Thermal Management of Flexible Electronic Systems

(what are the unique thermal/mechanical design features of a flexible electronic system)

Sammakia 4-06 Modes of Heat Transfer in Electronic Systems

Sammakia 4-06 Modes of heat transfer

•Conduction (relatively simple analysis, will introduce today) •Convection (mostly empirical and numerical) •Radiation (often negligible at low operating temperatures) •Multimode (combinations of the above modes)

Sammakia 4-06 Classification of levels of packaging…why ???

Thermal Mechanical Electrical Reliability Functional

Sammakia 4-06 Thermal aspects

First level….conduction heat transfer Second level….convection and conduction System level….thermodynamic considerations, overall system balance, application

Sammakia 4-06 •The design of a system should not be a set of individual requirements such as thermal, mechanical, electrical and functional. There should be one design that is optimal and meets all of the requirements. •Case in point thermal and mechanical requirements.

Sammakia 4-06 •Thermal and mechanical requirements are often conflicting.

•For example a large Cu heat sink is likely to adversely impact interconnect reliability (fatigue, shock, vibration)

Sammakia 4-06 •Interconnects are vulnerable failure points in all systems •Chip level interconnects are the most vulnerable (size and materials) •This has a direct impact on thermal management and the mechanical design of the system •Flexible electronics offer an advantage

Sammakia 4-06 Modes of heat transfer

Sammakia 4-06 Conduction

Heat transfer mode in solids and stationary fluids. Heat is transferred via random molecular interactions.

In gases: random molecular collisions (translational + vibration + rotational components)

In solids: combination of free electron transport and lattice vibrations

In liquids: similar to gases but closer bonding between molecules

Sammakia 4-06 Conduction Rate of heat transfer: Fourier’s “Law” (isotropic material): ~ dT q~" = −k∇T ; q" = −k 1-D conduction dx

Temperature predictions: Heat diffusion equation (Fourier Law + energy balance)

∂ 2T ∂ 2T ∂ 2T q ρc ∂T Rectangular coordinates; + + + & = ∂x2 ∂y 2 ∂z 2 k k ∂t k is constant

• Need 6 boundary conditions + 1 initial condition

Sammakia 4-06 Concept of Thermal Resistance Assuming: • 1-D x T = ()T −T +T 2 1 L 1 • No internal heat or Slab: generation: q& = 0 ∆T k R = = L / kA • Steady d 2T q" = (T −T ) th q = 0 1 2 L state: dx2 or Cylindrical shell: L " ⎛kA⎞ 1 ⎛ r ⎞ q = q A=⎜ ⎟∆T R = ln⎜ 2 ⎟ L th ⎜ ⎟ T1• ⎝ ⎠ 2πLk ⎝ r1 ⎠ Analogous to V= IR q′′ Spherical shell: •T 2 Current (I) 1 ⎛ 1 1 ⎞ Voltage (V) ⎜ ⎟ Rth = ⎜ − ⎟ 4πk ⎝ r1 r2 ⎠ x Sammakia 4-06 Concept of Thermal Resistance

In electronic packaging, a single chip package contains many materials. An overall resistance is defined:

Junction temperature Case temperature T −T R = j c : Internal thermal resistance jc q

Typical values: 80 K/W: plastic package, no spreader 12 -20 K/W: plastic package with spreader 5 - 10 K/W: ceramic package

Sammakia 4-06 Modes of heat transfer

Sammakia 4-06 Thermal management in a second level package Governing Equations for fluids in motion:

Assuming the flow to be steady with constant properties except for the thermal conductivity in general and the density in the buoyancy term specifically, and neglecting viscous dissipation, the governing equations are,:

Continuity (mass conservation):

∇. V = 0

Momentum conservation:

2 ρ (V.∇)V= - ∇p + µ∇ V+ ρg β(T-T∞)i

Energy conservation:

ρcp (V. ∇)T = ∇.(k∇T) Sammakia 4-06 Sammakia 4-06 Thermal management in a second level package…cont. •Navier Stokes equations fairly complex to solve •Most practical applications require a numerical solution •Several commercial codes are available, provide good design tools •It is possible to solve conjugate conduction/convection./radiation problems FLOTHERM (TM)

Sammakia 4-06 diffuser ducts

13.42 m long

6.05 m wide cold aisles (chilled air supply) return vents computer for hot exhaust air equipment racks (on parallel walls)

