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Thermal Analysis of Spray Cooled 3-D Interconnected Diamond Substrate MCMs:

Comparison with Experimental Measurements

Paul J. Boudreaux1, Richard C. Eden2

1Laboratory for Physical Sciences, College Park, MD, 2Technology Applications, Austin, TX Abstract - With high speed computation now driving with clock rates in the tens of gigahertz, changes have to be made to thermal management and packaging to respond to the increasing power density in such systems. The authors describe one successful approach to a sub nanosecond cycle time supercomputer design. Thermal measurements and modeling prove that this design is scalable to power dissipation levels as high as 25kiloWatts, while still achieving the sub nanosecond cycle times that were originally targeted. To the author’s knowledge, this is the first time a true three-dimensional electronic interconnected spray cooled thermal management scheme using polycrystalline diamond to handle the extraordinary heat loads has been described and demonstrated at these power levels. Index Terms - Polycrystalline diamond, 3-D cube computer, MCMs, z-axis interconnect, spray cooling, fuzz button, thermal modeling, fluorinert, phase change cooling, benzocyclobutene (BCB) die attach, thermal conductivity. INTRODUCTION In today’s age of advancing technology, researchers and scientists are looking for innovative solutions to problems encountered in the fields of microelectronics packaging and high performance computing. The desire to build computers with faster cycle times brings along with it problems of increased power density and heat build-up. Because of the finite speed of light, size restrictions are placed on modern supercomputing architectures. To realize subnanosecond cycle time performance in such a machine, no critical dimension can be larger than roughly 15cm, since light will only travel 30 cm in one nanosecond in a vacuum and the data has to be able to store and fetch within a cycle. This imposes an enormous power density within the machine which could cause catastrophic heat related failures.

Spray cooling and polycrystalline diamond are two technologies that have demonstrated the ability to solve these thermal management problems [1]. *Copyright ©2004 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purpose must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org.

Figure 1. (a) Vertically stacked and interconnected, diamond based multi-chip modules form a cube shape and the basis for an advanced 3-D architecture; (b) Photograph of the top of a MCM with mounted chips on the diamond substrate. It also shows the two protruding diamond substrate tabs that form the cooling fins.

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The authors realized their potential for thermal management after seeing the dramatic reliability improvements brought about by the use of these technologies [2]. Recent advancements in synthetic diamond manufacturing have produced diamond based microelectronic packages. This led directly to the development of a 3-dimensional cube computer architecture based on diamond packaging [3], see Figure 1(a), and spray cooling. These advances have been made possible because of the extraordinary room temperature thermal conductivity properties of polycrystalline diamond, (12 – 20W/cm°K) [4], and the heat extraction capabilities of spray cooling (50 – 150 W/cm2) [5]. One of the goals of this research was to carefully model the 3-D diamond multi-chip-module (MCM) structure and use that model to obtain the critical operating parameters obtained for the spray-cooled structure. The principal unknown parameters to be evaluated by this method include the heat transfer coefficient, h, obtained from the spray-cooled diamond cooling fins at the edge of the diamond substrate MCMs, the die attach thermal resistance, Rth(die), and the lateral thermal conductivity, k, of the diamond substrate itself. A further derived quantity is the effective thermal resistance of the spray cooling fins, Rth (Lc), as measured as the temperature difference, Tref-Tsat, between the base of the cooling fins and the coolant saturation temperature, Tsat, divided by the power into the fins. This paper documents some of the technical data obtained from a series of experimental measurements made over the period of a year on the initial design for an operating 3-D cube system. Many researchers from government, industry and private organizations contributed to the success of this research effort to determine the reliability impact of the thermal management system described below. Background There are several reliability and performance issues that arise in the area of high performance computing. One of these issues is thermal management. Overheating, thermal gradients, and rapid temperature changes can all lead to decreased reliability in silicon chips and other component parts. Another issue

concerns the match in the coefficient of thermal expansion (CTE) between components and packaging materials. CTE mismatch problems are directly caused by the temperature differences created in the electronic components and the materials of which they are made. In the case of polycrystalline diamond and single crystal silicon, there is an exceptionally good CTE match (polycrystalline diamond: 1.2 x 10-6 /

°K; silicon: 2.3 x 10-6 /°K) because of the similarity of elemental characteristics in the periodic table’s column of elements. This close match results in less stress/strain between the two materials as they undergo temperature change. Compared to other CTE values for packaging materials, which range from a low of 5 to a high of 285 x 10-6 / °K [6], the diamond-silicon match is a more reliable. To extract an even greater benefit from this CTE match, a new and innovative die attach methodology was developed for a different project that uses a 100 times thinner bond to adhere the silicon die to the diamond substrate than is typically used throughout the semiconductor industry. Since the temperature difference across this bond is directly proportional to the thickness of the bond, a one-hundred-fold reduction in the temperature difference results in a dramatic reliability enhancement. For example, in a typical “standard” die attach that uses solder, eutectic, or epoxy, the thickness of this material can vary between 75 and 200 microns. The new “thin attach” process uses a 1 to 2 micron thick polymer, called benzocyclobutene, BCB, to form the die attach. This very thin bond ensures a thermal dead short from the silicon chip to the

Figure 2. Schematic of MCM diamond substrate showing locations of active integrated circuits and their associated temperature sensing diodes located on each IC along with the two cooling fins.

