Determination of constitutive and morphological parameters of columnar thin films by inverse homogenization

A dielectric columnar thin film (CTF), characterized macroscopically by a relative permittivity dyadic, was investigated theoretically. The CTF was assumed, on the nanoscale, to be an assembly of parallel, identical, elongated ellipsoidal inclusions made of an isotropic dielectric material that has a different refractive index from the bulk material that was evaporated to fabricate the CTF. The inverse Bruggeman homogenization formalism was developed in order to estimate the refractive index of the deposited material, one of the two shape factors of the ellipsoidal inclusions, and the volume fraction occupied by the deposited material, from a knowledge of relative permittivity dyadic of the CTF. A modified Newton-Raphson technique was implemented to solve the inverse Bruggeman equations. Numerical studies revealed how the three nanoscale parameters of CTFs vary as functions of the vapor incidence angle.

[1]  L. Ward,et al.  The Optical Constants of Bulk Materials and Films , 1988 .

[2]  Dilip K. Paul,et al.  Sculptured Thin Films: Nanoengineered Morphology and Optics , 2005 .

[3]  E. Teller,et al.  ADSORPTION OF GASES IN MULTIMOLECULAR LAYERS , 1938 .

[4]  A. Lakhtakia,et al.  Theory of light emission from a dipole source embedded in a chiral sculptured thin film. , 2007, Optics express.

[5]  Tom J. Smy,et al.  Modelling and characterization of columnar growth in evaporated films , 1993 .

[6]  Akhlesh Lakhtakia,et al.  Characterization of sculptured thin films , 2004, SPIE Optics East.

[7]  W Steckelmacher,et al.  Thin-film optical filters, 3rd Edition , 2002 .

[8]  A. Lakhtakia.  On bioluminescent emission from chiral sculptured thin films , 2001 .

[9]  A. Lakhtakia,et al.  Significance of cross-sectional morphology for Motohiro-Taga interfaces , 1999 .

[10]  A. Lakhtakia,et al.  On calibration of a nominal structure–property relationship model for chiral sculptured thin films by axial transmittance measurements , 2002, 1907.10740.

[11]  A. Lakhtakia,et al.  Bruggeman model for chiral particulate composites , 1992 .

[12]  I. Hodgkinson,et al.  Empirical equations for the principal refractive indices and column angle of obliquely deposited films of tantalum oxide, titanium oxide, and zirconium oxide. , 1998, Applied optics.

[13]  Geoffrey B. Smith.  Effective medium theory and angular dispersion of optical constants in films with oblique columnar structure , 1989 .

[14]  Qi Hong Wu,et al.  Birefringent Thin Films and Polarizing Elements , 1998 .

[15]  CORRECTION TO ''MAXWELL GARNETT AND BRUGGEMAN FORMALISMS FOR A PARTICULATE COMPOSITE WITH BIANISOTROPIC HOST MEDIUM'' , 1999 .

[16]  A. Lakhtakia,et al.  On the surface plasmon polariton wave at the planar interface of a metal and a chiral sculptured thin film , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[17]  Akhlesh Lakhtakia,et al.  Maxwell Garnett and Bruggeman formalisms for a particulate composite with bianisotropic host medium , 1997 .

[18]  Elena Cherkaev,et al.  Inverse homogenization for evaluation of effective properties of a mixture , 2001 .

[19]  K. Barla,et al.  Pore Size Distribution in Porous Silicon Studied by Adsorption Isotherms , 1983 .

[20]  Rolf E. Hummel,et al.  The Optical Constants , 1993 .

[21]  Craig F. Bohren,et al.  Clouds in a glass of beer : simple experiments in atmospheric physics / Craig F. Bohren , 1987 .

[22]  Ian J. Hodgkinson,et al.  Sculptured-thin-film spectral holes for optical sensing of fluids , 2001 .

[23]  Elmar Ritter,et al.  Properties of TiO(x) films prepared by electron-beam evaporation of titanium and titanium suboxides. , 2003, Applied optics.

[24]  Selected papers on scattering in the atmosphere , 1989 .

[25]  E. Clothiaux,et al.  Fundamentals of Atmospheric Radiation , 2006 .

[26]  O. Heavens.  Thin-film Optical Filters , 1986 .

[27]  Toward optical sensing of metal nanoparticles using chiral sculptured thin films , 2007 .

[28]  F. Chiadini,et al.  Gaussian model for refractive indexes of columnar thin films and Bragg multilayers , 2004 .

[29]  R. Messier.  The nano-world of thin films , 2008 .

[30]  A. Lakhtakia,et al.  Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film , 2008 .

[31]  T. Mackay.  Lewin's homogenization formula revisited for nanocomposite materials , 2008 .

[32]  Vijayakumar C. Venugopal,et al.  Origin and evolution of sculptured thin films , 2000 .

[33]  Russell Chipman,et al.  Dielectric tensor measurement from a single Mueller matrix image. , 2007, Journal of The Optical Society of America A-optics Image Science and Vision.

[34]  R. E. Alley,et al.  What Light Through Yonder Window Breaks , 1991 .

[35]  Jeremy C. Sit,et al.  Nanostructured gradient index optical filter for high-speed humidity sensing , 2006 .

[36]  Z. Kam,et al.  Absorption and Scattering of Light by Small Particles , 1998 .

[37]  Peter A. Stark.  Introduction to Numerical Methods , 1970 .

[38]  R. Roy,et al.  Structure–composition variation in rf‐sputtered films of Ge caused by process parameter changes , 1976 .

[39]  Ibrahim Abdulhalim,et al.  Overview of Optical Biosensing Techniques , 2008 .

[40]  Haiming Wang.  Assessment of optical constants of multilayer thin films with columnar-structure-induced anisotropy , 1995 .