Handbook of ellipsometry (Norwich, 2005). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаHandbook of ellipsometry / ed. by H.G.Tompkins, E.A.Irene. - Norwich: William Andrew Pub.; Heidelberg: Springer, 2005. - xvi, 870 p.: ill. - Incl. bibl. ref. - Ind.: p.857-870. - ISBN 0-8155-1499-9; ISBN 3-540-22293-6
 

Оглавление / Contents
 
Part 1: Theory of Ellipsometry .................................. 1

1.  Polarized Light and Ellipsometry ............................ 3
    1.1.  A Quick Guide to Ellipsometry ......................... 4
          1.1.1.  Light Waves and Photons ....................... 4
          1.1.2.  Polarization of Light ......................... 6
          1.1.3.  Ellipsometric Configurations .................. 9
          1.1.4.  Null Ellipsometry ............................ 12
          1.1.5.  Photometric Ellipsometry and Polarimetry ..... 13
    1.2.  Maxwell and Wave Equations ........................... 19
          1.2.1.  Linear Local Response ........................ 20
          1.2.2.  Linear Non-Local Response .................... 22
          1.2.3.  Dipole Moment, Susceptibility and
                  Inductions ................................... 23
          1.2.4.  Relationships Between Optical Constants ...... 24
          1.2.5.  Wave Equation for Monochromatic Fields ....... 26
          1.2.6.  Plane Waves in Isotropic Medium .............. 29
    1.3.  Representations of Polarization ...................... 31
          1.3.1.  Representation by Ellipsometric Angles ....... 32
          1.3.2.  Special Cases: Linear and Circular
                  Polarization ................................. 35
          1.3.3.  Orthogonal Polarization States ............... 37
          1.3.4.  Representation by Complex Numbers ............ 37
          1.3.5.  Light Intensity, Detection of Polarization
                  State ........................................ 40
    1.4.  Propagation of Polarized Light ....................... 45
          1.4.1.  Jones Vectors ................................ 45
          1.4.2.  Jones Matrices ............................... 48
          1.4.3.  Quantum Mechanical Description, Partial
                  Polarization ................................. 53
          1.4.4.  Stokes Vectors ............................... 56
          1.4.5.  Mueller Matrices ............................. 59
    1.5.  Reflection and Transmission of Polarized Light at
          Planar Interfaces .................................... 67
          1.5.1.  Matching Plane Waves at a Planar Interface ... 67
          1.5.2.  Fresnel Coefficients ......................... 72
          1.5.3.  Special Values of the Angle of Incidence ..... 74
          1.5.4.  Ratio of Amplitude Reflectivities ............ 76
          1.5.5.  Propagation Matrices, Stratified
                  Structures ................................... 80
          1.5.6.  Substrate-Film-Ambient System ................ 85
    1.6.  References ........................................... 90

2.  Optical Physics of Materials ............................... 93
    2.1.  Introduction ......................................... 93
    2.2.  Propagation of Light in Solids ...................... 102
          2.2.1.  Optically Isotropic Solids and the Complex
                  Dielectric Function ......................... 102
          2.2.2.  Optically Anisotropic Solids and the
                  Dielectric Tensor ........................... 110
          2.2.3.  Dispersion Relationships .................... 124
    2.3.  Classical Theories of the Optical Properties of
          Solids .............................................. 125
          2.3.1.  Semiconductors and Insulators: the Lorentz
                  Oscillator Model ............................ 125
          2.3.2.  Metals: The Drude Free Electron Model ....... 129
          2.3.3.  Plasmons .................................... 132
          2.3.4.  Optical Sum Rules ........................... 136
    2.4.  Quantum Mechanical Theories of the Optical
          Properties of Solids ................................ 137
          2.4.1.  Quantum Theory of Absorption and
                  Dispersion .................................. 138
          2.4.2.  Direct Interband Transitions in Solids ...... 146
          2.4.3.  Band Structure and Critical Points in
                  Solids ...................................... 150
          2.4.4.  Indirect Interband Transitions in Solids .... 153
          2.4.5.  Intraband Transitions in Metals ............. 157
    2.5.  Modeling the Optical Properties of Solids ........... 159
          2.5.1.  Classical Lorentz Oscillator Models ......... 159
          2.5.2.  Classical Drude Models ...................... 172
          2.5.3.  Generalized Quantum Mechanical Models ....... 178
          2.5.4.  Specialized Quantum Mechanical Models ....... 207
    2.6.  Overview and Concluding Remarks ..................... 227
          Acknowledgments ..................................... 230
    2.7.  References and Bibliography ......................... 230
          2.7.1.  Numbered References ......................... 230
          2.7.2.  Bibliography ................................ 233

