# Spatial First-passage Statistics of Al/Si(111)-(root 3X root 3) Step Fluctuations

## Abstract

Step edge fluctuations on a multi-component surface of Al/Si(111)-( ) were measured via scanning tunneling microscopy over a temperature range of 720K-1070K, for step lengths of 65-160 nm. Even though the time scale of fluctuations of steps on this surface varies by orders of magnitude over the indicated temperature ranges, measured first-passage spatial persistence and survival probabilities are shown to be temperature independent over the temperature and spatial range. The power law functional form for spatial persistence probabilities is confirmed and the spatial persistence exponent is measured to be 0.71 ± 0.13 in contrast to theoretical predictions of a value ≤ ½. The survival probability is found to scale directly with x/L, where x is the step edge displacement and L is the step length anallyzed, with minor corrections for the discrete measurement interval. The form of the survival agrees quantitatively with theoretical predictions, which reduce to an exponential decay at short distances (x/L <~ 0.3). The decay constant is found experimentally to be (0.076 ± 0.033)L Also, the functional form of the stationary single site height distribution is found to agree with predictions.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 903239

- Report Number(s):
- PNNL-SA-51908

Journal ID: ISSN 1063-651X; PLEEE8; KP1504020; TRN: US200719%%519

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 75(2 PT 1):443-448; Journal Volume: 75; Journal Issue: 2 PT 1

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; ALUMINIUM; SILICON; SURFACE PROPERTIES; MORPHOLOGY; FLUCTUATIONS

### Citation Formats

```
Conrad, Brad R., Cullen, W. G., Dougherty, D. B., Lyubinetsky, Igor, and Williams, E. D.
```*Spatial First-passage Statistics of Al/Si(111)-(root 3X root 3) Step Fluctuations*. United States: N. p., 2007.
Web. doi:10.1103/PhysRevE.75.021603.

```
Conrad, Brad R., Cullen, W. G., Dougherty, D. B., Lyubinetsky, Igor, & Williams, E. D.
```*Spatial First-passage Statistics of Al/Si(111)-(root 3X root 3) Step Fluctuations*. United States. doi:10.1103/PhysRevE.75.021603.

```
Conrad, Brad R., Cullen, W. G., Dougherty, D. B., Lyubinetsky, Igor, and Williams, E. D. Thu .
"Spatial First-passage Statistics of Al/Si(111)-(root 3X root 3) Step Fluctuations". United States.
doi:10.1103/PhysRevE.75.021603.
```

```
@article{osti_903239,
```

title = {Spatial First-passage Statistics of Al/Si(111)-(root 3X root 3) Step Fluctuations},

author = {Conrad, Brad R. and Cullen, W. G. and Dougherty, D. B. and Lyubinetsky, Igor and Williams, E. D.},

abstractNote = {Step edge fluctuations on a multi-component surface of Al/Si(111)-( ) were measured via scanning tunneling microscopy over a temperature range of 720K-1070K, for step lengths of 65-160 nm. Even though the time scale of fluctuations of steps on this surface varies by orders of magnitude over the indicated temperature ranges, measured first-passage spatial persistence and survival probabilities are shown to be temperature independent over the temperature and spatial range. The power law functional form for spatial persistence probabilities is confirmed and the spatial persistence exponent is measured to be 0.71 ± 0.13 in contrast to theoretical predictions of a value ≤ ½. The survival probability is found to scale directly with x/L, where x is the step edge displacement and L is the step length anallyzed, with minor corrections for the discrete measurement interval. The form of the survival agrees quantitatively with theoretical predictions, which reduce to an exponential decay at short distances (x/L <~ 0.3). The decay constant is found experimentally to be (0.076 ± 0.033)L Also, the functional form of the stationary single site height distribution is found to agree with predictions.},

doi = {10.1103/PhysRevE.75.021603},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 75(2 PT 1):443-448},

number = 2 PT 1,

volume = 75,

place = {United States},

year = {Thu Feb 01 00:00:00 EST 2007},

month = {Thu Feb 01 00:00:00 EST 2007}

}