THERMAL MANAGEMENT OF MICROELECTRONIC EQUIPMENT · 2019. 9. 12. · THERMAL MANAGEMENT OF MICROELECTRONIC EQUIPMENT HEAT TRANSFER THEORY, ANALYSIS METHODS, AND DESIGN PRACTICES L.

THERMAL MANAGEMENTOF MICROELECTRONICEQUIPMENTHEAT TRANSFER THEORY, ANALYSIS METHODS, AND DESIGN PRACTICES

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ASME Press Book Series on Electronic PackagingDereje Agonafer, Editor-in-Chief

Associate Technical Editors Administrative Editors

Cristina Amon, Carnegie Mellon University Damena Agonafer A. Haji-Sheikh, University of Texas, Arlington University of Texas, ArlingtonYung-Cheng Lee, University of Colorado, BoulderWataru Nakayama, ThermTech International Senayet AgonaferShlomo Novotny, Sun Microsystems Princeton UniversityAl Ortega, University of Arizona, TucsonDonald Price, Raytheon Electronic SystemsViswam Puligandla, NokiaKoneru Ramakrishna, Motorola, Inc.Gamal Refai-Ahmed, Ceyba Inc.Bahgat Sammakia, SUNY, BinghamtonRoger Schmidt, IBMMasaki Shiratori, Yokohama National UniversitySuresh Sitaraman, Georgia Institute of TechnologyEphraim Suhir, Iolon, Inc.

About the Series

Electronic packaging is experiencing unprecedented growth, as it is the keyenabling technology for applications ranging from computers and telecommuni-cations, to automobiles and consumer products. Although technology improve-ments are still possible, these solutions are becoming quite expensive. Inaddition, technology enhancements seem to be reaching physics-based limits.Therefore, packaging can present an opportunity for performance improvementswithout the need for new CMOS technology. At InterPACK 1999, the flagship con-ference of the Electronic and Photonic Packaging Division, the electronic pack-aging business worldwide was estimated to be over $100 billion per year. Therapidly changing technology necessitates current and up-to-date technical knowl-edge on the subject for both practicing engineers and academic researchers. Itwas with this background that this book series was initiated.

The book series will cover broad topics in packaging ranging from electroniccooling, interconnects, thermo/mechanical challenges, including thermallyinduced stress and vibration, and various aspects of failures in electronic sys-tems. The important field of design tools, including thermal, mechanical andelectrical, and the corresponding important issues of integration of these variousdesign tools will also be topics for future books. Other topics include the growingfield of micro-electronics mechanical systems, optoelectronics, and nanotechnol-ogy packaging. Please contact the Editor-in-Chief or one of the outstanding asso-ciate technical editors listed above, or Mary Grace Stefanchik of ASME Pressshould you be interested in suggesting a particular book topic or have an interestin authoring a book.


THERMAL MANAGEMENTOF MICROELECTRONICEQUIPMENTHEAT TRANSFER THEORY, ANALYSIS METHODS, AND DESIGN PRACTICES

L. T. Yeh, Ph.D., P.E. R. C. Chu

ASME PRESSNEW YORK2002

ASME Press Book Series on Electronic PackagingDereje Agonafer, Editor-in-Chief


Copyright © 2002The American Society of Mechanical Engineers

Three Park Ave., New York, NY 10016

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INFORMATION CONTAINED IN THIS WORK HAS BEEN OBTAINED BY THE AMERI-CAN SOCIETY OF MECHANICAL ENGINEERS FROM SOURCES BELIEVED TO BERELIABLE. HOWEVER, NEITHER ASME NOR ITS AUTHORS OR EDITORS GUARAN-TEE THE ACCURACY OR COMPLETENESS OF ANY INFORMATION PUBLISHED INTHIS WORK. NEITHER ASME NOR ITS AUTHORS AND EDITORS SHALL BE RESPON-SIBLE FOR ANY ERRORS, OMISSIONS, OR DAMAGES ARISING OUT OF THE USE OFTHIS INFORMATION. THE WORK IS PUBLISHED WITH THE UNDERSTANDING THATASME AND ITS AUTHORS AND EDITORS ARE SUPPLYING INFORMATION BUT ARENOT ATTEMPTING TO RENDER ENGINEERING OR OTHER PROFESSIONAL SER-VICES. IF SUCH ENGINEERING OR PROFESSIONAL SERVICES ARE REQUIRED,THE ASSISTANCE OF AN APPROPRIATE PROFESSIONAL SHOULD BE SOUGHT.

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Library of Congress Cataloging-in-Publication Data

Yeh, L.-T. (Lian-Tuu), 1944-Thermal management of microelectronic equipment: heat transfer theory,

analysis methods, and design practices / L.-T. Yeh and R. C. Chu.p. cm.ISBN 0-7918-0168-31. Electronic apparatus and appliances – Cooling. 2. Electronic apparatus and appli-

ances – Thermal properties. 3. Heat – Transmission. I. Chu, R. C. (Richard C.), 1933. II.Title.

