A Uniform Temperature, Ultra High Heat Flux
`Liquid Cooled, Power Semi-Conductor Package
`
`Arthur H. Iversen
`Coriolis Corporation
`Campbell, California 95008
`
`and
`
`Stephen Whitaker
`Department of Chemical Engineering
`University of California
`Davis, California 95616
`
`Abstract - A new type of heat exchange process is described for use
`in semiconductor heat sinks. This involves the use of subcooled,
`nucleate boiling at concave curved surfaces where radial
`acceleration. v%, can be used to develop significant and beneficial
`buoyancy forces. This system provides a heat transfer surface with
`a uniform temperature, i.e.. the boiling point of the fluid, and
`requires no vapor-liquid separation process since all vapor bubbles
`are immediately condensed in the subcooled liquid. Use of low
`boiling point dielectric fluids, e.g. FC 72 (BP 56'C), establishes a
`uniform heat sink temperature that is independent of location or
`environment and does not require elaborate coolant and/or
`environmental conditioning. The low junction to fluid specific
`thermal resistance, 0jf-0.1' C/WcmZ, and high heat flux
`dissipation capability, -6,000 W/cm2, inherent in this design lends
`itself to a
`system design with high reliability and lower
`manufacturing costs. Failure rates are reduced and leakage currents
`are lowered by virtue of lower device operating temperatures, i.e.
`low boiling point coolants. Elimination of dry contacts and large
`mechanical forces, e.g. Disc Type Package, substantially reduces
`life shortening thermal stresses and lowers thermal resistance. The
`design lends itself to compact lightweight construction for high
`voltage series operation of devices and permits simplified parallel
`operation of high power devices.. Experimental studies at Coriolis
`Corporation have demonstrated a heat flux of 6300 watts/cm2 using
`FC77 with a pressure drop of only 2.70 pounds per square inch,
`over a one centimeter long heat transfer channel. In this paper we
`describe the design, construction, and operdtion of a liquid-cooled
`high power semi-conductor package and cooling technique for
`improved device reliability, simplified parallel operation of multiple
`devices, and efficient high voltage series construction.
`
`I. INTRODUCTION
`
`The performance of high power devices such as diodes,
`thyristors, GTO's, MOSFETS etc. is often limited by the heat
`removal capabilities of the thermal package. To achieve reasonable
`heat flux removal rates, device packages are often bulky and heavy,
`and this can complicate the packaging of these devices for series,
`parallel or series-parallel operation. For parallel operation, the need
`to maintain uniform junction temperatures is further complicated by
`those applications subject to surge-current overloads that can cause
`hot spots within a device.
`A common method for power device cooling is the use of high
`mechanical forces (up to 10 tons) to press the Disc Type package
`against the external heat sink which employs massive and bulky
`clamping springs and insulators. The sliding contacts resulting
`from this method have relatively high thermal resistance so the
`performance of the device in both steady state and surge is limited,
`and this construction additionally suffers from degradation of
`thermal fatique life (Glascock and Webster, 1983)[ 11.
`In this paper we propose a novel packaging and cooling scheme
`that addresses the shortcomings of conventional packaging and
`cooling techniques for high power devices, e.g. Disc Type Package.
`
`is pinned at the boiling temperature of the coolant thereby
`providing uniform device junction temperatures system wide,
`from cabinet to cabinet and room to mom;
`a) Simplifies parallel operation of devices.
`b) Thermal resistance change with transient or steady state
`operation should be minimal and confine substantially to
`that due to the silicon temperature rise by virtue of the
`elimination of mechanical pressure contacts and their
`associated degration of thermal fatigue life.
`c) Combined with (2) provides suppression of hot
`spots.
`d) Combined with (2) enables sustained surge current
`operation.
