Efficient numerical integrators for highly oscillatory dynamic systems based on modified magnus integrator method

李文成,; 邓子辰,; 黄永安,

doi:10.1007/s10483-006-1010-z

Cited by 1 publication

(1 citation statement)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(26) has been previously used to solve linear differential equations with a very high accuracy. 21,22 Figure 2 shows the difference between using just X 1 and using both X 1 and X 2 in Eq. (26) in solving the KI equations.…”

Section: Numerical Solution Of the Krieger And Iafrate Equations Imentioning

confidence: 99%

Modeling of multi-band drift in nanowires using a full band Monte Carlo simulation

Hathwar

Saraniti

Goodnick

2016

Journal of Applied Physics

View full text Add to dashboard Cite

We report on a new numerical approach for multi-band drift within the context of full band Monte Carlo (FBMC) simulation and apply this to Si and InAs nanowires. The approach is based on the solution of the Krieger and Iafrate (KI) equations [J. B. Krieger and G. J. Iafrate, Phys. Rev. B 33, 5494 (1986)], which gives the probability of carriers undergoing interband transitions subject to an applied electric field. The KI equations are based on the solution of the time-dependent Schr€ odinger equation, and previous solutions of these equations have used Runge-Kutta (RK) methods to numerically solve the KI equations. This approach made the solution of the KI equations numerically expensive and was therefore only applied to a small part of the Brillouin zone (BZ). Here we discuss an alternate approach to the solution of the KI equations using the Magnus expansion (also known as "exponential perturbation theory"). This method is more accurate than the RK method as the solution lies on the exponential map and shares important qualitative properties with the exact solution such as the preservation of the unitary character of the time evolution operator. The solution of the KI equations is then incorporated through a modified FBMC freeflight drift routine and applied throughout the nanowire BZ. The importance of the multi-band drift model is then demonstrated for the case of Si and InAs nanowires by simulating a uniform field FBMC and analyzing the average carrier energies and carrier populations under high electric fields. Numerical simulations show that the average energy of the carriers under high electric field is significantly higher when multi-band drift is taken into consideration, due to the interband transitions allowing carriers to achieve higher energies. Published by AIP Publishing.

show abstract

Section: Numerical Solution Of the Krieger And Iafrate Equations Imentioning

confidence: 99%

Modeling of multi-band drift in nanowires using a full band Monte Carlo simulation

Hathwar

Saraniti

Goodnick

2016

Journal of Applied Physics

View full text Add to dashboard Cite

show abstract

Efficient numerical integrators for highly oscillatory dynamic systems based on modified magnus integrator method

Cited by 1 publication

References 12 publications

Modeling of multi-band drift in nanowires using a full band Monte Carlo simulation

Modeling of multi-band drift in nanowires using a full band Monte Carlo simulation

Contact Info

Product

Resources

About