Appl. Phys. Lett. 115, 254102 (2019); https://doi.org/10.1063/1.5133795 115, 254102

© 2019 Author(s).

Tunable, passive thermal regulation throughliquid to vapor phase changeCite as: Appl. Phys. Lett. 115, 254102 (2019); https://doi.org/10.1063/1.5133795Submitted: 26 October 2019 . Accepted: 26 November 2019 . Published Online: 17 December 2019

Tanya Liu , James W. Palko , Joseph S. Katz , Ercan M. Dede , Feng Zhou, Mehdi Asheghi, andKenneth E. Goodson

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Tunable, passive thermal regulation through liquidto vapor phase change

Cite as: Appl. Phys. Lett. 115, 254102 (2019); doi: 10.1063/1.5133795Submitted: 26 October 2019 . Accepted: 26 November 2019 .Published Online: 17 December 2019

Tanya Liu,1 James W. Palko,2 Joseph S. Katz,3 Ercan M. Dede,4 Feng Zhou,4 Mehdi Asheghi,1

and Kenneth E. Goodson1,a)

AFFILIATIONS1Department of Mechanical Engineering, Stanford University, Stanford, California 94305, USA2Department of Mechanical Engineering, University of California, Merced, Merced, California 95343, USA3Department of Electrical Engineering, Stanford University, Stanford, California 94305, USA4Electronics Research Department, Toyota Research Institute of North America, Ann Arbor, Michigan 48105, USA

a)Author to whom correspondence should be addressed: goodson@stanford.edu

ABSTRACT

The increasing complexity and power density of electronic systems have necessitated the development of thermal circuits that can not onlyremove but actively redirect the flow of heat. Passive thermal regulators are promising as heat routing components that can mitigate largetemperature spikes by transitioning between high and low resistance states without external actuation. Existing regulators, however, are ofteneither limited to fixed temperature regulation ranges due to solid-state material property limitations or are difficult to package in a compactform factor. Here, we present a passive, compact (1 � 1 cm2 active area), and tunable thermal regulator that functions based on the dynamicsof vapor transport through a noncondensable gas cavity. The device demonstrates a switching resistance ratio of 4 in response to variationsin the input power ranging from approximately 0.6 W to 14 W. The device is also able to set the temperature difference across the hot andcold sides to a fixed, “clamped” value that is reasonably independent of heat flow. Both the overall resistance and the clamped temperaturedifference can be easily tuned by presetting the pressure of the noncondensable gas. We present a brief analysis of the physical operatingprinciples of the device and lay the groundwork for the development of future passive and tunable thermal circuitry components.

Published under license by AIP Publishing. https://doi.org/10.1063/1.5133795

The ability to route heat analogously to electricity is a compellingconcept with promising applications in various space-constrained,power dense systems. Conventional thermal management solutionstargeting merely heat dissipation are nonoptimal for systems withspatially nonuniform and highly transient heat generation.1,2 Thesesystems can benefit from the addition of nonlinear, switchable thermalcomponents for temperature regulation,3 heat flow inversion,4,5 andthermal isolation.6,7 The current library of such components availableto researchers includes thermal switches, diodes, and regulators.6,8–13

Passive components requiring no external input power areparticularly useful and promising. Solid-state devices have leveragedmetal-insulator phase transitions14 or thermal expansion induced flex-ing15 to switch effectively between high thermal resistance “off” statesand low thermal resistance “on” states. These devices, however, areoften limited to fixed temperature regulation ranges tunable onlythrough permanent procedures such as doping16 or may experiencemechanical fatigue after repeated deformation.17 Liquid-vapor phasechange is a relatively tunable, nonlinear thermal process that can be

harnessed for thermal regulation.18–20 One challenge, however, ispackaging the devices in a compact form factor that can be easily inte-grated with existing electronic systems. Variable conductance heatpipes, for instance, are highly effective temperature regulators butrequire a large condenser area to function, limiting their use to large-scale devices such as Stirling engines.21

In this work, we present a passive, tunable thermal device thatutilizes vapor transport in a noncondensable gas (NCG) cavity toachieve a switchable thermal resistance in response to varying levels ofheat flow. Compared to existing liquid-vapor phase change regulators,the device is relatively compact with an active working area of1� 1 cm2. In addition to a switchable resistance, the device is able toclamp the hot and cold sides to a heat flow independent temperaturedifference. The resistance switching and clamped temperature differ-ence, DTc, are tunable based on the pressure of the NCG. We assessthe effectiveness of our device in terms of a conventional switchingratio metric, as well as a nonlinearity coefficient, bc, which evaluatesthe strength of the DT clamping.

