Jumping-droplet electronics hot-spot cooling

Recent advances in electronic materials and circuit architectures have catalyzed an increase in the power density (power-to-volume ratio) and the specific power (power-to-weight ratio) of both stationary and mobile systems.¹ The trend of replacing bulky pneumatic and mechanical systems with smaller electrical systems in more-electric and fully electric vehicles ranging from automobiles to aircrafts has created a demand for lighter and more compact power electronics. Yet, the ability to remove heat from internal hot spots constrains the design of converters and inverters.² Phase change heat transfer offers a platform to efficiently remove heat from electronic devices and transfer it via the generated vapor phase (evaporation in heat pipes and vapor chambers) to the outside environment.³ However, recent advances utilizing wide bandgap semiconductors have shown that the majority of heat can be generated locally near spatially distributed hot spots.^2,4 Traditional cooling schemes can also be stymied by the temporal variation in hot spot locations concurrent with electro-thermal optimization and novel circuit architectures.⁵ 

In this work, we experimentally demonstrated jumping droplet-based active cooling of electronics hot spots with nanoengineered superhydrophobic surfaces. Recent studies have shown that when small water droplets (≈1–100 μm in diameter) merge on superhydrophobic nanostructured surfaces, droplets can spontaneously eject via the release of excess surface energy irrespective of gravity.^6,7 A number of works have since fabricated superhydrophobic nanostructured surfaces to achieve spontaneous droplet removal for a variety of applications, including self-cleaning,⁸ condensation heat transfer enhancement,^9,10 thermal diodes,¹¹ vapor chambers,¹² electrical energy harvesting,¹³ and anti-icing.¹⁴ Furthermore, we recently discovered that these jumping droplets are positively charged (≈10–100 fC), due to electric-double-layer charge separation at the hydrophobic coating/condensate interface,¹⁵ and can be manipulated with electric fields.^15–17 Here, we take advantage of this unique droplet-charging phenomenon to demonstrate electric-field-enhanced (EFE) jumping-droplet hot spot cooling, where the charged droplets jump between superhydrophobic copper oxide (CuO) condensers and either single or multiple high power gallium nitride (GaN) transistors acting as local hot spots to remove heat via droplet evaporation. We experimentally demonstrated spatially and temporally controllable jumping-droplet based cooling of ≈1 W/cm² and describe near term approaches to increase heat fluxes to 120 W/cm².

The utilization of droplet-jumping and active electric fields to locally cool mobile hot spots builds on state-of-the-art vapor chamber designs with several significant advantages as follows: (i) The electronics act directly as the evaporator and minimize thermal resistance as typically observed through the utilization of thermal-interface-materials and channel walls.¹⁸ If integrated into a jumping-droplet vapor chamber geometry due to electrical isolation concerns, the mass flow rate of the liquid inside the jumping-droplet vapor chamber is not dictated by the height of the wick structure, but by the jumping frequency since the condenser liquid is returned through the vapor space.¹² (ii) Spatial and temporal control of the jumping droplet motion is possible with electrostatic fields such that mobile hot spots can be sensed and cooled as needed.¹⁶ (iii) The low Bond number of the jumping droplets (⁠$Bo$ ∼ 10⁻³) allows operation independent of gravitational orientation. (iv) The out-of-plane jumping return is scalable and particularly suitable for planar systems, unlike conventional vapor chambers with capillary return along wicked walls, where longer liquid return paths are expected for devices of larger areas.^11,12