3.  Data Analysis for Spectroscopic Ellipsometry .............. 237
    3.1.  Introduction ........................................ 237
    3.2.  Ellipsometry Parameters ............................. 239
          3.2.1.  Calculated Parameters: Jones Matrices ....... 240
          3.2.2.  Measured Parameters: Mueller Matrices ....... 241
          3.2.3.  Mueller-Jones Matrices ...................... 242
    3.3.  Calculation of Complex Reflection Coefficients ...... 246
          3.3.1.  Isotropic, Homogeneous Systems .............. 246
          3.3.2.  Anisotropic Systems ......................... 248
          3.3.3.  Inhomogeneous Layers ........................ 251
    3.4.  Models for Dielectric Functions ..................... 252
          3.4.1.  Tabulated Data Sets ......................... 253
          3.4.2.  Lorentz Oscillator Model .................... 254
          3.4.3.  Optical Functions of Amorphous Materials .... 255
          3.4.4.  Models for Crystalline Materials ............ 258
          3.4.5.  Effective Medium Theories ................... 260
    3.5.  Fitting Models to Data .............................. 262
          3.5.1.  Figures of Merit ............................ 263
          3.5.2.  Errors in Spectroscopic Ellipsometry ........ 265
          3.5.3.  Convergence Routines ........................ 268
          3.5.4.  An Example: (a-SixNy:H)...................... 271
    3.6.  Determination of Optical Functions from
          Spectroscopic Ellipsometry Data ..................... 276
          3.6.1.  Optical Functions from Parameterization ..... 278
          3.6.2.  Newton-Raphson Algorithm .................... 280
          3.6.3.  Optical Functions of Bulk Isotropic
                  Semiconductors and Insulators ............... 282
          3.6.4.  Optical Functions of Anisotropic
                  Materials ................................... 285
          3.6.5.  Optical Functions of Thin Films ............. 286
    3.7.  Depolarization ...................................... 289
          Acknowledgements .................................... 293
    3.8.  Further Reading and References ...................... 293
          Optics and Ellipsometry ............................. 293
          Data Reduction ...................................... 294
          Numbered References ................................. 294

Part 2: Instrumentation ....................................... 297

4.  Optical Components and the Simple PCSA (Polarizer,
    Compensator, Sample, Analyzer) Ellipsometer ............... 299
    4.1.  General ............................................. 299
    4.2.  The Components ...................................... 301
          4.2.1.  Methods of Obtaining Polarized Light ........ 301
          4.2.2.  Double Refraction ........................... 302
          4.2.3.  Calcite Crystals ............................ 303
          4.2.4.  Polarizers and Analyzers .................... 305
          4.2.5.  Wollaston Prisms ............................ 307
          4.2.6.  Compensators, Quarter-Wave Plates, and
                  Retarders ................................... 308
          4.2.7.  Photoelastic Modulators ..................... 316
          4.2.8.  Monochromators .............................. 317
          4.2.9.  Goniometers ................................. 321
    4.3.  Ellipsometer Component Configurations ............... 322
          4.3.1.  Early Null Ellipsometer Configurations ...... 322
          4.3.2.  Photometric Ellipsometer Configurations ..... 323
          4.3.3.  Spectroscopic Ellipsometers ................. 324
          4.3.4.  Other Configurations ........................ 326
    4.4.  References .......................................... 327

5.  Rotating Polarizer and Analyzer Ellipsometry .............. 329
    5.1.  Introduction ........................................ 329
    5.2.  Comparison of Ellipsometers ......................... 333
    5.3.  Instrumentation Issues .............................. 343
          5.3.1.  Optical Configuration ....................... 343
          5.3.2.  Optical Components and Spectral Range ....... 345
          5.3.3.  Alignment ................................... 351
          5.3.4.  Electronic Design and Components ............ 356
    5.4.  Data Reduction for the Rotating Polarizer and
          Analyzer Ellipsometers .............................. 364
          5.4.1.  Ideal PXSAr Configuration ................... 364
          5.4.2.  Errors in the PXSAr Configuration ........... 371
          5.4.3.  PrXSA Configuration ......................... 378
    5.5.  Precision Considerations ............................ 386
    5.6.  Calibration Procedures .............................. 392
          5.6.1.  Ideal Rotating Polarizer and Analyzer
                  Ellipsometers ............................... 394
          5.6.2.  Detecting and Correcting Errors in
                  Calibration ................................. 407
          5.6.3.  Detecting and Correcting Compensator
                  Errors ...................................... 423
    5.7.  Summary: Recent and Future Directions ............... 425
    5.8.  References .......................................... 429