Appl. Phys. Lett. 115, 254102 (2019); doi: 10.1063/1.5133795 115, 254102-1

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Figure 1(a) shows a cross-sectional schematic highlighting theworking principles of the device. The device is composed of two piecesof silicon bonded to a Pyrex insert to form a 500 lm thick cavity.Pyrex is utilized in order to reduce parasitic heat conduction outsideof the active phase change region. A 1� 1 cm2 serpentine thin-filmplatinum resistor is patterned onto each side of the device and servessimultaneously as a heater and a resistance temperature detector(RTD) during the experiments. Micropillar arrays are etched into thesilicon by ultraviolet laser ablation to form porous wicks [Fig. 1(b)],and the chamber is filled with a mixture of de-ionized water and NCG(overall fabrication and charging details are given in the supplemen-tary material). As water in the heated wick evaporates, the vapor isdriven through the NCG and condenses on the cold side. The liquidthen recirculates to the hot side through capillary action via groovesetched into the insert sidewalls [Fig. 1(c)]. The NCG acts as a diffusionbarrier to the vapor transport and has an equivalent thermal resistance,RNCG, which varies based on the pressure of the NCG, PNCG, as well asthe temperature difference between the hot and cold sides, DT. As DTincreases, the vapor mass fraction gradient also increases and has a non-linear effect on the vapor transport, reducing RNCG. Figure 1(d) showsthe resistance stack in the active phase change region of the device,which includes the micropillar wick resistances (Rw,h and Rw,c) andliquid-vapor interfacial resistances (Rint,h and Rint,c) in series with RNCG.Parallel heat conduction occurs through the cavity sidewalls (Rp).

The effective thermal resistance across the device is defined as Rth¼ DT/Q, where DT is calculated as the difference in the area-averaged

temperatures of the hot and cold sides, Th,avg � Tc,avg, and Q is thetotal heat input. The uncertainty in the experimentally measured tem-perature using the calibrated heaters as RTDs ranges from approxi-mately 60.4 �C to 60.7 �C (the details are given in the supplementarymaterial). During experiments,Q is incremented steadily to one heaterwith a DC power supply, while the other side of the device is cooledwith a cold plate. The heat flow rate Q is limited in each experiment toapproximately 14 W to prevent degradation of certain experimentalcomponents above 95 �C (the details are given in the supplementarymaterial).

The device was characterized at four different NCG pressures ofPNCG < 0.1 kPa and PNCG ¼ 12 kPa, 23 kPa, and 34 kPa. Rth for eachPNCG is plotted vs Q in Fig. 2. For the baseline case of PNCG < 0.1 kPa,the overall resistance decreases slightly with increasing Q andapproaches a minimum value of approximately 0.55 �C/W. With sig-nificant amounts of NCG present, increasing PNCG directly increasesRth for a given Q and shifts the entire curve upwards. This is particu-larly evident at low Q, as increasing PNCG to 34 kPa raises Rth byalmost 400% over the baseline case. AsQ increases, however, the vapormass fraction gradient between the hot and cold sides also increasesand reduces the effect of the NCG. This is evidenced by the steadydecline of Rth with increasing Q for the different PNCG values consid-ered. With NCG present, the device essentially acts like a thermalswitch that responds passively to variations in Q. When placed in par-allel with a temperature sensitive component of comparable resistance,the switchable Rth behavior could be leveraged in combination with aheat spreader or similar to act as a heat flow surge protector. If anactive regulation scenario is desired, the amount of NCG could beutilized as the switching mechanism by dynamically modulating PNCGat a given heat flow input. The dynamic scenario opens up a largerrange of possibilities for device operation but would require theimplementation of a freezing cycle or additional system level compo-nents to prevent excess loss of water vapor during multiple chamber

FIG. 1. (a) Operating principles of the device. The NCG acts as a diffusion barrierfor vapor transport and results in a variable thermal resistance, RNCG. (b) Scanningelectron micrograph (SEM) of the laser ablated micropillar wick structure. (c)Closeup of the laser-etched sawtooth groove in Pyrex for condensate return. (d)Thermal resistance network for the device. RNCG is in series with the micropillarwick resistances (Rw,h and Rw,c) and liquid-vapor interfacial resistances (Rint,h andRint,c) and in parallel with conduction through the cavity sidewalls (Rp).

FIG. 2. Rth vs input power, Q, for a range of PNCG values. RNCG dominates forhigher PNCG and causes Rth to decrease passively with increasing Q.

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evacuation/pressurization cycles. For the remainder of this paper, wetherefore focus primarily on the passive scenario, where PNCG wouldbe tuned and preset during device fabrication to obtain the desiredoperating characteristics.

