DOCSLIB.ORG

Spectroscopic Ellipsometry

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Spectroscopic Ellipsometry Spectroscopic Ellipsometry: What it is, what it will do, and what it won’t do by Harland G. Tompkins • Introduction • Fundamentals • Anatomy of an ellipsometric spectrum • Analysis of an ellipsometric spectrum • What you can do, and what you can’t do 1-1 H. Tompkins Ellipsometry Introduction Perspective • Spectroscopic Ellipsometry is an optical technique used for analysis and metrology • A light beam is reflected off of the sample of interest • The light beam is then analyzed to see what the sample did to the light beam • We then draw conclusions about the sample • thickness • optical constants • microstructure • Model based •allmeasurement techniques are model based 1-2 H. Tompkins Ellipsometry Fundamentals Polarized Light • The Name • “Ellipsometry” comes from “elliptically polarized light” • better name would be “polarimetry” + • Linearly Polarized = • combining two light beams in phase, gives linearly polarized light 1-3 H. Tompkins Ellipsometry Fundamentals Polarized Light (continued) • Elliptically Polarized • combining two light beams + out of phase, gives elliptically polarized light • Two ways = • pass through a retarder • reflect off a surface • absorbing material • substrate with film 1-4 H. Tompkins Ellipsometry Fundamentals Laws of Reflection and Refraction • Reflection φ = φ i r • Refraction (Snell’s law) • for dielectric, i.e. k = 0 n sin φ = n sin φ 1 1 2 2 • in general Ñ sin φ = Ñ sin φ 1 1 2 2 • sine function is complex • corresponding complex cosine function 2 φ + 2 φ = sin 2 cos 2 1 1-5 H. Tompkins Ellipsometry Fundamentals Reflections (orientation) • Electric Field Vector • Plane-of-Incidence • incoming Ep • normal • outgoing Plane of Incidence Es • s-waves and p-waves • “senkrecht” and “parallel” 1-6 H. Tompkins Ellipsometry Fundamentals Equations of Fresnel • Fresnel reflection coefficients, r p r s • complex numbers 12 12 • ratio of Amplitude of outgoing to incoming • different for p-waves and s-waves φ − φ p Ñ cos Ñ cos φ − φ = 2 1 1 2 s Ñ 1 cos 1 Ñ 2 cos 2 r12 r = Ñ cos φ + Ñ cos φ 12 φ + φ 2 1 1 2 Ñ 1 cos 1 Ñ 2 cos 2 • Reflectance ℜ • ratio of Intensity • square of Amplitude • for a single interface 2 ℜ p = p 2 ℜs = s r12 r12 1-7 H. Tompkins Ellipsometry Fundamentals Brewster Angle (for dielectrics) • r s always negative and non-zero • r p passes through zero •ℜ p goes to zero • The Brewster Angle • sometimes called the principal angle, polarizing angle • Reflected light is s-polarized • ramifications n φ = 2 • tan B n1 φ = φ • cos 2 sin B 1-8 H. Tompkins Ellipsometry Fundamentals “Brewster” Angle, for metals • if k is non-zero, r s and r p are complex • cannot plot r s and r p vs angle of incidence • However, we can still plot the Reflectance •ℜ p has a minimum, although not zero • Actually called the “principal angle” 1-9 H. Tompkins Ellipsometry Fundamentals Reflections with Films φ • Ellipsometry, 1 • Amplitude, phase of outgoing vs Ñ1 incoming φ Ñ 2 d • Reflectometry 2 • Intensity of outgoing vs incoming Ñ3 φ • Total Reflection Coefficient 3 • corresponds to Fresnel Coefficients • complex number rp + r p exp(−j2β) r s + rs exp(−j2β) Rp = 12 23 Rs = 12 23 + p p − β + s s − β 1 r12 r23 exp( j2 ) 1 r12r23 exp( j2 ) d • β is phase change from top to β = 2π Ñ cosφ bottom of film λ 2 2 1-10 H. Tompkins Ellipsometry