TK7870.25.Y44 2002621.381’04 – dc21

2001034086


List of Figures xi

List of Tables xvii

Nomenclature xix

Foreword xxiii

Preface xxv

Chapter 1 Introduction 1

1.1 Need for Thermal Control ...............................................................1

1.2 Reliability and Temperature............................................................3

1.3 Levels of Thermal Resistance...........................................................4

1.4 Thermal Design Considerations ......................................................5

1.5 Optimization and Life-Cycle Cost ...................................................6

Chapter 2 Conduction 9

2.1 Fundamental Law of Heat Conduction ..........................................9

2.2 General Differential Equations for Conduction...........................10

2.3 One-Dimensional Heat Conduction..............................................16

2.4 Thermal/Electrical Analogy ...........................................................17

2.5 Lumped-System Transient Analysis ...............................................20

2.6 Heat Conduction with Phase Change...........................................25

TABLE OF CONTENTS


Chapter 3 Convection 31

3.1 Flow and Temperature Fields ........................................................31

3.2 Heat Transfer Coefficient ..............................................................34

3.3 Parameter Effects on Heat Transfer..............................................35

3.4 Pressure Drop and Friction Factor.................................................43

3.5 Thermal Properties of Fluids .........................................................46

3.6 Correlations for Heat Transfer and Friction .................................47

CHAPTER 4 RADIATION 53

4.1 Stefan-Boltzmann Law ..................................................................53

4.2 Kirchhoff’s Law and Emissivity ......................................................54

4.3 Radiation Between Black Isothermal Surfaces.............................55

4.4 Radiation Between Gray Isothermal Surfaces..............................58

4.5 Extreme Climatic Conditions .........................................................61

Chapter 5 Pool Boiling 67

5.1 Boiling Curve..................................................................................67

5.2 Nucleate Boiling.............................................................................70

5.3 Incipient Boiling at Heating Surfaces ...........................................72

5.4 Nucleate Boiling Correlations .......................................................76

5.5 Critical Heat Flux Correlations ......................................................77

5.6 Minimum Heat Flux Correlations (Leidenforst Point)..................79

5.7 Parameters Affecting Pool Boiling................................................81

5.8 Effect of Gravity on Pool Boiling ..................................................87

Chapter 6 Flow Boiling 95

6.1 Flow Patterns .................................................................................95

6.2 Heat Transfer Mechanisms ............................................................95

6.3 Boiling Crisis ...................................................................................98

6.4 Heat Transfer Equations ................................................................99

6.5 Thermal Enhancement ................................................................109

6.6 Pressure Drop ...............................................................................109

vi • Table of Contents


Chapter 7 Condensation 115

7.1 Modes of Condensation ..............................................................115

7.2 Heat Transfer in Filmwise Condensation....................................116

7.3 Improvements Over Nusselt Analysis..........................................121

7.4 Condensation Inside a Horizontal Tube .....................................123

7.5 Noncondensable Gas in a Condenser .........................................127

Chapter 8 Extended Surfaces 131

8.1 Uniform–Cross Section Fins .........................................................131

8.2 Fin Efficiency ................................................................................134

8.3 Selection and Design of Fins .......................................................137

Chapter 9 Thermal Interface Resistance 141

9.1 Factors Affecting Thermal Contact Resistance...........................141

9.2 Joint Thermal Contact Resistance ...............................................145

9.3 Methods of Reducing Thermal Contact Resistance ...................147

9.4 Solder and Epoxy Joints...............................................................159

9.5 Practical Design Data...................................................................160

Chapter 10 Components and Printed Circuit Boards 169

10.1 Chip Packaging Technology ......................................................169

10.2 Chip Package Thermal Resistance.............................................172

10.3 Chip Package Attachment.........................................................173

10.4 Board-Cooling Methods ............................................................176

10.5 Board Thermal Analysis .............................................................177

10.6 Equivalent Thermal Conductivity..............................................178

Chapter 11 Direct Air Cooling and Fans 185

11.1 Previous Work ............................................................................185

11.2 Heat Transfer Correlations ........................................................187

11.3 Pressure Drop Correlations........................................................190

11.4 Heat Transfer Enhancement......................................................194

11.5 Fans and Air-Handling Systems.................................................197

Table of Contents • vii


Chapter 12 Natural and Mixed Convection 213

12.1 Parallel Plates .............................................................................214

12.2 Straight-Fin Arrays .....................................................................220

12.3 Pin-Fin Arrays .............................................................................229

12.4 Enclosures...................................................................................234

12.5 Mixed Convection in Vertical Plates .........................................237

Chapter 13 Heat Exchangers and Cold Plates 243

13.1 Compact Heat Exchangers.........................................................243

13.2 Flow Arrangement of Heat Exchangers ...................................244

13.3 Overall Heat Transfer Coefficient .............................................244

13.4 Heat Exchanger Effectiveness ...................................................245

13.5 Heat Exchanger Analysis ...........................................................246

13.6 Heat Transfer and Pressure Drop ..............................................248

13.7 Geometric Factors ......................................................................250

13.8 Cold-Plate Analysis.....................................................................251

13.9 Correlations................................................................................255

Chapter 14 Advanced Cooling Technologies I:Single-Phase Liquid Cooling 261

14.1 Coolant Selection.......................................................................261

14.2 Natural Convection....................................................................265

14.3 Forced Convection .....................................................................267

Chapter 15 Advanced Cooling Technologies II: Two-Phase Flow Cooling 283

15.1 Figure of Merit...........................................................................283

15.2 Direct-Immersion Cooling .........................................................285

15.3 Enhancement of Pool Boiling ...................................................287

15.4 Flow Boiling ...............................................................................300

Chapter 16 Heat Pipes 309

16.1 Operation Principles ..................................................................309

16.2 Useful Characteristics.................................................................309

viii • Table of Contents


16.3 Construction...............................................................................311

16.4 Operation Limits ........................................................................312

16.5 Materials Compatibility .............................................................318

16.6 Operating Temperatures ...........................................................320

16.7 Operation Methods ...................................................................321

16.8 Thermal Resistances...................................................................323

16.9 Applications ...............................................................................325

16.10 Micro Heat Pipes ......................................................................330

Chapter 17 Thermoelectric Coolers 335

17.1 Basic Theories of Thermoelectricity ..........................................335

17.2 Net Thermoelectric Effect..........................................................337

17.3 Figure of Merit...........................................................................338

17.4 Operation Principles ..................................................................339

17.5 System Configurations...............................................................339

17.6 Performance Analysis ................................................................340

17.7 Practical Design Procedure........................................................344

Appendices 349

A. Material Thermal Properties ........................................................349

B. Thermal Conductivity of Silicon and Gallium Arsenide..............351

C. Properties of Air, Water, and Dielectric Fluids ............................353

D. Typical Emissivities of Materials ...................................................371

E. Solar Absorptivities and Emissivities of Common Surfaces .........................................................................................373

F. Properties of Phase-Change Materials .........................................375

G. Friction Factor Correlations..........................................................377

H. Heat Transfer Correlations ...........................................................381

I. Units Conversion Table .................................................................403

Index 405

About the Authors 413

Table of Contents • ix


1.1 Increase in circuit complexity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Major causes of electronics failures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Effect of part placement on component junction temperature.. . . . . . . . . . 61.4 Example of current thermal design practice. . . . . . . . . . . . . . . . . . . . . . . . . . 72.1 Cylindrical and spherical coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Thermal resistance factor Φ at heat source center

for rectangular solids with W = L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Thermal resistance factor Φ at heat source center

for cylindrical solids.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Thermal network for a multilayer composite wall. . . . . . . . . . . . . . . . . . . . 192.5 Temperature profile in a thermal-energy storage system.. . . . . . . . . . . . . . 252.6 Moving solid-liquid interface for melting and solidification. . . . . . . . . . . . 262.7 Temperature profile with natural convection in liquid region. . . . . . . . . . 272.8 Cross section of microencapsulated phase-change material particle. . . . . 283.1 Boundary-layer development for fluid in a tube. . . . . . . . . . . . . . . . . . . . . . 323.2 Flow regimes for flow over a flat plate.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3 Boundary-layer formation and separation on a circular cylinder

in crossflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4 Velocity profile and flow separation for a circular cylinder

in crossflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.5 Boundary layer over a vertical plate in natural convection. . . . . . . . . . . . . 393.6 Friction factor versus Reynolds number for round tubes. . . . . . . . . . . . . . 454.1 Geometrical relation between two radiative surfaces. . . . . . . . . . . . . . . . . 554.2 View-factor algebra for pairs of surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.3 Hottel crossed-string method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.4 Equivalent network for radiative heat exchange

between two gray surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.5 Solar heat flux and ambient air temperature. . . . . . . . . . . . . . . . . . . . . . . . 625.1 Constant-pressure heating process.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.2 Regimes in pool-boiling heat transfer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.3 Boiling mechanism for heat flux–controlled

and temperature-controlled conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.4 Nucleation from a cavity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.5 Bubble shapes with various values of contact angle (surface tension).. . . 725.6 Vapor trapped in cavities by advancing liquid. . . . . . . . . . . . . . . . . . . . . . . 73

LIST OF FIGURES


5.7 Conditions required for nucleation in a temperature gradient. . . . . . . . . 745.8 Schematic representation of wall superheat excursion (overshoot). . . . . 755.9 Predictions of critical heat flux for various heater configurations. . . . . . 78

5.10 Effect of pressure on pool-boiling curve. . . . . . . . . . . . . . . . . . . . . . . . . . . 825.11 Influence of subcooling on pool boiling. . . . . . . . . . . . . . . . . . . . . . . . . . . 835.12 Effect of surface roughness on boiling curve. . . . . . . . . . . . . . . . . . . . . . . 845.13 Effect of dissolved gas on boiling curve.. . . . . . . . . . . . . . . . . . . . . . . . . . . 855.14 Effect of dissolved gas and subcooling on CHF under

atmospheric pressure.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 865.15 Effect of agitation in methanol boiling at 1 atm.. . . . . . . . . . . . . . . . . . . . 875.16 Thermal hysteresis in pool boiling of R-113. . . . . . . . . . . . . . . . . . . . . . . . 885.17 Liquid nitrogen pool-boiling curve at earth and near zero gravity. . . . . . 895.18 Reduced-gravity CHF data for horizontal surfaces and wires.. . . . . . . . . 905.19 Reduced-gravity CHF data for vertical wires and spheres. . . . . . . . . . . . . 906.1 Typical flow patterns for a horizontal tube. . . . . . . . . . . . . . . . . . . . . . . . . 966.2 Heat transfer mechanisms and flow regions in upward

vertical flow.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 976.3 Heat transfer regions under various heat fluxes. . . . . . . . . . . . . . . . . . . . . 986.4 Effects of velocity and subcooling on flow boiling. . . . . . . . . . . . . . . . . . 1016.5 F factor for Chen correlation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036.6 S factor for Chen correlation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036.7 Relationship between ∆p and ∆Tsat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1046.8 Parametric effects on critical heat flux. . . . . . . . . . . . . . . . . . . . . . . . . . . 1056.9 Boiling in smooth and multilead ribbed tubes. . . . . . . . . . . . . . . . . . . . . 1107.1 Velocity and temperature profiles in liquid film. . . . . . . . . . . . . . . . . . . . 1177.2 Film condensation in horizontal tubes. . . . . . . . . . . . . . . . . . . . . . . . . . . 1207.3 Heat transfer for condensation on a vertical plate. . . . . . . . . . . . . . . . . . 1227.4 Baker flow regime map (horizontal flow). . . . . . . . . . . . . . . . . . . . . . . . . 1247.5 F factor in a horizontal tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1257.6 Circumferentially local heat transfer coefficient.. . . . . . . . . . . . . . . . . . . 1267.7 Effect of noncondensable gas in condensation. . . . . . . . . . . . . . . . . . . . . 1278.1 Model for fin analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1328.2 Various types of fin configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1358.3 Fin efficiency of commonly used fins.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1379.1 Two nominally flat surfaces in contact.. . . . . . . . . . . . . . . . . . . . . . . . . . . 1429.2 Various types of surfaces in contact. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1439.3 Effect of pressure on interface resistance. . . . . . . . . . . . . . . . . . . . . . . . . 1449.4 Increasing contact surface with same projected area.. . . . . . . . . . . . . . . 1489.5 Contact resistance versus various foil thicknesses. . . . . . . . . . . . . . . . . . 1509.6 Insertion of a filler at interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1519.7 Contact of bare and coated joints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1529.8 Thermal contact conductance of various coating materials. . . . . . . . . . 1559.9 Effect of metallic coating thickness on contact conductance. . . . . . . . . 156

