equations including impact ionization (II) process are presented and are applied to study electron transport and impact ionization in ZnS with a $\ensuremath{\Gamma},$ X, and L conduction-band structure at high electric field up to 2000 kV/cm. Hot-electron transport properties, such as electron drift velocity, electron energy, intervalley electron transfer, and electron-hole pair generation, are calculated by taking account of the scattering from polar optical, deformation potential, and intervalley interactions. Quantitative agreement is obtained among the results for drift velocity and II coefficient derived from the present calculations, from the recent full-band Monte Carlo simulations, and from experiments, thus confirming the validity of the present multivalley nonparabolic balance-equation approach.

Full band Monte Carlo simulations of high-field electron transport in wide band-gap semiconductors

We perform ab initio band structure calculations within density functional theory using an exact exchange formalism and a local density approximation for correlations. Ensemble Monte Carlo simulations consider all relevant scattering mechanisms including a realistic impact ionization rate. This full-band ensemble Monte Carlo method is applied to study the high-field electron transport. Results can be given for the total electron–phonon scattering rate, the drift velocity, the mean kinetic energy, the valley occupations and the ionization coefficient. We show here exemplary results for the wide band-gap materials ZnS and GaN.

High-field transport of electrons and radiative effects using coupled force-balance and Fokker-Planck equations beyond the relaxation-time approximation

The dynamics of a many-electron system under both dc and infrared fields is separated into a center-of-mass and a relative motion. The first-order force-balance equation is employed for the slow center-of-mass motion of electrons, and the Fokker-Planck equation is used for the ultrafast relative scattering motion of degenerate electrons. This approach allows us to include the anisotropic energy-relaxation process which has been neglected in the energy-balance equation in the past. It also leads us to include the anisotropic coupling to the incident infrared field with different polarizations. Based on this model, the transport of electrons is explored under strong dc and infrared fields by going beyond the relaxation-time approximation. The anisotropic dependence of the electron distribution function on the parallel and perpendicular kinetic energies of electrons is displayed with respect to the dc field direction, and the effect of anisotropic coupling to an incident infrared field with polarizations parallel and perpendicular to the applied dc electric field is shown. The heating of electrons is more accurately described beyond the energy-balance equation with the inclusion of an anisotropic coupling to the infrared field. The drift velocity of electrons is found to increase with the amplitude of the infrared field due to a suppressed momentum-relaxation process (or frictional force) under parallel polarization but decreases with the amplitude due to an enhanced momentum-relaxation process under perpendicular polarization.

A multicell matrix solution to the Boltzmann equation applied to the anisotropic electron transport in silicon

A new method for solving the Boltzmann transport equation is introduced. The method is based on a discontinuous spline approximation of the distribution function in the whole phase space. This procedure enables us to avoid the widely used PN-approximation for the angle dependence of the distribution function, so that we are able to treat strong anisotropies. The method is applied to a nonparabolic multivalley model of silicon, which allows for the investigation of the anisotropic high field transport of electrons in n-type silicon. The results are compared to experimental data and Monte Carlo simulations.

Direction-dependent band nonparabolicity effects on high-field transient electron transport in GaN

Time-resolved electroabsorption measurements on an AlGaN/GaN heterojunction p–i–n diode provide evidence of electron velocity overshoot at fields as low as ∼130 kV/cm for transport in the c-direction of wurtzite GaN. Theoretical Monte Carlo calculations employing a full band structure indicate that at fields below ∼300 kV/cm, this velocity overshoot is associated primarily with band nonparabolicity in the Γ valley related to a negative electron effective mass rather than intervalley transfer. Similar calculations of transport in the basal plane indicate that in this case, both a higher threshold field for velocity overshoot and a lower steady-state velocity at a given field are expected.

Full-band Monte Carlo simulations of high-field electron transport in GaAs and ZnS

We study the high-field transport in GaAs and ZnS based on ab initio band structures determined within density-functional theory using an exact exchange formalism with a local-density approximation for correlations. The transport properties are gained from ensemble Monte Carlo simulations where all relevant scattering mechanisms are considered including a realistic impact ionization rate. Important results are shown for the drift velocity, the mean kinetic energy, and the valley occupation.

