Steady-state Drift Research Articles

Electronic transport studies of bulk zincblende and wurtzite phases of GaN based on an ensemble Monte Carlo calculation including a full zone band structure

The ensemble Monte Carlo technique including the details of the first four conduction bands within the full Brillouin zone is used to calculate the basic electronic transport properties for both zincblende and wurtzite crystal phases of bulk gallium nitride. The band structure throughout the Brillouin zone is determined using the empirical pseudopotential method. Calculations of the electron steady-state drift velocity, average energy, valley occupancy and band occupancy in the range of electric fields up to 500 kV/cm are presented. It is found that the threshold electric field for intervalley transfer is greater and that the second conduction band is more readily occupied in wurtzite than in zincblende GaN over the range of electric fields examined here.

Theoretical study of electron transport in gallium nitride

This paper describes characteristic electron transport properties for GaN in bulk and quantum well structures. First, ensemble Monte Carlo calculations of steady-state electron drift velocity in bulk GaN are presented as a function of applied electric field for different lattice temperatures. At 300 K, the calculated peak steady-state drift velocity is 2.8×107 cm/s and the threshold field is 160 kV/cm. It is found that the peak steady-state electron drift velocity decreases only slightly by about 20% as the temperature increases from 300 to 600 K while the threshold field increases slightly by about 20%. Therefore, in addition to its high temperature stability, GaN has a low temperature coefficient making it ideal for high temperature applications. For electron transport in heterostructures, quantum mechanical calculations of the electron capture rate in GaN-based quantum wells as a function of well thickness are also presented. An oscillatory behavior of the electron capture rate as a function of quantum well thickness is observed. It is found that the electron capture time oscillates between 2 and 30 ps, which is about an order of magnitude greater than capture times in GaAs quantum wells. The amplitude of oscillations decreased as the well thickness increased. These results suggest that electron transport and carrier collection in GaN are efficient processes for improved electronic and optoelectronic devices.

Identifying the distinct phases of carrier transport in semiconductors with 10 fs resolution.

We study the very early processes of photogenerated carrier transport in GaAs and Si using THz nonlinear spectroscopy with 10 fs time resolution. This ultrahigh time resolution allows us to clearly separate the instantaneous creation of polarized electron-hole pairs and the subsequent carrier motion for the first time. In addition, our results give the first clear demonstration of the distinct phases of carrier transport; ballistic transport, electron velocity overshoot, and steady-state drift.

The coupling of impurity ions with scrape-off layer plasma ions

One-dimensional analysis of momentum transport equations of electrons, plasma ions, and one impurity charge state shows that both the nonambipolar current and the thermal forces can influence the coupling of impurity and plasma ions. The solution indicates that, in general, a steady-state drift can exist between the impurity and plasma ions. In cases where thermal forces are negligible, the impurity ions are strongly coupled to the plasma ions only if the transport is ambipolar. In this case the plasma ions and the impurities move as a single fluid. However, if nonambipolar currents are present, a steady-state drift is possible between the plasma ions and the impurity ions even if thermal forces are neglected. In this case, the imbalance due to the electron frictional force (∼Z2) acting on the impurity charge state and the plasma ions is balanced by the impurity and plasma ion friction.

Monte Carlo study of hole transport in silicon

The steady state and transient drift velocity of holes in silicon have been investigated using Monte Carlo techniques. The valence band is modeled by warped nonparabolic heavy and light hole bands, and a spherical spin-orbit band. The nonparabolicity of the heavy and light hole bands is included using piecewise continuous functions. The calculated velocities are in better agreement with experimental steady state drift velocity values compared to previous Monte Carlo calculations using only a heavy hole band. Transient calculations show the magnitude of the velocity overshoot for holes is smaller than electrons in silicon but is significantly higher than the steady state drift velocity when high fields are applied.

Effects of collision retardation on hot-electron transport in a two-dimensional electron gas.

The effect of collision retardation on hot-electron transport in a two-dimensional electron gas is examined using an ensemble Monte Carlo simulation. We find that collision retardation (i.e., a nonzero collision duration) tends to make the electrons hotter by suppressing energy-relaxing collision events. Collision retardation also increases the steady-state drift velocity and high-field mobility by suppressing momentum-relaxation events. Finally, it also increases velocity overshoot somewhat

Theory of the electron-plasmon interaction in Monte Carlo calculations through the direct solution of the Poisson equation

Ensemble Monte Carlo calculations of the steady-state electron drift velocity in degenerate bulk GaAs using a self-consistent algorithm specially tailored to directly include the electron-plasmon interaction are presented. The critical issues implicit in the direct approach are the mesh size, charge assignment to the mesh nodes, interpolation of the field at the particle location, and the frequency with which the solution of the Poisson equation is updated. All of these factors determine the stability of the system, the accuracy, and the computational time required in the calculation. Comparison is made to quantum mechanically based techniques in which the electron-plasmon interaction is treated as an additional scattering mechanism. It is found that the steady-state electron drift velocity in bulk degenerate GaAs calculated using the semi-classical approach for the electron-plasmon interaction is significantly less than that calculated assuming no electron-plasmon interaction is present. The steady-state drift velocity calculated using the quantum mechanical approach, wherein the electron-plasmon interaction is treated as a separate scattering mechanism, is affected in the opposite way, i.e., the velocity is greater than in the absence of the electron-plasmon interaction. Neither model can at present be considered complete and caution should be exercised in adopting either approach in device simulation until a more satisfactory model has been developed.