Fundamentals Ellipsometry and Reflectometry definitions 2 2 • Reflectance ℜp = Rp ℜs = Rs • Delta, the phase difference induced by the reflection •if δ is the phase difference before, and δ the phase difference after the 1 ∆ δ δ 2 reflection then = 1 - 2 • ranges from zero to 360º (or -180 to +180º ) • Psi, the ratio of the amplitude diminutions Rp • ranges from zero to 90º tan Ψ= R s • The Fundamental Equation of Ellipsometry p ∆ j∆ Rp ρ = R ρ = Ψ j tan Ψ = s tan e e s R R 1-11 H. Tompkins Ellipsometry Fundamentals More Perspective • Ellipsometers measure ∆ and Ψ (sometimes only cos ∆ ) • Properties of the probing beam • Quantities such as thickness and index of refraction are calculated quantities, based on a model. • Properties of the sample • Values of ∆ and Ψ are always correct • Whether thickness and index are correct depend on the model • Both precision and accuracy for ∆ and Ψ • Precision for thickness • Accuracy, ??? 1-12 H. Tompkins Ellipsometry The Anatomy of an Ellipsometric Spectrum Examples 180 150 film-free • Thin oxides on Silicon 10 Å 25 Å 120 60 Å 100 Å 90 50 ( ° ) ∆ 60 40 film-free 10 Å 25 Å 30 60 Å 30 100 Å 0 ( ° ) 200 400 600 800 1000 20 Ψ Wavelength (nm) 10 0 200 400 600 800 1000 Wavelength (nm) Si Optical Constants 7.0 6.0 6.0 5.0 n Ext. Coeff. ' k SiO2 Optical Constants 1.58 0.10 ' 5.0 4.0 n 1.56 n 4.0 3.0 0.08 Ext. Coeff. ' k ' 1.54 n Index ' Index 3.0 2.0 0.06 k ' 2.0 1.0 1.52 0.04 1.50 1.0 0.0 ' Index k 200 400 600 800 1000 ' 0.02 Wavelength (nm) 1.48 1.46 0.00 200 400 600 800 1000 Wavelength (nm) 1-13 H. Tompkins Ellipsometry The Anatomy of an Ellipsometric Spectrum Examples • Thicker oxide on Silicon 90 360 2200 Å 2500 Å 60 240 2200 Å 2500 Å 30 120 180 in degrees in degrees ∆ Ψ 150 0 0 200 400 600 800 1000 200 400 600 120800 1000 2200 Å 2500 Å Wavelength (nm) Wavelength (nm)∆ 90 60 30 200 400 600 800 1000 Si Optical Constants 7.0 6.0 Wavelength (nm) 6.0 5.0 n Ext. Coeff. ' k ' 5.0 4.0 n 4.0 3.0 SiO2 Optical Constants 1.58 0.10 Index ' Index 3.0 2.0 k ' 1.56 n 0.08 Ext. Coeff. ' 2.0 1.0 k ' 1.54 1.0 0.0 n 0.06 200 400 600 800 1000 1.52 Wavelength (nm) 0.04 1.50 Index ' Index k ' 1.48 0.02 1.46 0.00 200 400 600 800 1000 Wavelength (nm) 1-14 H. Tompkins Ellipsometry The Anatomy of an Ellipsometric Spectrum Examples • Polysilicon on oxide on silicon 3 srough 25 Å 2 polysilicon 3000 Å 1 sio2 1000 Å 0 si 1 mm 180 90 120 60 ∆ 60 30 in degrees Ψ 0 200 400 600 800 1000 0 200 400 600 800 1000 Wavelength (nm) Wavelength (nm) polysilicon OC's 6.0 5.0 5.0 4.0 Ext. Coeff. ' ' n 4.0 3.0 3.0 2.0 Index ' Index n k 2.0 k 1.0 ' 1.0 0.0 200 400 600 800 1000 Wavelength (nm) 1-15 H. Tompkins Ellipsometry The Anatomy of an Ellipsometric Spectrum Examples 1 cr 300 Å • Thin chromium on silicon 0 si 1 mm 180 60 film-free 50 Å 120 40 100 Å 200 Å film-free 300 Å 50 Å Ψ 60 100 Å 20 in degrees 200 Å ∆ 300 Å 0 0 300 400 500 600 700 800 300 400 500 600 700 800 Wavelength (nm) Wavelength (nm) Chromium OC's 5.0 4.5 4.2 4.0 Ext. Coeff. ' 3.9 ' n 3.0 n 3.6 • caveats k 2.0 3.3 Index ' Index 3.0 k 1.0 ' 2.7 0.0 2.4 300 400 500 600 700 800 Wavelength (nm) 1-16 H. Tompkins Ellipsometry Analysis of an Ellipsometric Spectrum Determining Film properties from SE spectra • Except for substrates, we cannot do a direct calculation What Ellipsometry Measures: What we are interested in: Film Thickness Refractive Index Psi (Ψ) Surface Roughness ∆ Interfacial Regions Delta ( ) Composition Crystallinity Anisotropy Desired information must be extracted Through a model-based analysis using Uniformity equations to describe interaction of light and materials 1-17 H. Tompkins Ellipsometry Analysis of an Ellipsometric Spectrum How we analyze data: 1-18 H. Tompkins Ellipsometry Analysis of an Ellipsometric Spectrum Building the model • Optical Constants • Tabulated list • when OC’s are very well known • single-crystal 1 cauchy 0 Å 0 si 1 mm • thermal oxide of Si, LPCVD nitride • Dispersion Equation • Cauchy equation • dielectrics, primarily • empirical • not K-K consistent λ = + Bn + Cn n( ) An λ2 λ4 1-19 H. Tompkins Ellipsometry Analysis of an Ellipsometric Spectrum Building the model • Optical Constants 2 polysilicon 0 Å • Dispersion Equation 1 sio2 1000 Å • Oscillator equation 0 si 1 mm 6.0 5.0 5.0 ' 4.0 k ' 4.0 n 3.0 3.0 2.0 Index ' Index 2.0 1.0 Ext. Coeff. ' 1.0 0.0 0.0 0 300 600 900 1200 1500 1800 0 300 600 900 1200 1500 1800 Wavelength (nm) Wavelength (nm) 5.0 4.0 4.0 30 20 3.0 3.0 ' 25 ' n 2.0 k ' 15 2.0 ' 1.0 20 1.0 10 0.0 2 0 300 600 900 1200 1500 1800 15 0.0 ε 0 300 600 900 1200 1500 1800 1 5 Wavelength (nm) Wavelength (nm) ε 10 0 5 -5 0 -10 0 2 4 6 8 10 0 2 4 6 8 10 Photon Energy (eV) Photon Energy (eV) 1-20 H. Tompkins Ellipsometry Analysis of an Ellipsometric Spectrum Building the model • Optical Constants 3 srough 0 Å •Mixture 2 polysilicon 2000 Å 1 sio2 1000 Å • EMA, effective medium 0 si 1 mm approximation • Graded Layers • Anisotropic Layers • Superlattice 1-21 H.
Load more

Recommended publications
  • Characterization of an Active Metasurface Using Terahertz Ellipsometry Nicholas Karl, Martin S
    Characterization of an active metasurface using terahertz ellipsometry Nicholas Karl, Martin S. Heimbeck, Henry O. Everitt, Hou-Tong Chen, Antoinette J. Taylor, Igal Brener, Alexander Benz, John L. Reno, Rajind Mendis, and Daniel M. Mittleman Citation: Appl. Phys. Lett. 111, 191101 (2017); View online: https://doi.org/10.1063/1.5004194 View Table of Contents: http://aip.scitation.org/toc/apl/111/19 Published by the American Institute of Physics APPLIED PHYSICS LETTERS 111, 191101 (2017) Characterization of an active metasurface using terahertz ellipsometry Nicholas Karl,1 Martin S. Heimbeck,2 Henry O. Everitt,2 Hou-Tong Chen,3 Antoinette J. Taylor,3 Igal Brener,4 Alexander Benz,4 John L. Reno,4 Rajind Mendis,1 and Daniel M. Mittleman1 1School of Engineering, Brown University, 184 Hope St., Providence, Rhode Island 02912, USA 2U.S. Army AMRDEC, Redstone Arsenal, Huntsville, Alabama 35808, USA 3Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 4Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA (Received 11 September 2017; accepted 19 October 2017; published online 6 November 2017) Switchable metasurfaces fabricated on a doped epi-layer have become an important platform for developing techniques to control terahertz (THz) radiation, as a DC bias can modulate the transmis- sion characteristics of the metasurface. To model and understand this performance in new device configurations accurately, a quantitative understanding of the bias-dependent surface characteristics is required. We perform THz variable angle spectroscopic ellipsometry on a switchable metasur- face as a function of DC bias. By comparing these data with numerical simulations, we extract a model for the response of the metasurface at any bias value.