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diamond substrate (which is already the world’s best thermal conductor) even though the thermal conductivity of the BCB is relatively poor (k= 0.29W/m°K @25oC). The BCB process described above was used reliably in many other projects and has proven quite successful in dramatically reducing the thermal impedance of assembled packages. In many systems, 50% of the thermal impedance occurs across the die attach so any reduction here improves the reliability proportionately. However, in the cube design described below, the standard die attach methodology that is used throughout the semiconductor industry was used in order to give a better insight into the silicon/diamond thermal interface and to allow for future performance improvements. It also establishes a basis for comparison with other published data in the literature. A third performance issue is the electrical insulating capacity of the diamond packaging material. Diamond is one of the very best dielectrics and can withstand exceptionally high electric fields without breakdown. This is a critical characteristic. Even though the voltage used in modern integrated circuits is low, the thickness of the insulator is thin in keeping with the submicron geometry of today’s integrated circuits. Since electric field is voltage divided by thickness, diamond’s dielectric strength makes it very useful for high performance applications. These factors all play an important role in designing electronic circuits for computing applications. Synthetic polycrystalline diamond is commercially produced by plasma methods and is relatively inexpensive. It has excellent thermal conductivity properties at operating temperature, as already stated, and relates well to the above reliability issues. At operating temperatures, thin polycrystalline diamond plates have a thermal conductivity as high as five times that of copper and a hundred times better than ceramic, allowing for more efficient heat extraction and improved thermal management. This improvement continues to rise as the operating temperature is lowered until it maximizes at 100 degrees Kelvin (k ~100W/cm°K) where it then begins to fall off. Spray cooling is another technology utilized by the authors in to attack the problems presented by high performance computing. This

Figure 4. The plastic Fuzz button board with a blowup insert shows individual fuzz buttons mounted in 0.010cm diameter holes on 0.051cm pitch.

Figure 3. Two views of the mechanically assembled supercomputer made of 3-D Z-axis interconnected diamond MCM substrates.

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technology has the ability to extract quantities of heat from very small and irregular surfaces, or volumes, with exceptional efficiency. In contrast, thermal engineers tend to spread out the heated area to make the largest possible surface in order to remove the heat easily. That is why fins, heat sinks and similar techniques work well in open spaces to easily remove heat from electronic circuits. Spray droplets can conformably cover all the exposed surfaces with a thin liquid film that is continuously evaporating. It is the evaporating dielectric liquid film adhering to the hot surface that extracts most of the heat. This electrically insulating liquid film is designed to be very thin

so the evaporation rate is maximized. The liquid is replenished by the constant arrival of tiny liquid droplets shot out of a spray nozzle, hence the name spray cooling. The physical characteristics of typical spray fluids are given in Table I. This fluid is very similar to those used by semiconductor manufacturers to wash and clean processed silicon wafers just prior to wafer dicing to separate the chips from the wafer. Thus it is fully compatible with contact to the bare processed silicon chip surface. This surface contact capability will also offer spray cooling a tremendous advantage in certain types of cooling systems.

Table I

Fluorinert Dielectric Fluid Data

Fluorinert Dielectric Fluid Data

Ref.: Handbook of Chemistry & Physics, Vol. 75, PP 6-59

0°K =

-273.15°C

MPa/psi= 145.037

Fluid Name

Boiling Point

Composition Pure Chemical Data: Boiling Point

Melting Point

Critical Temperature

Critical Pressure

Critical Volume

(°C) (Nominal) Tb (°K) Tm (°K) Tc (°K) Mpa cm^3/mol

FC87 31°C C5F12 Perfluoropentane 302.4 263 420.59 2.045 473

FC72 56°C C6F14 Perfluorohexane 329.8 186 448.77 1.868 606

Perfluoro-2-methylpentane 330.81 455.3 1.923 532

Perfluoro-3-methylpentane 331.52 450 1.69

Perfluoro-2,3-dimethylbutane 332.93 463 1.87 525

FC84 80°C C7F16 Perfluoroheptane 355.66 195 474.8 1.62 664

FC77 97°C C8F18 Perfluorooctane 379 502 1.66

FC104 101°C C9F20 Perfluorononane 398.5

Unlike the cooling process used in the Cray I supercomputer, where the entire electronic circuitry is submerged in a liquid bath, spray cooling only uses a mist of droplets on the heated surfaces. The physical heat extraction process is entirely different between the two methods. In the Cray I, it is primarily the warming of the liquid (by a property called the specific heat) that is used to remove the heat. In other words, the liquid is heated and the hot liquid is pumped away to a heat exchanger. In

spray cooling, the thin film of liquid is also warmed by the substrate but it also is converted directly into a gas by contacting the hot surface (by a process using both the specific heat and the latent heat of the liquid as it undergoes a phase change). This process requires many more calories of heat than simply warming the liquid and hence it can remove much larger quantities of heat with far less liquid. This two-phase process (liquid state to vapor state) has the property that all evaporating surfaces are nearly