`4) Compact, light weight construction results from efficient
`heat transfer from the silicon chip substrate, e.g. negligible
`lateral heat transfer resulting in a heat transfer surface, i.e. the
`substrate, that is the same size as that of the chip. The dielectric
`coolant is an excellent insulator, e.g. 38 KV/O.l" for FC72 and
`therefore package size is principally dictated by external
`electrical breakdown characteristics of the housing. For
`example, 60 Thyristors (4500V/2000A) could be seriesed to
`provide 120KV/2000A.operation. It is estimated that package
`size might be about 3 0 long, 8" diameter and weigh about 50
`lbs. Curved surface cooling could increase device rating to
`8.009 A at the expense of the long term surge current safety
`margin.
`5 ) Cost effective design is provided on two levels; more
`efficient heat transfer permits higher device ratings, that is a
`53mm device can be substituted for a 77Mm or lOOmm device,
`e.g. a doubling or quadrupling of heat flux removal,
`alternatively or in combination, substantial perfomnce margin
`can be achieved to permit sustained operation under surge
`current conditions. Compact design reduces system space
`requirements and uniform junction temperatures simplifies
`fail-safe circuit design. Incorporating a large number of devices
`in a hermetically sealed housing eliminates the individual device
`packaging costs, e.g. ceramic housing and associated
`component and labor costs.
`
`11. CONSTRUCTION
`
`- HELIARC FLANQE
`
`,
`
`I
`
`I i
`
`A. Benefits Include;
`1) Operation of devices at higher ratings, e.g. substitution of
`53mm devices for 77mm or l0Omm devices with attendant cost
`savings.
`2) Longer device life by virtue of lower junction temperatures
`[24] and reduced leakage, as provided by low thermal
`resistance construction and low boiling point coolants.
`3) Improved system reliability as provided by subcooled
`nucleate boiling heat transfer wherein the heat exchange surface
`89<382792-0/89/0000-1340S01.00 0 1989 IEEE
`
`,- HELIARC FLAN=
`d
`
`Figure 1
`
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`
`LIBERTY EXHIBIT 1042, Page 1
`
`

`

`Figure 1 illustrates an insulating structure to house an assembly
`of power devices. The housing may be cast from a suitable epoxy
`such as is employed for HV insulators. Alternative insulating
`materials of construction include ceramic or glass. Flanges for
`heliarc welds are employed at both the positive and negative
`terminals to provide hermetic seals.
`
`/ HV ELECTRODE
`
`curved surface coolant channels. The coolant, being a dielectric,
`contributes to the electrical insulation of the package, e.g.
`38KV/O.1" for FC72 fluorocarbon. In addition to cooling the
`device, coolant channels may be provided to divert a predetermined
`coolant flow over the device electrical interconnects to remove
`resistive heat losses. For clarity of illustration of the curved surface
`cooling concept, single curved surface cooling is shown. For
`power devices of large dimensions, periodic curved surface cooling
`as described in U.S. Patent #4,712,609 [23] would be employed.
`
`m
`
`i
`
`+ ELECTRODE
`
`
`
`CHIP
`
`\- ELECTRODE
`
`FLOW DIVERTER
`
`SERIES CONNECTION
`
`QND ELECTRODE
`HELIARC FLANQE
`
`Figure 2 illustrates a preassembled stack of power devices
`shown for convenience as electrically connected in series.
`Alternative connections are parallel or a combination of
`series-parallel connections as might be employed for fail-safe
`ogartioa.
`
`Positive Terminal
`
`Housing
`
`Flow
`Diverter
`
`Curved
`Heat Transfer
`Substrate
`
`Chip
`
`Coolan i t Out/et
`
`,/'
`
`Coolant Inlet-
`Figure 3 illustrates an angled cross section view of the stack of
`power devices of Fig. 2 mounted in the housing of Fig. 1. Coolant
`flow is shown progressing up the input coolant conduit and then
`branching off at 90' to progressively feed, in parallel, each of the
`
`INPUT
`COOLANT
`CONDUIT
`
`Figure 4 illustrates a top-down, cross section view of the
`packaged devices to show input and discharge coolant channels and
`the method for alignment of the preassembled power device stack
`within the housing.