9.10 Insertion of phase-change materials at interface. . . . . . . . . . . . . . . . . . . 1579.11 Microcapillary thermal interface concept. . . . . . . . . . . . . . . . . . . . . . . . . 1589.12 Measured and calculated thermal resistances of an epoxy joint.. . . . . . 1609.13 Contact resistance for transistor mounting.. . . . . . . . . . . . . . . . . . . . . . . 1629.14 Thermal contact conductance for various materials. . . . . . . . . . . . . . . . 163

xii • List of Figures


10.1 Scale comparison of MCM and SCP. (a) Dual in-line package (DIP) and pin-grid array. (b) MCM containing various types of individual chips. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

10.2 Drawings of common packages: (a) DIP; (b) PGA. . . . . . . . . . . . . . . . . 17110.3 Interconnection between pin and board: (a) DIP; (b) PGA. . . . . . . . . . 17210.4 Thermal conductivity and CTE of various materials. . . . . . . . . . . . . . . 17410.5 Thermal conductivity and CTE of copper-invar. . . . . . . . . . . . . . . . . . . 17510.6 Thermal path for a common board in an electronic box. . . . . . . . . . . . 17610.7 Typical PCB construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17810.8 Dimensions of board and card guides for Example 10.2. . . . . . . . . . . . 18111.1 Array of rectangular modules in a channel. . . . . . . . . . . . . . . . . . . . . . . 18611.2 Airflow over the PCB of Example 11.1.. . . . . . . . . . . . . . . . . . . . . . . . . . 19211.3 Local heat transfer coefficient over the DIPs of Example 11.1. . . . . . . 19311.4 Diagrams of heat sinks applied to PGAs: (a) pin-fin, (b) disk-fin,

and (c) straight-fin heat sinks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19511.5 Flow patterns in a heat sink: (a) free plates, s >> δ (L);

(b) developing flow, s ≈ δ (L); (c) interfering, s

12.9 A vertical straight-fin array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22512.10 U-channel apparent emittance εa for different values of ε. . . . . . . . . . . 22712.11 Horizontal fin array configuration.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22812.12 Heat transfer coefficients for pin-fin arrays:

(a) arrays with vertical base plate; (b) arrays facing up; (c) arrays facing down. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

12.13 Pin-fin configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23312.14 Dimensionless shape factors for conduction. . . . . . . . . . . . . . . . . . . . . 23612.15 Flow reversal of buoyancy-assisted flow in vertical plates.. . . . . . . . . . 23812.16 Reversed-flow zone in buoyancy-assisted flow. . . . . . . . . . . . . . . . . . . . 23812.17 Nusselt numbers and flow reversal for isoflux-isoflux. . . . . . . . . . . . . . 24013.1 Effectiveness of parallel- and counterflow heat exchangers. . . . . . . . . 24813.2 Effectiveness of various flow arrangements at Cmin/Cmax = 1. . . . . . . . . 24913.3 Sketch of a heat exchanger. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25113.4 Electronics on a finned cold plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25213.5 Cross-sectional view of the heat exchanger of Example 13.1. . . . . . . . 25614.1 Sketch of a counterflow system for electronic cooling.. . . . . . . . . . . . . 26714.2 Cold-wall temperature distribution for unidirectional

and counterflow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26814.3 Schematic of heat source array with finned pins. . . . . . . . . . . . . . . . . . 26914.4 Average Nusselt number for unaugmented heat source array. . . . . . . . 27014.5 Average Nusselt number for each row of pin-fin heat source. . . . . . . . 27114.6 Heat transfer data for smooth and microstud surfaces. . . . . . . . . . . . . 27214.7 Fin dimensions and cutaway view of thick offset fins. . . . . . . . . . . . . . 27314.8 Rectangular (thin) offset fins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27314.9 Friction factor and Nusselt number for offset fins

in a narrow passage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27414.10 Friction factor vs. Reynolds number in microchannels.. . . . . . . . . . . . 27614.11 Variations of heat transfer coefficient with wall temperature.. . . . . . . 27715.1 Pool-boiling data for a plain tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28615.2 Typical boiling for small heaters immersed in R113. . . . . . . . . . . . . . . 28815.3 Pool-boiling curves for plain and ABM surfaces.. . . . . . . . . . . . . . . . . . 28915.4 Bubble generation heater and bubble paths for various spacings. . . . 29015.5 Falling liquid film.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29115.6 Liquid-vapor exchange at a nucleation site. (a) Pool boiling

on a vertical surface. (b) Boiling in a falling liquid film.. . . . . . . . . . . . 29115.7 Boiling curve of a falling liquid film.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29215.8 Surface enhancement for falling liquid film. . . . . . . . . . . . . . . . . . . . . . 29315.9 Boiling data for microfin and microstud surfaces. . . . . . . . . . . . . . . . . 293

15.10 Boiling data for a microfin surface with and without a deflector. . . . . 29415.11 Jet-impingement boiling curve for R-113. . . . . . . . . . . . . . . . . . . . . . . . 29615.12 Boiling curves for jet-impingement and spray cooling. . . . . . . . . . . . . 29715.13 Variation of peak heat flux with liquid mass flux in spray cooling.. . . 29915.14 Curved-surface semiconductor cooling system. . . . . . . . . . . . . . . . . . . 30115.15 Flow boiling over a small heater.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30215.16 Boiling curves of smooth and microstud surfaces. . . . . . . . . . . . . . . . . 30315.17 Boiling curves for mini- and microchannel heat sinks. . . . . . . . . . . . . 30415.18 Fluid exit temperature for mini- and microchannels. . . . . . . . . . . . . . . 304

xiv • List of Figures


15.19 Comparison of performance between mini- and microchannel heat sinks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

16.1 Heat pipe structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31016.2 Heat pipe nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31316.3 Heat pipe operating limits.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31916.4 Heat pipe operating temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32016.5 Control techniques for heat pipe operations. . . . . . . . . . . . . . . . . . . . . . 32216.6 Electrothermal analog for a heat pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . 32316.7 Effect of orientation on heat pipe performance. . . . . . . . . . . . . . . . . . . 32516.8 Performance of double-condenser heat pipe.. . . . . . . . . . . . . . . . . . . . . 32616.9 Performance of circuit-card heat pipes. . . . . . . . . . . . . . . . . . . . . . . . . . 327

16.10 Cutaway view of heat pipe–cooled SEM. . . . . . . . . . . . . . . . . . . . . . . . . 32716.11 Edge-cooled heat pipe printed wiring board.. . . . . . . . . . . . . . . . . . . . . 32816.12 Direct heat pipe cooling of a semiconductor.. . . . . . . . . . . . . . . . . . . . . 32816.13 Temperatures of a PCB rack with and without heat pipes. . . . . . . . . . 32916.14 Heat pipe heat exchanger for cooling enclosed electronics. . . . . . . . . . 33016.15 Micro heat pipes.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33216.16 Data for rectangular and triangular heat pipe arrays.. . . . . . . . . . . . . . 33317.1 Base configuration of a Peltier couple. . . . . . . . . . . . . . . . . . . . . . . . . . . 34017.2 Interconnected thermoelectric couples. . . . . . . . . . . . . . . . . . . . . . . . . . 34017.3 Thermoelectric device for gas flow systems. . . . . . . . . . . . . . . . . . . . . . . 34117.4 Two-stage cascaded thermoelectric module.. . . . . . . . . . . . . . . . . . . . . . 34117.5 Cooling capacity and COP of a typical thermoelectric device. . . . . . . . 34317.6 Thermoelectric module for cooling electronics inside an enclosure. . . 34517.7 Temperature difference vs. net heat transfer rate. . . . . . . . . . . . . . . . . . 346

List of Figures • xv


1.1 Effect of Thermal Conditions on Part Failure. . . . . . . . . . . . . . . . . . . . . 42.1 Equations of Heat Conduction in Various Geometrical

Configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2 Analogous Quantities between Thermal and Electrical Systems. . . . . 182.3 Conduction Thermal Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1 Nusselt Number and Friction Factor in Fully Developed

Laminar Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.2 Nusselt Number NuT for Rectangular Tubes in Fully Developed

Laminar Flow at T Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.3 Nusselt Number NuH1 for Rectangular Tubes in Fully Developed

Laminar Flow at H1Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.4 Absolute Surface Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.1 View Factor for Two Finite Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.2 Hot Dry Daily Cycle of Air Temperature and Solar Radiation . . . . . . . 635.1 Surface-Fluid Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 769.1 Typical Ranges of Parameters in Equations 9.2 and 9.3. . . . . . . . . . . 1479.2 Thermal Ratings for Solid Metal Interstitial Materials . . . . . . . . . . . 1499.3 Thermal Resistances with Alloy at Interface . . . . . . . . . . . . . . . . . . . . 1579.4 Typical Values of Thermal Contact Resistance . . . . . . . . . . . . . . . . . . 1619.5 Properties of Thermal Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . 1619.6 Maximum Torque Values for Alloy Steel Screws. . . . . . . . . . . . . . . . . 162

10.1 Thermal Conductivity of Basic PCB Materials . . . . . . . . . . . . . . . . . . 17711.1 Loss Coefficients for Various Physical Configurations. . . . . . . . . . . . 20412.1 Heat Transfer Correlations for Parallel Plates. . . . . . . . . . . . . . . . . . . 21912.2 Nusselt Numbers for Isoflux-Isoflux . . . . . . . . . . . . . . . . . . . . . . . . . . 23913.1 Fouling Factors for Some Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24514.1 Coolant Figures of Merit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26514.2 Empirical Constants for Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . 27814.3 Empirical Constants for Friction Factor . . . . . . . . . . . . . . . . . . . . . . . 27915.1 Differences between Jet-Impingement and Spray Cooling . . . . . . . . 29915.2 Summary Results of Experimental Data

on Mixing of Dielectric Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30015.3 Heat Transfer from a Small Heated Patch: Test Conditions

and Key Boiling Characteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30216.1 Expressions for Effective Capillary Radius . . . . . . . . . . . . . . . . . . . . . 314

LIST OF TABLES


16.2 Expressions for Wick Permeability . . . . . . . . . . . . . . . . . . . . . . . . . . . 31516.3 Effective Thermal Conductivity of Liquid and Wick . . . . . . . . . . . . . 31816.4 Heat Pipe Material Compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31916.5 Comparative Values of Heat Pipe Resistances . . . . . . . . . . . . . . . . . . 324C.1 Properties of Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355C.2 Properties of Water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356C.3 Properties of FC-43. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357C.4 Properties of FC-75. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358C.5 Properties of FC-77. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359C.6 Properties of FC-78. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360C.7 Properties of Coolanol-20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361C.8 Properties of Coolanol-25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362C.9 Properties of Coolanol-35. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

C.10 Properties of Coolanol-45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364C.11 Properties of Freon E2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365C.12 Properties of Glycol-Water Mixture. . . . . . . . . . . . . . . . . . . . . . . . . . . 366C.13 Properties of PAO (2 CST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367C.14 Properties of PAO (4 CST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368C.15 Properties of PAO (6 CST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369C.16 Properties of PAO (8 CST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370H.1 Common Correlations for External Forced Convection . . . . . . . . . . 382H.2 Common Correlations for Internal Forced Convection . . . . . . . . . . . 386H.3 Common Correlations for External Free Convection . . . . . . . . . . . . 392H.4 Common Correlations for Free Convection in Enclosures

or from Parallel Vertical Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394H.5 Common Correlations for Forced Convection in Tube Banks. . . . . . 398

xviii • List of Tables


Letter Symbols

A cross-sectional area or surface area, ft2

Af fin surface area, ft2

At total heat transfer surface area, ft2

cp specific heat, Btu/(lbm·°F)D diameter, ftDh hydraulic diameter, ftE emissive power, Btu/(hr·ft2)f Fanning friction factor,F black body view factor for radiationg acceleration of gravity = 32.1739 ft/s2

gc gravitational constant or conversion factor= 32.1739 lbm·ft/(lbf·s2) = 4.17 × 108 lbm·ft/(lbf·hr2)

G mass velocity, lbm/(hr·ft2)h heat transfer coefficient, Btu/(hr·ft2·°F)hc contact conductance, Btu/(hr·ft2·°F)hfg latent heat of vaporization, Btu/lbmhg gap conductance, Btu/(hr·ft2·°F)H hardness of solid, psiI electrical current, Aℑ gray body view factor for radiationJ radiosity, Btu/(hr·ft2·°F)k thermal conductivity, Btu/(hr·ft·°F)ks harmonic mean thermal conductivity, Btu/(hr·ft·°F)kxy thermal conductivity in xy plane, Btu/(hr·ft·°F)kz thermal conductivity in z direction, Btu/(hr·ft·°F)K fluid loss coefficientL length or characteristic length, ftL latent heat of fusion or solidification, Btu/lbmm mass flow, lbm/hrm RMS absolute surface asperity slopeNs specific speed of fanP fluid pressure or apparent contact pressure, psi∆Pa pressure drop due to flow acceleration (or momentum change), psi

NOMENCLATURE


xx • Nomenclature

∆Pf pressure drop due to flow friction, psi∆Pg pressure drop or gain due to gravity in vertical flow, psi∆Ps pressure drop due to inlet, exit, expansion, contraction, bends,

fittings, etc., psi∆Pt total pressure drop, psiq heat transfer rate, Btu/hrq″ heat flux, Btu/(hr·ft2)R thermal resistance, °F·hr/BtuR electrical resistance, Ωs fin spacing, inT temperature, °Ft fin thickness, inU overall heat transfer coefficient, Btu/(hr·ft·°F)V velocity of fluid, ft/hrV voltage, Vw plate width or heat sink width, in

Greek Symbols

α absorptivity of radiationα Seebeck coefficientα thermal diffusivity, ft2/hrβ coefficient of thermal expansion, °R–1δ boundary-layer thickness, ftε emissivityε heat exchanger effectivenessε a apparent emissivityηf fin efficiencyη0 overall surface efficiencyθ angle, degreesθ time, hrµ viscosity of fluid, lbm·ft/sν dynamic viscosity, ft2/sξ pump efficiencyπ Peltier coefficientρ density of fluid, lbm/ft3σ RMS surface roughness, ftσ Stefan-Boltzmann constant = 0.1714 × 10–8 Btu/(h·ft2·°R4)σ surface tension, lbf·ftτ Thomson coefficientτ transmissivity of radiation

Dimensionless Groups

B Biot number = hL/kGr Grashof number = βρ2gL3 ∆T/µ2


Gz Graetz number = mcp/kLJ Colburn factor = Nu/(Pr Re) Pr2/3

Nu Nusselt number = hL/kPe Peclet number = Pr RePr Prandtl number = µcp/kRa Rayleigh number = Gr PrRe Reynolds number = ρVL/µSt Stanton number = Nu/(Pr Re) or h/ρVcp

Subscripts

amb ambient conditionc cold side of heat exchangerCHF critical heat fluxf liquid conditionfg difference between liquid and vapor statesg gas or vapor conditionl liquid conditionsat saturation conditionsub subcooling conditionw wall conditionw value for wick material in heat pipe

Nomenclature • xxi


Thermal Management of Microelectronic Equipment: Heat Transfer Theory, Analy-sis Methods, and Design Practices is the first book in this series and is on the veryimportant subject of electronic cooling. It has been well documented that over 50percent of electronic failures are thermally related. According to National Elec-tronics Manufacturing Report (NEMI 2000), electronics cooling is a key enablingtechnology in the development of advanced packaging systems and has helpedsustain the technology trends as predicted by “Moore’s Law”. The report predictsthat maximum chip power for high performance chips will be approaching 300watts in the next decade. This increasing power trend extends to all key productsincluding computers, telecommunication, handhelds, automotive, and militaryelectronics. This book is written to serve engineers in industry, as well for use inacademia for a senior/graduate level course. Dr. Yeh and Dr. Chu have done anoutstanding job of including both the fundamental and practical aspects of ther-mal management of electronic systems.

Dereje AgonaferUniversity of Texas, Arlington

FOREWORD


Developing reliable microelectronic devices capable of operating at high speedswith complex functionality requires a better understanding of the factors thatgovern the thermal performance of electronics. With an increased demand onsystem reliability and performance combined with miniaturization of thedevices, thermal consideration has become a crucial factor in the design of elec-tronic packages, from chips to systems.