Sammakia 4-06 z=0.8m y

z=6.5m z

z=12m

z=16m

z=20m

Most Racks ~19 kW

Sammakia 4-06 On the other hand there are very interesting small scale problems at the micro level; Example of micro-channel cooling

Sammakia 4-06 Channels in Perpendicular Direction Temperature Distribution

n io ct e ir d w lo f id lu F

F lu id

flo w di re c tio n

Sammakia 4-06 Temperature at various cross-sections along the length

Sammakia 4-06 Variation of Maximum Temperature with Velocity (Single Channel with Adiabatic BCs)

160 Simulated Data Second order exponential decay 140

Chi^2/DoF = 2.77172 120 R^2 = 0.99924

y0 31.89508 ±1.50026 A1 224.53191 ±16.14905 100

C) t1 0.03871 ±0.00338 o A2 41.0406 ±3.37751 t2 0.62888 ±0.12918 80 y0 + A1e^(-x/t1) + A2e^(-x/t2)

60 Temperature ( 40

0 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 Velocity (m/s)

Sammakia 4-06 Variation of Pressure Drop with Velocity (Single Channel with Adiabatic BCs)

28000 B Polynomial Fit of Data2_B Y = A + B1*X + B2*X^2 24000 Parameter Value Error ------A -30.44094 18.76507 20000 B1 4372.04107 37.73392 B2 630.1282 9.51187 16000

12000

Pressure (Pa) 8000

4000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Velocity (m/s)

Sammakia 4-06 Modes of heat transfer

Sammakia 4-06 Example using thermal grease as the interface material

Sammakia 4-06 Thermal grease in a ceramic single chip package

Without grease With grease R = 10 C/W int Rint = 3.5 C/W

Why not use adhesive ?

Sammakia 4-06 Air Air

Rcap-air

Rcard-air1

Rcard-air2

Air

Sammakia 4-06 Resistance Equation Value oC/W

Spreading in Si Rj-c = ln(ro-ri)/2 π kt 0.6

Through a solder joint Rc4 = l/kA 1.1 (Assume all solder joints conduct in parallel)

Spreading in the substrate Rsubstrate= ln(ro-ri)/2 π kt 6.4

Through a copper pin Rpin = l/kA 0.0

Spreading in the card Rcard= ln(ro-ri)/2π kt 1.8

Convection to air Rcap-air = 1/hA 5.0

Convection to air Rcard-air1= 1/hA 30.0

without grease

Rint = 10.7; Rext = 4.8 R = 15 total Sammakia 4-06 Air Air

Rcap-air

Rcard-air1

Rcard-air2

Air

Sammakia 4-06 Resistance Equation Value oC/W

Thermal grease resistance Rgrease = l/kA 2 to 4

With grease

Rint = 2.5; Rext = 5.2

Rtotal = 7.7

Sammakia 4-06 Example using an adhesive as a thermal interface material

Sammakia 4-06 THERMAL ADHESIVE HEAT SINK ENCAPSULANT BGA C4s

CHIP STIFFENER

PRINTED CIRCUIT BOARD

Power planes ORGANIC SUBSTRATE

Sammakia 4-06 Rint = 0.5 to 1.5 C/W Air

Air

Convective resistance or external resistance REXT Heat sink resistance (legs) Rhsl

Heat sink resistance (top) Rhs

Adhesive resistance Radh

Chip(heat source) Rchip Air C4 resistance Rc4 Substrate resistance Rsubst.

BGA resistance RBGA

Card spreading resistance Rspr Sammakia 4-06 Rint = 3 to 9 C/W Air

Air

Convective resistance or external resistance REXT Heat sink resistance (legs) Rhsl

Heat sink resistance (top) Rhs

Chip(heat source) R Air chip C4 resistance Rc4 Substrate resistance Rsubst.

BGA resistance RBGA

Card spreading resistance Rspr Sammakia 4-06 Thermal Resistances of Electronic Packages • A number of resistances are used, often poorly defined.

()TTjc− Junction-to-case: R = jc q ()TT− R = ca Case-to-ambient: ca q ()TT− Junction-to-ambient: R = ja ja q Problems: Measurement location, substrate conduction, ambient fluid properties, flow regime, accounting of system boundaries.

