We present a comprehensive study of the transport dynamics of electrons in the ternary compounds, Al Ga 1 N and In Ga 1 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 steadystate 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.Index Terms-Monte Carlo method, semiconductor materials, wide bandgap semiconductors.

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 valleys are tabulated as well in order to facilitate analytical Monte Carlo transport simulations.

This work presents detailed information on the band structures of the III-nitride wurtzite ternary alloys, computed through the virtual crystal approximation approach. The key ingredient of this study is the set of realistic atomic effective potentials described in Part I of the present work, dedicated to the constituent binary compounds. The model relies on the linear interpolation of the structural parameters and of the local and nonlocal effective potentials: no further empirical corrections are included. The dependence on the mole fraction is computed for the energy gaps at all the high-symmetry points, the valence-band width, and the electron effective masses in the valleys relevant for carrier-transport simulation.

The time evolution of Bloch electrons (holes) moving in a constant electric field has been studied for GaN and 2H-SiC using a numerical model based on realistic band structures. The large band gap of GaN and the SiC polytypes provide much larger critical fields than in conventional semiconductors, which allows device operation at very high electric fields. At sufficiently high electric fields the carriers may change band during drift due to tunneling. GaN has a direct band gap, while the hexagonal SiC polytypes have indirect band gaps. In spite of this difference the valence band structure is very similar due to the wurtzite symmetry. In this work the GaN and the 2H-SiC polytype are considered as wurtzite prototype semiconductors in order to study valence band to band tunneling in wurtzite semiconductors for electric fields directed along the c axis. A large valence band to band tunneling probability was found for both materials at electric fields above 400 kV/cm. This shows the importance of considering band to band tunneling in studies of high field hole transport in wide band-gap hexagonal semiconductor materials. The proposed numerical approach can be used to enhance the interband tunneling models used in Monte Carlo simulation of carrier transport in hexagonal semiconductors.