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isothermal. Thus, with virtually no temperature difference between components, the reliability of the system is improved dramatically, i.e., the CTE induced strains are minimized. This condition also allows two highly dissimilar materials to be joined together without a reliability penalty as long as they are spray cooled. In addition, spray cooling allows the thermal designer to sever the thermo-mechanical heat path, thus eliminating the pathway for shock or vibration from entering the system while the heat is extracted. This can be an enormous benefit in military systems. Huge reductions in weight and volume can be realized (15:1 in weight and 18:1 in volume) for some military systems [7]. This often leads directly to cost reductions of 10:1 over existing rugged military designs. For the first time, commercial-off-the-shelf (COTS) components can be used in rugged and shockproof equipment. This technique can reduce costs even more and get new technology into the field in record time. II. DIAMOND BASED MULTI-CHIP MODULES AND A 3-D CUBE COMPUTER ARCHITECTURE At the speed of light, a signal can travel 30 cm in one nanosecond in vacuum. To achieve subnanosecond cycle times, the entire computer is confined to a 10 cm cube with a diagonal and maximum path length of about 15 cm. The MCMs in this design are based on 10 cm x 10 cm x 1 mm thick polycrystalline diamond substrates, since these were commercially available from multiple vendors. The 100cm2 area of the square MCM substrate determined the maximum useable size that could easily be incorporated into fin areas, as illustrated in Figure 1b & 2. A supercomputer of such small dimensions would generate enormous amounts of heat. However, it was predicted that diamond substrates combined with spray cooling could efficiently handle the heat build-up and extraction in a single MCM with an upper surface fin area of 12cm2 [8]. A proof-of-principle program directed at the 3-D cube architecture used by the authors was funded by the Defense Advanced Research Projects Agency (DARPA Contract Number MDA972-91-C-0035) and successfully demonstrated these principles. Thin polycrystalline diamond substrates are used as the basis for constructing MCMs. Silicon chips are bonded to this 1mm thick diamond

substrate which has a copper/gold and dielectric thin film process applied to it. Standard die attach methods are used to bond the silicon chips to the diamond. Temperature sensing diodes

Figure 5. The actual, (A), and schematic, (B), I/O flex bus connector handles power distribution and signal I/O with its ten layer transmission line structure.

Turn Around Board

Fuzz Button Board

Fuzz Button Board

MCMFuzz Button Board

I/O Board

Fuzz Button Board

Turn Around Board

MCM

MCM

Fuzz Button Board

Fuzz Button Board

I/O Board

I/O Board

Fuzz Button Board

Heat Out

Signal I/O

Heat Out

Power In

Figure 6. The representative stack of boards, MCMs, fuzz buttons and turn around cards is shown for the Cube architecture tested.

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(whose positions on the chip are given in Figure 2) are used to measure and approximate junction temperatures. The central square 7.6cm x 7.6 cm area forms the MCM on the diamond substrate and is pictured in Figure 1(b). Part of the remaining area is used to form the two fins after notches are laser cut from the four corners of the substrate. These substrates have demonstrated an improved thermal performance when tested against similar MCMs that use ceramic substrates [9]. The diamond based MCMs were used to build the 3-D cube computer architecture shown in Figure 3. A 3-D cube architecture was envisioned to decrease both the physical size and cycle time of current supercomputing machines with the goal being to achieve subnanosecond performance. In this 3-D architecture, diamond based MCMs are stacked vertically to form a cube. Vertical interconnect to MCMs above and below is achieved by way of 7,200 laser drilled via holes in the diamond substrates which are then filled with metal. These metal vias through the diamond connect to the layers of copper and polyimide thin films on both sides of the diamond to effectively make printed circuit boards bonded to each side of the diamond substrate. These copper and polyimide thin film interconnect layers have wiring densities and lithography comparable to that of the metal interconnect on the integrated circuit itself. Five layers of copper and polyimide form the backside of the diamond substrate while seven layers of copper and polyimide form the front surface. The outer surfaces of copper are gold coated and patterned into 7,200 tiny squares to form one side of a pliable z-axis interconnect system that electrically interconnects adjacent MCM substrates. This pliable z-axis interconnection is made with “fuzz buttons” [10]. A ‘fuzz button” is similar to a gold plated “Brillo pad” that is only 0.10 millimeter in diameter and 1.2 millimeters long. Each of the 7,200 fuzz buttons is inserted through a 1.00millimeter thick plastic “fuzz button retainer” board (also called a spacer board) so that 0.1mm protrudes above each side of the retainer board surface. These 7,200 buttons filling the holes align with the 7,200 gold squares on the diamond MCM substrate surfaces to form the z-axis electrical interconnection. The fuzz buttons act as tiny gold-coated springs that make an electrical path

