Carrier Transport In Wurtzite GaN Using Monte Carlo Method

There has been considerable interest in GaN recently owing to its large band gap and favorable material properties, such as high electron mobility and very high thermal conductivity.It has been studied intensively for high temperature electronics, ultraviolet detectors and blue electroluminescent devices. GaN is one of the best candidates among other wide-band-gap materials for optoelectronic and electronic applications. For example, light emitting diodes (LEDs) and lasers using InGaN/GaN and AlGaN/GaN heterostructures have already been demonstrated. The direct nature of its band gap makes GaN ideal for optical detection and emission within the ultraviolet portion of the electromagnetic spectrum. Furthermore, the large band gap results in a large breakdown field, which together with its high thermal conductivity, makes GaN especially suitable for high-power and high-speed applications.The Monte Carlo method is often used in novel device simulations. It provides a useful tool for the analysis, and understanding of semiconductor devices. The single particle Monte Carlo method, as applied to charge transport in semiconductors, consists of a simulation of the motion of one electron inside the crystal, subject to the action of external forces due to applied electric field and of given scattering mechanisms. The motion of electron is determined by collisions and external forces. The effect of external forces is deterministic, but the collision processes affect the motion in a probabilistic manner. The former effect may be calculated by applying the classical laws of motion, but the latter effect is required to be evaluated by applying the probability theory. The duration of the carrier free flight and the scattering events involved in the simulation are selected stochastically in accordance with some given distribution probabilities describing microscopic processes. As a consequence, any Monte Carlo method relies on the generation of a sequence of random numbers with given distribution probabilities.We present velocity-field simulations of wurtzite-phase GaN at 300K using an single particle Monte Carlo technique. A three-valley model of the band structure is assumed, and the ionized impurity, polar optical phonon, acoustic phonon, piezoelectric, andintervalley scattering mechanisms are considered. Nonparabolicity is considered in three valleys. For the calculations the ionized impurity concentration was fixed as 10I7cm~3 and 101 cm"3 respectively. In the simulations we considered the effect of the lattice temperature on the steady-state electron drift velocity-field relation in GaN. The influence of time on displacement was obtained, and the curve slope was approximate equal to drift velocity of electrons. Drift velocity decreases with increasing lattice temperature due to the increased total scattering rate for the applied electric fields considered. In our simulation for 300K lattice temperature, there is a region of negative differential electron mobility for field strengths exceeding about 1.6x10 V/m with ionized impurity concentration of 1x10 cm" and field strengths exceeding about 1.4x 107 V/m with ionized impurity concentration of 1 x 1018 cm'3.