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


Simulation of
Thermoelectric Devices


ausgeführt zum Zwecke der Erlangung des akademischen Grades
eines Doktors der technischen Wissenschaften

eingereicht an der Technischen Universität Wien
Fakultät für Elektrotechnik und Informationstechnik
von


Martin Wagner


Bad Mitterndorf 284
A-8983 Bad Mitterndorf, Österreich

Matr. Nr. 9925860
geboren am 9. Juli 1979 in Wien


Wien, im November 2007

It is unwise
to be too sure
of one's own wisdom.
It is healthy
to be reminded that
the strongest might weaken
and the wisest might err.

Mahatma Gandhi

To Lena and Jakob

• Kurzfassung
• Abstract
• Acknowledgment
• Contents
• List of Symbols
  • Notation
  • Physical Quantities
  • Constants
  
  
• List of Figures
• List of Tables
• 1. Introduction
• 2. Fundamentals of Thermoelectric Devices
  • 2.1 Thermoelectric Phenomena
    • 2.1.1 Seebeck Effect
    • 2.1.2 Peltier Effect
    • 2.1.3 Thomson Effect
    • 2.1.4 Thermodynamic Relations
  • 2.2 Applications of Thermoelectric Devices
  • 2.3 Future Applications
  
  
• 3. Electrical Transport
  • 3.1 A Hierarchy of Simulation Strategies
  • 3.2 The Basic Equations
    • 3.2.1 Poisson's Equation
    • 3.2.2 Boltzmann's Equation
  • 3.3 Band Structure Model
  • 3.4 The Distribution Function
  • 3.5 Macroscopic Transport Models
    • 3.5.1 Microscopic and Macroscopic Quantities
    • 3.5.2 Method of Moments
    • 3.5.3 A Hierarchy of Transport Models
    • 3.5.4 Relaxation Time Approximation
    • 3.5.5 Stratton's Approach
    • 3.5.6 Bløtekjær's Approach
    • 3.5.7 Non-Diagonal Relaxation Time Ansatz
    • 3.5.8 Summary of Equations
    • 3.5.9 Onsager Relations
    • 3.5.10 Electrothermal Transport Model
    • 3.5.11 Phenomenological Approach
    • 3.5.12 Seebeck Coefficient
  
  
• 4. Materials for Thermoelectric Devices
  • 4.1 Characterization of Materials
  • 4.2 Optimization of Device Performance
  • 4.3 Silicon-Germanium
  • 4.4 Lead Telluride and its Alloys
  • 4.5 Bismuth Telluride and its Alloys
  
  
• 5. Physical Modeling of PbTe and PbSnTe
  • 5.1 Lattice Properties
    • 5.1.1 Lattice Constant, Thermal Expansion, and Mass Density
    • 5.1.2 Dielectric Constant
    • 5.1.3 Elastic Moduli and Sound Velocities
  • 5.2 Thermal Properties
    • 5.2.1 Specific Heat Capacity
    • 5.2.2 Thermal Conductivity
    • 5.2.3 Thermoelectric Powers
  • 5.3 Band Structure
    • 5.3.1 Band Gap
    • 5.3.2 Effective Masses, Density of States, Intrinsic Carrier Density
  • 5.4 Carrier Mobility
  • 5.5 Generation and Recombination
    • 5.5.1 Direct Recombination
    • 5.5.2 Shockley-Read-Hall Recombination
    • 5.5.3 Auger Recombination
  
  
• 6. Case Studies
  • 6.1 Ideal Classical Thermoelectric Generators
  • 6.2 Non-Ideal Devices and Thermal Environment
  • 6.3 Reduced Thermal Conductivity by Alloys
  • 6.4 Stacked Lead Telluride Thermoelectric Devices
  • 6.5 Pn-Junctions as Thermoelectric Devices
    • 6.5.1 Temperature Control by Graded Material Alloys
    • 6.5.2 Generation Enhancement by Additional Traps
    • 6.5.3 Optimization of Device Characteristics
  
  
• 7. Summary and Conclusions
• A. Poisson Brackets Formulation
• B. Useful Identities
• Bibliography
• Own Publications
• Curriculum Vitae
• About this document ...

M. Wagner: Simulation of Thermoelectric Devices