between adjacent diamond substrate MCMs and the I/O bus boards. A fuzz button board, as seen in Figure 4, is located on each side of the MCM substrate. Each MCM substrate is also connected to the outside world by means of a ten layer flexible interconnect I/O bus containing transmission lines for signal I/O and power distribution as illustrated in Figure 5. The I/O bus has a printed circuit pad area similar to the gold square contacts that align with the fuzz button board and open spaces for the integrated circuits. These pads can also act as a pass through via to the fuzz buttons in the adjacent MCM substrate. Each I/O bus can deliver up to 500 Watts of power to each MCM substrate. When all of the MCM substrates, I/O boards and retainer boards are stacked up, a true 3-D z-axis interconnected design is realized that is capable of subnanosecond performance. The schematic of such a stack is given in Figure 6. All the heat generated by the operation of the devices is

Spray Cooling System

Spray Cooling

HeatHeatAcquisitionAcquisition

Delivery and ReturnDelivery and ReturnTubes (Can be Part ofTubes (Can be Part ofChassis Frame withChassis Frame withQuick-Disconnects)Quick-Disconnects)

Cooled MCMCooled MCMor IC Packageor IC Package

Liquid OutLiquid Out

Vapor ReturnVapor Return

FanFan

PumpPump FilterFilter

Compact Pump-Condenser UnitCompact Pump-Condenser UnitTypically Mounted at Rear of Enclosure or ExternallyTypically Mounted at Rear of Enclosure or Externally

Condenser/Condenser/Heat ExchangerHeat Exchanger

HeatHeatRejectionRejection

Figure 7. The mechanical aerosol spray cooling system is illustrated in this drawing showing how the heat is extracted and deposited into the environment.

Figure 8. Schematic representation of the aerosol spray pattern from the nozzles onto the diamond substrate MCM with the protruding fins is shown in two views for the 3-D cube architecture of Figure 9. Both surfaces of each fin are sprayed.

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extracted from the diamond substrate fins that protrude from the side of the stack by the aerosol spray apparatus schematically illustrated in Figure 7. This projection of part of the diamond substrate out of the side of the stack acts as an effective fin. Each substrate has two fins - 1.0 cm wide and 6.0 cm long as seen in Figure 1(b). The central area is the MCM portion of the substrate. The two holes in the diagonal corners are there to align all the stacked substrates when mounted on the alignment pins in the mechanical housing. Both sides of each fin’s surface are constantly sprayed with liquid droplets ejected from an array of tiny nozzles, see Figure 8. The constant mist of evaporating liquid from the hot surfaces of the protruding fins removes the heat during the operation of the computer as seen in Figure 9 (a) and (b). The waste heat is transferred to the environment as portrayed in Figure 7; the hot vapor is recovered and recycled through filters

and a compressor pump after passing through a heat exchanger. The cooled compressed vapor condenses to a high-pressure liquid where it is once again injected into the spray nozzles to repeat the cooling process. This closed cycle spray cooling process is mechanically similar to the normal air conditioning process. In this early spray cooling design, no feedback mechanism was implemented to control the flow rate of sprayed droplets arriving at the fins. It was assumed that in this design the heat load would be constant during operation. This proved to be the case, but later designs could incorporate an active feedback system to ensure that the optimum fluid droplet rate was always present on the heated substrate. A big advantage of spray cooling over other heat removal techniques is that it directly extracts the heat uniformly from the hot surface without the use of a thermo-

Figure 10. A functioning 3-D Cube computer is made up of z-axis interconnected MCM diamond substrates. The backside of one of the two aerosol spray modules is seen on the side of the cube assembly. Both fins of each stacked MCM are sprayed on the top and bottom surfaces on both the left and right sides. 2,500 watts of power is delivered to the five MCMs by the orange lines to the left. High speed I/O is attached to the vertical PC board on the right. The aerosol spray controller and pump are shown below the assembly.

Figure 9. (a) Photo of a 3-D cube with projecting diamond fins exposed during assembly; a spray head module is subsequently mounted to each side of the cube. (b) An aerosol spray pattern is generated by the spray module. The aerosol spray module uses multiple rows of nozzles to create the pattern impinging on the glass plate during this test prior to mounting on the system.

