Patent Publication Number: US-9835363-B2

Title: Evaporative heat transfer system

Description:
This non-provisional application claims priority to provisional application Ser. No. 61/752,013 filed on Jan. 14, 2013, the contents of which are incorporated herein by reference in their entirety. 
    
    
     This invention was made with Government support under Grant No. N00014-09-1-1000 awarded by the Office of Naval Research. The Government has certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates to heat transfer and more particularly to a heat transfer system using a nanoporous membrane to provide capillary pressure for high heat transport and decoupled from fluidic delivery. 
     Increasing power densities in high performance systems have led to significant demands for advanced thermal management technologies. Evaporative microfluidic cooling strategies have received significant interest to address the stringent heat flux requirements in high performance systems while significantly reducing size, weight, and power consumption (SWaP). In particular, flow boiling in microchannels has been an active research area [3-5, 24-27] where typical dissipated heat fluxes of q″=200 W/cm 2  and heat transfer coefficients of h=10 W/cm 2 K using water have been demonstrated for exit qualities below 20% [24]. While heat transfer can be improved when in the annular flow regime with much higher exit quality, challenges exist with flow instabilities [3-5, 25-27]. Despite incorporating surface features and using various water mixtures allowing q″=600 W/cm 2  and h=8.8 W/cm 2 K, the performance remains fundamentally limited by instabilities [28]. Accordingly, flow restrictors have been proposed [29], but lead to significant increases in pumping power requirements. 
     Recent developments in thermal ground planes have utilized micro/nanostructured wicks, including sintered copper mesh coated with carbon nanotubes [30], titanium nanopillars [31], and oxidized copper microposts [32], to develop high flux evaporators. A typical value of q″=550 W/cm 2  and h=15.4 W/cm 2 K over a heated area of 5×5 mm 2  was demonstrated with an evaporator area of 2×2 cm 2  [30]. However, the performance of such wick is fundamentally limited due to the coupling between the capillary pressure generated by the wick and the liquid transport through the wick. To decrease the transport distance within the wick, liquid supply arteries [33] or bi-porosity [34, 35] have been introduced, and as a result, q″=380 W/cm 2  with h=20 W/cm 2 K was demonstrated [33]. Even in this configuration, the liquid transport remains in the wick, and limits the maximum heat flux. Meanwhile, to achieve the flow rates required for higher heat fluxes, the height of the wick structure should be &gt;100 μm, which increases the thermal resistance. 
     A recent study using evaporation through a nanoporous membrane, similar to our concept disclosed herein, demonstrated a maximum q″˜600 W/cm 2  with h=9.4 W/cm 2 K [36]. However, the configuration required heat conducting through a liquid layer that limited the thermal resistance, and active pumping, instead of capillarity, to drive the liquid to the membrane, which increased the power consumption. 
     SUMMARY OF THE INVENTION 
     The evaporative heat transfer system according to the invention includes a substrate and a plurality of substantially parallel, spaced-apart ridges extending from the substrate forming vertical liquid manifolds therebetween. A nanoporous membrane is supported on the ridges and a pump delivers a dielectric fluid across the edges. The fluid is drawn through the liquid manifolds via capillarity provided by the nanoporous membrane and evaporates to dissipate heat flux through the substrate. A preferred dielectric fluid is pentane. The pore size in the nanoporous membrane is selected to provide high capillary pressures. In one embodiment, the pore size is approximately 40 nm and capillary pressure is approximately 1.1 MPa. 
     In a preferred embodiment, membrane porosity varies across the membrane to tailor thermal resistances to limit temperature rises. In a preferred embodiment, the system is configured to dissipate greater than 1 kW/cm 2  on a 1 cm 2  area having a 200 by 200 μm hotspot dissipating greater than 5 kW/cm 2 . It is preferred that a condenser be provided to capture vapor to recirculate liquid to the pump. A suitable substrate is SiC. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         FIG. 1  is a perspective view of an embodiment of a high flux membrane-enhanced evaporative microfluidic device for dissipation of high heat fluxes according to the invention. 
         FIG. 2  is a detailed schematic diagram of an embodiment of the evaporative microfluidic thermal management system according to the present invention. 
         FIG. 3 a    is a schematic diagram showing a single pore in a nanoporous membrane used in the invention. 
         FIG. 3 b    is a graph of transmission probability as a function of available pressure budget. 
         FIG. 4  is a schematic illustration of a thin-film wick for an embodiment of the invention showing a portion of the nanoporous membrane removed to reveal supporting ridges. 
         FIG. 5 a    is a graph of ridge channel pressure drop for a background flux area. 
         FIG. 5 b    is a graph of ridge channel pressure drop for hotspot ridges according to an embodiment of the invention. 
         FIG. 6 a    illustrates temperature distribution in COMSOL simulations of membrane geometry. 
         FIG. 6 b    is a graph showing stress distribution in a plane under a pressure load. 
         FIGS. 7   a, b, c, d  and  e  are process flow diagrams for fabrication of the heat transfer system disclosed herein. 
         FIG. 8 a    is an exploded view showing an embodiment of the evaporative microfluidic device disclosed herein interfaced to a hot chip. Pumped liquid supply in microchannels drawn through vertical liquid manifold by capillarity. 
         FIG. 8 b    is an exploded view of an embodiment of the invention, showing vapor exiting from the evaporating membrane through outlet ports. 
         FIG. 8 c    is a magnified, perspective view of the device disclosed herein cross section. 
         FIG. 9 a    illustrates the geometry and prescribed boundary for thermal simulations. 
         FIG. 9 b    is a graph of maximum temperature at a hotspot as a function of accommodation coefficient based on simulation results. 
         FIG. 10  is a graph of simulated temperature distribution from the center to the edge of a chip with a hot spot and background fluxes. 