We evaluate the resistance switching in terms of the conventionalswitching ratio metric, Roff/Ron. As the off and on states of our devicedepend on Q, we define Roff and Ron as Rth at the minimum and maxi-mum input powers considered of approximately 0.6 W and 14 W,respectively. With this definition, the maximum switching ratioobserved in the experiments is 4 for PNCG¼ 12 kPa. This is not neces-sarily the maximum potential switching ratio for the device, however,as the full ranges of Q and PNCG were not explored. To estimate themaximum potential switching ratio, we examine the limitations forRoff and Ron. Roff at low Q is limited by the parasitic conduction resis-tance Rp, which we estimate using a finite element simulation to beapproximately 6.7 �C/W (the details are given in the supplementarymaterial). As Q increases and RNCG declines, the minimum value forRon is measured to be 0.55 �C/W from the results for minimal non-condensable gas (PNCG < 0.1 kPa), representing the contributionfrom the wick and interfacial resistances. Based on these estimates,the maximum switching ratio of the current device must be less thanor equal to 12. For future optimization, minimizing the area for side-wall conduction could increase Rp, and using a lower resistance wick-ing structure such as biporous sintered copper could reduce the wickand interfacial resistances within the device.22 Both optimizationstrategies would have interdependent effects on Rth, however, andfurther experimentation is necessary to identify the overall impact onRoff and Ron.

An interesting trend emerges in Fig. 3(a) when Rth is plottedagainst DT as opposed to Q. Except for the baseline case, Rth decreasesrapidly at a given critical temperature difference, DTc, which dependson PNCG. Varying PNCG shifts the critical DTc where the resistancebegins to decline. The values of DTc for PNCG ¼ 12 kPa, 23 kPa, and

34 kPa are approximately 16 �C, 20 �C, and 26 �C, respectively.Further details are given in Fig. 3(b), where DT is plotted vs Th,avg. Inthe presence of NCG, DT becomes clamped to a relatively fixed valueof DTc at a certain threshold temperature, Th,c, which varies based onPNCG. We define the initiation of clamping as the point when DT iswithin 1 �C of DTc. With these criteria, Th,c equals 61 �C, 71 �C, and78 �C for PNCG¼ 12 kPa, 23 kPa, and 34 kPa.

We examine the physics of mass transport in the NCG cavity toelucidate the dependence of DTc and Th,c on PNCG. We assume thatvapor can evaporate and condense freely at the vapor/liquid interfacesabove the porous wick, but there is no significant dissolution of NCGinto the liquid, and the net mass flux of NCG must therefore equalzero. As a mass fraction gradient in NCG naturally exists due to thecomplementary vapor mass fraction gradient, however, the zero fluxcondition for the NCG is preserved through an induced counterdiffu-sion velocity that counteracts the mass fraction gradient driven motionof the NCG. This creates a net advective and diffusive effect on thevapor transport. The vapor mass flux in this scenario can be describedby Maxwell-Stefan diffusion23,24 (further details are given in thesupplementary material). The hot side vapor mass fraction, xh, isrelated to the heat input as

xh ¼ 1þ xc � 1ð Þexp �QzqmDvghfgA

� �; (1)

where qm is the mixture density, Dvg is the binary diffusion coefficient,hfg is the latent heat of vaporization of water, xc is the cold side vapormass fraction, A is the area normal to the vapor transport, and z is thecavity height. Assuming for the moment that all the heat input goestoward phase change, analyzing the behavior of Eq. (1) reveals that asxh approaches 1, dxh=dQ decays exponentially with increasing Q. Interms of temperature, as Th,avg approaches the saturation temperatureof water at the total cavity pressure, Tsat(Ptot), the NCG mass transportresistance decreases such that large increases in heat input lead to

FIG. 3. (a) Rth vs DT for four different NCG pressures. The resistance Rth decreases rapidly at a different critical DTc value for each PNCG other than the baseline case. (b)The temperature difference DT vs Th,avg for the range of PNCG values considered. DT becomes clamped to DTc at a different Th,c value depending on the value of PNCG.

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relatively smaller increases in xh and subsequently Th,avg. This causesdTh,avg/dQ to decline, potentially initiating the clamping behavior forDT. We confirm our theory by estimating Tsat(Ptot) for each PNCG atthe onset of clamping when Th,avg ¼ Th,c (the details are given in thesupplementary material). In each case, the experimentally observedTh,c is within 8%–12% of the estimation for Tsat(Ptot). Note that asTh,avg approaches Tsat(Ptot), there is also the possibility of the initiationof boiling within the wick. In this case, the hot side wick resistancewould potentially decrease and further reduce the total deviceresistance.