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mechanical extraction path. It uses the latent heat of vaporization in addition to the specific heat of the liquid to extract heat. This “two phase” method is many times more efficient than single-phase methods that only use the specific heat of the liquid to extract heat. In addition, the mechanical reliability of the hermetically sealed commercial pump has been measured and warranted by the manufacturer to exceed 100,000 hours MTBF (Mean-Time-Between-Failures). Unlike the Cray I cooling system, this approach typically uses only one or two liters of liquid Fluorinert, depending on the amount of fluid held in a pressurized reserve canister controlled by a sensor relay valve that detects main bus power failures. If a power failure occurs, the relay opens on the pressurized fluid canister to bypass the pumps and supply fluid to the spray nozzles for a controlled thermal cool down of the system. In the cube arrangement described above, three MCMs, two “turn-around-boards” (at the top and bottom of the stack), three I/O boards and seven fuzz button boards were employed to produce the thermal data from the machine illustrated in Figure 10. The turn-around–boards were used to send the signal down a different path through the stack so that even though only three MCM diamond substrates were used in one test, there would be a signal propagation length equivalent to a stack of 24 MCMs. In addition, only five of the integrated circuits per MCM (the clock and four center chips) were active during these specific tests as illustrated in Figure 2. A summary of the data modeled along with its relative significance is illustrated in APPENDIX I. When all chips are powered on at full clock rate, an MCM can dissipate close to 500 Watts. Forty such MCM substrates are equivalent to the computing power of a Cray YMP supercomputer dissipating 20 kilowatts operating at subnanosecond clock speeds. III. SUMMARY OF RESULTS: A satisfactory thermal model was developed and values for the operating parameters were derived by careful comparison between measured operating junction temperatures under different operating conditions of the 3-D diamond MCM. The best performance was obtained with the 3-D MCM operated at a 45° angle so that gravity assistance was available to avoid flooding of the spray cooling chambers. This flooding could occur because the spray manifold was initially

designed for a stack of six diamond substrate MCMs, whereas the actual stack that was measured had only three diamond substrate MCMs. This meant that many nozzles were not spraying heated surfaces, thus adding liquid to the chamber. Further, only four die on each MCM were powered during these measurements (plus the center clock die which was operated at lower power) instead of the usual nine. The effect of this is to force all of the power to pass through four (instead of eight, neglecting the clock chip) die-substrate thermal resistances in parallel, raising junction temperatures for any given power level. As mentioned previously, the nozzle design was sized for more boards than were actually present in this test and the initial fixed liquid flow rate was sized for the full heat load design. Since no control feedback system was employed in this design, it was possible to flood the spray chamber with too much fluid. As a consequence of powering only three MCMs instead of the six that it was designed for, the maximum power level evaluated was only 304 Watts per MCM, instead of the 400 Watts per MCM nominal design value, which meant that instead of 6x400=2400 Watts module dissipation, there was a maximum of 3x304=912 Watts, with many measurements carried out at lower power levels. Under conditions where the actual power is far below the nominal design power, the spray cooling chamber may become flooded, with a type of jet impingement cooling obtained instead of true spray cooling. This was observed in the horizontal orientation (MCM substrates and fins horizontal) of the module, in which the excess liquid had to flow “up hill” to escape into the suction line. By temporarily tilting the MCM housing at a 45° angle, with the suction outlets at the bottom, excellent operation with good heat transfer coefficient values were obtained. The best-fit heat transfer coefficient value obtained for this work was h=1.15 W/cm2°K (or 2018BTU/HrFt2°F) with the FC87 (or PF5070 with nominal Tsat=31°C) Fluorinert fluid supplied by the manufacturer, with the cooling system. This value seems appropriate for a geometry in which the angle between the spray and most of the sprayed diamond tab surface is quite low. At this h, the effective thermal resistance of the 5.9cm wide by 0.8cm long spray-cooled tabs (from tab base to Tsat) was 0.129°K/Watt for each tab (0.0645 °K/W for the two tabs on each diamond MCM). Hence, at P=304 Watts, the base of the spray cooled

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diamond tabs was only Tref-Tsat =19.6°K above the fluid saturation temperature. The best fit value for lateral thermal conductivity of the z =1.00mm thick diamond substrate material was found to be k=12.00 W/cm°K, in excellent agreement with the values claimed by the diamond substrate supplier for this material. Note that this k value is obtained after the 7200 via holes were laser drilled through the substrate and all metal and MCM processing were completed. This value eliminated concerns that drilling and processing might seriously degrade the thermal performance of the diamond substrate material [11]. The final critical thermal parameter evaluated was the die to substrate thermal resistance, Rth (die). The best-fit value obtained for this parameter was Rth (die) =0.55 °K/Watt. This is a rather high value for a 1 cm x 1cm chip in a thermally sensitive application. For example, it leads to a junction-to-substrate temperature rise of 39.3 °K at the maximum power level tested of P=304 Watts per MCM or P=71.44 Watts in each of the four side chips. Considering that the total temperature rise caused by lateral heat flow through the z =1.0mm thick diamond substrate over the 33mm path from the cooling fin base to the hottest point on the MCM is only 47 °K, wasting nearly 40 °K in die attach thermal resistance is unsatisfactory. There is every reason to believe, however, that this could be greatly improved by optimizing the die attach technology with the above mentioned 1 – 2 micron thick BCB process. Other than the higher than desired Rth(die) values, however, the thermal results measured for the 3-D diamond MCM built in this program exceeded the initial expectations for such a novel design. A clear demonstration of the viability of this 3-D diamond MCM concept was presented. Thermal Model Calculation: While a full discussion of all of the technical details of the thermal model would be too lengthy to include here, it is appropriate to discuss key aspects, and then provide additional backup material, which can be examined for details of the calculational approaches and results. There are three steps to the thermal modeling: 1, calculating the temperature at the base of the spray cooled heat sink fins; 2, calculating (by 2-D Poisson’s equation simulation) the substrate temperature rise (caused by lateral thermal conduction in the