         FIG. 11 a    is an illustration showing geometry and prescribed boundary conditions for stress simulations. 
         FIG. 11 b    is a graph for a sensitivity analyses of the maximum stress on pore diameter. 
         FIG. 12  is a schematic illustration of a flow loop for the device according to the invention. 
         FIG. 13  is a cross-sectional view of the membrane-ridge device layer is SiC substrate bonded with the liquid-vapor microchannel device layer in Si substrate. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     We disclose a unique intrachip two-phase evaporative cooling solution capable of dissipating &gt;1 kW/cm 2  for a 1 cm 2  chip area with a local 200×200 μm 2  hot spot &gt;5 kW/cm 2  ( FIG. 1 ). A mechanical pump delivers a dielectric fluid, such as pentane, across microchannels whereby liquid is drawn in through the vertical liquid manifolds towards the heated surface via capillarity using a thin nanoporous membrane. The membrane provides an important functionality to the approach and allows the delivery of the necessary flow rates to dissipate the requisite heat fluxes. Subsequently, the vapor generated by evaporation exits through the backside and is guided to an external condenser where the liquid is recirculated back to the pump. A detailed design of the proposed concept is shown in  FIG. 2 , which has several important innovations. 
     A nanoporous membrane  10  is supported by parallel ridges  12  forming vertical channels  14  therebetween. Liquid is supplied through liquid supply lines  16 . Vapor exits through an outlet  18 . Liquid is drawn to the membrane via capillarity through the microfluidic network, which includes the ridges  12  that serve as mechanical supports for the membrane  10  and reduces the thermal resistance between the surface and evaporating region. Hot spot and background heat flux are both mitigated using different membrane, pore and ridge geometries. The desired dimensions for an embodiment of the invention for a nanoscale pore for a desired capillary pressure is shown in the inset. 
     The device architecture disclosed herein leverages nanoporous membranes to decouple the heat dissipation from the pressure drop of the device. With nanopores of diameter ˜40 nm, high capillary pressures (˜1.1 MPa) can be generated to achieve high mass flow rates (˜2.9-5.8 g/s) necessary for evaporation with low liquid inlet to outlet pressure drops (&lt;8 kPa=0.05 P sat ). By relying on capillarity as the main pumping mechanism, the thermofluid CoP is &gt;100. 
     Both the hotspot and background fluxes can be dissipated using the same ridge-supported membrane concept by varying key geometries within the wick, e.g., membrane porosity, to tailor thermal resistances to limit the temperature rise of the hotspot ΔT hs &lt;5 K over the background. This approach of using the same mechanism offers increased reliability, reduces complexities in fabrication to create a monolithic device, and offers the flexibility to be integrated with advanced solid-state solutions in the future. 
     The fluidic delivery to the evaporative region from the inlet microchannels is self-regulated by the capillarity of the membrane and eliminates the need for additional fluidic valves and active control on chip. 
     Parallel ridges in SiC provide both mechanical support for the nanoporous membranes and enhanced thermal conductivity to minimize the thermal resistance between the chip substrate and evaporation region to ensure that the temperature rise above the inlet is ΔT&lt; 30  K. The combined heat transfer coefficient of the membrane and supported ridge for the hotspot can therefore be as high as h=0.18 kW/cm 2 K, an order of magnitude higher than any state-of-the-art two-phase cooling solution. The overall can be easily scaled to larger areas to tackle thermal management needs of multiple devices on the same substrate. 
     The disclosed intrachip evaporative cooling approach will target applications in GaN electronics with silicon carbide (SiC) substrates and typical device dimensions of ˜1 cm 2  area and &gt;100 μm thickness. The strategy seeks to maintain the backside chip temperature at ˜75-80° C. The membrane and the supporting ridge structures will be fabricated in SiC which has a large bulk thermal conductivity of ˜450 W/mK. 
     In the hot spot region (q″=5 kW/cm 2 ), the target characteristic pore diameter of 40 nm will generate capillary pressures of ΔP cap ˜1.1 MPa ( FIG. 3 a   ) with pentane as the working fluid. The thickness of the membrane will be ˜300 nm, which is determined by the requirement to maintain the meniscus at the mouth of the pore to maximum the vapor transmission probability [14]. With a 300 nm membrane thickness ( FIG. 3 b   ), 50% of the capillary pressure budget is available to drive flow within the device without hindering the evaporative heat transfer behavior of the membrane. Meanwhile, parallel ridges will support the membrane ( FIG. 4 ) and also provide the liquid path to the membrane. The ridges have dimensions of thickness t=200 nm, height h=2 μm, and spacing w=1.5 μm. The pressure drops across each ridge with distance x for the background and hot spot flux areas are shown in  FIGS. 5 a  and  b   , respectively. The results indicate that the capillary pressure from the membrane can not only drive the flow from the ridges, but also in the low-pressure-drop liquid manifolds (not shown) to dissipate the large fluxes. 
     While the liquid in the wick can reach negative absolute pressures (˜−0.4 MPa at L/2), nucleation/cavitation is not expected until T=422 K or P cav ˜−13 MPa at T=343 K based on the kinetic limit of homogenous nucleation for pentane [15, 16]. The chosen ridge geometry ensures that the maximum temperature drop across the thin-film region from the substrate to the saturated vapor is ΔT&lt;30 K, where the conduction resistance of the ridges and fluid, as well as the liquid-vapor interfacial resistance were considered in the estimates. To address both the background and hot spot heat flux with the membrane approach, the thermal resistance of the entire wick (membrane and ridges) over the background flux area will be increased to limit the temperature difference between the hot spot and the background flux to &lt;5 K. We conservatively estimate that for a membrane porosity φ p =0.5 and a dissipated heat flux of q″=5 kW/cm 2 , the temperature rise will be ΔT=27.9 K (with an interfacial heat transfer coefficient, h interface =0.69 kW/cm 2 K [17]) ( FIG. 6 a   ) with maximum pressure difference across the membrane is ΔP=0.545 MPa. This result includes the ballistic phonon transport in nanoscale geometries, i.e., the thermal conductivity of the ridges and membrane are estimated as 350 W/mK and 35 W/mK, respectively [18]. In addition, we assessed the mechanical integrity of the membrane subject to stress generated by the capoillary pressure ( FIG. 6 b   ) and show that the maximum stress was ˜17 MPa, which is well below the fracture strength of SiC, σ f =500-1500 MPa [19]. 