    [Show full text]
  • Optical Characterization of Ultra-Thin Films of Azo-Dye-Doped Polymers Using Ellipsometry and Surface Plasmon Resonance Spectroscopy
    hv photonics Article Optical Characterization of Ultra-Thin Films of Azo-Dye-Doped Polymers Using Ellipsometry and Surface Plasmon Resonance Spectroscopy Najat Andam 1,2 , Siham Refki 2, Hidekazu Ishitobi 3,4, Yasushi Inouye 3,4 and Zouheir Sekkat 1,2,4,* 1 Department of Chemistry, Faculty of Sciences, Mohammed V University, Rabat BP 1014, Morocco; [email protected] 2 Optics and Photonics Center, Moroccan Foundation for Advanced Science, Innovation and Research, Rabat BP 10100, Morocco; [email protected] 3 Frontiers Biosciences, Osaka University, Osaka 565-0871, Japan; [email protected] (H.I.); [email protected] (Y.I.) 4 Department of Applied Physics, Osaka University, Osaka 565-0871, Japan * Correspondence: [email protected] Abstract: The determination of optical constants (i.e., real and imaginary parts of the complex refractive index (nc) and thickness (d)) of ultrathin films is often required in photonics. It may be done by using, for example, surface plasmon resonance (SPR) spectroscopy combined with either profilometry or atomic force microscopy (AFM). SPR yields the optical thickness (i.e., the product of nc and d) of the film, while profilometry and AFM yield its thickness, thereby allowing for the separate determination of nc and d. In this paper, we use SPR and profilometry to determine the complex refractive index of very thin (i.e., 58 nm) films of dye-doped polymers at different dye/polymer concentrations (a feature which constitutes the originality of this work), and we compare the SPR results with those obtained by using spectroscopic ellipsometry measurements performed on the Citation: Andam, N.; Refki, S.; Ishitobi, H.; Inouye, Y.; Sekkat, Z.
    [Show full text]
  • Use of Spectroscopic Ellipsometry and Modeling in Determining Composition and Thickness of Barium Strontium Titanate Thin-Films
    Use of Spectroscopic Ellipsometry and Modeling in Determining Composition and Thickness of Barium Strontium Titanate Thin-Films A Thesis Submitted to the Faculty of Drexel University by Dominic G. Bruzzese III in partial fulfillment of the requirements for the degree of MS in Materials Science and Engineering June 2010 c Copyright June 2010 Dominic G. Bruzzese III. All Rights Reserved. Acknowledgements I would like to acknowledge the guidance and motivation I received from my advi- sor Dr. Jonathan Spanier not just during my thesis but for my entire stay at Drexel University. Eric Gallo for his help as my graduate student mentor and always making himself available to help me with everything from performing an experiment to ana- lyzing some result, he has been an immeasurable resource. Keith Fahnestock and the Natural Polymers and Photonics Group under the direction of Dr. Caroline Schauer for allowing the use of their ellipsometer, without which this work would not have been possible. I would like to thank everyone in the MesoMaterials Laboratory, espe- cially Stephen Nonenmann, Stephanie Johnson, Guannan Chen, Christopher Hawley, Brian Beatty, Joan Burger, and Andrew Akbasheu for help with experiments, as well as Oren Leffer and Terrence McGuckin for enlightening discussions. Claire Weiss and Dr. Pamir Alpay at the University of Connecticut have both contributed much to the the field and I am grateful for their work; also Claire produced the MOSD samples on which much of the characterization and modeling was done. Dr. Melanie Cole and the Army Research Office and Dr. Marc Ulrich for funding the project under W911NF-08-0124 and W911NF-08-0067.