The authors understand that the challenge in the field of thermal managementof electronic systems resides not only with very-high-performance and high-heat-dissipation devices, but also with the intermediate and lower-power devices, whereimproved reliability objectives require cooler operation of chips. The authors fur-ther realize that no one design method is best suited for all applications. It is com-mon to employ several different heat transfer modes simultaneously in a system;therefore, this book includes a wide range of subjects related to various heat trans-fer technologies that can be utilized for thermal design of electronic equipment.

This book places a great deal of emphasis on understanding the physics ofeach subject, and thus a high level of mathematics is kept to a minimum. Thereare 17 chapters in the book. Among them, Chapters 2 through 8 deal with thefundamentals of various heat transfer modes, while the rest focus on specificsubjects of practical importance to the design of electronic systems. For exam-ples, Chapter 9 gives a detailed discussion of the thermal interface resistances.(Daily cycles of the ambient air and solar flux on a hot, dry day are also given inChapter 4 to be used in the design of outdoor equipment.) Appendix 8 presents acomprehensive catalog of topics in convective heat transfer that includes heattransfer correlations for various physical configurations and thermal boundaryconditions. Property tables for solids and 16 types of fluids such as air, water, anddielectric fluids are also included, in appendices.

This book has been developed to serve many types of readers. It will guideupperclass undergraduates or graduate students through practical approaches tosolving real-world problems of vast complexity. Professional engineers will findthis book a valuable reference resource for both refreshing their knowledge of thefundamentals in heat transfer and reading up on the latest thermal control tech-nology. Furthermore, this book also contains a great deal of practical design dataand correlations to be used in the analysis and design of electronic equipment.

L. T. YehR. C. Chu

PREFACE


Electronics are the heart of any modern equipment. Thermal control of elec-tronic equipment has long been one of the major areas of application of heattransfer technologies. Many improvements in reliability, power density, andphysical miniaturization of electronic equipment over the years can be attributedin part to improved thermal analysis and design of systems. Improved thermaldesign has been made possible through advances in heat transfer technologies aswell as computational methods and tools.

The primary function of cooling systems for electronic equipment is to pro-vide an acceptable thermal environment in which the equipment can operate. Toachieve this goal, it is necessary to maintain a thermal path with a minimumresistance from equipment heat sources to the ultimate heat sink.

1.1 NEED FOR THERMAL CONTROL

Because of advances in circuit and component technologies, electric circuitshave become more efficient, and thus heat dissipation from individual devicessuch as transistors has also become less. Miniaturization of circuits greatlydecreases the size of individual devices, however, and increases the number ofsuch devices that can be integrated on a single chip. The net result is that the chipheat flux (heat flow per unit surface area) has significantly increased in recentdecades as chip development has moved from small-scale integration (SSI) tovery large-scale integration (VLSI), and further to ultra-large-scale integration(ULSI). The chronology of advances in the integrated circuit (IC) is outlined inthe following steps, with the trends shown in Figure 1.1.

1960—Small-scale integration (SSI), fewer than 100 devices per chip1966—Medium-scale integration (MSI), fewer than 1000 devices per chip1969—Large-scale integration (LSI), fewer than 10,000 devices per chip1975—Very-large-scale integration (VLSI), fewer than 107 devices per

chip1990—Ultra-large-scale integration (ULSI), more than 107 devices per

chip

Decreasing the temperature of a component increases its performance aswell as its reliability. In addition to lowering the junction temperatures within a

Chapter 1

INTRODUCTION


component, it is sometimes also important to reduce the temperature variationbetween components that are electronically connected in order to obtain opti-mum performance. Thermal considerations become an important part of elec-tronic equipment because of increased heat flux.

An increased demand on system performance and reliability also intensifiesthe need for good thermal management of electronic equipment. Further evi-dence of the importance of thermal management to electronic systems is shownin Figure 1.2, based on a survey by the U.S. Air Force and indicating that morethan 50% of all electronics failures are caused by shortcomings in temperaturecontrol [1].

Although a great deal of attention has recently been paid to high-heat-fluxsystems, the opportunity also exists to improve thermal performance andreliability in low-heat-flux equipment. Therefore, the challenge in the field ofthermal management of electronic equipment resides not only with very-high-performance (high-heat-dissipation) devices, but also with intermediate- and

2 • THERMAL MANAGEMENT OF MICROELECTRONIC EQUIPMENT

FIGURE 1.1 Increase in circuit complexity.


lower-power components where improved reliability objectives require cooleroperation of chips.

1.2 RELIABILITY AND TEMPERATURE

Reliability—that is, the reciprocal of the mean time between failures (MTBF)—isdescribed as the statistical probability that a device or system will operate with-out failure for a specific time period. Each component or device has its failurerate curve. The reliability of a system is determined by combining many individ-ual part failure rates in series and/or parallel. System reliability is also affected bythe relative importance of the individual part to the system, and it can beimproved by redundancy at the component, packaging, or system level.

Table 1 lists the possible effect of temperature on the part failure under vari-ous thermal conditions such as thermal shock, temperature under continuousoperation (steady state), and temperature cycling. In the temperature range spe-cific to electronic equipment, it is an established fact that the reliability of elec-tronics is a strongly inverse function (a near exponential dependency) of acomponent’s temperature. The reliability of a silicon chip is decreased by about10% for every 2°C of temperature rise [2]. A typical temperature limit for a siliconchip is 125°C; however, a much lower design limit is commonly sought to main-tain the desired reliability, especially in military products.

The component failure rate is also related to temperature cycling, whichresults from either device power cycling or cycling of environmental conditions.In a U.S. Navy–sponsored study [3], an eightfold increase in failure rate was

Introduction • 3

FIGURE 1.2 Major causes of electronics failures [1].


encountered in equipment subjected to a deliberate temperature cycling of morethan 20°C.

1.3 LEVELS OF THERMAL RESISTANCE

The component-level resistance, which is often referred to as a component’s inter-nal resistance, is defined as the thermal resistance from the device junction (heatsource) to some predetermined reference point on the outside surface of thecomponent or package. In most component assemblies, heat must be transferredthrough a number of different materials and interfaces. The total thermal resist-ance is the sum of several individual resistances in series and/or parallel. The pri-mary heat transfer mode inside the component or package is conduction. Inwell-designed component packaging, the number of interfaces should be mini-mized, and bonding and sealing operations should also be selected to create thelowest interface resistance. The coefficient of thermal expansion (CTE) is a majorconcern at the interfaces of all materials laminated together. Any mismatch of thecoefficient of thermal expansion would increase the thermal resistance, and even


Table 1.1 Effect of Thermal Conditions on Part Failure

Condition Cause Effect Possible failure

Steady-state(hot)

Ambient exposure,equipment-induced

Aging—discolorationInsulation

deteriorationOxidationExpansionViscosity decreaseSoftening/hardeningEvaporation/dryingChemical changes

Alteration ofproperties

ShortingRustPhysical damage,

increased wearLoss of lubricationPhysical breakdownDielectric loss

Steady-state(cold)

Ambient exposure,mission-induced

ContractionViscosity increaseEmbrittlementIce formation

Wear, structuralfailure, binding

Loss of lubricityStructural failure,

cracked partsAlteration of electric

propertiesLoss of resilience—

seal leaks

Thermal cycling Ambient-induced,mission operation

Temperaturegradients

Expansion/contraction

Mechanical failure ofparts, solder joints,and connections

Delimitation ofbonding line

Thermal shock Mission profile High temperaturegradients

Mechanical failure,cracks, rupture


cause part failure. Note that the thermal designer may have no control over theinternal resistance if commercial components are used.

The packaging-level resistance is generally defined as the thermal resistancefrom the aforementioned surface reference point (the terminal point for measur-ing component-level resistance) to some designated point in a convective stream.For example, this designated point may be the local air temperature over a givencomponent or the local fluid or wall temperature of a cold plate.

The system-level resistance is defined as the thermal resistance from the desig-nated terminal point for measuring the packaging-level resistance to the ultimateheat sink of the equipment or system. The ultimate heat sink is the environmentin which the system operates. Sometimes, the combined resistance of packagingand system levels is referred to as the external thermal resistance.

The foregoing definitions are somewhat arbitrary; however, they give aninsight into the contribution of each level of resistance to the total resistance of asystem, and thus provide thermal engineers an opportunity to optimize the over-all thermal resistance by working at the individual levels.