     With this design, liquid will enter the device at T inlet =323 K with an inlet quality of 0 and vapor will exit at T sat =323 K with an exit quality of 1. The self-regulating microfluidic manifolds with the membrane design alleviates the overall pumping requirements ( FIG. 1 , liquid inlet-outlet) with ΔP˜5 kPa and the flow rate Q˜300-600 mL/min. Therefore, the CoP=Q/W p , where Q is the total thermal power dissipated from the device and W p  is the power input, can be &gt;100 with an off-the shelf pump (MZR®-11508, Micropump). These estimates suggest that the proposed evaporative membrane based approach is viable to dissipate the requisite power densities. 
     Pentane is chosen as the dielectric working fluid owing to the favorable thermophysical properties compared to other dielectrics including high latent heat (350 kJ/kg), thermal conductivity (0.11 W/mK), and low specific volume of vapor (0.22 m 3 /kg). Pentane has been investigated for potential electronic cooling applications [20, 21] due to its non-polar and non-toxic nature, and good dielectric constant and strength of 1.84 and ˜1.4 kV/mm [22], respectively. Other suitable dielectric fluids will be apparent to those of skill in this art. 
     The membrane and ridges are fabricated in Si first, and then later in SiC, while the microfluidic network for liquid and vapor flow will be fabricated in Si using standard lithography and DRIE. We plan first to develop test devices in Si to minimize cost and validate the design and fabrication strategies. The fabrication steps for a SiC based device is shown in  FIG. 7  and described in detail below. The SiC substrate is attached to the Si microfluidic manifolding layer using eutectic bonding [23]. The slight thermal expansion mismatch between Si (α≈3e−6/° C.) and SiC (α≈2.8e−6/° C.) will generate minimal stresses due to the small temperature differences (&lt;30 K). The overall thickness of the cooling device is &lt;2 mm, such that the heat density removed is &gt;1 kW/cm 3 . Hermetically scaled connectors are added by evaporating Ti/Ni/Au as the metallization layer for soldering. A Cu insert with tubing attached is then soldered into each fluidic opening, which is a fluxless process, eliminating contamination issues. 
     The intrachip two-phase evaporative cooling solution disclosed herein is capable of dissipating &gt;1 kW, &gt;1 kW/cm 2  for a 1 cm 2  chip area with a local 200×200 μm 2  hot spot &gt;5 kW/cm 2  ( FIG. 8 , also see  FIGS. 1&amp;2 ). An important element that enables the requisite high performance is the utilization of the nanoporous membrane. The nanometer pores (diameter ˜40 nm) provide the requisite capillary pressure to deliver the liquid to the high flux surface. Through the evaporation process, the latent heat of vaporization of pentane effectively dissipates the generated heat from the surface. Meanwhile, this high capillary pressure is decoupled from liquid transport, which allows for low viscous losses. This is a critical aspect to achieve the desired metrics. The dielectric fluid, pentane, is pumped across microchannels (top layer,  FIG. 8 a   ), whereby liquid is drawn in through the vertical liquid manifolds (arrows) towards the heated surface via capillarity using a thin nanoporous membrane. The capillarity of the membrane also self-regulates the fluid delivery to the evaporative region, which eliminates the need for active fluidic control on chip. The vapor generated by evaporation within the membrane exits ( FIG. 8 b   ) to an external condenser where the liquid is recirculated back to the device. A magnified view is also shown ( FIG. 8 c   ) with detailed dimensions. The overall thickness of the cooling device will be &lt;2 mm, such that the heat density removed is &gt;1 kW/cm 3 . 
     Compared to previous high flux heat transfer approaches, our disclosed membrane solution offers the following advantages: 1. The liquid transport is completely decoupled from the capillary pressure generation. The capillary pressure is generated by the nanopores in the membrane while the liquid transport is through the supporting ridges, allowing the flexibility to scale down the nanopore size to achieve large driving pressures without significantly increasing the viscous losses. 2. The vapor escape above the membrane is separate from the liquid flow path such that flow instabilities are avoided with 100% vapor exit quality. 3. The heat is dissipated primarily via evaporation, which improves the heat transfer coefficient and the stability. 4. The primary heat conduction path is through the SiC supporting ridges and membrane structure, which decreases the overall thermal resistance. 
     Our preliminary modeling efforts suggest that all of the metrics can be achieved with our proposed approach. Here, we describe the wick (membrane and ridges,  FIG. 4 .) and fluidic supply geometry capable of dissipating the 5 kW/cm 2  “hotspot” over a characteristic area of 200×200 μm 2  with the temperature, power, and other requirements. We demonstrate the viability 
     of the approach using the more severe heat flux case, and suggest that the requirements for the background case can also be achieved with the same approach with proper optimizations. 
     The membrane pores provide the capillary pressure to dissipate the requisite heat flux. The maximum capillary pressure associated with a pore radius, r p , ( FIG. 3 a   ) is given by the Young-Laplace equation, 
                         Δ   ⁢           ⁢     p   cap       =       2   ⁢           ⁢     γ   lv     ⁢           ⁢   cos   ⁢           ⁢   θ       r   p         ,     ⁢                   Eq   .           ⁢   1               
where θ is the wetting angle. For a pore radius of 20 nm, the membrane is capable of generating capillary pressures of ΔP cap ˜1.1 MPa with pentane as the working fluid (θ˜0 20   for well-wetting pentane). The membrane porosity was specified as φ p,m =πr p   2 /l p   2 ≈0.5 with a pore pitch of l p =50 nm, indicating a pore-level average heat flux of q i  ″=q″/(φ p,m φ p,r )=11.3 kW/cm 2 .
 