    [Show full text]
  • Ellipsometry
    AALBORG UNIVERSITY Institute of Physics and Nanotechnology Pontoppidanstræde 103 - 9220 Aalborg Øst - Telephone 96 35 92 15 TITLE: Ellipsometry SYNOPSIS: This project concerns measurement of the re- fractive index of various materials and mea- PROJECT PERIOD: surement of the thickness of thin films on sili- September 1st - December 21st 2004 con substrates by use of ellipsometry. The el- lipsometer used in the experiments is the SE 850 photometric rotating analyzer ellipsome- ter from Sentech. THEME: After an introduction to ellipsometry and a Detection of Nanostructures problem description, the subjects of polar- ization and essential ellipsometry theory are covered. PROJECT GROUP: The index of refraction for silicon, alu- 116 minum, copper and silver are modelled us- ing the Drude-Lorentz harmonic oscillator model and afterwards measured by ellipsom- etry. The results based on the measurements GROUP MEMBERS: show a tendency towards, but are not ade- Jesper Jung quately close to, the table values. The mate- Jakob Bork rials are therefore modelled with a thin layer of oxide, and the refractive indexes are com- Tobias Holmgaard puted. This model yields good results for the Niels Anker Kortbek refractive index of silicon and copper. For aluminum the result is improved whereas the result for silver is not. SUPERVISOR: The thickness of a thin film of SiO2 on a sub- strate of silicon is measured by use of ellip- Kjeld Pedersen sometry. The result is 22.9 nm which deviates from the provided information by 6.5 %. The thickness of two thick (multiple wave- NUMBERS PRINTED: 7 lengths) thin polymer films are measured. The polymer films have been spin coated on REPORT PAGE NUMBER: 70 substrates of silicon and the uniformities of the surfaces are investigated.
    [Show full text]
  • A Dissertation Entitled Spectroscopic Ellipsometry Studies of Thin Film Si
    A Dissertation entitled Spectroscopic Ellipsometry Studies of Thin Film Si:H Materials in Photovoltaic Applications from Infrared to Ultraviolet by Laxmi Karki Gautam Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Physics _________________________________________ Dr. Nikolas J. Podraza, Committee Chair _________________________________________ Dr. Robert W. Collins, Committee Member _________________________________________ Dr. Randall Ellingson, Committee Member _________________________________________ Dr. Song Cheng, Committee Member _________________________________________ Dr. Rashmi Jha, Committee Member _________________________________________ Dr. Patricia R. Komuniecki, Dean College of Graduate Studies The University of Toledo May, 2016 Copyright 2016, Laxmi Karki Gautam This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author. An Abstract of Spectroscopic Ellipsometry Studies of Thin Film Si:H Materials in Photovoltaic Applications from Infrared to Ultraviolet by Laxmi Karki Gautam Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Physics The University of Toledo May 2016 Optimization of thin film photovoltaics (PV) relies on the capability for characterizing the optoelectronic and structural properties of each layer in the device over large areas and correlating these properties with device performance. This work builds heavily upon that done previously by us, our collaborators, and other researchers. It provides the next step in data analyses, particularly that involving study of films in device configurations maintaining the utmost sensitivity within those same device structures. In this Dissertation, the component layers of thin film hydrogenated silicon (Si:H) solar cells on rigid substrate materials have been studied by real time spectroscopic ellipsometry (RTSE) and ex situ spectroscopic ellipsometry (SE).