`b. Devicecooling
`Conventional high power device cooling, e.g. Disc Type
`Packages, are reputed to have maximum heat flux removal rates of
`about 150 W/cm2 and utilize massive and bulky clamping springs
`and insulators. Curved surface cooling has demonstrated 17
`KW/cm2 (Gambill 19 Greene, 1958)[2], 24 KW/ cm2 (Leslie et al
`1983)[3] and 6.3 KW/ cm2 (Iversen and Whitaker 1984)[4].
`Sub-cooled nucleate boiling heat transfer for flow over concave
`curved heat exchange surfaces offers substantial advantages.
`Curved surface sub-cooled nucleate boiling at the device heat
`exchange surface acts effectively as an infinite heat sink thereby
`maintaining a substantially constant heat sink temperature over a
`broad range of device heat fluxes from device to device and package
`to package independent of environment or location. Junction
`temperature is then the product of the heat flux and thermal
`resistance of a thin high thermal conductivity substrate, e.g.
`tungsten, plus the boiling point of the coolant, to which is added a
`superheat which depends upon the heat flux. Low boiling point
`fluorocarbon coolants, e.g. FC 87(32' C), or FC 72(56' C), enable
`high heat fluxes to be obtained while maintaining junction
`temperatures within acceptable limits. Thus, the heat transfer
`characteristics of the heat sink are no longer limited by mechanical
`contacts and thick heat sink members.
`Device junction-to-fluid thermal resistance, 06 is strongly
`influenced by the construction technique utilized. By employing
`diffusion bonded device construction, Glascock [ 11 demonstrated a
`substantial drop in junction -to -case thermal resistance, Ojc. over
`dry contact construction while still using Disc Type Package heat
`sinking. With liquid cooling, the dry sliding Disc Type Package
`heat sink contact is replaced with one of high compliance, negligible
`pressure and total contact for optimum performance. To simplify
`calculations and to provide a conservative design, the thermal
`resistance is calculated for single sided cooling. With double sided
`cooling. e.g. the use of structured copper, thermal resistance of
`about 60% of that for single sided cooling may be obtained. Using
`Nuegebauer's [13] junction to fluid specific thermal resistance Ojf of
`0.1' Wan* for bonded structures resulting in a thermal resistance
`of -0.002' W for a 77mm device and -.0012' c/w for a 100 mm
`device would provide a junction temperature rise AT of 15' C at the
`conventional maximum heat flux of 150 W/cm 2 . Using FC72 (BP
`56' C) as a coolant would result in a conservative junction
`temperature of 71' C (56' C + 15' C) plus superheat resulting in
`1341
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`LIBERTY EXHIBIT 1042, Page 2
`
`

`

`lower leakage currents and enhanced device life. With double sided
`cooling, the thermal resistance of the 77mm devices would reduce to
`about 0.0012' C/W, as contrasted to greater than 0.01' C/W for
`Digital Type Package construction. Thermal resistance change with
`transient or steady state operation should be minimal and confined
`substantially to that due to the silicon temperature rise by virtue of
`the elimination of mechanical pressure contacts. Direct liquid
`cooling eliminates Disc Type Package related thermal stress and
`associated device life degradation.
`B. Coolant ComDatibility
`
`With respect to coolant compatibility, the use of pure
`fluorocarbons, e.g. 3M, FC72 (BP 56' C) or FC87 (BP32.C)
`appears to present no difficulties for device cooling. In an ongoing
`experiment, 3M has been operating bare chip devices in FC72 for
`over 4 1/2 years with no difficulties[5]. The Cray 3 will employ 3M
`fluorocarbon bare chip cooling. Virtually all prior work reported
`with fluorocarbon cooling has been with the chloro-fluorocarbon
`R-113 (BP47.C). R113 has been reported as reactingwith
`aluminum, copper and other similar metals, Eriksson et a1[6]. The
`authors experience has been similar to the above with respect to
`copper and zinc in addition to experiencing corrosion of 400 series
`stainless steel. The pure fluorocarbons do not seem to present any
`difficulties for packaged or bare chip cooling nor do they appear to
`present a threat to the environment.