To investigate jumping-droplet electronics cooling, a printed circuit board (PCB) with a single active integrated GaN field effect transistor (FET, EPC2034)¹⁹ was positioned above the nanostructured superhydrophobic CuO surface. The circuit board was placed on top in order to test the worst case scenario of droplet jumping against gravity (Figures 1(a)–1(c)). The CuO nanostructures (Fig. 1(d), inset) were grown on commercially purchased 800 μm thick Cu tabs with overall dimensions of 50 × 50 mm. Each tab was cleaned in an ultrasonic bath with acetone for 10 min and rinsed with ethanol, isopropyl alcohol, and deionized (DI) water. The tabs were then dipped into a 2.0 M hydrochloric acid solution for 10 min to remove the native oxide film on the surface, then triple rinsed with DI water, and dried with clean nitrogen gas. Nanostructured CuO films were formed by immersing one of the cleaned tabs into a hot (≈98 °C) alkaline solution composed of NaClO₂, NaOH, Na₃PO₄ • 12H₂O, and DI water (3.75:5:10:100 wt. %).²⁰ During the oxidation process, a thin (≈300 nm) Cu₂O layer was formed that then re-oxidized to form sharp, knife-like CuO oxide structures with heights of $h$ ≈ 1 μm, a solid fraction $φ$ ≈ 0.02, and a roughness factor $r$ ≈ 10. To render the CuO tabs superhydrophobic, a C₄F₈ hydrophobic coating was applied with chemical vapor deposition. This process allowed for the development of a highly conformal (≈50 nm thick) polymer layer on the CuO surface. Goniometric measurements (MCA-3, Kyowa Interface Science) of ≈300 nL droplets on a smooth C₄F₈-coated silicon wafer surface showed advancing and receding contact angles of $θa$ = 121 ± 5.1° and $θr$ = 105 ± 9°, respectively. Meanwhile, the advancing and receding contact angles on the superhydrophobic CuO surface were measured to be $θaapp$ = 166 ± 6° and $θrapp$ = 156 ± 7°, respectively.

To initiate jumping-droplet hot spot cooling, the temperature of the CuO tab was reduced to ≈5 °C via a cooling water flow (Figs. 1(a) and 1(c)) until jumping-droplet-condensation occurred. To visualize the behavior, a gap between the parallel devices was observed with a high speed camera. Due to electric-double-layer charge separation at the liquid-hydrophobic coating interface,¹⁵ the jumping droplets departed the surface with a droplet radius dependent electrostatic charge (∼10 fC). The jumping droplets travelled from the CuO surface to the circuit board, resulting in evaporative cooling of the hot GaN FET. In order to quantify cooling, EFE jumping droplet condensation for a single GaN device for cases with and without an external electric field of −100 V for the guard ring or the source pin potential of the GaN FET was studied.

Using rear lighting and long exposure time imaging, images and videos of jumping droplet phenomena in the gap were obtained. In the no-field condition, droplets jumping with insufficient inertia fall back to the superhydrophobic surface. In contrast, an external electric field provides sufficient force to guide droplet's with insufficient inertia along electric field lines to the GaN device as depicted in Figure 1(d). The unique parabolic path in the right hand side of Figure 1(d) also reveals how the droplets accelerate toward the power devices due to the presence of an electric field. Accelerations between 3 and 6 m/s² for the droplets attracted by the electric fields were observed from measurements when a −100 V potential was applied across a 3 mm spacing between the cold plate and the GaN transistor, thus enhancing the cooling capability by improving the rate and the number of droplets that reach the GaN FET. The applied fields (200–300 V/cm) are similar to the critical fields needed to overcome gravitational and drag forces as shown in previous studies.¹⁷ 