1.4 THERMAL DESIGN CONSIDERATIONS

Thermal control of electronic equipment may employ several different heattransfer modes simultaneously and may consist of up to three tasks: (1) removingheat from the sources (components), (2) transporting heat to system internalheat sinks, and (3) rejecting heat from the internal heat sinks to the ultimate heatsink, the environment. Sometimes, tasks 2 and 3 are lumped into a single task.

The purpose of a thermal design is to provide equipment that will induce ther-mal energy to flow properly from heat sources to the ultimate heat sinks. Thegoal of thermal control is to prevent part failures and also to achieve desired sys-tem performance and reliability. Another goal of thermal control is to obtain anoptimum design. The optimum system will result from a series of trade-off stud-ies considering several factors:

1. Performance. The primary and foremost consideration is that the sys-tem must be able to perform its required functions and the specifictasks for which it is designed.

2. Producibility. The system under consideration must be produciblewithout involving a very complicated manufacturing process.

3. Serviceability (or maintainability). The equipment under design mustbe readily and easily accessible for testing, repair, or replacement. Thedesign approach may also be affected by the system maintenancemethods—e.g., whether the equipment will be maintained in the fieldor in the shop.

4. Compatibility. The system, including the coolant used, must be com-patible with the environment in which it is being used.

5. Cost. The final product must be cost-effective. Cost may be the mostimportant factor in product design. In determining the cost of aproduct, one should consider not only manufacturing but also main-tenance costs.

Introduction • 5


The relative importance of these five individual factors is mission-related; forexample, the cost may become a secondary issue for some military equipment,where performance and reliability are the major concerns. A concurrent engi-neering approach must be adopted in the development of a new product. Thedesign philosophy or basic rule is that the best design is the simplest and lowest-cost one that will meet the specified requirements.

1.5 OPTIMIZATION AND LIFE-CYCLE COST

Because of the strong dependence of microelectronic device reliability on tem-perature, it is important and desirable in the thermal management of electronicsystems to pursue temperature distributions that are not merely acceptable butare optimal. Mayer [4] discusses the opportunities for optimization at all pack-aging levels. These opportunities include (1) optimal thermal placement of elec-tronic components on circuit boards and optimal arrangement of boards withinboxes or assemblies, and (2) optimal distribution of thermally conductive lay-ers and optimal distribution of coolant flow rates. As an example of the firsttype, Figure 1.3 compares junction temperatures with and without optimiza-tion at different component positions on a printed circuit board cooled byforced-air convection. The left diagram in the figure is for the purpose of illus-tration and does not include all components. By switching component loca-tions, a significant improvement in overall temperature (near 40°F reductionfor half of the components) is found with optimization, even though the maxi-mum temperature is about the same for both cases. This in turn improves theoverall system reliability.

It is important to involve thermal design in the early phase of the equipmentdesign process. The design approach should place emphasis at the system levelfor optimizing the thermal control unit. However, since for most electronics there


FIGURE 1.3 Effect of part placement on component junctiontemperature.


is a direct relationship between a component’s junction temperature and its fail-ure rate, the current design practice is often to establish an upper temperaturelimit that is below the maximum allowable temperature set by manufacturers,ensuring that no component junction temperatures exceed this temperaturelimit. Currently, an upper limit of 105°C for semiconductor devices is being usedby the U.S. Air Force and Navy [4, 5]. In theory, the actual temperature limitshould be determined by the required reliability of each individual piece ofequipment.

As pointed out by Berger [6], the problem with this temperature limit designapproach stems from the attempt to analyze the reliability of equipment by look-ing at the individual components in terms of their temperature rather than theiractual part failure rate. The goal should not be to minimize component tempera-tures but to minimize component failure rates that directly impact the reliabilityof the equipment.

A simplified example given by Berger as shown in Figure 1.4 illustrates thepreceding statement. Component B, in the center of the layout diagrammed inthe figure, is at 110°C and thus is the hottest component. A redesign is in order, toget the temperature of all parts below 105°C, if that particular standard is to beapplied. One of the simplest ways to redesign is just to switch component B withcomponent A at left, thereby placing the hot component close to the heat sink.Acceptable design criteria would be met under the standard if components A andB both turned out to be at 100°C. The graph in the figure reveals, however, thatthe increase in the failure rate of component A for a 10°C rise outweighs the ben-efits obtained for a 10°C reduction in temperature for component B. The man-dated redesign actually results in a reduction of the overall reliability of theequipment. Any design change, therefore, should not be initiated unless it will bean overall improvement in equipment reliability and the change can also be justi-fied on the basis of a system life-cycle cost (LCC) reduction. In short, the equip-

Introduction • 7

FIGURE 1.4 Example of current thermal design practice.


ment design should be thermally optimized to minimize the LCC and maximizethe reliability and operation life of the system.

REFERENCES

1. U.S. Air Force Avionics Integrity Program (AVIP) notes, 1989.2. A. Bar-Cohen, A. D. Kraus, and S. F. Davidson, “Thermal Frontiers in the

Design and Packaging of Microelectronic Equipment,” Mech. Eng., June1983.

3. W. F. Hilbert and F. H. Kube, “Effects on Electronic Equipment Reliability ofTemperature Cycling in Equipment,” Report No. EC-69-400 (Final Report),Grumman Aircraft Corp., Bethpage, NY, February 1969.

4. A. H. Mayer, “Opportunities for Thermal Optimization in Electronics Packag-ing,” Proc. 1st Int. Electronics Packaging Soc. Conf., 1981.

5. “Thermal Design, Analysis, and Test Procedures for Airborne ElectronicEquipment,” MIL-STD-2218, 1987.

6. R, L. Berger, “A System Approach—Minimizing Avionics Life-Cycle Cost,”SAE Technical Paper Series 831107, 13th Intersociety Conf. on EnvironmentalSystems, San Francisco, 1983.

7. L. T. Yeh, “Future Thermal Design and Management of Electronic Equip-ment,” in Wei-Jei Yang and Yasuo Mori, eds., Heat Transfer in High Technol-ogy and Power Engineering, Hemisphere, New York, 1987.

8. A. D. Kraus, Cooling Electronic Equipment, Prentice-Hall, Englewood Cliffs,NJ, 1965.

9. J. H. Seely and R. C. Chu, Heat Transfer in Microelectronic Equipment: A Prac-tical Guide, Marcel Dekker, New York, 1972.

10. A. W. Scott, Cooling of Electronic Equipment, Wiley, New York, 1974.11. D. S. Steinberg, Cooling Techniques for Electronic Equipment, Wiley, New

York, 1980.12. A. D. Kraus and A. Bar-Cohen, Thermal Analysis and Control of Electronic

Equipment, Hemisphere, New York, 1983.13. G. N. Ellison, Thermal Computation for Electronic Equipment, Van Nostrand

Reinhold, New York, 1984.14. L. T. Yeh, “Review of Heat Transfer Technologies in Electronic Equipment,”

J. Electronic Packaging 117, 1995.15. M. Pecht, “Why the Traditional Reliability Prediction Models Do Not Work—

Is There an Alternative?” Electronics Cooling 2(1), 1996.



Heat conduction is a process by which heat flows from a region of higher tem-perature to a region of lower temperature through a solid, liquid, or gaseousmedium, or between different media in intimate contact. Generally, heat con-duction is due to movement and interaction of molecules. Therefore, a solid issuperior to a liquid in transferring heat by conduction because of its shorter dis-tance between molecules. Similarly, a liquid has better thermal conductioncharacteristics than a gas. Generally, a good conductor of electricity is also agood conductor of heat.

2.1 FUNDAMENTAL LAW OF HEAT CONDUCTION

The fundamental law of heat conduction is attributed to Fourier [1], who statedthat the rate of heat conduction in a medium is proportional to the product of thearea normal to the path and the temperature gradient along the path. Mathemat-ically, the Fourier law for the one-dimensional case can be expressed as follows:

(2.1)

where q is the heat transfer rate, A is the area normal to the heat flow path, anddT is the temperature gradient over the distance dx. The negative sign is assignedto allow a positive heat flow when the temperature decreases along the path.With an insertion of a proportionality constant, Equation 2.1 becomes

(2.2)

where k is the proportionality constant, also referred to as the thermal conductiv-ity of the medium.

Thermal conductivity is a material property. The thermal conductivity of gasesis an order of magnitude smaller than that of liquids, and likewise that of liquidsis an order of magnitude smaller than that of solids. Thermal conductivity of

q kAdTdx

= −

q AdTdx

∝ −

Chapter 2

CONDUCTION


materials within a limited temperature range is generally a function of tempera-ture and can be approximately expressed in the form

k(T) = k0(1+βT) (2.3)

where k0 is the thermal conductivity of a medium at T = 0 °F and β is the temper-ature coefficient of thermal conductivity. Generally, the value of β is negative formost pure metals and is positive for most alloys, gases, and liquids with an excep-tion in high temperature ranges for some alloys and liquids.