Superlattice Bloch electron conduction and negative differential mobility

Force and energy balance equations are formulated for hot electron transport in an arbitrary superlattice miniband, and are analyzed for negative differential conductivity using a tight binding approximation for GaAs/AlAs superlattices. Both impurity and phonon scatterings are treated. The calculated steady-state peak drift velocity v p for transport across the superlattice, and the critical field E c at which the drift velocity peaks, are analyzed as functions of the miniband width. The present theory predicts for the first time an increase in E c d ( d is the superlattice period) with decreasing miniband width, in favorable comparison with the experimental observations of Sibille et al., indicating that Bloch miniband transport is responsible for negative differential velocity even for the samples of narrowest miniband width in their experiment.

Calculated electron and hole steady-state drift velocities in lattice matched GaInP and AlGaInP

We present calculations based on an ensemble Monte Carlo program of the steady-state electron and hole drift velocities in bulk Ga0.52In0.48P 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. The calculations are made including a realistic treatment of both the conduction and valence energy bands based on the k*p method. All of the principal phonon scattering agents are included in our simulation as well.

Multiple trapping in strong electric fields.

The time-dependent and steady-state drift mobilities of photoexcited carriers are calculated within a framework of a multiple-trapping model incorporating nonlinear effects due to a strong electric field. Tunneling processes from localized states to the transport edge and vice versa are taken into account. We discuss the application of the proposed theory to recent experiments and compare it with hopping theory.

Ballistic transport in alkaline earth sulfides

Monte-Carlo calculations are based on the Fröhlich theory of electron/polar optical phonon scattering, taking into account the full energy and momentum balance and dependence of phonon creation and annihilation. Covering the range from well below to runaway field strength of about 10 5 V/cm, steady state drift velocities and mobilities have been obtained, as well as the gradual change to ballistic transport above 5 X 10 5 V/cm. A “travelling spike” electron energy distribution indicative of loss-free acceleration is consistent with very recent results obtained in thin film electroluminescence sample with high quality earth alkaline sulfide active films.

Theory of electronic transport in two-dimensional Ga0.85In0.15As/Al0.15Ga0.85As pseudomorphic structures

We present calculations of the electron drift velocity and valley populations as a function of applied electric field in two different Ga0.85In0.15As/Al0.15Ga0.85 As heterostructure systems which show two-dimensional size quantization effects. Electronic transport in both a pseudomorphic, double heterostructure system formed by use of three separate semiconductor layers is examined and compared to that of a simpler two-layer, single heterostructure. The calculations are made based on an ensemble Monte Carlo simulation which includes the full physics of the two-dimensional system. The double heterostructure consists of a Ga0.85In0.15 As quantum well bordered on one side by a highly doped (1×1018 1/cm3 ) Al0.15Ga0.85 As layer and on the other by a nearly intrinsic GaAs layer consistent with the design of most pseudomorphic high electron mobility transistors. In order to assess the effect of the electronic confinement within the quantum well on the resulting carrier velocities, the results are compared to calculations of the electron drift velocity in a single heterostructure. The single-heterostructure system consists of two separate layers of doped Al0.15Ga0.85 As and nearly intrinsic Ga0.85In0.15 As. It is found that the electron drift velocity and mobility is much larger within the double heterostructure than within the single heterostructure over a wide range of applied electric field strengths. The presence of the surrounding GaAs layer in the double heterostructure acts to confine the electrons within the two-dimensional system resulting in a significant increase in the average steady-state electron drift velocity.

Theoretical comparison of electron real-space transfer in classical and quantum two-dimensional heterostructure systems

We present a comparison of the effect of real-space transfer on the electron drift velocities in both classical heterostructure systems, those in which spatial quantization effects do not occur, and in two-dimensional heterostructure systems using an ensemble Monte Carlo simulation. The calculations for the two-dimensional system are based on a first-principles formulation of electron transport in a triangular quantum well system using an ensemble Monte Carlo code tailored to include the basic physics of two-dimensional systems. In addition, we present an analysis, again based on a complete ensemble Monte Carlo simulation, of real-space transfer from classical systems, ones in which no two-dimensional gas is formed at the heterointerface. Electron drift velocities within the classical system greater than that possible in the constitutive bulk materials are thwarted by either real-space transfer out of the high mobility material into the adjacent low mobility material or k-space transfer within the narrow gap material itself. In contrast, higher electron drift velocities than that achievable in the bulk occur in a system in which two-dimensional effects are present. In this case, when the electrons are confined within the two-dimensional gas, their corresponding drift velocities are somewhat larger than within the bulk three-dimensional system. We conclude that in electronic devices in which the electric field is applied parallel to the heterostructure layers, that the highest steady-state electron velocities are achieved for transport within the two-dimensional gas. In structures in which either a two-dimensional system is not present or the carriers all reside outside of the quantized states, the steady-state electron drift velocity is always less than or equal to the corresponding velocity in the bulk material due to the combined actions of real-space and k-space transfer.