     The thickness of the membrane is determined by the requirement to maintain the meniscus at the mouth of the pore to maximize the vapor transmission probability [14] given by 
                   η   =     1   +       l   2     4     -         l   ^     4     ⁢           l   ^     2     +   4         -           [         (     8   -       l   ^     2       )     ⁢           l   ^     2     +   4         +       l   ^     2     -   16     ]     2         72   ⁢     l   ^     ⁢           l   ^     2     +   4         -     288   ⁢           ⁢     ln   ⁡     [       l   ^     +           l   ^     2     +   4         ]         +     288   ⁢           ⁢   ln   ⁢           ⁢   2         .               Eq   .           ⁢   2               
where {circumflex over (l)}=l p /r p . Once the meniscus begins to recede into the pore, the effective heat transfer coefficient, h p =ηh i  becomes the product of the transmission probability, η and the interfacial heat transfer coefficient, h i . We model pressure drop in an :individual pore as a laminar tube flow (fRe p =64) since Re p =q i 2r p /(h fg μ)˜0.1. Thus, the maximum length of the pore (membrane thickness) associated with dissipating a pore level heat flux While maintaining the pore completely full with liquid is given by
 
                       l     p   ,   max       =       1   f     ⁢     (       Δ   ⁢           ⁢     p   cap       -     p   in       )     ⁢   4   ⁢     r   p     ⁢           p   l     ⁡     (       h   fg       q   l   ″       )         2         ,           Eq   .           ⁢   3               
where p in  is the pressure at the inlet to the pore from the ridges. As shown in  FIG. 3 b   , for a membrane thickness of l mem =300 nm, ˜50% of the capillary pressure budget is available to drive the flow in the ridges without hindering membrane heat transfer. Doubling the thickness of the membrane to 600 nm reduces the available budget to ˜1%. This analysis indicates that further thinning of the membrane can have significant fluidic advantages by providing more capillary budget without hindering phase-change mass (heat) transfer in the pore. However, further reducing the thickness or the membrane must be balanced against the need to maintain a suitable conduction path to the pores from the ridges and the mechanical integrity of the membrane (see below).
 
