# Simulation of Epitaxial Film–Substrate Interaction Potential

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## Abstract

**:**

## 1. Introduction

## 2. Substrate Potential Modeling

## 3. Ground State of Monoatomic Film

## 4. Structural Phase Transition

## 5. Discussion

_{8}Sb

_{92}transition from the amorphous phase to the crystalline phase when the substrate is heated [37]. The crystallinity of the thermoelectric thin film Ag-Sb-Te at room temperature depends on the state of the substrate [38]. The crystalline silicon thin film is a two-phase structure of the amorphous phase and the crystalline phase [39]. The transition temperature from the amorphous phase to the crystalline phase shifts under the influence of the substrate.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The dependence of amplitudes ${A}_{k}\left({z}^{\prime},{\sigma}^{\prime}\right)$ on the parameter ${\sigma}^{\prime}$ at ${z}^{\prime}=1$.

**Figure 3.**Plots for ${A}_{1}\left({z}^{\prime},{\sigma}^{\prime}\right)$ (

**a**) and ${A}_{2}\left({z}^{\prime},{\sigma}^{\prime}\right)$ (

**b**) versus ${\sigma}^{\prime}$ near ${\sigma}_{0}\mathrm{}({A}_{1}\left({z}^{\prime},{\sigma}_{0}\right)=0)$ at different ${z}^{\prime}$.

**Figure 4.**The plot of the ratio ${A}_{2}\left({z}^{\prime},{\sigma}^{\prime}\right)/{A}_{1}\left({z}^{\prime},{\sigma}^{\prime}\right)$ coefficients to ${\sigma}^{\prime}$ at ${z}^{\prime}=1$.

**Figure 5.**The plot of the parameter ${\sigma}_{0}$ dependence on the distance to the film ${z}^{\prime}$.

**Figure 6.**The dependence of the coefficient $B\left(1,1\right)$ on the number of atoms in the chain.

**Figure 7.**A plot for the potential $U\left({x}^{\prime},{z}^{\prime}\right)$ versus ${x}^{\prime}$ at ${z}^{\prime}=1$, ${\sigma}^{\prime}=1$, and $\epsilon =1$ for different numbers of atoms in the chain $N$. FK is the Frenkel–Kontorova potential.

**Figure 8.**The arrangement of film atoms for elasticity modulus equal to substrate amplitude ($g/A=1$) and different values of parameter $B$: (

**a**) $B=0.1$, (

**b**) $B=0.5$, (

**c**) $B=1.0$, (

**d**) $B=2$.

**Figure 9.**Substrate potential surfaces for different values of parameter $B$: (

**a**) $B=0.1$, (

**b**) $B=0.5$, (

**c**) $B=1.0$, (

**d**) $B=2$.

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**MDPI and ACS Style**

Belim, S.V.; Tikhomirov, I.V.; Bychkov, I.V.
Simulation of Epitaxial Film–Substrate Interaction Potential. *Coatings* **2022**, *12*, 853.
https://doi.org/10.3390/coatings12060853

**AMA Style**

Belim SV, Tikhomirov IV, Bychkov IV.
Simulation of Epitaxial Film–Substrate Interaction Potential. *Coatings*. 2022; 12(6):853.
https://doi.org/10.3390/coatings12060853

**Chicago/Turabian Style**

Belim, Sergey V., Ilya V. Tikhomirov, and Igor V. Bychkov.
2022. "Simulation of Epitaxial Film–Substrate Interaction Potential" *Coatings* 12, no. 6: 853.
https://doi.org/10.3390/coatings12060853