diamond) between the base of the fins and the various points of interest under the integrated circuit die; and 3, calculating the junction-to-substrate temperature rise and adding it to the substrate temperature to get the junction temperatures at the points on the die corresponding to the experimentally-monitored temperature diode points for comparison to the experimental data. Calculation of Temperature at Base of Spray-Cooled Diamond Fins: Two heat flow processes are taking place simultaneously within the spray-cooled diamond fins; lateral thermal conduction within the diamond, which leads to a temperature gradient in the fins, and heat transfer from the top and bottom surfaces of the fin to the spray. Because this heat transfer to ambient is sensitive to the temperature difference between the fin and the saturation temperature of the fluid, Tsat, it is necessary to solve a differential equation to obtain the T(x) temperature distribution in the fin. For a diamond fin of uniform width, w, thickness, z, and thermal conductivity, k, the temperature gradient along the x direction in the fin (x=0) is taken at the base of the fin, where it meets the MCM) will be given by dT(x)/dx=-P(x)/ (kzw), Eq. 1. where P(x) is the heat flow in Watts conducting along the diamond fin at point x and where P(x=0) =P, is the total power into the fin. The heat flow out of the diamond fin leads to a gradient in the power remaining in the fin. If one assumes a constant heat transfer coefficient, h, from spray cooling from a surface at temperature, Ts, such that in an area, A, the heat loss is given by

Ps = hA(Ts - Tsat,) = hAT(x) [where T(x)=Ts- Tsat] Eq. 2.

This heat loss at a point, x, leads to a gradient in P(x) as

dP(x)/dx = -Ps(x) = -hAT(x) = -2hwT(x) [for two surfaces sprayed] Eq. 3.

where the factor of 2 comes from the fact that both the top and bottom surfaces of the fins are being sprayed. Differentiating Eq.1 and substituting Eq. 3 for dP(x)/dx gives the

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differential equation for temperature distribution within the spray-cooled fin as d2T(x)/dx2 = (2h/kz)T(x), Eq. 4. This differential equation has solutions of the form of growing and decaying sum of exponentials. For example, if the length of the fin, Lc, is infinite, only the decaying exponential solution meets the boundary condition of T=0 at x=infinity, thus the solution is T(x) = T(0) exp(-x/Leff) (for Lc >> Leff ), Eq. 5 where the characteristic temperature attenuation length in the fin, Leff, is given by Leff = Sqrt(kz/2h). Eq. 6 Using Eq. 5 for T(x) in Eq. 1 and evaluating at x=0, to obtain the effective thermal resistance of the fin, Rth(Lc=inf) Rth(Lc=inf)=T(x=0)/P= (1/w)(1/Sqrt(2hkz)) (for Lc >> Leff ). Eq. 7 In fact, for the h, k and z values appropriate for the diamond 3-D MCMs in this work, the value of the characteristic temperature attenuation length in the fin, Leff, is found to be 0.7223 cm, so Eq. 7 will not be very accurate when the fin length is only Lc = 0.777 cm. The math is slightly messier for this case as the T(x) solution is the sum of exp(-x/Leff) and exp(+x/Leff) terms. The result of the calculation is shorter than that derived by Incropera and DeWitt, [12], and is presented here for this finite Lc case as

Rth(Lc)=(1/w)(1/Sqrt(2hkz)) [(1+exp(-Lc/Leff))/(1-exp(-2Lc/Leff))]. Eq. 8 Since the exponential portion of this is just the reciprocal of the hyperbolic tangent, 1/Tanh(Lc/Leff), and the first part is the same as Eq. 7, this can also be written Rth(Lc) = 1/(wSqrt(2hkz)Tanh(Lc/Leff))

= Rth(Lc=inf)/Tanh(Lc/Leff). Eq. 9 In the 3-D diamond MCM thermal model calculation, the absolute temperature at the base of the spray-cooled diamond fins is calculated from the total MCM power, P, and the Rth(Lc) value from Eq. 9 as