    [Show full text]
  • 1. Introduction & Theory
    1. Introduction & Theory Neha Singh October 2010 Course Overview Day 1: Day 2: Introduction and Theory Genosc Layer Transparent Films Absorbing Films Microstructure – EMA If time permits: – Surface roughness Non-idealities – Grading (Simple and Ultra thin films function-based ITO) Uniqueness test – Thickness non-uniformity UV Absorption Review – Point-by-point fit Actual Samples © 2010, All Rights Reserved 2 Introduction & Theory Light Materials (optical constants) Interaction between light and materials Ellipsometry Measurements Data Analysis © 2010, All Rights Reserved 3 Light Electromagnetic Plane Wave From Maxwell’s equations we can describe a plane wave ⎛ 2π ⎞ E(z,t) = E0 sin⎜ − (z − vt) + ξ ⎟ ⎝ λ ⎠ Amplitude Amplitude arbitraryarbitrary phase phase X Wavelength Wavelength VelocityVelocity λ Electric field E(z,t) Y Z Direction Magnetic field, B(z,t) of propagation © 2010, All Rights Reserved 4 Intensity and Polarization Intensity = “Size” of Electric field. I ∝ E 2 Polarization = “Shape” of Electric field travel. Different Size Y •Y E More Intense Less (Intensity) Intense E Same Shape! X (Polarization) •X © 2010, All Rights Reserved 5 What is Polarization? Describes how Electric Field travels through space and time. X wave1 Y E wave2 Z © 2010, All Rights Reserved 6 Describing Polarized Light Jones Vector Stokes Vector Describe polarized light Describe any light beam with amplitude & phase. as vector of intensity ⎡S ⎤ ⎡ E2 + E2 ⎤ iϕx 0 x0 y0 ⎡Ex ⎤ ⎡E0xe ⎤ ⎢ ⎥ ⎢ 2 2 ⎥ = S1 ⎢ Ex0 −Ey0 ⎥ ⎢ ⎥ ⎢ iϕy ⎥ ⎢ ⎥ = E E e ⎢ ⎥ ⎢ ⎥ ⎣ y ⎦ ⎣⎢ 0y ⎦⎥ S2 2Ex0Ey0 cosΔ ⎢ ⎥ ⎢ ⎥ ⎣S3 ⎦ ⎣⎢2Ex0Ey0 sinΔ⎦⎥ © 2010, All Rights Reserved 7 Light-Material Interaction velocity & c wavelength vary v = in different n materials n = 1 •n = 2 Frequency remains constant v υ = λ © 2010, All Rights Reserved What are Optical Constants n , k Describe how materials and light interact.
    [Show full text]
  • Optical Properties of Teflon AF Amorphous Fluoropolymers
    J. Micro/Nanolith. MEMS MOEMS 7͑3͒, 033010 ͑Jul–Sep 2008͒ Optical properties of Teflon® AF amorphous fluoropolymers MinK.Yang Abstract. The optical properties of three grades of Teflon® AF— Roger H. French AF1300, AF1601, and AF2400—were investigated using a J.A. Woollam DuPont Co. Central Research VUV-VASE spectroscopic ellipsometry system. The refractive indices for Experimental Station each grade were obtained from multiple measurements with different film Wilmington, Delaware 19880-0400 thicknesses on Si substrates. The absorbances of Teflon® AF films were E-mail: [email protected] determined by measuring the transmission intensity of Teflon® AF films on CaF2 substrates. In addition to the refractive index and absorbance per cm ͑base 10͒, the extinction coefficient ͑k͒, and absorption coefficient Edward W. Tokarsky ͑␣͒ per cm ͑base e͒, Urbach parameters of absorption edge position and DuPont Fluoropolymer Solutions edge width, and two-pole Sellmeier parameters were determined for the Chestnut Run Plaza three grades of Teflon® AF. We found that the optical properties of the Wilmington, Delaware 19880-0713 three grades of Teflon® AF varied systematically with the AF TFE/PDD composition. The indices of refraction, extinction coefficient ͑k͒, absorp- tion coefficient ͑␣͒, and absorbance ͑A͒ increased, as did the TFE con- tent, while the PDD content decreased. In addition, the Urbach edge position moved to a longer wavelength, and the Urbach edge width became wider. © 2008 Society of Photo-Optical Instrumentation Engineers. ͓DOI: 10.1117/1.2965541͔ Subject terms: fluoropolymer; absorbance absorption coefficient; VUV ellipsometry. Paper 07086R received Oct. 24, 2007; revised manuscript received May 16, 2008; accepted for publication Jun.