Sammakia 4-06 Other resistances that need to be added: • Interfaces (interfacial voids and defects) • Spreading (bottlenecks)

Sammakia 4-06 Contact Resistance

∆T (K/W) Rt,c = qx

T1 ∆T 2 Rt′′,c = (m K/W) ∆T q′x′

: available from tables Rt′′,c T2 qx Depends upon: contact surface materials, Line of contact interface pressure, interfacial material

Sammakia 4-06 Conduction Spreading Resistance

Near the chip, the conduction is 2 or 3-D. Need to solve heat

diffusion equation exactly to get Rth. For many cases this can be done in closed form (if chip approximated as uniform heat flux circular source) H ⎛ a w ⎞ Rth = H⎜ , ⎟ Available from charts kπ a ⎝ b b ⎠ b r r a r

(a)z (b)z (c) z adiabatic boundary Sammakia 4-06 Thermal and Mechanical designs are intertwined

Sammakia 4-06 • During every thermal cycle interconnections must ‘absorb’ the CTE mismatch • They must be designed to survive (at an acceptable failure rate) through end of life of the product

Sammakia 4-06 Underfill or encapsulation

Converts some of the shear loading to bending

Sammakia 4-06 • Chip not mechanically coupled(strongly) to chip carrier + • Long slender wire bonds = excellent fatigue life

Soft interface

Sammakia 4-06 Thermal grease provides a flexible heat transfer path, (phase change, low modulus materials, etc…)

Sammakia 4-06 CTE value for different packaging materials, PPM/Degree K.

Invar 80 Silicon Cu Invar Cu 60 Al203 40 Kovar 20 Quartz Fe 0 Cu Al Fe

Fr-4 Al Invar Cu Kovar solder Cu Invar Cu Fr-4 Adhesives

Sammakia 4-06 At room temperature

At elevated temperature

At room temperature

Sammakia 4-06 Fundamentals of Electronics Packaging; B. Sammakia Additional examples from actual systems

Sammakia 4-06 Sammakia 4-06 IBM system 3081 ES/3090 ES9000 Chapter 12 Figure 3b Year 1980 1985 1990

Max chip power (W) 4 7 27

Max module power (W) 300 600 2000

o Rint ( C/W) 11.6 7.7 1.8 Chip heat flux (W/cm2) 19 33 64

Module heat flux (W/cm2) 3.7 5.3 11.8

Table 1. Showing the relative incremental improvements made to the TCM, from Simons (1995).

Sammakia 4-06 Sammakia 4-06 Sammakia 4-06 Incoming air

Nozzle

Impingement heat sink

Ceramic cap

Thermal Ceramic grease substrate

Chapter 12 Figure 2 Schematic diagram of the IBM 4381

Sammakia 4-06 Sammakia 4-06 Sammakia 4-06 Sammakia 4-06 fluorocarbon liquid, FC-77, under single phase forced convection conditions. The flow velocity is about 1 m/s over the single chip packages.

fluorocarbon liquid, FC-77

Chapter 12 Figure 8 Cray 2 system

Sammakia 4-06 Bellows provides mechanical spring

Sammakia 4-06 Flex provides mechanical spring

Sammakia 4-06 Sammakia 4-06 Sammakia 4-06 •In all of the designs shown here there is a flexible part of the system designed to protect the interconnects at the chip level. •Examples: pistons, bellows and springs (weakly coupled to the chip) •Grease: allows the chip and heat-sink to expand independently •Flexible chip carrier: the chip carrier deforms and reduces the stresses on the interconnect

Sammakia 4-06 Metal heat sink IBM TCM (308X,309X,ES9000) IBM 4381 Gas gap/Spring/Thermal grease/Oil Hitachi M680 Solder interconnections Mitsubishi high thermal (no underfill) conduction module Substrate Fujitsu bellows system

Metal heat sink

High modulus adhesive VAX 9000 NECSX3 Wire bond/TAB/Solder Bumps with Under fill Substrate

Sammakia 4-06 Technology Thermal Characteristics Thermal and Mechanical design features

P Q Q” Q”’ Rint Rext

Mitsubishi HTCM 36 4 0.83 0.4 3 4.3 Thin air gap between cap and heat spreader on the chip. This reduces the stresses. Hitachi RAM 6 1 0.8 0.5 10.1 24.6 Air cooling, CTE matching by using SiC heat spreader Honeywell SLIC 60 >0.5 0.9 0.2 Total Water cooled. 60 NEC SX LCM 250 >5.4 1.6 0.3 Total Water cooling, studs touching chips. 5 IBM 4381 90 3.8 2.2 0.5 9 8 Air cooling, impingement heat sink. Ceramic cap and thermal grease reduce stress IBM 3090 500 7 2.2 0.4 7.2 1.5 Water cooling, aluminum pistons touching chips. IBM ES 9000 2000 27 Water cooling, copper pistons touching chips.