Tref = Ts(x=0) = Tsat + P Rth(Lc), Eq. 10 where Tsat=31.0°C was taken for the FC87 Fluorinert fluid. And for a total spray cooling fin width w=11.786 cm with kz=1.20 W/°K and h=1.15 W/cm2°K, a value of Rth(Lc) = 0.0645 °K/Watt was obtained. Note that it is assumed here that the power density into the fin is uniform in the y direction, which would make the temperature along the fin base constant. In fact, this is not precisely true in the case of diamond MCMs in which the cooling tab is somewhat narrower than the body of the MCM substrate. However, as long as this assumption is consistently carried into the 2-D Poisson’s equation analysis, the resulting error will be small except for points very near the edge of the fin. At the highest power level measured, P=304 Watts per diamond MCM, the temperature rise above saturation was P Rth(Lc) = 19.6°K, or Tref = 50.6°C at the base of the spray cooling fin for Tsat=31.0°C. At P=229 Watts per MCM, these are P Rth(Lc) = 14.77°K and Tref = 45.77°C. Calculation of Temperature Distribution in Diamond MCM Substrate: The lateral thermal conduction in the diamond MCM substrate from the powered IC chips to the spray cooling fins leads to temperature gradients in the diamond substrate. Because of the complex geometry of the heated chip and cooling fin/MCM shape, solving for the ∆T(x,y) temperature distribution (where ∆T = Ts - Tref) analytically (as was done for the fin region above) would be impractical. What was done was to write a 2-D Poisson’s equation solver in HiQ script that does a finite difference simulation of the problem. Because of the horizontal and vertical symmetry of the MCM substrate and chip locations, only 1/4 of the substrate needs be simulated. A 1.0 mm simulation mesh size was taken, so the 1/4 substrate is simulated with a 33 x 38 mesh, or 35 x 40 including boundary points. All of the boundaries are taken as insulating except for the portion of the side that is the base of the spray cooled fin which is taken at a fixed reference temperature of ∆T=0. It is assumed that the chip power is uniformly applied over the area of the chips, and the enhancement of the lateral thermal conductivity of the diamond substrate due to the

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addition of the silicon IC chip on it is considered, although the effect is not very large with a z =1.0 mm thick diamond substrate. The numerical values of temperature rise from the cooling fin base, ∆T(x,y), were calculated for the P=304 Watt case (four side chips powered with 71.439 W and the center clock chip at 18.07 W) and for the P=229 Watt case (four side chips powered with 52.72 W and the center clock chip

still at 18.07 W). These results can be used to determine the substrate temperature value at any point under any powered or unpowered IC chip. These data are also shown in the form of a “3-D” surface graph in Figures 11and 12 for these two cases. The location of the cooling fin base (at ∆T=0) is indicated by the heavy line. The graph for the P=229 Watt case also shows the outline of the powered and unpowered IC die locations. Note that the maximum temperature rise is ∆Tmax=35.7°K for P=229W or ∆Tmax=47.4°K for the P=304W case. Calculation of IC Junction Temperatures and Using Thermal Model for Parameter Fitting: In both the 2-D Poisson’s equation simulation of ∆T(x,y) and in the calculation of the difference in temperature between the IC junctions (or thermal sensing diode) temperatures and the diamond substrate temperature underneath, it is assumed that the

power dissipation is uniform over any given IC chip. It is also assumed that all IC chips have the same die attach thermal resistance, Rth(die). Hence the absolute junction temperature at any point on an IC die will be given from Tj(x,y) = Tref + ∆T(x,y) + PIC Rth(die), Eq. 11 where Tref is obtained for the whole MCM from Eq. 10, ∆T(x,y) is from the 2-D thermal

spreading calculation results as shown in the two figures, and the junction to substrate temperature rise is calculated for each chip based on its power dissipation, PIC. For convenience, this entire calculation process has been put into an Excel 4.0 spreadsheet so that key parameters can be varied to obtain best fit to the experimentally measured diode temperature data. The ∆T(x,y) data was put into the spreadsheet for the ten temperature sensing points used for this evaluation by looking up the diode location within the IC chip, and the location of the chip on the MCM, to obtain the x,y location of each diode. The ∆T(x,y) value for each location was either read from, or interpolated between data points in the ∆T(x,y) tables that had been calculated. The procedure was done separately for the two (P=229W and P=304W) cases. Adjustment of the three critical parameters h,

Figure 11. This temperature versus area plot for ¼ of the measured the 3-D diamond MCM substrate shows the powered chip locations and temperatures measured by the on-chip diodes.

Figure 12. This is a temperature versus area plot of ¼ of the diamond substrate MCM showing the power dissipation on the MCM. The power dissipation equals 304 Watts when five of the nine chips in the MCM are active. The entire MCM thermal map can be found by using symmetry arguments.