`C. Reliability
`A recent field study by the military provided a correlation
`between failure rate models and real life situations. From the data,
`device temperatures of 5@ 100' C are acceptable and 100-125'C are
`marginal [24]. Employing the temperature related failure rate table
`of Corman et al. [24] a comparison of relative failure rates for Disc
`Type Packages and curved surface cooling can be made. At a 110'C
`ju'nction temperature for Disc Type Packages, the failure rate would
`be 10 times higher for CMOS and 4 times higher for Bipolar as
`compared to a 71'C (FC72) junction temperature, i.e. 150 W/cm2,
`with curved surface cooling. At a 47'C (FC87) junction
`temperature, Disc Type Package failure rate would be 38 times
`higher for CMOS and 13 times higher for Bipolar as compared to
`curved surface cooling. At a junction temperature of 125'C, the Disc
`Type Package failure rate increases to 20X for CMOS and 6.4X for
`Bipolar over 71'C(FC72) curved surface cooling. Compared to
`47'C operation (FC87), it is 80X higher for CMOS and 20X for
`Bipolar. A further failure mode is caused by thermal stresses which
`arise from 1)the clamping forces employed in Disc Type Package
`heat sinking, and 2) the high temperature excursions that Disc Type
`Packages undergo. In the proposed design, (1 above) is eliminated
`and (2 above) is minimized.
`D. Extended Slarpe Current Tolerance
`By increasing the coolant velocity and using a lower boiling
`point coolant, e.g. FC87 (BP 32'C), high surge currents can be
`tolerated for extended periods. For example, using FC87 (BP
`32'C) and a 125'C max junction temperature, the permissible AT
`temperature rise is 93'C. Assuming 1O'C for super-heat. the
`junction to heat exchange surface AT is 83'C. Using the junction to
`heat exchange surface specific thermal resistance Ojc of 0.1 C.W
`cm2, the dissipated power is then 830 W/cm2, an almost 6X
`increase over the Disc Type package maximum heat flux of 150
`W/cm2. For a 77mm device, this corresponds to a continuous
`dissipation of 38KW. With double sided cooling, the overall
`specific thermal resistance would decrease to about 0.06' C/W cm2
`thereby increasing the power dissipation for a AT of 83'C to about
`1,380 W/cm2 resulting in a 9X increase in the continuous surge
`c m n t rating over standard operational ratings, e.g a 2,000A rated
`device (150 W/cmz dissipation) could be operated at a sustained
`surge cument of 18,000 A (1,3980 W/cm2 dissipation). It should be
`noted that the above value of 1.380 W/cm2 is well below the 6
`~ w / c m 2 demonstrated in the Iversen-Whitaker experimenti41..
`E. Subcooled Nucleate Bo iling
`The process of subcooled. nucleate boiling is an especially
`efficient means of heat removal. Nucleate boiling traditionally
`produces extremely high heat fluxes, and when the liquid is
`subcooled we have the advantage of a heat transfer system in which
`
`1 -
`
`only a single phase is present in the entrance and exit smams. In
`subcooled boiling. the vapor bubbles leave the heat transfer surface
`and then collapse in the liquid as illustrated in Figure 5.
