Terrace-width distributions on vicinal surfaces: generalized Wigner surmise and extraction of step–step repulsions

We have measured the terrace width distribution on copper (111) vicinal surfaces with (100) steps. For all surfaces, the distribution is well fitted by a Gaussian. The width of the Gaussian scales with the mean terrace width L, which is indicative of a repulsive 1/L2 interaction potential between steps. We determine an interaction strength of the potential of 3.2± 0.2 meV per atom length. From the temperature-dependent analysis of the step–step distance distribution, we find a kink formation energy for (100) steps of 0.12± 0.03 eV, which is consistent with previous measurements of the kink energy on copper (100) vicinal surfaces.

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Terrace-width distributions and step–step repulsions on vicinal surfaces: symmetries, scaling, simplifications, subtleties, and Schrödinger

Surface Science ◽

10.1016/s0039-6028(01)01254-7 ◽

2001 ◽

Vol 493 (1-3) ◽

pp. 460-474 ◽

Cited By ~ 27

Author(s):

T.L. Einstein ◽

Howard L. Richards ◽

Saul D. Cohen ◽

O. Pierre-Louis

Keyword(s):

Vicinal Surfaces ◽

Terrace Width ◽

Step Step

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Vicinal surfaces: free energy, terrace width distribution and step correlation functions

Surface Science ◽

10.1016/s0039-6028(99)00499-9 ◽

1999 ◽

Vol 432 (1-2) ◽

pp. 139-154 ◽

Cited By ~ 29

Author(s):

E. Le Goff ◽

L. Barbier ◽

L. Masson ◽

B. Salanon

Keyword(s):

Free Energy ◽

Correlation Functions ◽

Vicinal Surfaces ◽

Terrace Width ◽

Width Distribution

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Spontaneous Formation of Ridges on Patterned Mesas and Their Role in the Evolution of

MRS Proceedings ◽

10.1557/proc-854-u2.5/jj2.5/kk2.5 ◽

2004 ◽

Vol 854 ◽

Author(s):

Step Arrays ◽

Kee-Chul Chang ◽

Jack M. Blakely

Keyword(s):

Computer Simulations ◽

One Dimensional ◽

Step Motion ◽

Spontaneous Formation ◽

Terrace Width ◽

Sinusoidal Shape ◽

Step Dynamics ◽

Step Step

ABSTRACTMesa structures fabricated on Si(111) surfaces have been found experimentally to develop step arrays with large spacing of the order of a micron or more after annealing at temperatures where sublimation becomes important. Ridges around the edges initially develop during annealing and form barriers to step motion before eventually breaking down. This produces an array of steps of the same sign with a few wide terraces. Computer simulations using one dimensional Burton, Cabrera and Frank (BCF) theory including attachment-detachment rates and step-step repulsion for this configuration show that the terraces evolve under different dynamics depending on the terrace widths. For large terrace widths, sublimation dominates the step dynamics and the Ehrlich-Schwoebel effect is negligible. Sinusoidal terrace width distributions result in this case. The experimentally measured step distribution has such a sinusoidal shape suggesting that the step dynamics is sublimation dominated on the mesas after ridge breakdown.

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Narrowing of terrace-width distributions during growth on vicinal surfaces

EPL (Europhysics Letters) ◽

10.1209/0295-5075/88/26005 ◽

2009 ◽

Vol 88 (2) ◽

pp. 26005 ◽

Cited By ~ 8

Author(s):

A. BH. Hamouda ◽

A. Pimpinelli ◽

T. L. Einstein

Keyword(s):

Vicinal Surfaces ◽

Terrace Width

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Quantifying the Effect of Step–Step Exclusion on Dynamically Unstable Vicinal Surfaces: Step Bunching without Macrostep Formation

Crystal Growth & Design ◽

10.1021/acs.cgd.0c00927 ◽

2020 ◽

Vol 20 (11) ◽

pp. 7246-7259

Author(s):

Hristina Popova ◽

Filip Krzyżewski ◽

Magdalena A. Załuska-Kotur ◽

Vesselin Tonchev

Keyword(s):

Vicinal Surfaces ◽

Step Bunching ◽

Step Step

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Spontaneous Formation of Ridges on Patterned Mesas and Their Role in the Evolution of Step Arrays

MRS Proceedings ◽

10.1557/proc-849-kk2.5/jj2.5/u2.5 ◽

2004 ◽

Vol 849 ◽

Author(s):

Kee-Chul Chang ◽

Jack M. Blakely

Keyword(s):

Computer Simulations ◽

One Dimensional ◽

Step Motion ◽

Spontaneous Formation ◽

Terrace Width ◽

Sinusoidal Shape ◽

Step Dynamics ◽

Step Step

AbstractMesa structures fabricated on Si(111) surfaces have been found experimentally to develop step arrays with large spacing of the order of a micron or more after annealing at temperatures where sublimation becomes important. Ridges around the edges initially develop during annealing and form barriers to step motion before eventually breaking down. This produces an array of steps of the same sign with a few wide terraces. Computer simulations using one dimensional Burton, Cabrera and Frank (BCF) theory including attachment-detachment rates and step-step repulsion for this configuration show that the terraces evolve under different dynamics depending on the terrace widths. For large terrace widths, sublimation dominates the step dynamics and the Ehrlich-Schwoebel effect is negligible. Sinusoidal terrace width distributions result in this case. The experimentally measured step distribution has such a sinusoidal shape suggesting that the step dynamics is sublimation dominated on the mesas after ridge breakdown.

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