D I S S E R T A T I O N

Photolithography Simulation

ausgeführt zum Zwecke der Erlangung des akademischen Grades
eines Doktors der technischen Wissenschaften
eingereicht an der Technischen Universität Wien
Fakultät für Elektrotechnik

von

Heinrich Kirchauer

Arthaberplatz 11/38
Wien X.
Matrikelnummer 8825186
geboren am 11. Dezember 1969 in Wien

Wien, im März 1998

 

• Kurzfassung
• Abstract
• Acknowledgment
• Contents
• List of Figures
• List of Tables
• List of Symbols
• List of Abbreviations
• 1. Introduction
  • 1.1 Semiconductor Technology
    • 1.1.1 Unit Processes
    • 1.1.2 Process Integration
  • 1.2 The Role of Technology CAD
  • 1.3 Outline of the Thesis
• 2. The Photolithography Process
  • 2.1 Some Fundamental Considerations
  • 2.2 Operation Principle
  • 2.3 Illuminator
    • 2.3.1 Light Source
    • 2.3.2 Condenser Lens
    • 2.3.3 Partial Coherence and Advanced Apertures
  • 2.4 Photomask
    • 2.4.1 Binary Masks
    • 2.4.2 Phase-Shifting Masks
  • 2.5 Optical System
    • 2.5.1 Contact and Proximity Printing
    • 2.5.2 Projection Printing
  • 2.6 Photoresist
    • 2.6.1 Contrast and Important Properties
    • 2.6.2 Composition of DQN Resist
    • 2.6.3 Processing Issues
    • 2.6.4 Advanced Resist Systems
  • 2.7 Nanolithography
    • 2.7.1 Extreme Ultraviolet
    • 2.7.2 X-Ray
    • 2.7.3 Electron-Beam
    • 2.7.4 Ion-Beam
• 3. Photolithography Simulation
  • 3.1 Modeling Phases and Basic Simulator Structure
  • 3.2 Practical Characterization
    • 3.2.1 Focus Effects and Process Window
    • 3.2.2 Point Optimization of the Aerial Image
    • 3.2.3 Lumped Parameter Model
  • 3.3 Modeling of Technology Innovations
    • 3.3.1 Die-Size Simulation of Optical Proximity Correction
    • 3.3.2 Feature-Size Simulation and Advanced Physical Modeling
  • 3.4 Existing Simulators and Future Perspectives
• 4. Aerial Image Simulation
  • 4.1 Principles of Fourier Optics
    • 4.1.1 Scalar Diffraction Theory
    • 4.1.2 Phase Transformation Properties of a Lens
    • 4.1.3 Fourier Analysis of an Imaging System
    • 4.1.4 Köhler Illumination of a Periodic Mask
    • 4.1.5 Vector-Valued Extension
  • 4.2 Lens Aberrations and In-Lens Filter
    • 4.2.1 Defocus
    • 4.2.2 Power Series Representation of Primary Seidel Aberrations
    • 4.2.3 Zernike Polynomials for General Aberration Terms
    • 4.2.4 In-Lens Filters
  • 4.3 Advanced Illumination Aperture
    • 4.3.1 Abbe's Method
    • 4.3.2 Hopkins' Method
  • 4.4 Numerical Implementation
    • 4.4.1 ``Alias Free'' Forward Transform
    • 4.4.2 Numerical Backward Transform
• 5. Photoresist Exposure/Bleaching Simulation
  • 5.1 Exposure Kinetics
    • 5.1.1 Absorption in a Dilute Solution
    • 5.1.2 Modeling of Conventional Resists
    • 5.1.3 Modeling of Chemically Amplified Resists
    • 5.1.4 Simulation Flow
  • 5.2 Field Calculation over Planar Topography
    • 5.2.1 Vertical Propagation Method
    • 5.2.2 Scaled Defocus Method
    • 5.2.3 Transfer Matrix Method
    • 5.2.4 Beam Propagation Method
  • 5.3 Field Calculation over Nonplanar Topography
    • 5.3.1 Rigorous Electromagnetic Solution
    • 5.3.2 Approximate Electromagnetic Solution
• 6. Differential Method
  • 6.1 Fundamentals
    • 6.1.1 Problem Formulation
    • 6.1.2 Operation Principle
  • 6.2 Lateral Discretization of the Maxwell Equations
    • 6.2.1 First Maxwell Equation
    • 6.2.2 Second Maxwell Equation
    • 6.2.3 Elimination of the Vertical Field Components
    • 6.2.4 Scaling of the Ordinary Differential Equation System
    • 6.2.5 Truncation of the Fourier expansions
    • 6.2.6 Vector-Matrix Notation
  • 6.3 Formulation of the Boundary Conditions
    • 6.3.1 Air/Resist Interface
    • 6.3.2 Resist/Substrate Interface
    • 6.3.3 Vector-Matrix Notation
  • 6.4 Vertical Discretization of the Maxwell Equations
    • 6.4.1 Two-Point Boundary Value Problem
    • 6.4.2 Numerical Solution Techniques for Boundary Value Problems
    • 6.4.3 Shooting Method
      • Single Shooting
      • 6.4.3.1 Shooting with Reduced Superposition
      • 6.4.3.2 Multiple Shooting
  • 6.5 Discussion
    • 6.5.1 Performance
    • 6.5.2 Limitations
    • 6.5.3 Comparison with the Waveguide Method
• 7. Photoresist Bake and Development Simulation
  • 7.1 Bake Steps
    • 7.1.1 Prebake
    • 7.1.2 Post-Exposure Bake
  • 7.2 Development
    • 7.2.1 Development Rate Modeling
    • 7.2.2 Surface Advancement
• 8. Simulation Examples
  • 8.1 Aerial Image Simulation of the Layout of a Multiplexer
    • 8.1.1 Entire Layout
    • 8.1.2 Imaging Enhancement Techniques
  • 8.2 Photoresist Exposure and Development Simulation
    • 8.2.1 Printing of a Contact Hole over Planar Substrate
    • 8.2.2 Printing of a Contact Hole over Dielectric Step
    • 8.2.3 Printing of a Contact Hole over Reflective Step
    • 8.2.4 Two-Dimensional Cross Sections of the Printed Contact Holes
• 9. Conclusion and Outlook
  • Aerial image simulation.
  • Differential method.
  • Physical modeling.
• A. Approximation of the Inclination Factor
• B. Analytical Fourier Transformations
  • B.1 Triangular Patterns
  • B.2 Rectangular Patterns
  • B.3 Numerical Evaluation
• C. Stratified Medium
  • C.1 One Homogeneous Planar Layer
    • Electric Field
    • Magnetic Field
    • Matrix Notation
    • Matrix Factorization
    • Propagation Matrix
  • C.2 Stack of Homogeneous Planar Layers
• D. Nonplanar Material Interface
• Bibliography
• List of Publications
• Curriculum Vitae