# Computational stochastic model of ions implantation

## Abstract

Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.

- Authors:

- M.V. Keldysh Institute of Applied Mathematics RAS, 4,Miusskaya sq., 125047 Moscow (Russian Federation)
- VNII Geosystem Russian Federal Center, Varshavskoye roadway, 8, Moscow (Russian Federation)
- Scuola di Lettere e BeniCulturali, University di Bologna, sede di Ravenna, via Mariani 5, 48100 Ravenna (Italy)

- Publication Date:

- OSTI Identifier:
- 22391061

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1648; Journal Issue: 1; Conference: ICNAAM-2014: International Conference on Numerical Analysis and Applied Mathematics 2014, Rhodes (Greece), 22-28 Sep 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BROWNIAN MOVEMENT; CRYSTALS; DIELECTRIC MATERIALS; DIFFERENTIAL EQUATIONS; DISTRIBUTION FUNCTIONS; GASES; ION IMPLANTATION; IRRADIATION; KINETIC EQUATIONS; NUCLEATION; PHASE TRANSFORMATIONS; POROSITY; STOCHASTIC PROCESSES; STRESSES; SURFACES; THIN FILMS; VACANCIES; XENON IONS

### Citation Formats

```
Zmievskaya, Galina I., E-mail: zmi@gmail.ru, Bondareva, Anna L., E-mail: bal310775@yandex.ru, Levchenko, Tatiana V., E-mail: tatlevchenko@mail.ru, and Maino, Giuseppe, E-mail: giuseppe.maino@enea.it.
```*Computational stochastic model of ions implantation*. United States: N. p., 2015.
Web. doi:10.1063/1.4912495.

```
Zmievskaya, Galina I., E-mail: zmi@gmail.ru, Bondareva, Anna L., E-mail: bal310775@yandex.ru, Levchenko, Tatiana V., E-mail: tatlevchenko@mail.ru, & Maino, Giuseppe, E-mail: giuseppe.maino@enea.it.
```*Computational stochastic model of ions implantation*. United States. doi:10.1063/1.4912495.

```
Zmievskaya, Galina I., E-mail: zmi@gmail.ru, Bondareva, Anna L., E-mail: bal310775@yandex.ru, Levchenko, Tatiana V., E-mail: tatlevchenko@mail.ru, and Maino, Giuseppe, E-mail: giuseppe.maino@enea.it. Tue .
"Computational stochastic model of ions implantation". United States.
doi:10.1063/1.4912495.
```

```
@article{osti_22391061,
```

title = {Computational stochastic model of ions implantation},

author = {Zmievskaya, Galina I., E-mail: zmi@gmail.ru and Bondareva, Anna L., E-mail: bal310775@yandex.ru and Levchenko, Tatiana V., E-mail: tatlevchenko@mail.ru and Maino, Giuseppe, E-mail: giuseppe.maino@enea.it},

abstractNote = {Implantation flux ions into crystal leads to phase transition /PT/ 1-st kind. Damaging lattice is associated with processes clustering vacancies and gaseous bubbles as well their brownian motion. System of stochastic differential equations /SDEs/ Ito for evolution stochastic dynamical variables corresponds to the superposition Wiener processes. The kinetic equations in partial derivatives /KE/, Kolmogorov-Feller and Einstein-Smolukhovskii, were formulated for nucleation into lattice of weakly soluble gases. According theory, coefficients of stochastic and kinetic equations uniquely related. Radiation stimulated phase transition are characterized by kinetic distribution functions /DFs/ of implanted clusters versus their sizes and depth of gas penetration into lattice. Macroscopic parameters of kinetics such as the porosity and stress calculated in thin layers metal/dielectric due to Xe{sup ++} irradiation are attracted as example. Predictions of porosity, important for validation accumulation stresses in surfaces, can be applied at restoring of objects the cultural heritage.},

doi = {10.1063/1.4912495},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1648,

place = {United States},

year = {Tue Mar 10 00:00:00 EDT 2015},

month = {Tue Mar 10 00:00:00 EDT 2015}

}