`/ / " " " / / " " ~ ~ ~ ~ ~ ~ ' ~ ' ' ' '
`
`SUBCOOLED
`
`a
`
`Fig. 5 Bubble Generation and Collapse During Subcooled Boiling
`The high rates of heat transfer that occur during nucleate boiling
`are caused by the intense liquid motion that is generated by the
`growth and subsequent departure of the vapor bubbles from the heat
`transfer surface. These vapor bubbles, which generate the desired
`fluid motion, are also the source of the boiling crisis known as the
`critical heat flux or "burnout" condition. As the heat flux rises, the
`number of active nucleating sites (one of which is indicated in
`Figure 5 ) increases and the concentration of vapor bubbles in the
`neighborhood of the heat transfer surfaces increases. When
`sufficient bubble coalescence occurs, a stable vapor film develops
`and this usually leads to system failure. A high rate of vapor bubble
`removal from the heat trqnsfer surface is the key to an efficient heat
`transfer process, and there are two principal mechanisms which can
`be used to enhance the rate of removal of vapor bubbles: 1) the
`effect of shear and turbulent dispersion caused by a forced flow of
`liquid past the heat transfer surface, and 2) the effect of an increased
`body force caused by an acceleration of the liquid normal to the heat
`transfer surface. This increase in the body force can be generated by
`flow past a goncave surface.
`The effect of forced flow on the critical heat flux has been
`reviewed by Katto [21] for a wide variety of configurations. While
`the critical heat flux depends on the flow configuration and the
`nature of the heated surface, one can conclude that the critical heat
`flux is roughly proportional to the square root of the liquid velocity,
`i.e.,
`
`qc-vlR , forced flow
`(1)
`Clearly this is an approximation since experimental results can be
`found for which qc is proportional to vln and for which qc is
`proportional to vm. For our purposes the representation given by
`Equation 1 is very attractive since it nicely descriks the work of
`Gambill and Greene [2] and the follow-up study of Mayersak et a1
`[7]. The effect of shear flow on the boiling process is extremely
`complex and not yet completely understood. However, it is clear
`that a turbulent shear flow tends to break vapor bubbles away from
`the heat transfer surface and transport them into the surrounding
`liquid. This enhances the boiling process and gives rise to an
`increase in the critical heat flux as indicated by Equation 1. While
`the critical heat flux must be avoided in the operation of most
`systems, Equation 1 is still quite useful since it describes the effect
`of a shear flow.
`The influence of buoyancy effects on the nucleate boiling
`process is clearly evident in the process of "pool boiling" such as
`one observes when a pan of water is heated on a stove. In that case
`the buoyancy force, generated by the difference in the vapor and
`liquid densities and the gravitational force, causes the vapor bubbles
`to be propelled upwards away from the heat transfer surface As
`early as 1950 Kutateladze [8] was able to deduce that the critical heat
`flux during pool boiling was proportional to the fourth root of the
`acceleration normal to the heat transfer surface, i.e..
`qc - (a/g)I" , pool boiling
`is the standard
`Here a
`represents the acceleration and g
`gravitational acceleration, i.e., one "gee". Kutateladze's result was
`corroborated by the hydrodynamic stability analysis of Zuber [9]
`and confirmed by the experimental studies of Usisken and Siege1
`[ 10). The implications of Equation 2 for micro-gravity environments
`are obvious, and a survey of this general problem was presented by
`Siege1 [Ill in 1967.
`
`(2)
`
`1342
`
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`
`LIBERTY EXHIBIT 1042, Page 3
`
`

`

`F. Flow Past Curved Surfaces
`When a liquid flows past a concave surface at which nucleate boiling
`occurs, two flow phenomena influence the critical heat flux. First,
`the boiling process is enhanced because of the shear generated by
`the tangential fluid motion as illustrated in Figure 5 and suggested
`by Equation 1. In addition, the radial acceleration, a = v2/r, gives
`rise to a buoyance force which propels the vapor bubbles away from
`the heat transfer surface as illustrated in Figure 6.
`
`NUCLEATING SITE
`Figure 6 Bubble Generation and Collapse During Subcooled
`Boiling in a Curved Channel.
`This effect was first investigated by Gambill and Greene [2] who
`used a swirl flow to achieve a critical heat flux of 17 kw/cm2. This
`represented the highest known heat flux in 1958 and it clearly
`indicated that curved surface flow could be used to generate an
`exceptionally efficient boiling process. This exceptional efficiency
`results from the fact that the liquid velocity is used to generate a
`buoyance force that is normal to the heat transfer surface, whereas
`the drag force generated in linear flow is ginpent to the heat transfer
`surface. Thus, with curved surface flow the vapor bubbles are
`subject to a force which propels them directlv awav from the heat
`m s f e r surface and into the subcooled liquid where they collapse.