     Meanwhile, parallel ridges ( FIG. 4 ) support and provide a liquid path to the membrane where the geometry is given by height, h, thickness, t, gap spacing, w, and corresponding porosity defined as φ p,r =1−[t/(w+t)]. The maximum height of the ridges is constrained by a maximum feature aspect ratio dictated by etching limitations for SiC, h max =10t [37]. Thus, for t =200 nm, h max =2 μm, a maximum w=1.5 μm was set to minimize conduction resistances and mechanical integrity issues. To ensure that the pumping capillary pressure is sufficient, the pressure drop between the parallel ridges was determined using the expression for laminar flows (Re˜50), 
                             dp   l     dx     ⁢     (   x   )       =     -       fRe   ⁢           ⁢     ρ   l     ⁢           ⁢         v   l     ⁡     (   x   )       2             ,     ⁢                   Eq   .           ⁢   4               
where fRe, the Pouiseille number, is taken from [38], v l (χ) is the χ-dependent mean velocity calculated from an energy balance from evaporation through the membrane, Re(χ)=ρ l v l (χ)D h /μ l  is the χ-dependent Reynolds number, and D h =2wh/(w+h) is the hydraulic diameter and ρ l  is the liquid density.  FIG. 5 a    shows that the maximum pressure drop for the required mass flow rates to dissipate 1 kW/cm 2  is significantly smaller than the maximum capillary pressure (˜0.2Δp cap ) where the flow length is L=W/2 (˜0.5Δp cap  for q″=2.75 kW/cm 2 ). Similarly,  FIG. 5 b    shows that for the hotspot, the maximum pressure drop for the required mass flow rates is approximately half the maximum capillary pressure (˜0.5Δp cap ) where the average flow length is L=W/ 4 . While the liquid in the wick can reach negative pressures (˜−0.4 MPa at the center of the patch), nucleation/cavitation is not expected until T=422 K or P cav ˜−13 MPa at T=343 K based on the kinetic limit of homogenous nucleation for pentane [15, 16], provided that we avoid introducing nucleation sites that lower the activation energy during fabrication.
 
     We similarly determined the pressure drop in the microfluidic manifold to supply liquid to the wick for a geometry with liquid flow length of L ls =5 mm, width W ls =50 μm, height H ls =250 μm (Re ls ˜1500). The pressure drop was ˜1×10 −2  ΔP cap , indicating that the capillary pressure from the membrane also drives the flow in the supply lines connected to the low-pressure-drop liquid manifold. 
     These results suggest that a key advantage and novelty of the proposed approach is that by using capillarity with a nanoporous membrane, we can achieve a self-regulating system that alleviates the need for external valves, and decreases the overall pumping requirements of the system. While such capillarity-driven systems have been successfully demonstrated in numerous previous studies [30-36], including our own [39], an important aspect of this invention is demonstrating the ability achieve the high capillary pressures in the fabricated nanoporous membranes seamlessly integrated with the supported ridge structures and liquid supply lines. 
     In addition to the requirement to dissipate the high heat fluxes, the overall thermal resistance of the wick needs to be considered because it determines the temperature of the device. The temperature drop from the substrate to the vapor during heat transfer is dictated by the following two resistances. Note that due to the large q″ and small size of the wick, the two resistances are of the same order and need to be considered carefully. For our preliminary calculations, we used classical kinetic theory [17, 46] to capture the liquid vapor interface resistance. The local heat flux at the interface of the pore, q i ″=q″/(φ p,m φ p,r ), can be determined for the non-negligible velocity of vapor away from the interface during evaporation [17, 46], For the specified T v =323 K and q i ″=11.3 kW/cm 2  (q i ″=5 kW/cm 2 ) and assuming that an accommodation coefficient, {circumflex over (σ)}=0.9, the temperature drop across the liquid-vapor interface is ΔT i =15.05 K, indicating a characteristic interfacial heat transfer coefficient of h i =q i ″/ΔT i ˜0.69 kW/cm 2 K. 
     Note that there are several competing theories to predict the behavior of the liquid/vapor interface during phase change in addition to kinetic theory, such as statistical rate theory [47]. We seek to perform careful temperature measurements close to me interface based on our established experimental technique [48] to identify the appropriate theory for the modeling efforts. Accordingly, we can incorporate the liquid-vapor interface resistance as described above as a boundary condition to determine the overall resistance and associated temperature rise from the substrate to vapor. Given the complex conduction paths in the wick, we used 3D finite element simulations with COMSOL with material properties from Table 1 to model the heat transfer associated with the conduction resistance of the ridges and fluid.  FIG. 9 a    shows the simulated geometry with the pore and ridge dimensions (described above) with the prescribed boundary conditions, and thermal conductivities accounting for ballistic phonon transport in nanoscale geometries, i.e., the thermal conductivity of the ridges and membrane are 350 W/mK and 35 W/mK, respectively [18]. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Thermal and mechanical properties of the chip material 
               