Steady-state infrared imaging (Fig. 2(a)) of the active GaN FET (Fig. 2(b)) as well as transient time-lapse liquid crystal thermography (Fig. 2(c)) were able to provide qualitative information about the GaN device temperature and its high temperature localization (hot spots) and to highlight how heat spread in the PCB (see supplementary material, Section S2). Yet, the inability to view the device while integrated with the superhydrophobic surface required the use of thermocouples. By attaching thermocouples to the transistor and the cold plate, quantification of the GaN FET steady-state temperature for various spacings (2–4 mm) between the circuit and cold superhydrophobic sample was studied. Figure 2(d) shows the thermal circuit corresponding to the experimental setup. The GaN device was assumed to have a uniform temperature, $Tg$⁠, due to the low Biot number (⁠$Bi$ ∼ 10⁻²) for the cooling conditions and geometry studied here. Joule heating of 1.57 W was generated inside the GaN transistor at a rate of $RdsI2$⁠, where $Rds$ = 7 mΩ is the internal electrical resistance of the GaN FET, and $I$ = 15 A is the DC current flowing through the device. The heat is dissipated either to the backside (through the board, then to ambient air, $Ta$ = 23 ± 0.5 °C) or to the front side (towards the superhydrophobic sample, $Ts$ = 5 ± 0.5 °C). Miscellaneous losses to ambient air have been lumped into a thermal resistance, $Rlosses$⁠, which was determined through calibration during the no-jumping condition (see supplementary material, Section S1). Using the cross-sectional area of the GaN FET (⁠$Ag$ = 0.12 cm²),¹⁹ a total heat flux of 13.2 W/cm² was dissipated. The cooling benefit can be separated into its contributing factors of radiation, convection, conduction through the back of the PCB, and heat removed via jumping droplet condensation and subsequent evaporation from the GaN device. The thermal resistance network of Fig. 2(d) was solved by inputting the relevant experimentally measured temperatures and solving for all of the relevant heat transfer pathways during circuit operation for the no-jumping, no-field jumping, and EFE jumping cases (see supplementary material, Section S1). Table I summarizes the measured and calculated performance, showing that although only modest GaN FET temperature decreases (∼2 °C) were obtained by jumping droplet cooling, EFE condensation enhances the heat transfer from the hot spot by ≈200% and 20% when compared to cooling without jumping and non-EFE jumping, respectively. The relatively low heat fluxes dissipated by our device were mainly due to the presence of non-condensable gases (NCGs) in the vapor environment. The condensation of water vapor leaves behind NCGs (air) that blanket the superhydrophobic surface and act as a diffusion barrier for water vapor.²¹ The counter diffusion of water vapor to the surface, coupled with the diffusion of NCGs away from the surface, significantly deteriorate the condensation heat transfer process, and hence decrease the effective surface-to-vapor temperature difference.

To investigate the possibility of using jumping-droplet EFE condensation to achieve dynamic spatial-temporal control of cooling for mobile hot spots, we repeated the experiments with a modified two transistor circuit having two GaN devices spaced 3 mm apart in the horizontal direction (Fig. 2(e)). By observing droplet trajectories through high speed imaging, we were able to plot the trajectories of droplets from the superhydrophobic surface to the GaN devices with no-field, EFE condensation with the electric field biased towards only one GaN FET (GaN1) or the electric field biased towards the other GaN FET (GaN2) (Fig. 3). In contrast to Figure 3(a) where no external electric fields are employed, Figures 3(b) and 3(c) underscore how an external electric field dramatically increases the average number of droplet trajectories directed toward a specific GaN transistor, and demonstrates spatially controllable cooling. The droplet trajectories in Fig. 3(c), which appear to stop before reaching the GaN FET, are a good example of droplets leaving the plane of focus for the high resolution video camera. In this case, the droplets will reach the GaN device due to the external electric field. The droplets' initial velocity, as measured from the videos, did not show a significant deviation from the inertial-capillary scaled velocity, consistent with previous works^7,15,16 that have shown that the separation of charge on the superhydrophobic surface happens as a result of jumping, leading to electrostatic interaction contributions only after the jump occurs. However, we expect that over longer operational time periods, the field-mediated reduced droplet return to the surface will result in the indirect maintenance of a large density of small droplets, causing an increased jumping frequency when compared to a no-field surface. Electrically floating the source pin was found experimentally to direct the droplets closer to the GaN transistor than the external guard ring. Since the source pin approach involves electrically floating pins underneath approximately half of the total device surface as shown in Fig. 2(b), the electric field lines attract all of the droplets directly toward the GaN FET. In contrast, some of the droplets attracted by the external guard ring would have to wick from the guard ring toward the package of the GaN device.