6.  Polarization Modulation Ellipsometry ...................... 433
    6.1.  Introduction ........................................ 433
    6.2.  The Photoelastic Modulator (PEM) .................... 436
          6.2.1.  General Description and Historical
                  Perspective ................................. 436
          6.2.2.  Mathematical Description of a PEM ........... 440
          6.2.3.  Stokes Vector Descriptions of the PSG 
                  and PSA ..................................... 442
    6.3.  Experimental Configurations of Polarization
          Modulation Ellipsometers ............................ 446
          6.3.1.  Polarization Modulation Ellipsometry (PME)
                  with Analog Data Acquisition ................ 446
          6.3.2.  Phase Modulated Ellipsometry (PME) with
                  Digital Data Acquisition .................... 447
          6.3.3.  Two-Channel Spectroscopic Polarization
                  Modulation Ellipsometer (2-C SPME) .......... 449
          6.3.4.  Two-Modulator Generalized Ellipsometer 
                  (2-MGE) ..................................... 450
    6.4.  Light Intensity Through a Polarization Modulation
          Ellipsometer ........................................ 452
          6.4.1.  Mueller Matrices for Various Samples ........ 452
          6.4.2.  Intensity for a Standard PME ................ 455
          6.4.3.  Intensity for the 2-Modulator Generalized
                  Ellipsometer (2-MGE) ........................ 457
    6.5.  Waveform Analysis ................................... 461
          6.5.1.  Basis Function .............................. 463
          6.5.2.  Phase-Sensitive Detection ................... 465
          6.5.3.  Digital Waveform Analysis ................... 466
          6.5.4.  Two-Modulator Systems ....................... 467
    6.6.  Calibration Procedures .............................. 469
          6.6.1.  One-Modulator PMEs .......................... 470
          6.6.2.  Two-Modulator PMEs .......................... 472
    6.7.  Errors .............................................. 474
          6.7.1.  General Discussion .......................... 474
          6.7.2.  Systematic Errors of PMEs ................... 475
    6.8.  Further Reading and References ...................... 479
          6.8.1.  Further Reading ............................. 479
          6.8.2.  Numbered References ......................... 479

7.  Multichannel Eilipsometry ................................. 481
    7.1.  Introduction ........................................ 481
    7.2.  Overview of Instrumentation ......................... 483
          7.2.1.  Self-Compensating Designs ................... 483
          7.2.2.  Rotating-Element Designs .................... 487
          7.2.3.  Phase-Modulation Designs .................... 491
          7.2.4.  Design Comparisons .......................... 493
          7.2.5.  Errors Unique to Multichannel Detection
                  Systems ..................................... 497
    7.3.  Rotating-Element Designs ............................ 502
          7.3.1.  Rotating Polarizer .......................... 502
          7.3.2.  Single Rotating Compensator ................. 523
          7.3.3.  Dual Rotating Compensator ................... 546
    7.4.  Concluding Remarks .................................. 562
          Acknowledgements .................................... 564
    7.5.  References .......................................... 564

Part 3: Critical Reviews of Some Applications ................. 567

8.  SiO2 Films ................................................ 569
    8.1.  Introduction 569
          8.1.1.  Preeminence of SiO2 in Microelectronics:
                  the Eilipsometry Connection ................. 569
          8.1.2.  Electronic Passivation ...................... 570
          8.1.3.  Properties of SiO2 Films .................... 571
    8.2.  Historical Perspective - Prior to 1970 .............. 578
    8.3.  Modern Studies - Since 1970 ......................... 585
          8.3.1.  Thick SiO2 Films ............................ 585
          8.3.2.  Thin SiO2 Films ............................. 599
          8.3.3.  Recent Results on Ultra Thin SiO2 Films
                  and the Si-SiO2 Interface ................... 619
    8.4.  Conclusions ......................................... 632
          Acknowledgements .................................... 633
    8.5.  References .......................................... 633

9.  Theory and Application of Generalized Ellipsometry ........ 637
    9.1.  Introduction ........................................ 637
    9.2.  The Generalized Ellipsometry Concept ................ 638
          9.2.1.  Comments on Notations in GE ................. 638
          9.2.2.  The Optical Jones Matrix .................... 640
          9.2.3.  The Generalized Ellipsometry Parameters ..... 643
          9.2.4.  Generalized Ellipsometry Acquisition
                  Techniques .................................. 647
    9.3.  Theory of Generalized Ellipsometry .................. 650
          9.3.1.  Birefringence in Stratified Media ........... 650
          9.3.2.  4X4 Maxwell's Equations in Matrix Form ...... 652
          9.3.3.  Transmission and Reflection GE .............. 656
    9.4.  Special Generalized Ellipsometry Solutions .......... 657
          9.4.1.  Biaxial Films (Symmetrically Dielectric
                  Materials) .................................. 657
          9.4.2.  Bi-Biaxial or Magneto-Optical Films
                  (Non-Symmetrically Dielectric Materials) .... 661
          9.4.3.  Chiral Biaxial Films (Axially Twisted
                  Symmetrically Dielectric Materials) ......... 663
          9.4.4.  Isotropic Dielectric Films .................. 669
          9.4.5.  Further Solutions: [111] Superlattice
                  Ordering in III-V Compounds
                  (CuPt-Ordering) ............................. 671
    9.5.  Strategies in Generalized Ellipsometry .............. 675
          9.5.1.  Data Acquisition Strategies for
                  Anisotropic Samples ......................... 676
          9.5.2.  Strategies for Treatment of Sample
                  Backside Effects ............................ 679
          9.5.3.  Model Strategies ............................ 682
    9.6.  Generalized Ellipsometry Applications ............... 683
          9.6.1.  Anisotropic Bulk Materials .................. 684
          9.6.2.  Anisotropic Films ........................... 693
    9.7.  Conclusions ......................................... 710
          Acknowledgements .................................... 710
    9.8.  Further Reading and References ...................... 711
          9.8.1.  General Reading ............................. 711
          9.8.2.  Numbered References ......................... 712

