Transient Velocity Overshoot Research Articles

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 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.

Steady-state and transient electron transport within bulk ternary nitride semiconductors including GaInN, AlGaN and AlInN using a three-valley Monte Carlo method

An ensemble Monte Carlo simulation is used to compare bulk electron transport in wurtzite phase GaInN, AlGaN and AlInN materials. Electronic states within the conduction band valleys at theΓ, U and K are represented by non-parabolic ellipsoidal valleys centered on important symmetry points of the Brillouin zone. 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 ∼5×107 Vm-1, appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of ∼1.5×105 ms-1 with in 4 ps for all crystal structures. The steady-state and transient velocity overshoot characteristics are in fair agreement with other recent calculations. Keywords: Brillouin zone, gate-drain, transient, critical field, drift velocity, semiconductor

Steady-state and transient electron transport within bulk ternary nitride semiconductors including GaInN, AlGaN and AlInN using a three-valley Monte Carlo method

An ensemble Monte Carlo simulation is used to compare bulk electron transport in wurtzite phase GaInN, AlGaN and AlInN materials. Electronic states within the conduction band valleys at the Γ, U and K are represented by non-parabolic ellipsoidal valleys centered on important symmetry points of the Brillouin zone. 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 ~5×10 7 Vm -1 , appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of ~1.5×10 5 ms -1 with in 4 ps for all crystal structures. The steady-state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.

COMPARISON OF TRANSIENT BALLISTIC ELECTRON TRANSPORT IN BULK WURTZITE PHASE 6H-SiC and GaN

An ensemble Monte Carlo simulation is used to compare bulk electron ballistic transport in 6H - SiC and GaN materials. Electronic states within the conduction band valleys at Γ1, U, M, Γ3, and K are represented by nonparabolic ellipsoidal valleys centered on important symmetry points of the Brillouin zone. The large optical phonon energy (~120 meV) and the large intervalley energy separation between the Γ and satellite conduction band valleys suggest an increasing role for ballistic electron effects in 6H - SiC , especially when compared with most III-V semiconductors such as GaAs . Transient velocity overshoot has been simulated, with the sudden application of fields up to ~5×107 Vm -1, appropriate to the gate-drain fields expected within an operational field effect transistor. A peak-saturation drift velocity ratio of 2:1 is predicted for 6H - SiC material while that for GaN is 4:1. The electron drift velocity relaxes to the saturation value of ~2×105 ms -1 within 3 ps, for both crystal structures. The transient velocity overshoot characteristics are in fair agreement with other recent calculations.

Anisotropic Transient and Stationary Electron Velocity in Bulk Wurtzite GaN

The theoretical calculation of transient electron velocity overshoot in wurtzite <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> -axis GaN indicates a higher transient overshoot peak for transport in the basal plane ( Gamma- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> and Gamma- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> ) than along the growth direction (Gamma- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> ). Characteristic rise times for the transient overshoot peak are found to be shorter for transport along the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> -axis. Stationary electron velocity is significantly larger for transport oriented in the basal plane than along the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> -axis. No significant anisotropy is observed, however, in either the transient or steady-state electron velocity as a function of field orientation within the basal plane itself. The higher peak transient and stationary velocities in the basal plane are directly attributable to the anisotropy of the electronic dispersion, which exhibits lower effective mass along the Gamma- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> and Gamma- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> directions and greater nonparabolicity along the Gamma- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> direction.

MONTE CARLO MODELING OF HOT ELECTRON TRANSPORT IN BULK AlAs, AlGaAs AND GaAs AT ROOM TEMPERATURE

The results of an ensemble Monte Carlo simulation of electron drift velocity response on the application field in bulk AlAs , AlGaAs and GaAs are presented. All dominant scattering mechanisms in the structure considered have been taken into account. 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 1600 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 ~105 ms-1 within 4 ps, for all crystal structures. The steady state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.

COMPARISON OF STEADY-STATE AND TRANSIENT ELECTRON TRANSPORT IN InAs, InP AND GaAs

An ensemble Monte Carlo simulation 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 400 kVm-1 for the case of GaAs , 300 kVm-1 for InAs and 700 kVm-1 for InP . 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 GaAs sample to be a bout 3 ps. Similar calculations for InAs and InP yield 2.2 and 5 ps, respectively. The steady-state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.

