Kevin F. Brennan

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.

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.

Electron transport characteristics of GaN for high temperature device modeling

Monte Carlo simulations of electron transport based upon an analytical representation of the lowest conduction bands of bulk, wurtzite phase GaN are used to develop a set of transport parameters for devices with electron conduction in GaN. Analytic expressions for spherical, nonparabolic conduction band valleys at the Γ, U, M, and K symmetry points of the Brillouin zone are matched to experimental effective mass data and to a pseudopotential band structure. The low-field electron drift mobility is calculated for temperatures in the range of 300–600 K and for ionized impurity concentrations between 1016 and 1018 cm−3. Compensation effects on the mobility are also examined. Electron drift velocities for fields up to 500 kV/cm are calculated for the above temperature range. To aid GaN device modeling, the drift mobility dependences on ambient temperature, donor concentration, and compensation ratio are expressed in analytic form with parameters determined from the Monte Carlo results. Analytic forms are also...

Ensemble Monte Carlo study of electron transport in wurtzite InN

Electronic transport in wurtzite phase InN is studied using an ensemble Monte Carlo method. The model includes the full details of the first five conduction bands derived from the pseudopotential method and a numerically calculated impact ionization transition rate using a wave-vector- dependent dielectric function. Calculated results for electron transport at both low and high electric field are presented and compared with available results from simpler methods. The dependence of the relevant transport properties on the parameters is discussed, in particular in regards to the uncertainties in the band structure and coupling constants. It is found that at a field of 65 kV/cm that the peak electron drift velocity is 4.2×107 cm/s. The peak velocity in InN is substantially higher than in GaN. The velocity field curve presents a noticeable anisotropy with respect to field direction. The peak velocity decreases to 3.4×107 cm/s for a field of 70 kV/cm in the direction perpendicular to the basal plane. The elect...

High field electron transport properties of bulk ZnO

The Monte Carlo method is used to simulate electron transport for electric field strengths up to 350 kV/cm in bulk, wurtzite structure ZnO. The relevant parts of the conduction bands of a first-principles band structure are approximated by spherically symmetric, nonparabolic valleys located at the Γ and Umin symmetry points of the Brillouin zone. It is shown that the analytic expressions represent the band structure and the density of states well over a range of nearly 5 eV from the bottom of the conduction band. The simulated electron steady-state drift velocity versus electric field characteristics are calculated for lattice temperatures of 300, 450, and 600 K. For room temperature, drift velocities higher than 3×107 cm/s are reached at fields near 250 kV/cm. Examination of the electron energy distributions shows that the strong decrease of the differential mobility with increasing electric field in the field range studied is to be associated with the pronounced nonparabolicity of the central valley and...

Theory of hole initiated impact ionization in bulk zincblende and wurtzite GaN

In this article, the first calculations of hole initiated interband impact ionization in bulk zincblende and wurtzite phase GaN are presented. The calculations are made using an ensemble Monte Carlo simulation including the full details of all of the relevant valence bands, derived from an empirical pseudopotential approach, for each crystal type. The model also includes numerically generated hole initiated impact ionization transition rates, calculated based on the pseudopotential band structure. The calculations predict that both the average hole energies and ionization coefficients are substantially higher in the zincblende phase than in the wurtzite phase. This difference is attributed to the higher valence band effective masses and equivalently higher effective density of states found in the wurtzite polytype. Furthermore, the hole ionization coefficient is found to be comparable to the previously calculated electron ionization coefficient in zincblende GaN at an applied electric field strength of 3 ...

Theory of resonant tunneling in a variably spaced multiquantum well structure - An Airy function approach

A theoretical study of resonant tunneling in multilayered heterostructures is presented based on an exact solution of the Schrodinger equation under the application of a constant electric field. By use of the transfer matrix approach, the transmissivity of the structure is determined as a function of the incident electron energy. The approach presented herein is easily extended to many layer structures where it is more accurate than other existing transfer matrix or Wentzel–Kramers–Brillouin (WKB) models. The transmission resonances are compared to the bound‐state energies calculated for a finite square well under bias using either an asymmetric square‐well model or the exact solution of an infinite square well under the application of an electric field. The results show good agreement with other existing models as well as with the bound‐state energies. The calculations were then applied to a new superlattice structure, the variably spaced superlattice energy filter, which is designed such that under bias...

Monte Carlo calculation of electron initiated impact ionization in bulk zinc-blende and wurtzite GaN

Calculations of the high-field electronic transport properties of bulk zinc-blende and wurtzite phase gallium nitride are presented focusing particularly on the electron initiated impact ionization rate. The calculations are performed using ensemble Monte Carlo simulations, which include the full details of the band structure derived from an empirical pseudopotential method. The model also includes the numerically generated electron impact ionization transition rate, calculated based on the pseudopotential band structures for both crystallographic phases. The electron initiated impact ionization coefficients are calculated as a function of the applied electric field. The electron distribution is found to be cooler and the ionization coefficients are calculated to be lower in the wurtzite phase as compared to zinc-blende gallium nitride at compatable electric-field strengths. The higher electron energies and the resulting larger impact ionization coefficients in zinc-blende gallium nitride are believed to ...

Band structure nonlocal pseudopotential calculation of the III-nitride wurtzite phase materials system. Part I. Binary compounds GaN, AlN, and InN

This work presents nonlocal pseudopotential calculations based on realistic, effective atomic potentials of the wurtzite phase of GaN, InN, and AlN. A formulation formulation for the model effective atomic potentials has been introduced. For each of the constitutive atoms in these materials, the form of the effective potentials is optimized through an iterative scheme in which the band structures are recursively calculated and selected features are compared to experimental and/or ab initio results. The optimized forms of the effective atomic potentials are used to calculate the band structures of the binary compounds, GaN, InN, and AlN. The calculated band structures are in excellent overall agreement with the experimental/ab initio values, i.e., the energy gaps at high-symmetry points, valence-band ordering, and effective masses for electrons match to within 3%, with a few values within 5%. The values of the energy separation, effective masses, and nonparabolicity coefficients for several secondary valle...

Monte Carlo calculation of two-dimensional electron dynamics in GaN–AlGaN heterostructures

We present detailed Monte Carlo based calculations of the electron dynamics in GaN–AlGaN heterostructures in the presence of strain polarization fields. The model consists of a fully numerical self-consistent solution of the Schrodinger–Poisson equation with a Monte Carlo transport model. The two-dimensional sub-band energies, wave functions and carrier scattering mechanisms are computed numerically and included within a Monte Carlo simulation. The electron energy, steady-state and transient drift velocity and band occupancy are calculated as a function of electric field for different AlGaN–GaN heterostructure compositions. The effect of piezoelectrically induced strain fields on the transport dynamics is examined. A field dependent mobility model is also developed from the Monte Carlo results.