2.2 GENERAL DIFFERENTIAL EQUATIONS FOR CONDUCTION

With the aid of Fourier’s law along with the assumption of energy balance on adifferential element of a solid, the general differential equations of heat conduc-tion can be developed. Without including the detailed derivations, which areavailable in most textbooks, we can show the general differential equation forheat conduction as

(2.4)

where the internal heat generation and thermal conductivity can be functions oftime, space, and temperature. With proper initial and boundary conditions, thedifferential equation can be solved analytically or numerically.

For the case with constant thermal properties, Equation 2.4 can be simplifiedto the form

(2.5)

where α (= k/ρc) is thermal diffusivity, which represents an approximate measureof the ratio of heat conducted to heat stored.

Equation 2.5 can further be reduced under the following assumptions:

Fourier equation (no internal heat generation):

(2.6a)

Poisson equation (steady state):

(2.6b)∂∂

+ ∂∂

+ ∂∂

+ ′′′ =2

2

2

2

2

20

T

x

T

y

T

z

qk

∂∂

+ ∂∂

+ ∂∂

= ∂∂

2

2

2

2

2

2

1T

x

T

y

T

z

Ttα

∂∂

+ ∂∂

+ ∂∂

+ ′′′ = ∂∂

2

2

2

2

2

2

1T

x

T

y

T

z

qk

Ttα

∂∂

∂∂

+ ∂∂

∂∂

+ ∂∂

∂∂

+ ′′′ = ∂∂x

kTx y

kTy z

kTz

q cTtx y z

ρ



Laplace equation (no internal heat generation and steady state):

(2.6c)

The above discussions are limited to the Cartesian coordinate system. Again,without going through the detailed derivations, the final form of the general dif-ferential equation for heat conduction in cylindrical or spherical solids can beexpressed as follows:

For cylindrical systems:

(2.7)

For spherical systems:

(2.8)

It should be noted that Equations 2.7 and 2.8 can also be obtained from Equa-tion 2.4 through the following transformations with the coordinates given inFigure 2.1:

The solution to any three-dimensional heat conduction problem is alwayscomplicated, even in the steady-state condition. The problem becomes even morecomplex where multiple heat sources are applied to the top surface of the multi-layer structure to simulate heat conduction in microelectronics. The closed-formsolution, which is typically expressed by tediously long infinite series either ana-lytically or approximately, is not practical for engineering applications.

The steady-state solution for the simple case where a single heat source isapplied to the top surface of a medium was presented in papers by Lindsted andSurty [2] and Kennedy [3] for rectangular and cylindrical solids, respectively. Themaximum temperature occurs at the center of the heat source, and its correspon-ding temperature rise over the isothermal surface can be determined by

∆Tm = Rmq (2.9)

Cylindrical systems Spherical systems

x = r cos θ x = r sin φ cos θy = r sin θ y = r sin φ sin θz = z z = r cos φ

1 1

1

22

2 2

2 2

r rr k

Tr r

kT

rk

Tq c

Tt

r∂∂

∂∂

+ ∂∂

∂∂

+ ∂∂

∂∂

+ ′′′ = ∂∂

sin

sinsin

θ θ θ

φ φφ

φρ

θ

φ

1 12r r

rkTr r

kT

zk

Tz

q cTtr z

∂∂

∂∂

+ ∂∂

∂∂

+ ∂∂

∂∂

+ ′′′ = ∂∂θ θ

ρθ

∂∂

+ ∂∂

+ ∂∂

=2

2

2

2

2

20

T

x

T

y

T

z

Conduction • 11


where q is heat dissipation and Rm is the maximum thermal resistance. Rm isdefined for the two cases as follows:

where Φ is the thermal resistance factor, k is the thermal conductivity of thematerial, and linear dimensions A, B, and H are as listed in Figures 2.2 and 2.3.

Example 2.1

A chip with thermal conductivity of 2 W/(in · °C) dissipates 0.2 W at the junction.The bottom of the chip is assumed to be isothermal. Find the maximum temper-ature rise in the chip over the isothermal surface for the following cases:

Case I

Chip size: 0.1 by 0.1 by 0.05 in; thus, chip cross-sectional area = 0.01 in2

Heat source size: 0.005 by 0.005 in; thus, heat input area = 2.5 × 10–5 in2Heat source perimeter: 0.02 in, with

• W = L = 0.1/2 = 0.05 in• A = B = 0.005/2 = 0.0025 in• B/W = 0.0025/0.05 = 0.05• W/H = 0.05/0.05 = 1• A/B = 1

(2.10a)

(2.10b)

Rk AB H

k A

m =( )

Φ

Φ

rectangular solid

cylindrical solidπ


FIGURE 2.1 Cylindrical and spherical coordinates.


From Figure 2.2 with A/B = 1, we have

Φ = 0.014

From Equation 2.10a, one obtains

Rm = ×( ) = °0.014

2 0.0025 0.0025 0.00556 C/W

Conduction • 13

FIGURE 2.2 Thermal resistance factor � at heat source center for rec-tangular solids with W = L.


The maximum temperature rise for the chip can readily be computed accordingto Equation 2.9:

∆Tm = 56 × 0.2 = 11.2°C

Case II

Chip size: 0.1 by 0.1 by 0.05 in (chip cross-sectional area = 0.01 in2, sameas previous case)


FIGURE 2.3 Thermal resistance factor � at heat source center for cylin-drical solids.


Heat source size: 1.18 × 10–2 by 2.236 × 10–3 in (heat input area = 2.5 × 10–5in2, same as previous case)

Heat source perimeter: 0.0268 in, with

• W = L = 0.1/2 = 0.05 in• A = 1.118 × 10–2/2 = 5.59 × 10–3 in• B = 2.236 × 10–3/2 = 1.118 × 10–3 in• B/W = 1.118 × 10–3/0.05 = 0.0236• W/H = 0.05/0.05 = 1• A/B = 5

From Figure 2.2 with A/B = 5, we have

and

∆Tm = 48 × 0.2 = 9.6°C

Case III

Cylindrical chip with same cross-sectional areas for chip and heat source asthe previous two cases:

Chip diameter (2B): 0.11283 in (chip cross-sectional area = 0.01 in2, sameas previous cases)

Heat source diameter (2A): 0.0056419 in (heat input area = 2.5 × 10–5 in2,same as previous cases)

Heat source perimeter: 0.0177 in, with

• A = 0.0056419/2 = 0.002821 in• B = 0.112838/2 = 0.056419 in• H/B = 0.05/0.0056419 = 8.86• A/B =0.05

From Figure 2.3, we have

and

∆Tm = 84.6 × 0.2 = 16.9°C

Comment: The above results clearly indicate that for the same heat sourcearea, the thermal resistance decreases as the perimeter of the heat sourceincreases.

Φ = ⇒ = = °1.5 1.52 0.002821

84.6Rm πC/W

Φ = ⇒ =× × ×( ) = °− −0.012

0.012

2 5.59 10 1.118 10 0.0548

3 3Rm C/W

Conduction • 15


2.3 ONE-DIMENSIONAL HEAT CONDUCTION

Under certain limiting conditions, heat conduction in a three-dimensional sys-tem can be approximated by a one-dimensional problem. For example, a one-dimensional heat conduction problem may be assumed if the lateral dimensionsof a wall are very large as compared with its thickness. Another case is if thermalresistances in lateral directions are large as compared with the conductive resist-ance through the thickness of the wall.

2.3.1 Steady-State Condition

For a steady-state condition, the temperature of a medium is independent of thetime, and thus the energy entering must be equal to the energy leaving the sys-tem. The analysis of Equations 2.4, 2.7, and 2.8 is greatly simplified when heatconduction becomes a one-dimensional steady-state condition. For cases withoutinternal heat generation and with constant thermal properties, the temperatureprofile and the heat flow for a plane wall, hollow cylinder, and hollow sphere withprescribed wall temperatures can be summarized as in Table 2.1. The tempera-ture profile of a given geometry can easily obtained by a double integration ofEquation 2.4, 2.7, or 2.8 with the aid of the boundary conditions, i.e., prescribedtemperature at the two surfaces of the wall. Once the temperature profile isknown, the heat flux can be determined with Fourier’s law.