    [Show full text]
  • Ellipsometry for Csige Metrology
    Ellipsometry for cSiGe Metrology Saiqa Farhat, Srinivasan Rangarajan, Timothy J. Dawei Hu, Ming Dai Mcardle, Michael Steigerwalt Films Metrology Division 300mm East Fishkill KLA Tencor Corp. IBM Corp San Jose, CA Hopewell Jn, NY, USA Abstract— In this paper we report the effectiveness of sensitive to the refractive index and thickness of the films in optical ellipsometry in measuring thickness and Germanium % the stack. Next, the elliptically polarized light will pass through of channel SiGe on SOI substrate used in advanced node high the analyzer and become linear polarized light again. Finally, performance semiconductor devices. the detector will receive the linear polarized light signal. The value tanΨ and cosΔ are extracted as a function of wavelength. Keywords—cSiGe, Ellipsometry, Thickness, Ge These are called the measured spectra. Concentration, metrology. I. INTRODUCTION Optical metrology of film thickness is the “work-horse” technique in semiconductor fabrication for control of a wide variety of processes. The tools and their technology are well established, providing low cost of ownership (COO) to manufacturers by giving fast and reliable feedback to their processes. In this study we demonstrate the successful implementation of optical metrology for cSiGe process control replacing a X-ray diffraction technique. The performance of SiGe channel in devices is dependent on film thickness and %Ge. X-ray diffraction (XRD) technique measures the change Figure 1: SE measurement optics schematic in lattice spacing of the strained silicon which is well correlated with %Ge in the film [1]. The technique is slow and new, posing challenges in manufacturing. Optical metrology on the other hand is a model based technique relying on the ability to B.
    [Show full text]
  • Infrared Spectroscopy and Ellipsometry of Magnetic Metamaterials
    Invited Paper Infrared spectroscopy and ellipsometry of magnetic metamaterials W.J. Padilla1, Ta Jen Yen2, N. Fang2, D.C. Vier3, David R. Smith4, J.B. Pendry5, X. Zhang2, D.N. Basov3 1Los Alamos National Laboratory, MS K764 MST-10, Los Alamos, NM 87545. 2Department of Mechanical and Aerospace Engineering, University of California at Los Angeles, 420 Westwood Plaza, Los Angeles, CA 90095. 3Department of Physics, University of California San Diego, La Jolla, California 92093-0319. 4Department of Electrical & Computer Engineering, Durham, NC 27708-0291. 5Condensed Matter Theory Group, Blackett Laboratory, Imperial College, London SW7 2AZ, UK. ABSTRACT We present S and P polarized measurements of artificial bianisotropic magnetic metamaterials with resonant behavior at infrared frequencies. These metamaterials consist of an array of micron sized (~40µm) copper rings fabricated upon a quartz substrate. Simulation of the reflectance is obtained through a combination of electromagnetic eigenmode simulation and Jones matrix analysis, and we find excellent agreement with the experimental data. It is shown that although the artificial magnetic materials do indeed exhibit a magnetic response, care must be taken to avoid an undesirable electric dipole resonance, due to lack of reflection symmetry in one orientation. The effects of bianisotropy on negative index are detailed and shown to be beneficial for certain configurations of the material parameters. Keywords: THz, meta material, left handed, negative index, bianisotropy, chiral, ellipsometry 1. INTRODUCTION Recently the field of electromagnetism has seen significant excitement and rapid growth, due the discovery of left- handed metamaterials.i These artificially constructed materials are capable of achieving simultaneous values of negative electric (ε<0) and negative magnetic (µ<0) response, a feat that is difficult or impossible to achieve with naturally occurring materials.
    [Show full text]
  • 1 Narrowband Metamaterial Absorber for Terahertz Secure Labeling
    Narrowband Metamaterial Absorber for Terahertz Secure Labeling Magued Nasr *a, Jonathan T. Richard *d, Scott A. Skirlo *b, Martin S. Heimbeck c, John D. Joannopoulos,b Marin Soljacic b, Henry O. Everitt c†, Lawrence Domash a * Equal contributors a Triton Systems Inc., 200 Turnpike Rd #2, Chelmsford, MA 01824 b Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 c U.S. Army Aviation and Missile RD&E Center, Redstone Arsenal, AL 35898 d IERUS Technologies, 2904 Westcorp Blvd Suite 210, Huntsville, AL 35805 † Corresponding author: [email protected] Abstract Flexible metamaterial films, fabricated by photolithography on a thin copper-backed polyimide substrate, are used to mark or barcode objects securely. The films are characterized by continuous wave terahertz spectroscopic ellipsometry and visualized by a scanning confocal imager coupled to a vector network analyzer that constructed a terahertz spectral hypercube. These films exhibit a strong, narrowband, polarization- and angle-insensitive absorption at wavelengths near one millimeter. Consequently, the films are nearly indistinguishable at visible or infrared wavelengths and may be easily observed by terahertz imaging only at the resonance frequency of the film. 1 Introduction Terahertz radiation in the long wavelength 1 - 3 mm band penetrates dry dielectrics such as plastics, concrete, and fabric while being strongly absorbed by water and water vapor. This combination of characteristics may be exploited for numerous applications including short-range communications and radar, collision avoidance radar, non-destructive testing of materials and structures, security imaging, medical diagnosis, and spectroscopy.[1,2,3] Materials with interesting terahertz properties also play a role in numerous security applications due to their limited range and high bandwidth.