To provide insight into the experimental results and to project the maximum potential of jumping-droplet cooling, we estimated the maximum possible thermal concentration of droplets that could reach a GaN FET using the image processing techniques coupled to previous condensation heat transfer measurements in pure vapor environments.²² Assuming that all of the departing droplets leave the superhydrophobic surface and reach the GaN device, the maximum jumping-droplet cooling heat flux can be calculated as $q″=qc″AC/Ag$⁠, where $qc″$ is the critical flooding heat flux for CuO superhydrophobic surfaces having conformal hydrophobic polymer coatings (≈13 W/cm² from h= 10 000 W/m²K and ΔT = 10 °C), and $AC$ is the effective condenser area which is able to provide jumping droplets that move laterally from their jumping location to the GaN device (⁠$AC=L2$⁠, where $L$ is the maximum horizontal distance from which jumping droplets will travel to the device). Using more than 10 time lapse images analogous to Figure 1(d) to estimate $L$ during EFE condensation (⁠$AC≈9Ag$⁠), our analysis suggests that heat fluxes of $q″$ ≈ 120 W/cm² should be attainable in pure vapor environments for gap spacings of 3 mm and the GaN FET geometries studied here. Our analysis suggests that increasing in the charge per droplet is the most important parameter to obtain enhanced heat flux since the effect of the electric field attrition force and area ratio can be increased (⁠$AC∼L2$⁠). A secondary and more practical approach to increase the hot spot heat flux is to optimize the condenser-to-FET spacing or applied EFE voltage in order to attract more droplets. The experiments conducted here were limited to −100 V due to safety considerations; however, higher applied voltages are possible in closed systems.¹⁰ 

The EFE jumping droplet cooling method demonstrated here is similar to but fundamentally different from the jumping-droplet vapor chamber.¹² In the jumping droplet vapor chamber, spatial and temporal control of droplet motion is not possible, whereas in our device, active sensing of hot spots can be used as a feedback to locally direct droplets using electric fields. Furthermore, active application of electric fields may not be necessary, as the EFE concept developed here has future possibility of exploiting the inherent electric fields generated by the high voltage switching action (⁠$dv/dt$⁠) from power semiconductor devices to tailor the electric field to provide localized, directed cooling for the power devices. In addition to improved cooling, this effect may also realize a method to better equalize temperatures, a key design challenge for power sharing among parallel-connected devices. In the future, it would be interesting to investigate the performance of the device in pure vapor environments in vacuum due to: (i) the significant condensation thermal resistance added by NCGs, and (ii) the potential for droplet charge dissipation in the presence of NCGs. Indeed, a scaling analysis using previous EFE condensation visualization studies in pure vapor environments¹⁶ indicates that the thermal concentration ratio (⁠$AC/Ag$⁠) can be well over 100 for gap spacing of the same order of magnitude studied here (5 mm), inferring that $q″=qc″AC/Ag≈$ 1 kW/cm² can be achieved. Furthermore, future studies should also investigate the durability of the superhydrophobic surfaces on internal sealed condenser devices, as any practical implementation will require a longevity of years if not decades.¹⁰ 

In summary, we demonstrated jumping-droplet hot spot cooling, whereby charged droplets jump between superhydrophobic copper oxide condensers and electrical circuits to cool local hot devices actively with evaporation. Through experiments and modeling, we demonstrated heat flux dissipations of 1 W/cm² via evaporation, which can be improved in the near-term to 120 W/cm². Future enclosed devices with pure vapor environments, and optimized geometrical designs have the potential to achieve higher active cooling rates approaching 1 kW/cm². This work not only demonstrates EFE condensation based electronics cooling, but also provides a framework for the development of active jumping droplet based vapor chambers and heat pipes capable of spatial and temporal thermal dissipation control.

See supplementary material for thermal characterization, modeling, and analysis of the device jumping droplet experiments, as well as infrared and liquid crystal thermography experimental methods.

This work was supported by the National Science Foundation Engineering Research Center for Power Optimization of Electro Thermal Systems (POETS) with cooperative Agreement No. EEC-1449548 and by the Sandia Academic Alliance. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under Contract No. DE-AC04-94AL85000. N.M. gratefully acknowledges funding support from the Office of Naval Research (ONR) with Dr. Mark Spector as the program manager (Grant No. N00014-16-1-2625) and the support of the International Institute for Carbon Neutral Energy Research (WPI-I2CNER), sponsored by the Japanese Ministry of Education, Culture, Sports, Science and Technology. Electron microscopy was carried out in part in the Frederick Seitz Materials Research Laboratory Central Facilities, University of Illinois.