            
           
           
               
               
               
               
            
               
                   
                 Thermal conductivity, 
                   
                   
               
               
                   
                 k (W/mK) 
                   
                 Fracture 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 Nanorestricted, 
                 Elastic modulus, λ 
                 CTE, 
                   
                 strength 
               
               
                 Material 
                 Bulk 
                 characteristic length 20 nm 
                 (GPa) 
                 α (10 −6  K) 
                 Poisson ratio, ν 
                 (MPa) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Silicon (Si) 
                 149 [40] 
                 10 [41] 
                 130 in &lt;100&gt;; 
                   3 [40] 
                 0.28 &lt;100&gt;; 
                 300-600 
                 [43] 
               
               
                   
                   
                   
                 169 in &lt;110 &gt;[42] 
                   
                 0.064 &lt;110&gt; [42] 
                   
                   
               
               
                 Silicon carbide (SiC) 
                 450 [41] 
                 35 [41] 
                 400 [44] 
                 2.77[40] 
                 0.19 [44] 
                 500 
                 [45] 
               
               
                   
               
            
           
         
       
     
     The results of the simulation,  FIG. 6 a   , shows that the target imposed heat flux of q″=5 kW/cm 2  results in a total temperature rise of 27.9 K corresponding to a substrate temperature of T s =351 K and an overall heat transfer coefficient of h=0.18 kW/cm 2 K. Note that this overall heat transfer coefficient is an order of magnitude higher than those reported in previous works. To address both the background and hot spot heat flux with this approach, the thermal resistance of the entire wick over the background flux area will be increased by adjusting the wick geometry (e.g., porosity) to limit the temperature difference between the hot spot and the background flux to &lt;5 K.  FIG. 10  shows simulation results for the temperature distribution along the length of the device with the hotspot and background fluxes applied and effective heat transfer coefficients of 180 W/cm 2 K and 40 W/cm 2 K, respectively. The maximum temperature variation across the chip is &lt;4 K, which meets the ΔT across-heat-chip &lt;10 K requirement. 
     While these simulations suggest a viable approach, an important aspect that needs to be considered to achieve the high interfacial heat transfer coefficients is the accommodation coefficient, {circumflex over (σ)}. Using our model, we investigated the maximum temperature at the hotspot as a function of the accommodation coefficient at the evaporating interface ( FIG. 9 b   ). and show that {circumflex over (σ)}&gt;0.57 is needed to achieve the design goal. A significant body of previous work focused on measuring the accommodation coefficient for various liquids and report a large range from 0.001-1 depending on the purity of the interface [17, 49-52]. Previous results on non-polar fluids, such as benzene and carbon tetrachloride, show an accommodation coefficient closer to 1 can be obtained [50, 51]. As such, we anticipate that pentane can achieve similar results. Part of our detailed characterizations will be focused on achieving the requisite {circumflex over (σ)} values by attaining clean interfaces. 
     Due to the thin geometry of the membrane, we also assessed the mechanical integrity of the membrane subject to stress generated by the capillary pressure ( FIG. 11 ,  FIG. 6 b   ) with material properties in Table 1.  FIG. 11 a    shows the geometry and prescribed boundary conditions for the simulations with a pressure load of 0.545 MPa which is 50% of the capillary pressure and the pressure drop across the membrane to maintain the meniscus at the top opening of the pores (Eqn 3).  FIG. 6 b    shows that the maximum stress was ˜17 MPa, which is well below the fracture strength of SiC, σ 1 =500-1500 MPa [19]. We also note that if there is variability in the pore size, that there is little sensitivity to the maximum stress, therefore, mechanical failure should not be a critical failure mechanism. 
     These preliminary models suggest that the proposed evaporative membrane based approach is viable to dissipate the requisite power densities with the associated metrics. Also, given the expected variations of &lt;15% in pore radius and &lt;5% in membrane thickness which are the dominant fabrication factors affecting device performance, there is sufficient margin to meet the requirements. 
     A schematic of the flow loop is shown in  FIG. 12 . The constant temperature bath which also serves as a liquid reservoir maintains the dielectric fluid at near saturated conditions (x˜0). A pump (mzr-11508, Micropump) circulates pentane through a filter, a flow-meter, and temperature and pressure sensor to the test module ( 3 ). Since the proposed concept relies on the high capillary pressure generated by the membrane for efficient fluid delivery, the pump is only required to supply the fluid from the external reservoir ( 1 ) to the inlet manifold ( 3 ) through a series of ¼″ diameter copper tubings. The required liquid flow rate of 300 mL/min (5.1 cm 3 /s) implies a minimal pressure difference of 5-8 kPa (with 3 m long 0.25″ tubing, two 90° turns and a flow meter) to maintain the liquid flow (Δp˜0.05 p sat ). Vapor (100% quality) that exits the heated test module ( 4 ) is then condensed ( 5 - 6 ) using a custom heat exchanger and chiller (NeslabHX-75, Thermo Electron Corporation). The small pressure drop of ˜3 kPa to drive the Vapor from the exit manifolds to the condenser (1 meter long, ¼″diameter copper tube) only Lowers the saturation temperature difference (ΔT sat &lt;1° C.) that is available (T sat@evap −T sat@cond ˜20-25° C.). Such a small change in saturation temperature will mitigate condensation in the vapor removal lines and can safely account for the slight superheating of the vapor. The liquid is then recirculated back to the constant temperature reservoir ( 7 ). Total volume of the test fluid in the loop is estimated to be ˜600 mL. The liquid flow rates, pressure drops and required pumping power are detailed in Table 2. All of the measurement instruments in this setup, including thermocouples, flow and pressure sensors, will conform to the requirement for measurement errors &lt;10%. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Liquid and vapor flow rates, pressure drop, and power 
               