COMPARISON OF HIGH FIELD STEADY STATE AND TRANSIENT ELECTRON TRANSPORT IN WURTZITE GaN, AlN AND InN

An ensemble Monte Carlo simulation is used to compare bulk electron transport in wurtzite phase GaN , AlN and InN materials. Electronic states within the conduction band valleys at the Γ1, U, M, Γ3 and K are represented by non-parabolic ellipsoidal valleys centered on important symmetry points of the Brillouin zone. 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 ~5 × 107 Vm -1, appropriate to the gate-drain fields expected within an operational field effect transistor. The electron drift velocity relaxes to the saturation value of ~1.4 × 105 ms -1 within 4 ps, for all crystal structures. The steady state and transient velocity overshoot characteristics are in fair agreement with other recent calculations.

Nonparabolicity effect on bulk transport properties in wurtzite InN

We investigate the transient and steady-state electron transport properties in bulk wurtzite InN using the ensemble Monte Carlo method. The main emphasis is given to the origin of the negative differential mobility of the steady-state velocity-field characteristics and of the strong transient velocity overshoot. In general, these effects can be caused by intervalley transfer and by the nonparabolicity of the main valley of the conduction band. We analyze the relative importance of these two mechanisms and demonstrate that in wurtzite InN the negative differential mobility and drift velocity overshoot are governed by the strong nonparabolicity of the central valley.

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.

Strained-Si single-gate versus unstrained-Si double-gate MOSFETs

Self-consistent full-band Monte Carlo simulations are employed to compare the performance of nanoscale strained-Si single-gate (SG) and unstrained-Si double-gate (DG) MOSFETs for a gate length of 25 nm. Almost the same on-current as in the DG-MOSFET can be achieved by strain in a SG-MOSFET for the same gate overdrive. This is due to the compensation of the higher electron sheet density in the two inversion channels of the DG-MOSFET by the higher strain-enhanced velocity in the channel of the SG-MOSFET. The on-current of the strained-Si SG-MOSFET is almost 10% larger for a channel orientation along the crystallographic ⟨100⟩ direction than for the ⟨110⟩ direction. This confirms that the on-current is determined by quasi-ballistic transport, because the maximum enhancement of the in-plane velocity in bulk (001)-strained Si in the ⟨100⟩ direction is 5% at medium electric fields (the low-field mobilities and saturation velocities are the same and the difference in the thermal injection velocities is negligibly small), whereas the transient bulk velocity overshoot peak is 30% larger in the ⟨100⟩ direction.

Experimental and Theoretical Studies of Transient Electron Velocity Overshoot in GaN

We employ an optically detected time-of-flight technique with femtosecond resolution that monitors the change in the electroabsorption due to charge transport in an AlGaN/GaN heterojunction p-i-n diode to measure the electron velocity overshoot in GaN at room temperature. It has been found that electron velocity overshoot occurs at electric fields as low as 105 kV/cm, with the peak transient velocity increasing with E up to ∼320 kV/cm, at which field a peak velocity of 7.25 x 10 7 cm/s is attained within the first 200 fs after photoexcitation. At higher fields, the increase in transit time with increasing field suggests the onset of negative differential resistance due to intervalley transfer. The existence of transient velocity overshoot at fields lower than the calculated peak steady-state velocity suggests that it occurs while the electrons are primarily in the r valley. Full zone Monte Carlo calculations imply that the overshoot is associated more with band nonparabolicity in the Γ valley than with intervalley transfer at fields less than 325 kV/cm, and, in conjunction with theoretical calculations employing a semiclassical transport model, confirm the importance of this nonparabolicity for the determination of the temporal shape of the transient velocity overshoot curves.

Fullband Particle-Based Simulation of High-Field Transient Transport in III–V Semiconductors

Motivated by recent experimental measurements (A. Leitenstorfer et al., 2000. Physical Review B 61(24): 16642–16652), this work presents the transient analysis of photogenerated electron-hole pairs in GaAs and InP pin diodes (S. M. Sze, 1981. Physics of Semiconductor Devices, 2nd edn., John Wiley) using a fullband particle-based simulator (M. Saraniti and S. Goodnick, 2000. IEEE Transactions on Electron Devices 47(10): 1909–1915). The fullband simulation tool is based on a particle-based technique that has been developed to reduce the computational time required for modeling charge transport phenomena in semiconductors. Excellent agreement is found between experiment and simulation of transient acceleration and velocity overshoot in GaAs and InP pin diodes due the femto-second optical excitation of carriers.