NTT 377 15.1 4.2 8.4 2.8 0.5 Liquid cooling utilizing micro channels in substrate VAX 9000 30 at Chips backbonded to heat spreader using diamond chip paste. TAB bonding reduced mechanical stresses. level Cray 2 600-700 Uses direct liquid immersion cooling.

Fujitsu VP 2000 4600 30 0.56 Uses Bellows and water impingement cooling total

Where Sammakia 4-06 P = total module power, W Q = Max chip power, W Q” = heat flux, W/cm2 Q”’ = Heat density, W/cm3 Future flexible electronic systems that are completely integrated can be ‘wrapped’ around heat-sinks and cold plates for maximum thermal performance and reliability

Sammakia 4-06 References:

•Allen, E., Donohue, B. and Pei, H. (1987), “Cooling the VAX 8000 Family of Computers - An Overview,” Proc. of the Technical Conf., Seventh Annual Intl. Electronic Packaging Society Conf., v. 2, held in Boston, MA, pp. 712-717. •Bar-Cohen, A. (1987), “Thermal Management of Air- and Liquid Cooled Multi-Chip Modules,” IEEE Trans. Components, Hybrids and Manufacturing Technology, v. CHMT-10, no. 2, pp. 159-175. •Bar-Cohen, A. (1988), “An Addendum and Correction to Thermal Management of Air- and Liquid-Cooled Multi-Chip Modules,” IEEE Trans. Components, Hybrids and Manufacturing Technology, v. CHMT-11, no. 3, pp. 333-334. •Biskeborn, R.G., Horvath, J.L. and Hultmark, E.B. (1984), “Integral Cap Heat Sink Assembly for the IBM 4381 Processor,” Proc. of the Technical Conf., Fourth Annual Intl. Electronic Packaging Society Conf., held in Baltimore, MD (October 29-31, 1984), pp. 468-474. •Carlson, D.M., (1994), “Cray J90 Computer System Air-Cooled Supercomputer Packaging,” Proc. of the Technical Program, 1994 Intl. Electronics Packaging Conf., Atlanta, GA (September 25-28, 1999), pp. 708-721. •Chu, R.C., Hwang, U.P. and Simons, R.E. (1982), “Conduction Cooling for an LSI Package - A One-Dimensional Approach,” IBM J. of Research and Development, v. 26, no. 1, pp. 45-54. •Cray, S. R. (1986), “Immersion Cooled High Density Electronic Assembly,” U. S. Patent 4,590,538 (May, 1986). •Danielson, R.D., Krajewski, N. and Brost, J. (1986), “Cooling a Superfast Computer,” Electronic Packaging and Production, (July, 1986), pp. 44-45. •Emoto, Y, Tsuchiya, M., Ogiwara, S., Sasaki, T., Kobayashi, F.and Otsuka, K. (1986), “A High Performance Package Approach on 1st Level Packaging For Main Frame,” Proc. of the 36th Electronic Components Conf., Organized by the IEEE Components, Hybrids, and Manufacturing Technology, held in Seattle, WA (May 5-7, 1986), pp. 564-570. •.‘National Technology Roadmap for Semiconductors: Technology needs’, 1999, http://notes.sematech.org/PublNTRS.nsf/home.htm . •.”The Electronics Industry Report”, Prismark partners annual report, 1998-99.

