Full-band matrix solution of the Boltzmann transport equation and electron impact ionization in GaAs

Simulation of hole phonon-velocity in strained Si/SiGe metal-oxide-semiconductor transistor

“…Moreover, the subbands present at the Si/SiGe interface ͑parasitic channel͒, are described by a nonparabolic band with effective mass m* ϭ1.1 m 0 and a nonparabolic parameter ␣ϭ0.5. 10 In these bands, we obtain a mobility of about ϳ200 cm 2 V Ϫ1 s Ϫ1 in good agreement with value given by Fischetti and Laux in relaxed SiGe. 2 For the scattering mechanisms, we take into account acoustic and optical phonons with intra-as well as inter-subband scattering.…”

“…In a third step, using a Boltzmann transport equation matrix solution, 10 we investigate the transport process in the inversion layer for a spatially homogeneous channel with constant longitudinal ͓100͔-electric field. We consider the hole subbands ͑4 -8 subbands with LH, HH and spin-orbite character͒ where the wave functions are located in the strained-Si channel.…”

“…The calculation of the scattering rate between 2D holes and bulk phonons follows a conventional approach. 10,5 The parameters used for each type of phonon are listed in Table I. Figure 5 shows the average drift velocity obtained when solving the Boltzmann transport equation for holes in the 2D subband structure reported in Fig.…”

“…We use a 20 band k.p Hamiltonian method recently developed 1,6 for the determination of the valence-band structure and a self-consistent effective mass and onedimensional ͑1D͒ solver of the Schrödinger and Poisson equations for the subband structure calculation of the confined holes. Finally, a direct matrix solution of the Boltzmann transport equation, 10 The present article organized as follows. The theoretical methods employed are summarized in Sec.…”

Coupled Solution of Boltzmann Transport Equation, Maxwell’s and Navier Stokes equations

“…In a state of equilibrium a gas of particles has uniform composition with constant temperature and density. If the gas is subjected to a temperature difference or disturbed by externally applied electric, magnetic, or mechanical forces, it will be set in motion and the temperature, density, and composition may become functions of position and time, in other words, the gas moves out of equilibrium [6][7][8][9]. The Boltzmann Equation applies to a quantity known as the distribution function, which describes this non-equilibrium state mathematically and specifies how quickly and in what manner the state of the gas changes when the disturbing forces are varied.…”