DOCSLIB.ORG

Ellipsometry for Csige Metrology

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read 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. Test Material model the refractive index variation of the film caused by Epitaxial growth of SiGe in the channel is dependent on varying amounts of Ge. process parameters. The Ge and Silane flow rates determine the stoichiometry while the temperature and deposition times II. METROLOGY TOOL AND MODEL determine the thickness of the film. A set of wafers with predictable variations of the film thickness and composition A. Ellipsometer centered around the target process specification was generated Broadband Spectroscopic Ellipsometry (BBSE) technology is using these process variables Table 1. widely used in thin film thickness measurement; in this study cSiGe thickness and %Ge is measured by this technology. A high performance inline films metrology tool operating in the wavelength range 235nm~800nm that meets the tight process tolerances required for thickness, refractive index and stress measurements in modern semiconductor fabs is used in this study. An ellipsometer is designed to measure intensity ratio and Ψ phase shift (tan and cosΔ) between S polarized light and P * Thickness is for calibration with XRD polarized light. The basic optical path is shown in Figure 1. Broadband spectroscopic unpolarized light (235nm ~800nm) Table 1. Samples with designed variations for modeling is generated in the light source; linear polarized light can be and calibration. Thickness and Ge% are normalized to target. obtained after passing through the polarizer and the light interacts with the layer stack on the wafer; after that, the linear C. Modeling and recipe light will become elliptically polarized light carring intensity The metrology method used in this study is model based ratio and phase shift (tanΨ and cosΔ) information which are spectroscopic ellipsometry (SE). The tanΨ and cosΔ spectra 978-1-4799-3944-2/14/$31.00 ©2014 IEEE 42 ASMC 2014 are measured with the SE tool over a wavelength range from 250nm to 800nm using a broadband light source. A model spectra derived using predefined thickness and optical dispersions (T, n, k) for each of the distinct materials in the measured region is compared to the measured spectrum. A regression algorithm arrives at the solution for thickness and refractive index of the film layers using chi squared fitting across the model and measured spectrum. The film layers modeled for the particular application of measuring channel SiGe on SOI substrate is shown in Figure 2. a) Figure 2. Film stack modeled in the recipe b) All the modeling and analysis of spectra is performed using Figure 3. a) Spectra from samples with same thickness an off-line analysis software. The analysis of the spectra from (normalized 1.0) and varying Ge% b) Spectra from samples designed samples shows sensitivity to changes in thickness and with same Ge% (normalized 0.98) and varying thickness. % Ge. Figure 3. Optical response to thickness variation is more apparent than that to Ge% change because of the low nominal Ge dose and small variations being studied, thus making the metrology very challenging. The variation in Germanium content in silicon is observed as variation in the optical dispersion of the film (n,k) Figure 4. In order to report the Ge% a lookup table is established based on the correlation between the optical dispersion and Germanium content[2]. It is challenging to de-convolve the effects of thickness of cSiGe and superficial silicon and the Germanium content in the measured spectrum. A multi-pass regression is implemented that allows feeding forward the sub-layer thicknesses between passes to simplify the measurement of the layer of interest. For accurate reporting of Ge% the dispersions are correlated to reference XRD results. XRD is a more direct technique that measures the lattice spacing changes in Si due to substitution by Ge. But for a viable measurement the technique requires a much thicker film compared to the typical cSiGe film. This required parallel generation of thicker films in the set of designed samples spanning the Ge range for this calibration. Figure 4. N and K dispersion curves for different Ge% in Table 1. 43 ASMC 2014 III. RESULTS demonstrate that the measurement will be sensitive to process variations and correlates with physical process variables as A. Measurement Precision observed in Fig. 6 and 7. This is essential for establishing The measurement was evaluated on a fleet of 5 tools for process controls. long term repeatability and matching. The data was collected a by measuring the same patterned wafer on 21 sites of size 60um x 70um. The long term repeatability results had to be corrected for trending due to oxidation of the wafer by applying a linear correction factor. From Fig. 5 and table 2 it is clearly established that the tool has good repeatability and matching performance. Table 2. 