Sammakia 4-06 •Fitch, J.S. (1990), “A One-Dimensional Thermal Model for the VAX 9000 Multi-Chip Units,” in Thermal Modeling and Design of Electronic Systems and Devices, R. A. Wirtz and G. L. Lehman, (editors), presented at the ASME Winter Annual Meeting, Dallas, TX (November 25-30, 1990), American Society of Mechanical Engineers, New York, NY, HTD-Vol. 153, pp. 59-64. •Gani, L., Graf, M.C., Rizzolo, R.F. and Washburn, W.F. (1991), “IBM Enterprise System/9000 Type 9121 Model 320 Air-Cooled Processor Technology,” IBM J. of Research and Development, v. 35, no. 3, pp. 342-351. •Hopper, S., Edwards, D.L. and Young, S.P. (1992), “The Thermal Management of IBM's ES/9000 Advanced Thermal Conduction Module,” Proc. of the 42nd Electronic Components and Technogy Conf., Organized by IEEE Soc. on Components, Hybrids and Manufacturing Technology, held in San Diego, CA (May 18-20, 1992), pp. 997-1001. •Kaneko, K. Seyama, K. and Suzuki, M. (1990), “LSI Packaging and Cooling Technologies for Fujitsu VP2000 Series,”, Fujitsu Scientific & Technology J., v. 41, no. 1, pp. 12-19. •Kalita, B. and English, W. (1985), “Cooling the VAX 8600 Processor,” Digital Technical Journal, no. 1, (August 1985). •Kaneko, K., Kuwabara, K., Kikuchi, S. and Kano, T. (1991), “Hardware Technology for Fujitsu VP2000 Series,” Fujitsu Scientific & Technology J., v. 37, no. 2, pp. 158-168. •Knickerbocker, J.U., Leung, G.B., Miller, W.R., Young, S.P., Sands, S.A. and Indyk, R.F. (1991), “IBM System/390 Air-Cooled Alumina Thermal Conduction Module,” IBM J. of Research and Development, v. 35, no. 3, pp. 330-341. •Kobayashi, F., Anzai, A., Yamada, M., Takahashi, A., Yamazaki, S. and Toda, G.,(1986), “Packaging Technologies for the Ultrahigh- Speed Processor Hitachi M-680 H/M-682 H,” Proc. of the 36th Electronic Components Conf., Organized by the IEEE Components, Hybrids, and Manufacturing Technology, held in Seattle, WA (May 5-7, 1986), pp. 571-577. •Kohara, M., Nakao, S, Tsutsumi, K., Shibata, H., and Nakata, H. (1983), “High thermal conduction package technology for for flip chip devices,” IEEE Trans. Components, Hybrids, Manuf. Technology, Vol. CHMT-6, pp. 267-271. •Lyman, (1982), “Special Report - Supercomputers Demand Innovation in Packaging and Cooling,” Electronics, (September 22, 1982), pp. 136-142. •McElroy, J. (1984), “Packaging of a High Performance VAX,” Proc. of the Intl. Electronic Packaging Soc. Conf., •McElroy, J. (1985), “Packaging the VAX8600 Processor,” Digital Technical Journal, no. 1, (August 1985). •McPhee, M., O'Toole, T.S. and Yedvabny, M. (1990), “Cooling The VAX 9000,” Electro/90, Conference Record, pp. 288-292, Boston, MA (May 9-11, 1990). •Mizuno, T., Okano,M., Matsuo, Y. and Watari, T. (1987), “Cooling Technology for the NEC SX Supercomputers,” Proc. of the Intl. Symposium on Cooling Technology for Electronic Equipment, Hawaii, pp. 110-125.

