Abstract

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 Schrödinger 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 free-flight 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.

Original languageEnglish (US)
Article number044307
JournalJournal of Applied Physics
Volume120
Issue number4
DOIs
StatePublished - Jul 28 2016

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nanowires
simulation
Runge-Kutta method
Brillouin zones
electric fields
free flight
energy
perturbation theory
operators
expansion

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Modeling of multi-band drift in nanowires using a full band Monte Carlo simulation. / Hathwar, Raghuraj; Saraniti, Marco; Goodnick, Stephen.

In: Journal of Applied Physics, Vol. 120, No. 4, 044307, 28.07.2016.

Research output: Contribution to journalArticle

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