2.3.2 Transient Condition

For the case with constant properties, the differential equation for one-dimen-sional heat conduction is

(2.11)1 1

11

x xx T

xqk

Ttn

n−

−∂∂

∂∂

+ ′′′ = ∂∂α


Table 2.1 Equations of Heat Conduction in Various Geometrical Configurations

L = thickness of plane wall or length of cylinder.

Geometry Temperature profile Heat flow

Plane wall

Hollow cylinder

Hollow sphere

T TT T

/r /r/r /r

i

i o

i

i o

−−

= −−

1 11 1

qT T

(r r )/ krri o

o i i o= −

− 4π

T TT T

(r/r )(r /r )

i

i o

i

i o

−−

= lnln

qT T

(r /r )/ kLi o

o i= −

ln 2π

T TT T

xL

−−

= −11 2

qT TL kA

= −1 2/


where

Again, with proper initial and boundary conditions, Equation 2.11 can be solvedeither analytically or numerically. Solutions for the above problems are generallyavailable and are often expressed in graphical form for practical applications.For the case without internal heat generation, the charts of Heisler [4] can beapplied for a convection boundary condition.

In the case with thermal radiation at the boundary, the problem becomes non-linear and is typically solved numerically. The labor involved in repeatedly solv-ing these nonlinear problems further warrants the construction of solutioncharts, which will be of interest to thermal engineers in various fields. The graph-ical charts of the temperature history are available for a one-dimensional slab[5], cylinder[6], and sphere [7]. Chung and Yeh [8, 9] extended the above solu-tions by including the internal heat generations for a slab, cylinder, and sphereunder heating or cooling conditions. The heating case represents the conditionwhere the environment temperature is higher than the initial temperature of thesolid. On the other hand, the cooling case implies that the solid is initially hotterthan its environment. Numerical computations reveal that for the same parame-ters, the sphere cools most rapidly, followed by the cylinder, and finally the slab.The same sequence is found for radiant heating.

2.4 THERMAL/ELECTRICAL ANALOGY

Heat flow within a medium due to a temperature gradient is similar to the case ofan electrical system, where the current flows in a circuit according to Ohm’s law,which can be stated as

∆V = IR (2.12)

where ∆V is the voltage (electrical potential), I is the current, and R is the electri-cal resistance. The following relation may express the temperature in a heattransfer process:

∆T = qR (2.13)

where q is the heat transfer rate and R is the thermal resistance, equivalent to thedenominators of the heat flow equations in Table 2.1. Analogous quantitiesbetween the two kinds of systems are listed in Table 2.2.

The purpose of employing the analogy between electrical and thermal sys-tems is to simplify the calculation procedure for the latter. This approach isoften used to develop a general thermal analyzer for analysis and design of a

n =

1

2

3

for slabs

for cylinders

for spheres

Conduction • 17


thermal system. For physical systems encountered in practice, one rarely findsa problem that can be solved analytically. A complicated three-dimensionalsystem may be approximated by subdividing it into a large number of smallelements or nodes which have no internal temperature gradient. These nodesare then interconnected by thermal paths (thermal resistances) to form a net-work. Nodes represent discrete quantities of mass that may gain or lose ther-mal energy from or to neighboring nodes, or may gain energy from internalheat sources.

The thermal resistance for different heat transfer modes may be defined asfollows:

Conduction: (2.14a)

where

L = conduction lengthA = cross-sectional area normal to heat conduction path

Convection: (2.14b)

where

h = heat transfer coefficientA = heat transfer surface area (fluid-wall contacting surface)

Radiation: (2.14c)

where

σ = Stefan-Boltzmann constantℑ = gray body view factor

As can be seen from Equation 2.14c, the radiation thermal resistance is explicitlyexpressed as a nonlinear function of the surface temperature that is somewhat

RT T

A T T= −

ℑ −( )1 2

14

24σ

RhA

= 1

RLkA

=


Table 2.2 Analogous Quantities between Thermal and Electrical Systems

Thermal system Electrical system

Potential ∆T, °K or °R ∆V, voltsFlow q, W or Btu/hr I, amperesResistance R, °K/W or °R/(Btu/hr) R, ohmsCapacitance C, kJ/°K or Btu/°R C, farads


different from the cases of the conduction and convection thermal resistances.The heat transfer coefficient under natural convection is also a nonlinear func-tion of temperature. Convection and radiation heat transfer will be discussed inChapters 3 and 4, respectively.

As does an electrical network, a thermal network consists of series and paral-lel paths. For example, the thermal network of a multiple-layer composite wall isshown in Figure 2.4. It should be noted that a two-dimensional heat flow mightresult if the thermal conductivities of materials C, D, and E are significantly dif-ferent. Also, the thermal contact resistances at the interfaces are not shown inFigure 2.4. Generally, a thermal resistance exists at the interface when two bodiesare in contact. A detailed discussion of the interface thermal contact resistancewill be presented in Chapter 9.

Example 2.2

Referring to Figure 2.4, let L1, L2, and L3 be 0.5, 0.8, and 1 ft, respectively. It isassumed the total heat transfer rate, q, is 100 Btu/hr. Other assumptions are listedin the accompanying table. Determine the temperature difference between T1and T4.

Solution:

RLkA

R

R R R

A B

C E D

= =×

= =×

=

= =×

= =×

=

0 550 1

0 010 8

80 10 01

1100 0 3

0 0331

100 0 40 025

..

..

..

..

A B C D E

Thermal conductivity, Btu/(h · ft · °F) 50 80 100 100 100Cross-sectional area, ft2 1 1 0.3 0.4 0.3

Conduction • 19

FIGURE 2.4 Thermal network for a multilayer composite wall.


For parallel paths between T3 and T4, the net thermal resistance is

The total thermal resistance becomes

Rt = RA + RB + R′ = 0.01 + 0.01 + 0.01 = 0.03°F/(Btu/hr)

The temperature difference between T1 and T4 is

T1 – T4 = qRt = 100 × 0.03 = 3°F

To facilitate computations, the thermal resistance due to heat conduction for sev-eral common geometrical configurations is listed in Table 2.3. By applyingproper values of θ and φ in Equations 3 and 5 in Table 2.3, one obtains the fol-lowing equations:

2.5 LUMPED-SYSTEM TRANSIENT ANALYSIS

There is no material with an infinite thermal conductivity. However, many tran-sient problems may be treated approximately as a lumped system by assuminguniform temperature within the system at any instant. This simplification is jus-tified only for the case where the external thermal resistance between the systemand its surroundings is so large compared with the internal thermal resistancethat the latter can be neglected. The Biot number, hLc/k, which is the ratio of theinternal to the external resistance, is often used to measure the relative impor-tance of the external and internal thermal resistances; h is the average heat trans-fer coefficient, k is the thermal conductivity of the solid, and Lc is thecharacteristic length defined as the ratio of the volume of the body to its surfacearea. For regular-shaped bodies such as plates, cylinders, and spheres, the errorinduced by the assumption of a uniform internal temperature in the solid is lessthan 5% if the Biot number is less than 0.1. The following are characteristiclengths for several common geometric shapes:

(2.16a)

(2.16b)

(2.16c)

L

r

r

r

r LrL

r

L

L

L

c =

( )=

=

=

4 3

4 3

2 2

6 6

3

2

2

3

2

sphere

cylinder

cube

π

πππ

(2.15a)

(2.15b)

R

r r

kLr r

kr r

i

o i

o i

i o

=

( )

−

ln

2

4

π

π

hollow cylinder

hollow sphere

′ =+ +

= °RR R RC D E

11 1 1

0 01. F/(Btu/hr)



To understand the solution to the lumped-system transient, let us consider asolid body with an internal heat generation, q. The body is initially at a uniformtemperature of Ti and is suddenly exposed to an airstream at a temperature of Ta.The heat transfer coefficient is assumed to be relatively small compared with thethermal conductivity of the body, so that the Biot number is less than 0.1. Fromthe energy balance equation, we have

(2.17)c VdTdt

q hA T Taρ = − −( )

Conduction • 21

Table 2.3 Conduction Thermal Resistance

Geometry Thermal resistance

where θ1, θ2, φ1, and φ2 are angles in radians

(5)

(6)

(7)

Rr r

kr rro i

i o= −

−( ) −( )cos cosθ θ φ φ1 2 2 1

THERMAL MANAGEMENT OF MICROELECTRONIC EQUIPMENT · 2019. 9. 12. · THERMAL MANAGEMENT OF MICROELECTRONIC EQUIPMENT HEAT TRANSFER THEORY, ANALYSIS METHODS, AND DESIGN PRACTICES L.

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