Part 4: Emerging Areas in EUipsometry ......................... 719

10. VUV Ellipsometry .......................................... 721
    10.1. Introduction ........................................ 721
    10.2. Historical Review of Short Wavelength
          Ellipsometry ........................................ 722
          10.2.1. BESSY Ellipsometer .......................... 722
          10.2.2. EUV Ellipsometer ............................ 724
    10.3. VUV EUipsometry Today ............................... 726
          10.3.1. Current VUV Instrumentation ................. 726
    10.4. Importance of VUV Ellipsometry ...................... 732
    10.5. Survey of Applications .............................. 737
          10.5.1. Lithography ................................. 740
          10.5.2. Gate Dielectrics ............................ 748
          10.5.3. High-energy Optical Constants ............... 749
    10.6. Future of VUV Ellipsometry .......................... 757
    10.7. Acknowledgments ..................................... 757
    10.8. References .......................................... 757

11. Spectroscopic Infrared Ellipsometry ....................... 763
    11.1. Experimental Tools .................................. 763
          11.1.1. Two Kinds of Instruments .................... 763
          11.1.2. Optical Equipment for the
                  Infrared-EIlipsometry ....................... 768
          11.1.3. The Degree of Polarization .................. 771
          11.1.4. Linearity of the Detection System ........... 775
          11.1.5. Infrared Synchrotron Radiation .............. 775
    11.2. Applications ........................................ 776
          11.2.1. Optics of Absorbing Media ................... 776
          11.2.2. Vibration Modes - the Concept of Weak and
                  Strong Oscillators .......................... 778
          11.2.3. Inversion of Infrared Ellipsometric
                  Measurements ................................ 781
          11.2.4. Anisotropy Features in the Infrared
                  Ellipsometric Spectra ....................... 786
    11.3. References .......................................... 797

12. Ellipsometry in Life Sciences ............................. 799
    Poem and Dedication ....................................... 799
    12.1. Introduction ........................................ 800
    12.2. Historical Background ............................... 802
    12.3. The Interfaces Under Study .......................... 802
    12.4. From Optics to Biology .............................. 804
          12.4.1. The Unique Possibilities .................... 804
          12.4.2. Verification of Ellipsometric Results ....... 805
    12.5. Methodology for Data Evaluation - from ψ and Δ to
          Biologically Related Parameters ..................... 806
          12.5.1. A Thin Biolayer on a Flat Ideal Substrate ... 806
          12.5.2. A Thick Biolayer on a Flat Ideal
                  Substrate ................................... 817
          12.5.3. Adsorption of Biomolecules into Porous
                  Structures .................................. 817
          12.5.4. Surface Roughness ........................... 819
          12.5.5. Use of Dispersion Models .................... 820
          12.5.6. Anisotropy .................................. 820
    12.6. Methodology - Experimental .......................... 821
          12.6.1. Instrumentation ............................. 821
          12.6.2. Cell Designs ................................ 822
          12.6.3. In situ Considerations for Biological
                  Interfaces .................................. 824
          12.6.4. Some Model Surfaces ......................... 825
          12.6.5. Studies on Real Biological Surfaces ......... 827
          12.6.6. Complementary and Independent
                  Information ................................. 828
          12.6.7. Experimental Design ......................... 828
    12.7. Applications ........................................ 829
          12.7.1. Introduction ................................ 829
          12.7.2. Adsorption of Biomolecules to Model
                  Surfaces .................................... 830
          12.7.3. Spectroscopy ................................ 839
          12.7.4. Imaging ..................................... 841
          12.7.5. Biological Surfaces ......................... 843
          12.7.6. Biosensors Based on Ellipsometric Readout ... 844
          12.7.7. Engineering Applications .................... 845
    12.8. Outlook ............................................. 846
          Acknowledgements .................................... 847
    12.9. References .......................................... 847


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