`The original discovery of Gambill and Greene [2] has been
`utilized by researchers at Hewlett-Packard Laboratories (Leslie et al
`[3]) to develop an enhanced brightness X-ray source. Using a
`cone-shaped anode with a concave radius of curvature of 2
`centimeters and a fluid velocity of 10,OOO cm/s, Leslie et a1 were
`able to obtain a heat flux of 25 kw/cm2. However, this was not a
`critical heat flux and they suggested that their curved surface device
`was capable of producing a heat flux two to three times larger than
`the measured value of 25 KW/cmz. In 1984, experiments were
`carried out by Iversen and Whitaker [4] using FC 77 as a coolant
`and a curved channel similar to that illustrated in Figure 6. With a
`radius of curvature of 2.5 centimeters and a velocity of 1340 cm/s
`(a/g = 726). a "near-bumout" heat flux of 6.3 kw/cm2 was obtained.
`On the basis of the studies of Gambill and Greene [2] and our
`own experimental work, we have developed an empirical equation
`for the critical heat flux for FC 77. This is given by
`
`(3)
`
`where qc is in kw/cm2, v is in cm/s, and the subcooling, ATsub, in
`'C. When the radial acceleration is negligible, Equation 3 reduces to
`the form given by Equation 1. When a/g is large compared to one,
`we have
`
`(4)
`and under these circumstances the critical heat flux becomes a linear
`function of the velocity
`
`qc - v, forced flow past a concave surface
`
`(5)
`A comparison of this result with Equation 1 clearly indicates a
`dramatic improvement in the efficiency of the boiling process. and
`this improvement is directly related to the radial acceleration that is
`generated by concave surfaces,
`While the heat fluxes reported by Gambill and Greene [2], Leslie
`et al[3], and Iversen and Whitaker [4] are much higher than those
`
`currently encountered in semiconductor cooling processes, the
`efficiency of curved surface nucleate boiling is not to be ignored. In
`the next section we indicate how this efficiency can be successfully
`Utilized.
`G. Semiconductor Cooling
`
`In Figure 3 we have shown a power semiconductor cooling
`configuration [12]. The semiconductor chips are bonded to the
`substrated heat sinks with each having its own curved heat transfer
`surface. Alternatively, structured cooper or a suitable silicon
`substrate could be employed. The substrate shown is molybdenum
`or tungsten which provides a low thermal resistance and a good
`match in terms of coefficients of thermal expansion. From Table III
`of Neugebauer et al [I31 we find the thermal resistance of the
`chip-solder- molybdenum assembly to be 0.1 IO'C/(W/cm2). As an
`example of the use of this type of system, we consider the following
`conditions.
`
`, radius of curvature = 3cm
`fluid = FC 77
`, hTsub - 70'c
`fluid velocity = 54 cm/s
`
`(6)
`
`For these conditions, which provide a/g = 1, we can use Equation 3
`to predict a critical heat flux of
`
`qc = 370 watts/cm2
`
`(7)
`
`If the heat flux at a semiconductor chip is 200 watts/cm2, one could
`expect to safely operate under the conditions represented by
`Equation 6. The corresponding critical heat flux for a linear flow
`system (a/g = 0) would be 185 watts/cm2 and such a system would
`burnout if the operating heat flux were 200 watts/cm2.