Sammakia 4-06 •Okutani, K., Otsuka, K., Sahara, K. and Satoh, K. (1984), “Packaging Design of a SiC Ceramic Multi-Chip RAM Module,” Proc. of the Technical Conf., Fourth Annual Intl. Electronic Packaging Society Conf., held in Baltimore, MD (October 29- 31, 1984), pp. 299-304. •Pei, J., Heng, S., Charlantini, R., and Gildea, P. (1990), “Cooling Components Used in VAX 9000 Family of Computers,” Proc. of the Technical Conf. 1990 Intl. Electronics Packaging Conf., (Marlborough, MA, September 10-12, 1990), pp. 587- 601. •Sechler, R. F. (1993), “RISC System/6000 Central Processing Unit,” Proc. of the Intl. Conf. & Exhibition on Multichip Modules, (Denver, CO 14-16 April, 1993), SPIE vol. 1986, pp. 22-27. •Simons, Robert, E. (1995), “The evolution of IBM high performance cooling technology,” IEEE Transactions on Components, Packaging and Manufacturing Technology-Part A, Vol. 18, No. 4. •Watari, T. and Murano, H. (1985), “Packaging Technology for NEC SX Supercomputer,” Proc. of the 1985 IEEE Electronic Component Conference, organized by IEEE Components, Hybrids, and Manufacturing Technology, pp. 192-198. •Werbizky, G.G. and Haining, F.W. (1985), “Circuit packaging for large scale integration”, in Proc. IEEE Electronic Component Conf., pp. 187-191. •Yamamoto, Udagawa, Y. and Okada, T. (1986), “Cooling and Packaging for FACOM M-780,” Fujitsu, v. 37, no. 2, pp. 124-134. •Yamamoto, Udagawa, Y. and Suzuki, M. (1987), “Cooling System for FACOM M-780 Large-Scale Computer,” Proc. of the Intl. Symposium on Cooling Technology for Electronic Equipment, Hawaii, pp. 110-125. •.T.M.Niu, Bahgat Sammakia and Sanjeev Sathe “Void effect modeling of flip chip encapsulation on ceramic substrates”, Transactions of the ASME, IMECE 1997, Seattle WA •.P. Totta, S. Khadpe, N. Koopman, T. Reilly, M. Sheaffer, “Chip to Package Interconnections,” Chap. 8 of Microelectronics Packaging Handbook, Part II, ed. Rao Tummala, Eugene J. Rymaszewski, Alan G. Klopfenstein, 2nd ed., Chapman & Hall 1997. •.D. Suryanarayana, R. Hsiao, T.P. Gall, J.M. McCreary, “Flip-Chip Solder Bump Fatigue Enhanced by Polymer Encapsulation,” IEEE Trans. of Components and Hybrid Manufacturing Technology, Vol. 14, No. 1, 1991, p. 218. •.G. Moore, “Cramming More Components onto Integrated Circuits,” Electronics Magazine, Vol. 38, No. 8, April 19, 1965, p. 114. •.Schaller, R.R. “Moore’s Law: Past, Present and Future,” IEEE Spectrum, Vol. 34, No. 6, June 1997, p. 52. •.Chu, R. C. (1986), "Heat Transfer in Electronic Systems," Heat Transfer - 1986, Proc. of the 8th Intl. Heat Transfer Conf., held in San Francisco, Hemisphere Publishing Co., Washington, DC, v. I, pp. 293-305. •.Bar-Cohen, (1987), "Thermal Management of Air- and Liquid Cooled Multi-Chip Modules," IEEE Trans. Components, Hybrids and Manufacturing Technology, v. CHMT-10, no. 2, pp. 159-175.

Sammakia 4-06 •.Chu, R. C. and R. E. Simons, (1990), "Review of Thermal Design for Multi-Chip Modules," Proc. of the Technical Program, pp. 1633-1642, NEPCON-WEST, National Electronic Packaging and Production Conf., Anaheim, CA (February 26 - March 1, 1990). •Pei, J., Heng, S., Charlantini, R., and Gildea, P., (1990), “Cooling Components Used in VAX 9000 Family of Computers,” Proc. of the Technical Conf. 1990 Intl. Electronics Packaging Conf., (Marlborough, MA, September 10-12, 1990), pp. 587-601. •Oktay, S. and Kammerer, H.C. (1982), “A Conduction Cooled Module for High Performance LSI Devices,” IBM J. of Research and Development, v. 26, no. 1, pp. 55-66. •Oktay, S., Dessauer, B. and Horvath, J.L. (1983), “New Internal and External Cooling Enhancements for the Air-Cooled IBM 4381 Module,” ICCD '83, Proc. of the IEEE Intl. Conf. on Computer Design: VLSI in Computers, held in Port Chester, NJ (November 1, 1983). •Han and Guo,"Thermal Deformation Analysis of Various Electronic Packaging Products by Moire and Microscopic Moire Interferometry," Journal of Electronic packaging, Transaction of the ASME, Vol. 117, pp. 185-191, 1995. •Guo, Lim, Chen and Woychik,"Solder Ball Connect (SBC) Assemblies under Thermal Loading: I. Deformation Measurement via Moire Interferometry, and Its Interpretation," IBM Journal of Research and Development, Vol. 37, No. 5, pp. 635-648, 1993. Choi, Guo, LaFontaine, and Lim, "Solder Ball Connect (SBC) Assemblies under Thermal Loading: II. Strain Analysis via Image,Processing, and Reliability Considerations," IBM Journal of Research and Development, Vol. 37, No. 5,pp. 649-659, 1993. •Y. Joshi, “Thermal management in electronic packages”, professional course presented at ITherm 2002, San Diego.

Sammakia 4-06