Three-body bond-order (Tersoff-style) potential by Wang and Rockett (1991) v000

Ramanish Singh; Daniel S. Karls; Jun Wang; Angus Rockett

doi:10.25950/29dfb23c

Jump to: Files | Wiki

ThreeBodyBondOrder_WR__MD_817691861922_000

Title A single sentence description.	Three-body bond-order (Tersoff-style) potential by Wang and Rockett (1991) v000
Description	A modified form of the Tersoff empirical interatomic potential originally developed to model silicon surfaces. It includes a screened-Morse-potential tail to the bulk Tersoff interaction behavior which is important when tetrahedral coordination is disrupted.
Disclaimer A statement of applicability provided by the contributor, informing users of the intended use of this KIM Item.	None

Contributor	Ramanish Singh
Maintainer	Ramanish Singh
Implementer	Ramanish Singh Daniel S. Karls
Developer	Jun Wang Angus Rockett
Published on KIM	2019
How to Cite	This Model Driver originally published in [1] is archived in OpenKIM [2-4]. [1] Wang J, Rockett A. Simulating diffusion on Si(001) 2x1 surfaces using a modified interatomic potential. Phys Rev B. 1991;43(15):12571–9. doi:10.1103/PhysRevB.43.12571 [2] Singh R, Karls DS, Wang J, Rockett A. Three-body bond-order (Tersoff-style) potential by Wang and Rockett (1991) v000. OpenKIM; 2019. doi:10.25950/29dfb23c [3] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6 [4] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a Click here to download the above citation in BibTeX format.
Funding	Not available

Short KIM ID The unique KIM identifier code.	MD_817691861922_000
Extended KIM ID The long form of the KIM ID including a human readable prefix (100 characters max), two underscores, and the Short KIM ID. Extended KIM IDs can only contain alpha-numeric characters (letters and digits) and underscores and must begin with a letter.	ThreeBodyBondOrder_WR__MD_817691861922_000
DOI	10.25950/29dfb23c https://doi.org/10.25950/29dfb23c https://commons.datacite.org/doi.org/10.25950/29dfb23c
KIM Item Type	Model Driver
KIM API Version	2.0
Programming Language(s) The programming languages used in the code and the percentage of the code written in each one.	100.00% C

Models using this Model Driver

ThreeBodyBondOrder_WR_WangRockett_1991_Si__MO_081872846741_000

Files

CMakeLists.txt
LICENSE
README
ThreeBodyBondOrder.c
bondorder.inc
bondorder_aux.inc
kimprovenance.edn
kimspec.edn

Download

ThreeBodyBondOrder_WR__MD_817691861922_000.txz	Tar+XZ	Linux and OS X archive
ThreeBodyBondOrder_WR__MD_817691861922_000.zip	Zip	Windows archive

This bond-order potential, which is an extension to the Tersoff potential, was proposed by Jun Wang and A. Rockett in 1991 for modeling diffusion on silicon surfaces for applications in microelectronics devices. It addresses limitations of the Tersoff potential, which predicts the bulk properties of Si well, but does not give satisfactory results for surface diffusion.

<br/>
### Drawbacks of the original Tersoff Potential

Since the Tersoff potential is a covalent potential, it has a short interaction range and a soft angular dependence. This causes problems when it is applied to determine surface behavior because the atoms and adatoms on the surface have lower symmetry as compared to the atoms in the bulk.  
Moreover, the Tersoff cutoff functions leads to a steep (positive) slope at $$r = 0.285$$ nm. This means that an atom moving away will feel a sudden attractive force at $$r = 0.285$$ nm, which  leads to anomalous behavior of atoms on surfaces when there are large distortions during surface diffusion processes.
<br/>

### The modified Tersoff Potential

The modified potential takes into account both the metallic and directional (covalent) contributions to the bonding. It interpolates between screened long range and short range covalent bonding in surface Si atoms. For long range interactions, a modified Morse potential is used and for short range interactions, the Tersoff potential is used. A screened Morse potential tail is added to the bulk Tersoff potential to predict the behavior of atoms when tetrahedral geometry is disrupted. Also, both the repulsive and attractive part have an angle-dependent screening term.
<br/>

### Mathematical Description

\begin{equation}
V_{ij}=f_{c}(r_{ij})(A_{ij}e^{-\lambda_{1}r_{ij}}-BB_{ij}e^{-\lambda_{2}r_{ij}})
\end{equation}
  
  \begin{equation}
f_{c}(r_{ij}) =
\begin{cases}
1 & r < R-D \\
\tfrac{1}{2} - \tfrac{1}{2}\sin[\tfrac{\pi}{2}(r-R)/D] & R-D < r < R+D \\
0 & r > R + D
\end{cases}
\end{equation}

\begin{equation}
B_{ij}=[1+(\beta\zeta_{ij})^{n}]^{-1/2n}
\end{equation}

\begin{equation}
\zeta_{ij} = \sum_{k (\neq i,j) } g(\theta_{ijk})\exp\{[\lambda_3(r_{ij}-r_{ik})]^3\}
f_{c}(r_{ik}) 
\end{equation}

\begin{equation}
g^{}(cos\theta_{ijk}) = 1 + \left(\frac{c}{d}\right)^2 - \frac{c^2}{d^2 + (h-\cos\theta_{ijk})^2}
\end{equation}

\begin{equation}
A_{ij} =A
\begin{cases}
1 & r < R_a-D_a \\
B_{ij}+(1-B_{ij})\{\tfrac{1}{2} - \tfrac{1}{2}\sin[\tfrac{\pi}{2}(r-R_a)/D_a]\} & R_a-D_a < r < R_a+D_a \\
B_{ij} & r > R_a + D_a
\end{cases}
\end{equation}

<br/>
#### Note:
$$\alpha$$, which is a parameter defined in the original Tersoff potential is not used in this potential. However, to keep the functional form same, $$\alpha$$ appears in the Wang-Rockett driver code, but is set to zero and does not affect the calculations.

Wiki Contributors

2019-05-09T10:43:28.491643	tadmor
2019-05-08T22:29:18.191398	ramanish
2019-05-08T22:28:30.134496	ramanish
2019-05-08T22:28:10.409265	ramanish
2019-05-08T22:27:50.117024	ramanish
2019-05-08T22:27:25.131713	ramanish
2019-05-08T22:13:13.669810	ramanish
2019-05-08T22:10:34.715777	ramanish
2019-05-08T22:05:56.524903	ramanish