Theory of high-field electronic transport in bulk ZnS and ZnSe

We present ensemble Monte Carlo calculations of electron transport in bulk ZnSe and ZnS under conditions of high applied electric field strengths. The calculations include the full details of the first two conduction bands as well as the full-order treatment of the electron-phonon scattering mechanisms. The steady-state electron drift velocities as a function of applied electric field are determined for each material system as well as the total electron-phonon scattering rates. In addition, the high-field probability distribution function is presented for both ZnS and ZnSe. As expected, based on the values of the optical-phonon energy, the electron distribution is much cooler in bulk ZnS than in bulk ZnSe at comparable electric field strengths even in the absence of significant impact ionization in either material. Consequently, carrier heating to comparable energies is more difficult to achieve in ZnS than in ZnSe. This has relevance to the operation of electroluminescent devices made from these materials.

Theory of the velocity-field relation in AlGaAs

We present ensemble Monte Carlo calculations of the steady-state electron drift velocity as a function of applied electric field in Al0.32 Ga0.68 As. The effect of various material parameters on the calculated velocity is assessed by varying each parameter independently by ±20%. It is found that both the optical phonon energy and intervalley separation energy alter the peak electron velocity greatly. Variations in the dielectric constants and central valley effective mass have little effect upon the peak drift velocity, but act to alter the threshold electric field. It is further found that the threshold electric field is greater in Al0.32Ga0.68As than in GaAs even though the central-to-satellite valley separation energy is less in AlGaAs. The combined effects of a greater central valley effective mass and a larger phonon energy in AlGaAs result in a greater threshold field. Finally, we present sets of material parameters useful in Monte Carlo models for both GaAs and AlGaAs.

Monte Carlo Study of Hot Electron Transport in Quantum Wells

Monte Carlo simulations of hot electron transport in AlGaAs/GaAs /AlGaAs quantum wells were carried out in order to clarify the drift velocity overshoot and steady state drift velocity versus the electric-field relation. In the simulations, we took into account the nonparabolic isotropic energy band structures. Results are given for GaAs well widths of 500 and 100 Å and an electron sheet density of 1.0×1012 cm-2 at 77 K. The drift-velocity overshoot reaches about 7×107 cm/s at an electric field of 10 kV/cm in both quantum well structures. A negative differential mobility appears beyond 3 kV/cm in both structures due to electron transfer from the Γ valley to the L valleys.

Theory of the steady-state hole drift velocity in InGaAs

We present calculations of the steady-state hole drift velocity in Ga0.47In0.53As as a function of applied electric field based on an ensemble Monte Carlo method. The calculation uses no adjustable parameters in the determination of the scattering rates and contains the full details of the valence-band structure derived using the k*p method. It is found that the calculated values match recent experimental values within 20% in the saturated regime. The calculations are made over the applied field range of 10–250 kV/cm.

A test by Monte Carlo simulation of the lucky drift theory of impact ionisation for a model with energy-dependent parameters

The lucky drift theory of the impact ionisation coefficient is tested against a Monte Carlo simulation for a model semiconductor with a multi-valley band structure and energy-dependent parameters. The lucky drift formulation due to Burt (1985) is applied to this model to calculate the steady-state drift velocity, average electron energy, energy and momentum relaxation lengths and the impact ionisation coefficient. The lucky drift predictions for these quantities are compared with estimates derived from a Monte Carlo simulation over a range of values of the applied electric field. The agreement between the lucky drift predictions and Monte Carlo results is quite encouraging, given the extreme simplicity of the theory and the generality of the model.

Effect of loop-filter and non-linearity on carrier-frequency stabilization in WBFM

The generation of wide-band FM using direct frequency modulation generally requires a subsidiary loop to stabilize the carrier frequency. The steady-state carrier drift is shown to depend on the loop gain as well as the reference frequency of the frequency demodulator used in the feedback loop. The transient behaviour of the loop may be controlled by the loop filter which is used to separate modulating signal from drift. An appropriate low-Q second-order filter is preferable to one with sharp roll-off rate. The consequent overlapping of drift and signal spectra is resolved by the use of a suitable pre-emphasis filter between the modulating signal and the FM loop. The demodulator non-linearity has significant effect on the transient response when the drift size is large. Two types of demodulator characteristics are used in evaluating the step response of the loop. It is found that the pulse-counting type provides a faster loop response at large drift steps than the ‘S’ type.

Modeling Random Gyro Drift Rate by Data Dependent Systems

A new modeling procedure is presented in which a mathematical model for random gyro drift rate is obtained directly from the original observations without requiring any theoretical conjectures or preprocessing of the data. The adequate model so obtained confirms the presence of a random walk component causing the steady state drift and a stochastic component of the nature of correlated noise. It also provides a quantitative measure of the relative contribution of each component, useful in determining the quality of the gyro in guidance over extended periods.