Figure 4 provides more insights into the change in hot side tem-perature behavior for Th,avg greater than Th,c. Th,avg and Tc,avg are plot-ted as functions of the input power, Q, for PNCG¼ 34 kPa. The dashedlines are provided as visual guides to track the change in the slope forTh,avg vs Q. As the experimental cold side is not a fixed reservoir, Tc,avgshows a linear dependence on Q due to the constant heat transfer coef-ficient boundary condition enforced by the cold plate. At location 1 onthe plot, dTh,avg/dQ is greater than dTc,avg/dQ and DT increases withincreasing Q. For Th,avg > Th,c, however, dTh,avg/dQ begins to declineas RNCG decreases significantly based on the principles of Maxwell-Stefan diffusion and approaches a value equal to the slope of the coldside temperature. At locations 2 and 3 on the plot, dTh,avg/dQ isapproximately equal to dTc,avg/dQ, initiating the clamping behaviorfor DT.

The DT clamping behavior of the device is comparable to thecharacteristics of an electrical varistor, which demonstrates a current-independent clamping voltage beyond a critical transition voltage.Borrowing from the electrical varistor literature,25 we create a powerlaw fit for Q vs DT to assess the clamping effectiveness of the device.The relation can be written as

Q / DTb; (2)

where b is the nonlinearity coefficient that describes the strength of theDT clamping, and a higher b represents a stronger clamp. The fit is per-formed separately for the leakage region of the device and the clampingregion where DT is pulled to DTc. The fitted curves for Q vs DT basedon Eq. (2) are plotted against the experimental data for each of the dif-ferent NCG charge pressures in Fig. 5, with an average root mean squarediscrepancy between the fits and measurements of 61.8W. The averagefitted nonlinearity coefficients in the leakage and clamping regions arebl ¼ 1.4 and bc ¼ 8.56 1, respectively. The contrast between the twocoefficients delineates the clear change in DT behavior once clamping isinitiated. We note that commercial metal-oxide electrical varistors canachieve clamping coefficients of up to 80.25 A direct comparison of bc isnot necessarily relevant, as the voltage and current operating ranges ofelectrical systems are often orders of magnitude larger than thermal sys-tem analogies (DT and Q). However, as power dissipation levels con-tinue to increase in electronic packages, higher clamping coefficientsand further device optimization may be desirable.

In conclusion, we have demonstrated a passive thermal devicethat leverages vapor diffusion through a NCG barrier to exhibit aswitchable resistance over a range of power inputs. The resistancedecreases by up to 4 times as the input power increases, making thedevice concept suitable for use in passive surge protector systemsagainst sudden power spikes. The device also demonstrates the abilityto clamp the temperature difference across the hot and cold sides to aheat flow independent, fixed value of DTc. Both the resistance switch-ing behavior and the value of DTc are adjustable with the amount ofNCG charge, an advantage over many existing regulators that are lim-ited to fixed operating temperature ranges. The tunability of the devicepresented here provides a valuable addition to the current arsenal ofexisting thermal circuitry components and increases the opportunityfor electrothermal codesign in future systems.

FIG. 4. Th,avg and Tc,avg vs input power, Q, for PNCG ¼ 34 kPa. At location 1, Th,avg< Th,c and clamping has not initiated, causing DT to increase with increasing Q. Atlocation 2, Th,avg < Th,c and dTh,avg/dQ is approximately equal to dTc,avg/dQ (loca-tion 3), which results in the DT clamping behavior.

FIG. 5. Power fit for Q vs DT for PNCG ¼ 12 kPa, 23 kPa, and 34 kPa to extract anonlinearity coefficient, b, to describe the strength of the DT clamping. The averagenonlinearity coefficients for the leakage region and clamping region are bl ¼1.4and bc ¼ 8.56 1, respectively.

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See the supplementary material for further details on device fabri-cation, experimental components, and onset of clamping calculations.

This project was supported by the TOYOTA ResearchInstitute of North America (TEMA) and also partially funded bythe National Science Foundation Engineering Research Center forPower Optimization of Electro-Thermal Systems (POETS) withcooperative Agreement No. EEC-1449548. Part of this work wasperformed at the Stanford Nano-Shared Facilities (SNSF)/StanfordNanofabrication Facility (SNF), supported by NSF under AwardNo. ECCS-1542152. T. Liu acknowledges support from the NSFGraduate Research Fellowship Program. J. Katz acknowledges theSemiconductor Research Corporation (SRC) for support through aGraduate Research Fellowship. Any opinions, findings, andconclusions or recommendations expressed in this material arethose of the author(s) and do not necessarily reflect the views of theNational Science Foundation.

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