`The thickness of the flow channel illustrated in Figure 2 is a
`parameter in an optimization analysis; however, we have found that
`a channel depth on the order of 0.2 cm is generally acceptable. For
`this channel depth and a velocity of 54 cm/s, the pressure drop per
`centimeter of channel length is 0.004 psi when the channel is
`assumed to be hydraulically smooth. Under these circumstances a
`one meter long flow channel of the type illustrated in Figure 32 will
`give rise to a pressure drop on the order of one half pound per
`square inch. From these calculations we see that the pressure drop
`in the heat transfer channel is not a matter of serious concern. To
`emphasize this point, we remark again that experiments have been
`performed (Iversen and Whitaker [4]) in which a heat flux of 6300
`watts/cmz was obtained in a curved channel system for which the
`pressure drop was 2.70 psi per centimeter.
`As we mentioned earlier, it is the intense fluid motion generated
`by bubble growth and departure from the heat transfer surface that
`leads to the high heat fluxes associated with nucleate boiling. This
`intense fluid motion can also be obtained by the use of sufficiently
`high liquid velocities. A dramatic example of this is supplied by the
`work of Tuckerman [14] who used the classical method of extended
`surface heat transfer (Whitaker [ 151) to obtain a heat flux of 790
`watts/cmz using water in laminar flow. The absence of boiling
`would appear to give rise to a simpler heat transfer system;
`however, it leads to significant surface temperature gkdients in the
`direction of flow, high pressure drops, and relatively high
`In Table I we have shown the
`temperature driving forces.
`experimental result for water from Tuckerman's thesis [ 141, the
`conversion of these results to FC 77, and the results predicted by
`Equation 3. Both the surface temperam rise in the direction of
`flow and the pressure drop associated with Tuckerman's
`configuration indicate that laminar flow heat transfer is very
`inefficient compared to nucleate boiling at a curved surface. In
`calculating the Coriolis results listed in Table 1, we have used a
`radius of curvature of 3 cm, a liquid velocity of 143 c d s , and a
`subcooling of 70'C. While our experiments and calculations have
`been carried out with FC 77, we expect that semiconductor cooling
`would be carried out with FC 72 which boils at 56'C. At a heat flux
`of 200 watts/cm2 and a thermal resistance of 0.1 1o'C cmZ/watt, the
`temperature drop across the chip-solder-molybdenum assembly
`would be 22'C. If the steady-state superheat in the liquid were YC,
`If lower
`the maximum chip temperature would be 83'C.
`
`1343
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`LIBERTY EXHIBIT 1042, Page 4
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`

`

`Table 1 Comparison Between Laminar Flow cooling and Nucleate Boiling at a Curved Surface w
`
`surface temperature change in the
`direction of flow per centimeter
`
`Tuckenn-
`Water
`22'c
`
`#
`FC 77
`49'c
`
`negligible
`
`108'C
`790 watts/cm2
`
`-10'c
`790 watts/cm2
`
`temperature driving force
`35'C
`heat flux
`790 watts/cm2
`pressure drop per centimeter
`22 psi
`temperatures are required one could use the flmrcarbon R11 which
`boils at 24' C or FC87 (32' C BP).
`Temmture Overshw
`
`36 psi
`0.022 psi
`When the temperature of the solid is increased, the pressure of the
`vapor will increase and the region occupied by the vapor will expand
`until the vapor-liquid interface reaches the position shown in Fig. 8.
`Under these circumstances, the effect of surface tension is reversed
`and the pressure of the vapor is given by
`
`The increase in the pressure of the vapor in going from the
`configuration shown in Fig. 7 to that shown in Fig. 8 is given by
`
`inagase in vapor pressure
`in site gorn
`
`the nuleation) to Be from temperature
`
`overshoot site
`
`20[&
`
`E
`
`+ k]
`
`(1 0)
`
`For most systems the superheat required to maintain steady
`nucleate boiling is on the order of 5-10' C; however, the gansient
`suDerheat or "temperature overshoot" may be considerably larger.
`This effect was apparently first observed by Cory and Foust [ 161 in
`a study of pool boiling using ether, normal pentane, and Freon 113.
`They observed temperature overshoots on the order of 10-15' C,
`and their results were comparable to those obtained by Bankoff et al.