               
                 requirements. 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Flow 
                 Pressure 
                 Power 
                   
               
               
                   
                 rate 
                 drop 
                 required 
               
               
                   
                 (cm 3 /sec) 
                 (kPa) 
                 (mW) 
                 Pump Model/Make 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 Liquid 
                 5.1 
                 5-8 kPa 
                 40 mW 
                 mzr-11508/ 
               
               
                   
                   
                 (node (1)-(3)) 
                   
                 Micropump 
               
               
                   
                   
                   
                   
                 (0-20 mL/sec) 
               
               
                 Vapor 
                 670 
                 3-2 kPa 
                  2 W 
                 NA* 
               
               
                   
                   
                 (node (4)-(5)) 
               
               
                   
               
               
                 **driven by the sat. pressure difference between the evaporator and condenser 
               
            
           
         
       
     
     Under normal operating conditions, the pump only supplies the pressure required to deliver the liquid from the external reservoir ( 1 ) to the inlet manifold ( 3 ) through a series of macroscopic tubings (¼″) while the capillary pumping mechanism associated with the membrane drives pentane to the heated substrate through the microfluidic network. The minimal pumping pressure of 5-8 kPa required to drive the liquid from the reservoir to the inlet manifold implies that a CoP=Q/W p &gt;100, where Q is the total thermal power dissipated from the device and W p  is the power input (40 mW) of the liquid pump (mzr-11508) to supply liquid to the device. 
     Pentane was selected as the dielectric working fluid due to its favorable thermophysical properties such as the high latent heat and thermal conductivity, and low specific volume. While fluids such as water and methanol have significantly better thermophysical properties compared to pentane and other dielectric fluids (Table 3), they are not good dielectrics in practice because they contain dissolved ions, are good solvents, and have relatively low relaxation times, which all reduce the breakdown voltage considerably. Pentane has been investigated for electronic cooling applications [53-55] due to its non-polar and non-toxic nature, and good dielectric constant and strength of 1.84 and ˜1.4 kV/mm [56], respectively. Moreover, it has significantly better thermophysical properties than typical dielectric fluids such as FC-72 and HFE7100, which is important based on our preliminary estimates to achieve the desired targets. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 Thermophysical and dielectric properties of liquids. 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Latent 
                 Surface 
                 Thermal 
                 Vapor Specific 
                   
                 Relaxation 
                 Breakdown 
               
               
                   
                 Meat 
                 Tension 
                 Conductivity 
                 Volume 
                 Dielactric 
                 Time 
                 Voltage 
               
               
                   
                 [kJ/kg] 
                 [N/m] 
                 [W/m-K] 
                 [m 2 /kg] 
                 Constant 
                 [s] 
                 [kV/mm] 
               
               
                   
               
               
                 DECREASING 
                 Water 
                 Water 
                 Water 
                 HFE7100 
                 Water* 
                 HFE7100 
                 HFE7100 
               
               
                 PREFERNCE 
                 [2257] 
                 [0.058] 
                 [0.65] 
                 [0.075] 
                 [60.4]  
                 [—] 
                 [14] 
               
               
                   