    [Show full text]
  • SOLID STATE PHYSICS PART II Optical Properties of Solids
    SOLID STATE PHYSICS PART II Optical Properties of Solids M. S. Dresselhaus 1 Contents 1 Review of Fundamental Relations for Optical Phenomena 1 1.1 Introductory Remarks on Optical Probes . 1 1.2 The Complex dielectric function and the complex optical conductivity . 2 1.3 Relation of Complex Dielectric Function to Observables . 4 1.4 Units for Frequency Measurements . 7 2 Drude Theory{Free Carrier Contribution to the Optical Properties 8 2.1 The Free Carrier Contribution . 8 2.2 Low Frequency Response: !¿ 1 . 10 ¿ 2.3 High Frequency Response; !¿ 1 . 11 À 2.4 The Plasma Frequency . 11 3 Interband Transitions 15 3.1 The Interband Transition Process . 15 3.1.1 Insulators . 19 3.1.2 Semiconductors . 19 3.1.3 Metals . 19 3.2 Form of the Hamiltonian in an Electromagnetic Field . 20 3.3 Relation between Momentum Matrix Elements and the E®ective Mass . 21 3.4 Spin-Orbit Interaction in Solids . 23 4 The Joint Density of States and Critical Points 27 4.1 The Joint Density of States . 27 4.2 Critical Points . 30 5 Absorption of Light in Solids 36 5.1 The Absorption Coe±cient . 36 5.2 Free Carrier Absorption in Semiconductors . 37 5.3 Free Carrier Absorption in Metals . 38 5.4 Direct Interband Transitions . 41 5.4.1 Temperature Dependence of Eg . 46 5.4.2 Dependence of Absorption Edge on Fermi Energy . 46 5.4.3 Dependence of Absorption Edge on Applied Electric Field . 47 5.5 Conservation of Crystal Momentum in Direct Optical Transitions . 47 5.6 Indirect Interband Transitions .
    [Show full text]
  • Metrology Standards for Semiconductor Manufacturing Yu Guan and Marco Tortonese VLSI Standards, Inc., 3087 North First Street, San Jose, CA 95134, USA
    Metrology Standards for Semiconductor Manufacturing Yu Guan and Marco Tortonese VLSI Standards, Inc., 3087 North First Street, San Jose, CA 95134, USA Abstract made traceable to SI units because this gives us the guarantee that the results from any metrology In semiconductor manufacturing, the performance of instruments in any places that have been calibrated with metrology equipment directly impacts yield. Fabs and such standards are matched. For instance, it is desirable equipment suppliers depend on calibration standards to that dimensional standards are made traceable to the SI ensure that their metrology results are within tolerances unit of length. Actually, most calibration standards used and to maintain their ISO [1] and QS [2] quality in semiconductor fabrications (e.g. CD, film thickness, certifications. This task becomes more challenging as the step height, and particle size) are dimensional. It is, device features shrink and tolerances become tighter, to however, usually not straightforward to establish the extent of their physical limits in many cases. As the traceability for these quantities because the chain of industry keeps finding ways to meet the demanding comparison involved can be complex and the equipment metrology requirements, calibration standards have been required is not commonly available. In order to help the developed and enhanced for all essential measurements, industry obtain and maintain traceable standards, some i.e. critical dimensions, thin films, surface topography, governmental standard organizations, such as the overlay, doping, and defect inspections. This paper National Institute of Standards and Technology (NIST) provides an overview of such standards and in the US, have made available master standards that are demonstrates how they are certified and tested to be traceable to SI units, known as Standard Reference traceable to the International System (SI) unit of length Materials (SRMs).
    [Show full text]