`[ 171.using methanol. A detailed study of temperature overshoot was
`camed out by Bergles and Chu [ 181 for porous metallic surfaces,
`and they found that the temperature overshoot for Freon R-113 was
`about double that of water for pool boiling conditions. The
`maximum observed temperature overshoot for R-113 was about
`8' c.
`Bar-&hen and Simon [20] have pointed out that temperature
`overshoot can present a serious problem with the use of dielectric
`fluids such as FC77. Since the fluorocarbons characteristically have
`a low surface tension and contact angle they can penetrate deep into
`the pores and cavities that exist on any solid surface. In the absence
`of non-condensable gases, a re-entrant cavity must exist in order to
`produce a stable nucleating site. It seems clear that fluids with low
`surface tension and low contact angle will fill many potential
`nucleating sites, thus leaving only a small fraction of re-entrant
`cavities to provide nucleating sites. This situation is illustrated in
`Fig. 7 where we have shown a re-entrant cavity as a nucleation site.
`In the absence of non-condensable gases, the pressure of the vapor
`in the cavity can be expressed as
`
`Here Pvap represents the vapor pressure which can be determined as
`a function of the temperature by the Clausius-Clapeyron equation,
`Pliq represents a local ambient pressure in the liquid, and0 is the
`surface tension. The radius of curvature of the gas-liquid interface
`shown in Fig. 7 is designated by Rn, and it is important to note that
`the effect of surface tension is to reduce the pressure of the vapor in
`the cavity. It is this reduction of the pressure that generates a stable
`nucleating site.
`
`Pvap Pri-241 R"
`
`Fig. 7 Nucleating Site
`
`Fig. 8 Temperature Overshoot Site
`
`The temperature associated with this change in pressure will be
`described by the Clausius-Claypeyron equation, and if Ro is
`relatively small one can expect a large temperature overshoot. A
`further increase in the temperature will force the vapor-liquid
`interface beyond the constriction illustrated in Fig. 8 and the steady
`superheat condition shown in Fig. 9 will be achieved. Under these
`circumstances the pressure of the vapor will be given by;
`
`1344
`
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`
`LIBERTY EXHIBIT 1042, Page 5
`
`

`

`Fig. 9 Steady Superheat Site
`
`however, one must remember that the condition illustrated in Fig. 9
`is a dvnam ic condinon and the radius of curvature, Rs, should be
`thought of as some appropriate average value. An equation
`analogous to 4. 10 can be written as
`
`}
`
`in vapor pressure
`in going from the temperature
`overshoot site to the steady
`superheat site
`
`=
`
`4
`4
`
`-
`
`(' 2,
`
`force - pv2
`
`m
`
`loytr
`
`I
`
`bbyer
`
`Lomimr y b I o y J 1
`
`H i R q n d d s nu-
`M
`
`Fig. 10 Qualitative Description of Wall Effects in Turbulent Flow
`
` Dim region (Whitaker,
`This region of flow is known as the m h
`Sec. 8.2, 1191). On the basis of numerous experimental studies of
`flow in pipes the thickness of the laminar sublayer can be estimated
`by
`
`This result can be used to construct an estimate of the local velocity
`which is given by
`
`and a linearized version of the Clausius-Clapeyron equation can be
`used with this result to estimate the temperature overshoot as
`
`- (g), y
`
`6
`
`- v , y > 6
`
`"IOC
`
`Here y represents the distance measured from the mean radius
`illustrated in Fig. 4 and v represents the velocity in the turbulent
`core.
`It should be clear at this point that the cavik illustrated in Fig. 9
`is embedded in one of the roughnesses shown in Fig. 10. Because
`of the curved streamlines indicated in Fig. 9, the pressure in the
`liquid at the throat of the cavity is lowered by an amount which we
`estimate as
`
`{reduction} - Pvk h/r
`(18)
`Here h is the height of the protrusion illustrated in Fib. 9 and r is
`the radius of curvature of the streamlines over the protrusion. If we
`think of Eq. 9 as a static relation in which
`is determined by the
`geo