Theory of light scattering from self-affine surfaces: Relationship between surface morphology and effective medium roughness

Angel Yanguas-Gil, Brent A. Sperling, John R Abelson

Research output: Contribution to journalArticle

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 languageEnglish (US)
Article number085402
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume84
Issue number8
DOIs
StatePublished - Aug 18 2011

Fingerprint

Light scattering
Surface morphology
light scattering
roughness
Surface roughness
ellipsometry
surface roughness
slopes
rice
Scanning probe microscopy
Rayleigh scattering
Spectroscopic ellipsometry
Ellipsometry
exponents
microscopy
scanning
probes
products
approximation
scattering

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

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.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 84, No. 8, 085402, 18.08.2011.

Research output: Contribution to journalArticle

@article{58725428666c4b0c835aaa670d00f974,
title = "Theory of light scattering from self-affine surfaces: Relationship between surface morphology and effective medium roughness",
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.",
author = "Angel Yanguas-Gil and Sperling, {Brent A.} and Abelson, {John R}",
year = "2011",
month = "8",
day = "18",
doi = "10.1103/PhysRevB.84.085402",
language = "English (US)",
volume = "84",
journal = "Physical Review B-Condensed Matter",
issn = "0163-1829",
publisher = "American Institute of Physics Publising LLC",
number = "8",

}

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 -