Spectroscopic Ellipsometry and Reflectometry A User's Guide

by Tompkins, Harland G.; McGahan, William A.

• ISBN13: 9780471181729
• ISBN10: 0471181722
• Edition: 1st
• Format: Hardcover
• Copyright: 1999-03-18
• Publisher: Wiley-Interscience

Summary

While single wave ellipsometry has been around for years, spectroscopic ellipsometry is fast becoming the method of choice for measuring the thickness and optical properties of thin films. This book provides the first practical introduction to spectroscopic ellipsometry and the related techniques of reflectometry. A guide for practitioners and researchers in a variety of disciplines, it addresses a broad range of applications in physics, chemistry, electrical engineering, and materials science.

Author Biography

Harland Tompkins retired from full-time employment in 2001. During his full-time employment, he was employed by General Electric Co., Bell Laboratories, the Idaho National Engineering Lab, and Motorola.

William A. McGahan is the author of Spectroscopic Ellipsometry and Reflectometry: A User's Guide, published by Wiley.

Table of Contents

Preface	xiii
Perspective and History	1	(5)
Historical Aspects	1	(1)
Complementary Nature of the Techniques	2	(1)
Format and Purpose of the Book	3	(1)
References	4	(2)
Fundamentals	6	(17)
Description of an Electromagnetic Wave	6	(2)
The Effect of Matter on Electromagnetic Waves	8	(3)
The Complex Index of Refraction	8	(2)
Laws of Reflection and Refraction	10	(1)
Polarized Light	11	(3)
Sources	11	(1)
Linearly Polarized Light	11	(1)
Elliptically Polarized Light	12	(2)
Application of Elliptically Polarized Light	14	(1)
The Reflection of Light	14	(5)
Orientation	14	(1)
The Reflection Equations of Fresnel	15	(1)
The Brewster Angle	15	(3)
Reflections with Films	18	(1)
Ellipsometry and Reflectometry Definitions	19	(2)
Reflectance	19	(1)
Delta and Psi	20	(1)
The Fundamental Equation of Ellipsometry	20	(1)
References	21	(2)
Optical Properties of Materials and Layered Structures	23	(12)
The Physical Meaning of the Optical Constants	23	(1)
Conventions and More Basics	24	(2)
The Lorentz Oscillator	26	(2)
Insulators	28	(1)
Semiconductors	29	(2)
Metals	31	(2)
Kramers-Kronig Relations	33	(1)
Miscellaneous	33	(1)
References	34	(1)
Instrumentation	35	(19)
Introduction	35	(1)
Reflectometry in General	35	(1)
Reflectometer Hardware Configurations	36	(3)
Reflectometer Components	39	(1)
Sources	39	(1)
Beamsplitter	39	(1)
Lenses	39	(1)
Monochromators and Detectors	39	(1)
Ellipsometry in General	40	(1)
Optical Components Used in Ellipsometers	40	(4)
Sources	40	(1)
Polarizers	41	(1)
Compensators	42	(1)
Monochromators	42	(2)
Detectors	44	(1)
Ellipsometer Hardware Configurations	44	(5)
Null Ellipsometry	44	(1)
Rotating Element Photometric Ellipsometry	45	(3)
Modulation Ellipsometry	48	(1)
Single Wavelength Ellipsometers	49	(1)
Spectroscopic Ellipsometers	49	(1)
Instrument Parameter Characterization	50	(1)
Research vs. Production Ellipsometry	50	(2)
Errors in Reflectance and Ellipsometric Measurements	52	(1)
References	53	(1)
The Anatomy of a Reflectance Spectrum	54	(8)
General	54	(1)
Spectra for Substrates Only	54	(1)
With a Film: The Effect of Wavelength	55	(2)
Contribution of Film Thickness	57	(2)
Contribution of the Optical Constant Spectra of Film and Substrate	59	(2)
Summary	61	(1)
Aspects of Single-Wavelength Ellipsometry	62	(13)
General	62	(1)
Substrates: Delta and Psi and the Optical Constants	62	(4)
Calculating Delta/Psi Trajectories	66	(1)
Delta/Psi Trajectories for Transparent Films	67	(4)
Delta/Psi Trajectories for Absorbing Films	71	(1)
Trajectories for Two-Film Structures	72	(1)
Key Issues	73	(1)
References	74	(1)
The Anatomy of an Ellipsometric Spectrum	75	(10)
General	75	(1)
Typical Spectra	75	(2)
Spectra for Substrates Only	77	(1)
With a Film: Single-Wavelength Considerations	77	(2)
Effect of Wavelength	79	(2)
Contribution of the Optical Constant Spectra of Film and Substrate	81	(1)
Contribution of Film Thickness	82	(1)
Summary	83	(1)
References	84	(1)
Analytical Methods and Approach	85	(13)
General Approach	85	(1)
Sample Positioning	85	(1)
How Much Data?	86	(2)
Wavelength	86	(1)
Angle of Incidence	87	(1)
