A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories

A general method to calculate a lower bound and an estimated upper bound for the surface diffusion coefficient from jump frequencies of an adatom from one absorption site to another has been formulated. This method has been applied to the surface diffusion of Si on Si(111). Keating's potential...

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Main Authors:	Ibrahim Ali , Noorbatcha, Lionel M. , Raff, Donald L. , Thompson
Format:	Article
Language:	English
Published:	American Institute of Physics (AIP) 1985
Subjects:	QD Chemistry
Online Access:	http://irep.iium.edu.my/35865/ http://irep.iium.edu.my/35865/ http://irep.iium.edu.my/35865/ http://irep.iium.edu.my/35865/1/JCP1985.pdf

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spelling	iium-358652014-03-09T02:19:28Z http://irep.iium.edu.my/35865/ A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories Ibrahim Ali , Noorbatcha Lionel M. , Raff Donald L. , Thompson QD Chemistry A general method to calculate a lower bound and an estimated upper bound for the surface diffusion coefficient from jump frequencies of an adatom from one absorption site to another has been formulated. This method has been applied to the surface diffusion of Si on Si(111). Keating's potential has been used for the Si(111) lattice. The interaction potential between the adatom and the lattice is a pairwise sum of 60 Morse potentials involving the Si atoms in the first and second layers of the crystal. This potential formulation predicts the existence of two different types of adsorption sites on the Si(111) surface. The jump frequencies from these adsorption sites have been calculated by classical trajectory methods. Using these jump frequencies, a lower bound for the diffusion coefficient is calculated by solving a set of coupled phenomenological kinetic equations describing the jumping of adatoms between adjacent adsorption sites. The results at 800, 1000, 1200, and 1500 K yield a lower bound for the diffusion coefficient of D>(8.53±1.11)×exp{-(2430±270)/ RT} cm2/s. At 1500 K, the computed mean-square displacement and velocity autocorrelation function give diffusion coefficients of 7.11×10-4 and 8.69×10-4 cm2/s, respectively, which is in excess of the calculated lower bound at 1500 K by about a factor of 2. This suggests that diffusion of Si on Si(111) involves highly correlated motion. An estimate for the upper bound for the diffusion coefficient is obtained by removing from the set of coupled kinetic equations all terms involving adatom motion which leads back toward the original adsorption site. The upper bound calculated in this manner at 1500 K is 1.41×10-3 cm2/s, which is a factor of 2 greater than the computed diffusion coefficient. The calculated activation energy for surface diffusion (2.43 kcal/mol) suggests that the experimental value for this quantity obtained from the direct deposition of Si on Si(111) in ultra high vacuum most accurately represents the true zero-coverage limit on a Si(111) crystal free of kinks and steps. American Institute of Physics (AIP) 1985-02-15 Article PeerReviewed application/pdf en http://irep.iium.edu.my/35865/1/JCP1985.pdf Ibrahim Ali , Noorbatcha and Lionel M. , Raff and Donald L. , Thompson (1985) A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories. Journal of Chemical Physics , 82 (3). pp. 1543-1550. ISSN 0021-9606 http://scitation.aip.org/content/aip/journal/jcp/82/3/10.1063/1.448429 DOI: 10.1063/1.448429
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QD Chemistry
spellingShingle	QD Chemistry Ibrahim Ali , Noorbatcha Lionel M. , Raff Donald L. , Thompson A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories
description	A general method to calculate a lower bound and an estimated upper bound for the surface diffusion coefficient from jump frequencies of an adatom from one absorption site to another has been formulated. This method has been applied to the surface diffusion of Si on Si(111). Keating's potential has been used for the Si(111) lattice. The interaction potential between the adatom and the lattice is a pairwise sum of 60 Morse potentials involving the Si atoms in the first and second layers of the crystal. This potential formulation predicts the existence of two different types of adsorption sites on the Si(111) surface. The jump frequencies from these adsorption sites have been calculated by classical trajectory methods. Using these jump frequencies, a lower bound for the diffusion coefficient is calculated by solving a set of coupled phenomenological kinetic equations describing the jumping of adatoms between adjacent adsorption sites. The results at 800, 1000, 1200, and 1500 K yield a lower bound for the diffusion coefficient of D>(8.53±1.11)×exp{-(2430±270)/ RT} cm2/s. At 1500 K, the computed mean-square displacement and velocity autocorrelation function give diffusion coefficients of 7.11×10-4 and 8.69×10-4 cm2/s, respectively, which is in excess of the calculated lower bound at 1500 K by about a factor of 2. This suggests that diffusion of Si on Si(111) involves highly correlated motion. An estimate for the upper bound for the diffusion coefficient is obtained by removing from the set of coupled kinetic equations all terms involving adatom motion which leads back toward the original adsorption site. The upper bound calculated in this manner at 1500 K is 1.41×10-3 cm2/s, which is a factor of 2 greater than the computed diffusion coefficient. The calculated activation energy for surface diffusion (2.43 kcal/mol) suggests that the experimental value for this quantity obtained from the direct deposition of Si on Si(111) in ultra high vacuum most accurately represents the true zero-coverage limit on a Si(111) crystal free of kinks and steps.
format	Article
author	Ibrahim Ali , Noorbatcha Lionel M. , Raff Donald L. , Thompson
author_facet	Ibrahim Ali , Noorbatcha Lionel M. , Raff Donald L. , Thompson
author_sort	Ibrahim Ali , Noorbatcha
title	A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories
title_short	A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories
title_full	A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories
title_fullStr	A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories
title_full_unstemmed	A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories
title_sort	phenomenological approach to the calculation of the diffusion coefficient for si on si(111) using classical trajectories
publisher	American Institute of Physics (AIP)
publishDate	1985
url	http://irep.iium.edu.my/35865/ http://irep.iium.edu.my/35865/ http://irep.iium.edu.my/35865/ http://irep.iium.edu.my/35865/1/JCP1985.pdf
first_indexed	2023-09-18T20:51:22Z
last_indexed	2023-09-18T20:51:22Z
_version_	1777410016064569344

A phenomenological approach to the calculation of the diffusion coefficient for Si on Si(111) using classical trajectories

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