### Abstract

Using Rayleigh-Rice scattering theory we have studied the influence of surface morphology on the optical response of self-affine surfaces. We have established a mathematical relationship between the surface roughness (d) as determined by spectroscopic ellipsometry (SE) using the effective medium approximation (EMA) and the parameters controlling the morphology of the surface: root-mean-square roughness (w), correlation length (ξ), and roughness (Hurst) exponent (α). These three parameters affect the roughness value measured by ellipsometry. However, when the correlation length is smaller than the wavelength, the dependence is contained in a single parameter wδ that is proportional to the product of the surface roughness and the local slope δ=w/wξαξα. The fact that the local slope of a surface increases only very slowly during growth explains the linear dependence experimentally found between w as measured by scanning-probe microscopy and the vertical roughness determined by the effective medium approach.

Original language | English (US) |
---|---|

Article number | 085402 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 84 |

Issue number | 8 |

DOIs | |

State | Published - Aug 18 2011 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*84*(8), [085402]. https://doi.org/10.1103/PhysRevB.84.085402

**Theory of light scattering from self-affine surfaces : Relationship between surface morphology and effective medium roughness.** / Yanguas-Gil, Angel; Sperling, Brent A.; Abelson, John R.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 84, no. 8, 085402. https://doi.org/10.1103/PhysRevB.84.085402

}

TY - JOUR

T1 - Theory of light scattering from self-affine surfaces

T2 - Relationship between surface morphology and effective medium roughness

AU - Yanguas-Gil, Angel

AU - Sperling, Brent A.

AU - Abelson, John R

PY - 2011/8/18

Y1 - 2011/8/18

N2 - Using Rayleigh-Rice scattering theory we have studied the influence of surface morphology on the optical response of self-affine surfaces. We have established a mathematical relationship between the surface roughness (d) as determined by spectroscopic ellipsometry (SE) using the effective medium approximation (EMA) and the parameters controlling the morphology of the surface: root-mean-square roughness (w), correlation length (ξ), and roughness (Hurst) exponent (α). These three parameters affect the roughness value measured by ellipsometry. However, when the correlation length is smaller than the wavelength, the dependence is contained in a single parameter wδ that is proportional to the product of the surface roughness and the local slope δ=w/wξαξα. The fact that the local slope of a surface increases only very slowly during growth explains the linear dependence experimentally found between w as measured by scanning-probe microscopy and the vertical roughness determined by the effective medium approach.

AB - Using Rayleigh-Rice scattering theory we have studied the influence of surface morphology on the optical response of self-affine surfaces. We have established a mathematical relationship between the surface roughness (d) as determined by spectroscopic ellipsometry (SE) using the effective medium approximation (EMA) and the parameters controlling the morphology of the surface: root-mean-square roughness (w), correlation length (ξ), and roughness (Hurst) exponent (α). These three parameters affect the roughness value measured by ellipsometry. However, when the correlation length is smaller than the wavelength, the dependence is contained in a single parameter wδ that is proportional to the product of the surface roughness and the local slope δ=w/wξαξα. The fact that the local slope of a surface increases only very slowly during growth explains the linear dependence experimentally found between w as measured by scanning-probe microscopy and the vertical roughness determined by the effective medium approach.

UR - http://www.scopus.com/inward/record.url?scp=80052493790&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052493790&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.84.085402

DO - 10.1103/PhysRevB.84.085402

M3 - Article

AN - SCOPUS:80052493790

VL - 84

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 8

M1 - 085402

ER -