Band Structure Effects on the Transient Electron Velocity Overshoot in GaN

Time-resolved electroabsorption measurements on an AlGaN/GaN heterojunction p-i-n photodiode have been used to study the transient electron velocity overshoot for transport in the c-direction in wurtzite GaN. The velocity overshoot increases with electric field up to ∼320 kV/cm, at which field a peak velocity of 7.25 x 10 7 cm/s is attained within the first 200 fs after photoexcitation. However, theoretical Monte Carlo calculations incorporating a GaN full-zone band structure show that the majority of electrons do not attain sufficient energy to effect intervalley transfer until they are subjected to higher fields (> 325 kV/cm). Insight into this behavior can be gleaned from the band nonparabolicity deduced from the constant energy surfaces in the Γ valley, which shows that the effective mass in the c-direction can be viewed as becoming larger at high k values.

Time-resolved electroabsorption measurement of the transient electron velocity overshoot in GaN

A femtosecond time-resolved electroabsorption technique employing an AlGaN/GaN heterojunction p–i–n diode with a p-type AlGaN window layer and a semitransparent p contact has been used to measure the transient electron velocity overshoot in GaN. A peak transient electron velocity of 7.25×107 cm/s within the first 200 fs after photoexcitation has been observed at a field of 320 kV/cm. The increase in electron transit time across the device with increasing field beyond 320 kV/cm provides experimental evidence for a negative differential resistivity region of the steady-state velocity-field characteristic in this high field range.

Transient electron transport in wurtzite GaN, InN, and AlN

Transient electron transport and velocity overshoot in wurtzite GaN, InN, and AlN are examined and compared with that which occurs in GaAs. 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 4 kV/cm for the case of GaAs but much higher for the III–nitride semiconductors: 140 kV/cm for GaN, 65 kV/cm for InN, and 450 kV/cm for AlN. We find that InN exhibits the highest peak overshoot velocity and that this velocity overshoot lasts over the longest distances when compared with GaN and AlN. Finally, using a one-dimensional energy–momentum balance approach, a simple model is used to estimate the cutoff frequency performance of nitride based heterojunction field effect transistors (HFETs) and a comparison is made to recently fabricated AlGaN/GaN HFETs.

Monte Carlo study of electron transport in SiC

Temperature- and electric field-dependent electron transport in 3C–, 4H–, and 6H–SiC has been calculated by the Monte Carlo technique. Due to the freezeout of deep donor levels the role of ionized impurity scattering in 6H–SiC is suppressed and the role of phonon scattering is enhanced, compared to 3C– and 4H–SiC. There are indications of impurity band formation for impurity concentrations exceeding 1019 cm−3. It is found that ionized impurity scattering along with the deep donor ionization is responsible for the temperature dependence of mobility anisotropy ratio. Electron effective masses and electron-phonon coupling constants have been deduced from the comparison of Monte Carlo simulation results with available experimental data on low-field electron mobility. The extracted model parameters are used for high-field electron transport simulations. The calculated velocity-field dependencies agree with experimental results. The saturation velocities in all three polytypes are close, but the transient velocity overshoot at high electric field steps is much more pronounced in 3C–SiC.

Terahertz electromagnetic pulses as probes for transient velocity overshoot in GaAs and Si

Ultrafast dynamics of the transient velocity overshoot in GaAs and Si have been studied through the use of measurements of radiated and guided terahertz pulses whose time-domain waveforms are proportional to the acceleration and the velocity of carriers, respectively. These measurements have been compared with each other and also with a Monte Carlo simulation. The field-dependent free-space and guided waveforms are qualitatively consistent with Monte Carlo calculations. By correlation of the calculated velocities with a sampling gate function the observed ratio of peak-to-steady-state velocities is found to be in reasonable quantitative agreement. Also, by detecting the free-space radiation from a Si p-i-n structure, we have made the first, to our knowledge, direct experimental observation of transient velocity overshoot in Si.