3Sigma stability and offset on 3 tools as a percentage of the normalized value of the parameter. b a Figure 6. Correlation of optical measurements to process conditions a) Ge Flow Rate b) Deposition Time b Figure 5a & b. Wafer normalized thickness and Ge% over multiple days as measured on a fleet of 3 tools. Figure 7. Correlation of %Ge measured optically to XRD measurement on equivalent samples. B. Measurement Sensitivity The set of wafers for recipe development were designed to encompass the variations that might occur in a channel SiGe cSiGe channel thickness is found to be the most important deposition process. We can show results from these wafers to process parameter affecting threshold voltage Vth [3]. Figure 8 44 ASMC 2014 shows Vth decreasing with increasing cSiGe thickness as Figure 9. Optical Ge% correlates with Ieff due to the measured on wafers with designed variation. Fig. 9 shows effect of band gap modification. excellent correlation of Ieff with Ge% measured optically. With increasing Ge% (lower band gap) the device is able to support CONCLUSION a higher drive current. The optical response to changes in thickness and Ge% of thin SiGe films on SOI though subtle can be well characterized. Careful setup of regression in the recipe enables repeatable and sensitive measurement suitable for process control. This metrology can enable the control of significant device parameters like Vth and Ieff that are impacted by cSiGe thickness and Ge concentration. REFERENCES [1] Judson R. Holt, Anita Madan, Eric C. T. Harley, Matt W. Stoker, Teresa Pinto, Dominic J. Schepis, Thomas N. Adam, Conal E. Murray, Stephen W. Bedell and Martin Holt. Observation of semiconductor device channel strain using in-line high resolution X-ray diffraction. J. Appl. Phys. 114, 154502 (2013) [2] O. Fursenko, J. Bauer, P. Zaumseil, Y. Yamamoto, B. Tillack. Doping Figure 8. Optical cSiGe thickness correlates with pFET concentration control of SiGe layers by spectroscopic ellipsometry, Thin Solid Films 517 (2008) 259-261. threshold voltage providing a tool to control and optimize [3] C. Ortolland, D. Jaeger, T.J. Mcardle, C. Dewan, R.R. Robison1, K. device performance. Zhao, J. Cai2, P. Chang, Y. Liu, V. Varadarajan,G. Wang, A.I. Chou, D.P. Ioannou, P. Oldiges, P. Agnello, S. Narasimha, V. Narayanan & G. Freeman 2nd Generation Dual-Channel Optimization with cSiGe for 22nm HP Technology and Beyond. IEDM Dec., 2013 45 ASMC 2014.
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]
  • 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]
  • Spectroscopic Ellipsometry of Graphene and an Exciton-Shifted Van Hove Peak in Absorption
    PHYSICAL REVIEW B 81, 155413 ͑2010͒ Spectroscopic ellipsometry of graphene and an exciton-shifted van Hove peak in absorption V. G. Kravets, A. N. Grigorenko,* R. R. Nair, P. Blake, S. Anissimova, K. S. Novoselov, and A. K. Geim School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom ͑Received 3 March 2010; published 6 April 2010͒ We demonstrate that optical transparency of any two-dimensional system with a symmetric electronic spectrum is governed by the fine structure constant and suggest a simple formula that relates a quasiparticle spectrum to an optical absorption of such a system. These results are applied to graphene deposited on a surface of oxidized silicon for which we measure ellipsometric spectra, extract optical constants of a graphene layer and reconstruct the electronic dispersion relation near the K point using optical transmission spectra. We also present spectroscopic ellipsometry analysis of graphene placed on amorphous quartz substrates and report a pronounced peak in ultraviolet absorption at 4.6 eV because of a van Hove singularity in graphene’s density of states. The peak is asymmetric and downshifted by 0.5 eV probably due to excitonic effects. DOI: 10.1103/PhysRevB.81.155413 PACS number͑s͒: 72.80.Vp, 78.20.Ϫe, 78.40.Ϫq I. INTRODUCTION field in the 2D layer͒. The energy absorption of normal inci- dent light per unit area is given by the Fermi golden rule, Graphene, a recently isolated two-dimensional ͑2D͒ carbon-based material,1 attracted a lot of attention due to ␲ 2 g 2 2 W = ប␻ ͚ ͉͗f͉Vˆ ͉i͉͘ ͓n͑␧ ͒ − n͑␧ ͔͒␦͑pជ − pជ ͒␦͑␧ − ␧ unique physical, chemical, and mechanical properties.
    [Show full text]