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Rth(die) and k to obtain the best overall fit of the experimental temperature data for the two cases involves physical insight. The unpowered U3 die data is independent of Rth(die), and the U3 die is reasonably close to the spray-cooled fin, so this is a good place to focus for h adjustments. The clock die U5 has only 25% of the power of the side chips in the 304 Watt case, so it is somewhat less sensitive to Rth(die), and hence is a good place to look for k adjustments after a reasonably good Rth(die) value has been obtained (this particular diode gave somewhat erratic readings, however, so precise agreement is doubtful). The Rth(die) values are adjusted by looking at the heavily powered chips. The goal should be to get overall agreement. The Excel worksheet was used in selecting these critical parameter values, and it shows by the fitting accuracy obtained. For example, for P=229 W at the center of the unpowered U3 die Tj=64.2°C was calculated, vs. 64.8°C measured, while for the 304 W case it was 70.2°C calculated vs. 73.5°C measured. In the 304 W case, the clock die was calculated at Tj=99.6°C but measured at 96.0°C and 100.7°C in two measurements only about a minute apart. Most of the measurements are within about ±4°C of the calculated values, although one particular diode consistently gave values around 10-12°C lower than expected, which might well be an experimental problem with this diode. In general, the quality of fit to the experimental temperature data indicated that our model was very useful as a first order approximation for this design. IV. CONCLUSIONS AND POSSIBLE FUTURE IMPROVEMENTS Spray cooling and polycrystalline diamond substrates have demonstrated a critical capability that is essential to future high performance equipment. This technique demonstrated continuous heat extraction from the diamond MCM fins without exceeding a maximum set junction temperature of 90°C on the integrated circuits within the MCM during operation. This has been adequately demonstrated in this 3-D interconnected cube and shows the heat extraction capability of fluorochemical spray and synthetic polycrystalline diamond for reliably cooling microelectronic circuits. As already stated, further improvements in thermal performance can be made by: (1) an ultra thin die attach; (2) active fluid pressure control and feedback to keep the spray optimized

for the heat load; and (3) going to a more advanced z-axis pliable interconnect to improve high performance signal propagation. New types of non-fuzz button z-axis pliable interconnect technology have already demonstrated that they will handle an even higher density of pliable z-axis interconnects than fuzz buttons. Other performance enhancements could include flip-chip die attach and high density area array interconnect for the die. This is a natural technology extension to exploit the performance capability of the high density thin film copper polyimide interconnect transmission line wiring system available on both sides of the diamond MCM substrate. REFERENCES [1] Boudreaux, P. J., Thermal Aspects of High Performance Packaging with Synthetic Diamond, Applications of Diamond Films and Related Materials: Third International Conference, pp. 603-610, National Institute of Standards and Technology, Gaithersburg, MD, August 21-24, 1995. [2] Boudreaux, P.J., Conner, Z., Culhane, A., Leyendecker, A. J., “Thermal Benefits of Diamond Inserts and Diamond-Coated Substrates to IC Packages”, 1991 Digest of Papers of the Government Microcircuit Applications Conference, GOMAC 1991, pp. 251-256, DTIC number B-160081. [3] Jackson, K., Thurston, D., Boudreaux, P., Armstrong, R., “Fracturing of Industrial Diamond Plates,” Journal of Materials Science, Volume 32, 1997, pp. 5035-5045. [4] Davies, G., Editor, Properties and Growth of Diamond, INSPEC, the Institution of Electrical Engineers, London, England, 1994, p.34. [5] Tilton, D., Boudreaux, P., Murphy, J.,”Embedding High Performance COTS Electronics in Harsh Environments,” 1997 Digest of Papers of the Government Microcircuit Applications Conference, GOMAC, 1997, pp.239-242, DTIC number B-222171. [6] Pecht, M., Handbook of Electronic Package Design, Marcel Dekker, Inc., New York, 1991, p.484.

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[7] Sienski, K., Eden, R., Schaefer, D., “3-D Electronic Interconnect Packaging”, 1996 IEEE Aerospace Applications Conference, 1996. [8] Leyendecker, A. J., “Thermal Effects in Diamond Substrates”, Internal Technical Report - TR-R54-001-91, January 25, 1991. [9] Eden, R. C., “Application of Bulk Synthetic Diamond for High Heat Flux Thermal Management”, High Heat Flux Engineering II, SPIE, Volume 1997, 12-13 July 1993, pp.124-135. [10] Harris, D., Pecht, M., “A Reliability Study of Fuzz Button Interconnects”, Circuit World, Volume 21, No. 2, 1995, pp.12-18.

[11] Jackson, op. cit. [12] Incropera, Frank, DeWitt, David, Fundamentals of Heat and Mass Transfer, Fourth Edition, John Wiley & Sons, New York, 1996, pages 110-134.

APPENDIX I Thermal Analysis of Diamond 3-D MCM Results

Comparison of the Volume Power Density (Watts per cubic inch) and corresponding Peak Computational Throughput per cubic inch (Peak MFlops per cubic Inch), power limited, assuming DEC 21064 “Alpha” chip power-MFlops normalization. R.C. Eden