Effect of non-drifting hot phonons on high-field drift velocity in GaN/AlGaN

We report on the studies of steady-state high-field drift velocity in GaN/AlGaN HEMT structures. The results are compared with a model taking into account the effect of hot phonon production on the high-field transport of electrons. In the theoretical model Cerenkov effects and phonon drift are assumed to be negligible. Experimental results show that the drift velocity saturates at vd = 1.0 × 107 cm s−1 at electric fields in excess of F ≈ 7.5 kV cm−1 at TL = 77 K. Theoretical calculations indicate that the enhanced scattering rate due to the production of non-drifting hot phonons reduces the drift velocity. The reduction in the drift velocity increases with increasing population of non-drifting non-equilibrium phonons.

HIGH-FIELD ELECTRON TRANSPORT CONTROLLED BY OPTICAL PHONON EMISSION IN NITRIDES

We have investigated the problem of electron runaway at strong electric fields in polar semiconductors focusing on the nanoscale nitride-based heterostructures. A transport model which takes into account the main features of electrons injected in short devices under high electric fields is developed. The electron distribution as a function of the electron momenta and coordinate is analyzed. We have determined the critical field for the runaway regime and investigated this regime in detail. The electron velocity distribution over the device is studied at different fields. We have applied the model to the group-III nitrides: InN, GaN and AlN. For these materials, the basic parameters and characteristics of the high-field electron transport are obtained. We have found that the transport in the nitrides is always dissipative. However, in the runaway regime, energies and velocities of electrons increase with distance which results in average velocities higher than the peak velocity in bulk-like samples. We demonstrated that the runaway electrons are characterized by the extreme distribution function with the population inversion. A three-terminal heterostructure where the runaway effect can be detected and measured is proposed. We also have considered briefly different nitride-based small-feature-size devices where this effect can have an impact on the device performance.

High-field electron transport in GaAs/Al xGa 1− xAs p–i–n–i–p-structures investigated by ultrafast absorption changes

High-field electron transport is studied in a GaAs/Al x Ga 1− x As p–i–n–i–p-structure with a specially designed composition profile. Electron transfer in real space and energy relaxation is investigated via time-resolved measurements using various probe energies. We observe a transfer time of ∼10 ps for the transport of electrons over 600 nm . This time is found to be nearly independent of the reverse bias voltage. The experimental findings are in good agreement with Monte Carlo simulations.

High-field electron transport in Al xGa 1− x as diodes investigated tracing ultrafast absorption changes

The topic of this contribution is the investigation of transient, nonequilibrium high-field electron transport in GaAs. Our two key ingredients are a unique laser system, which provides fs pump and probe pulses of independently tunable wavelengths and an AlGaAs hetero p–i–n diode with sophisticated design. This combination allows us to obtain time- and spatially resolved information about the temporal evolution of a photo-generated electron ensemble from ballistic to side-valley dominated transport, without disturbing hole contributions. Fields ranging from 7 to 180 kV/cm are investigated. Results are compared successfully to Monte Carlo Simulations.

High-Field Electron Transport in Nanoscale Group-III Nitride Devices

Focusing on the short-size group-III nitride heterostructures, we have developed a model which takes into account main features of transport of electrons injected into a polar semiconductor under high electric fields. The model is based on an exact analytical solution of Boltzmann transport equation. The electron velocity distribution over the device is analyzed at different fields and the basic characteristics of the high-field electron transport are obtained. The critical field for the runaway regime, when electron energies and velocities increase with distance which results in the average velocities higher than the peak velocity in bulk-like samples, is determined. We have found that the runaway electrons are characterized by a distribution function with population inversion. Different nitride-based small-size devices where this effect can have an impact on the device performance are considered.

Lattice misfit versus performance of thin film electroluminescent structures

Thin polycrystalline electroluminescent thin films (TFEL) of ZnS:Mn (phosphor) and Y2O3 (insulator) were deposited individually or as multilayers onto Si (100) substrates. Their crystallinity and the luminescent efficiency of the phosphor films were investigated at varying thermal annealing temperatures. It is shown that the luminescent quality of the phosphor layer increases up to 700 °C, whereas the electroluminescence operating intensity of TFEL devices saturates at 500 °C. The structural analysis of the insulating and phosphor layers shows that they recrystallize at annealing temperatures of, respectively, 500 and 600 °C, and that their lattice misfit doubles at processing temperatures>=500 °C. Since TFEL devices should benefit from enhanced luminescence efficiency and crystallinity at high annealing temperatures, we suggest that the lack of improvement in device performance beyond 500 °C is due to interface alterations. According to previous works, we propose that the lattice misfit increase between the phosphor and dielectric thin films modifies the morphology of the phosphor–insulator boundary inducing a modification of the interface states density, and hence, modifying high field electron transport properties of TFEL devices.