Analytical Methods	88	(9)
General	88	(1)
Tabulated Optical Constants	89	(1)
Simple Mixtures of Tabulated Optical Constants	90	(3)
Dispersion Relationships	93	(2)
Point-by-Point Optical Constants	95	(1)
Regression Process	96	(1)
Summary	97	(1)
References	97	(1)
Optical Data Analysis	98	(10)
Introduction	98	(1)
Direct Calculation	99	(2)
Regression Analysis Methods	101	(2)
The Problem	101	(1)
The Merit Function	101	(1)
The Regression Algorithm	102	(1)
Hybrid Methods	103	(1)
Goodness of Fit	103	(1)
Uniqueness	104	(1)
Combined Analysis of Multiple Data Types	105	(1)
Multiple Sample Analysis	106	(1)
Errors---Systematic and Random	106	(1)
References	107	(1)
Quality Assurance	108	(5)
General	108	(1)
Precision vs. Accuracy	108	(1)
Standards	109	(1)
Quality Assurance Measurements	110	(2)
References	112	(1)
Very Thin Films	113	(10)
Introduction	113	(1)
Determining Thickness	113	(4)
For Reflectance	113	(2)
For Ellipsometry	115	(2)
Determining Optical Constants	117	(1)
Distinguishing Between Materials	118	(4)
References	122	(1)
Roughness	123	(10)
Introduction	123	(1)
Roughness in General	123	(1)
Approximation of Surface Roughness as an Oxide Layer	124	(1)
Effective Medium Approximations (EMAs)	125	(1)
Examples	126	(4)
Polysilicon	126	(1)
Sensitivity in the Visible	127	(1)
Roughness Effects when Determining Optical Constants	128	(1)
SOI Interface Roughness	128	(2)
References	130	(3)
PROTOTYPICAL ANALYSES
Thermal Oxide, LPCVD Nitride, or Photoresist on Silicon	133	(5)
Salient Feature	133	(1)
Thinner Films	133	(2)
Intermediate Films	135	(1)
Thicker Films	136	(2)
Silicon Oxynitrides, PECVD Silicon Oxides, and Polysilicon	138	(9)
Salient Feature	138	(1)
Polysilicon	138	(3)
PECVD Silicon Oxides	141	(1)
Silicon Oxynitrides	142	(4)
References	146	(1)
PECVD Silicon Nitride, Silicon Dioxide, and Photoresist on Silicon	147	(8)
Salient Feature	147	(1)
Cauchy Modeling	147	(8)
LPCVD Polysilicon and Amorphous Silicon	155	(6)
Salient Feature	155	(1)
The Problem	155	(1)
The Optical Constants	155	(1)
Using the EMA Model	156	(1)
Using the Lorentz Oscillator Dispersion Model	156	(4)
References	160	(1)
Substrate Optical Constant Determination	161	(5)
Salient Feature	161	(1)
Aluminum	161	(2)
Glass	163	(3)
Analysis of Films on Transparent Substrates	166	(7)
Salient Feature	166	(1)
The Structure of the Example	166	(1)
Transmission	166	(1)
Reflection	167	(2)
Ellipsometry	169	(1)
Reverse Ellipsometry	170	(1)
Summary	171	(1)
References	172	(1)
Very Thick Films	173	(5)
Salient Feature	173	(1)
Thick Photoresist on Silicon---Reflectometry	173	(2)
Thick Photoresist on Glass---Ellipsometry	175	(1)
Conclusion	176	(2)
Compositional Analysis of Materials	178	(3)
Salient Feature	178	(1)
Background	178	(1)
GaAs/AlGaAs/GaAs	179	(1)
References	180	(1)
Thin Metal Films	181	(7)
Salient Feature	181	(1)
Background	181	(1)
Thin Titanium on Silicon	182	(1)
Thin Titanium Nitride on Oxide on Silicon	182	(2)
Using Multiple Films of Thin Metal	184	(3)
Comments and Summary	187	(1)
References	187	(1)
Photoresist Optical Constants	188	(7)
Salient Feature	188	(1)
Background	188	(1)
Photoresist on Silicon	189	(1)
Summary	190	(5)
Appendices
A Regression Algorithms	195	(1)
A.1 The Merit Function	195	(1)
A.2 The Analysis Procedure	195	(1)
A.3 The Algorithms	196	(1)
A.4 The Combination	197	(1)
A.5 References	198	(1)
B Maxwell's Equations and the Wave Equation	199	(1)
B.1 Introduction	199	(2)
B.2 Differential Equation Form of Maxwell's Equations	201	(1)
B.3 The Wave Equation	201	(1)
B.3.1 Dielectric Media	201	(3)
B.3.2 Including Conductors	204	(1)
B.3.3 The Magnetic Field Wave	205	(2)
B.4 References	207	(1)
B.5 Vector Calculus Notation Review	207	(1)
B.5.1 Vector Algebra	207	(1)
B.5.2 Scalar and Vector Fields	208	(1)
B.5.3 Vector Calculus	208	(4)
C Snell's Law, Fresnel's Equations, and the Total Reflection Coefficient Derivations and Historical Perspective	212	(1)
C.1 Introduction	212	(1)
C.2 Reflection and Refraction (Snell's Law)	212	(4)
C.3 Fresnel's Reflection and Transmission Coefficients	216	(4)
C.4 Using the Complex Index of Refraction	220	(1)
C.5 Total Reflection Coefficient for a Film on a Substrate	221	(3)
C.6 References	224	(1)
Index	225