# A split-step method to include electron–electron collisions via Monte Carlo in multiple rate equation simulations

## Abstract

A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron–phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron–electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate how electron–electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.

- Authors:

- Department of Physics and OPTIMAS Research Center, University of Kaiserslautern (Germany)
- Department of Chemistry and OPTIMAS Research Center, University of Kaiserslautern (Germany)
- Department of Physics, Kennesaw State University, Kennesaw, GA 30144 (United States)

- Publication Date:

- OSTI Identifier:
- 22572363

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 322; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIELECTRIC MATERIALS; ELECTRON-ELECTRON COLLISIONS; ELECTRON-ELECTRON INTERACTIONS; FORTRAN; IONIZATION; MONTE CARLO METHOD; NONLINEAR PROBLEMS; PHONONS; PHOTONS; PULSES; SIMULATION; STOCHASTIC PROCESSES

### Citation Formats

```
Huthmacher, Klaus, Molberg, Andreas K., Rethfeld, Bärbel, and Gulley, Jeremy R., E-mail: jgulley@kennesaw.edu.
```*A split-step method to include electron–electron collisions via Monte Carlo in multiple rate equation simulations*. United States: N. p., 2016.
Web. doi:10.1016/J.JCP.2016.06.043.

```
Huthmacher, Klaus, Molberg, Andreas K., Rethfeld, Bärbel, & Gulley, Jeremy R., E-mail: jgulley@kennesaw.edu.
```*A split-step method to include electron–electron collisions via Monte Carlo in multiple rate equation simulations*. United States. doi:10.1016/J.JCP.2016.06.043.

```
Huthmacher, Klaus, Molberg, Andreas K., Rethfeld, Bärbel, and Gulley, Jeremy R., E-mail: jgulley@kennesaw.edu. Sat .
"A split-step method to include electron–electron collisions via Monte Carlo in multiple rate equation simulations". United States.
doi:10.1016/J.JCP.2016.06.043.
```

```
@article{osti_22572363,
```

title = {A split-step method to include electron–electron collisions via Monte Carlo in multiple rate equation simulations},

author = {Huthmacher, Klaus and Molberg, Andreas K. and Rethfeld, Bärbel and Gulley, Jeremy R., E-mail: jgulley@kennesaw.edu},

abstractNote = {A split-step numerical method for calculating ultrafast free-electron dynamics in dielectrics is introduced. The two split steps, independently programmed in C++11 and FORTRAN 2003, are interfaced via the presented open source wrapper. The first step solves a deterministic extended multi-rate equation for the ionization, electron–phonon collisions, and single photon absorption by free-carriers. The second step is stochastic and models electron–electron collisions using Monte-Carlo techniques. This combination of deterministic and stochastic approaches is a unique and efficient method of calculating the nonlinear dynamics of 3D materials exposed to high intensity ultrashort pulses. Results from simulations solving the proposed model demonstrate how electron–electron scattering relaxes the non-equilibrium electron distribution on the femtosecond time scale.},

doi = {10.1016/J.JCP.2016.06.043},

journal = {Journal of Computational Physics},

number = ,

volume = 322,

place = {United States},

year = {Sat Oct 01 00:00:00 EDT 2016},

month = {Sat Oct 01 00:00:00 EDT 2016}

}