                 Methanol 
                 Methanol 
                 Methanol 
                 FC-72 
                 Methanol* 
                 FC-72 
                 FC-72 
               
               
                   
                 [1100] 
                 [0.018] 
                 [0.19] 
                 [0.103] 
                 [32.6]  
                 [100] 
                 [11] 
               
               
                   
                 Pentane 
                 Pentane 
                 Pentane 
                 Pentane 
                 HFE7100 
                 Pentane 
                 Pentane 
               
               
                   
                  [358] 
                 [0.014] 
                 [0.11] 
                 [0.335] 
                  [7.38] 
                 [10 −4 ] 
                   [1.4] 
               
               
                   
                 HFE7100 
                 HFE7100 
                 HFE7100 
                 Methanol 
                 Pentane 
                 Water 
                 Water 
               
               
                   
                  [111] 
                 [0.014] 
                 [0.08] 
                 [0.811] 
                  [1.84] 
                 [10 −4 ] 
                 [—] 
               
               
                   
                 FC-72 
                 FC-72 
                 FC-72 
                 Water 
                 FC-72 
                 Methanol 
                 Methanol 
               
               
                   
                  [83] 
                 [0.000] 
                 [0.00] 
                 [1.675] 
                  [1.78] 
                 O[10 −11 ] 
                 [—] 
               
               
                   
               
               
                 *These values are not a good indicator of dielectric performance which should be concluded from corresponding relaxation time and experimental breakdown voltage data. 
               
            
           
         
       
     
     The Lower Explosive/Flammable Limit (LEL/LFL) of pentane is 1.4% [57]. Although pentane can form as explosive mixture in air, the design requirement of leak rates less than 1% per year will rule out the flammability hazard of pentane under normal operating conditions. Precautions will be taken in case of a large leak so as to minimize or eliminate any concerns with respect to fire and explosion. 
     The fabrication process for the SiC test device is shown in  FIG. 7 . First, thin film heaters to emulate the GaN device and a temperature sensor array will be fabricated on a SiC substrate. Conventional lithography will be used, where a thin Pt layer deposited using electron-beam evaporation is patterned using a metal lift-off technique ( FIG. 7 a   ). UV lithography is then carried out to create ridges on the backside of the wafer. This allows preparing features on a hard mask, such as SiO 2  or metal, which is subsequently used for etching SiC with reactive ion etching (RIE) [58-63] to fabricate ridges ˜0.2 μm thick, spaced ˜1 μm apart and ˜2 μm tall [64]. A conformal deposition of silicon oxide (˜2 μm) is then carried out using plasma enhanced chemical vapor deposition (PECVD) to fill the channels between the ridges. Subsequently, mechanical polishing of the substrate will result in a flat surface suitable for further processing steps,  FIG. 7 b   . SiC is then deposited (˜0.3 μm thick) using a PECVD, followed by deposition of titanium and nickel using e-beam evaporation ( FIG. 7 c   ). 
     Conventional lithography allows etching the nickel to produce square features ˜10 to 50 μm, which define the liquid ports for the coolant supply. Subsequently, a block copolymer film is used as an etch mask to transfer nanoscale patterns (˜40 nm diameter pores) in the underlying nickel metal [65-67], as shown in  FIG. 7 d   . Using the patterned metal layer as the hard mask, the underlying SiC substrate is then etched using inductively coupled plasma enhanced RIE [63], Ni is retained on the membrane for the subsequent wafer bonding process. The membrane is released by etching the silicon oxide chemically using buffered oxide etch (BOE), leaving behind a monolithic structure, consisting of freestanding membranes supported only at the ridges, as shown in  FIG. 7   e.    
     Microfluidic manifolds for the fluid supply and vapor removal will be separately etched and fusion bonded (not shown) in Si using well-established lithography and dry etching processes. Gold (Au)-tin (Sn) eutectic bonding will be used to join SiC substrate consisting of the membrane-ridge structure with the Si substrate consisting of the fluidic manifold. This is a crucial step to ensure hermetic sealing from the ambient environment [23]. Multiple layers of metallization Ti-100 nm, Ni-200 nm, Au-70 nm, Sn-2900 nm and then Au-80 nm, are deposited on wafer with the microfluidic manifolds ( FIG. 13 ). Ti acts as an adhesion promoter and Ni prevents diffusion of Sn into the substrate. A thin layer of gold is also deposited onto the SiC substrate using e-beam. At 280° C., Sn diffuses into Au and forms a strong wafer-bond. Note that the thermal budget of all the fabrication steps for our proposed cooling system in the SiC wafer (T&lt;400° C.) is compatible with SiC wafers with GaN devices already fabricated on them. Initially the membrane and ridges will be fabricated in Si due the well-established processes and expertise to demonstrate viability of the membrane approach. Meanwhile, SiC processing will be developed. 
     The numbers within square brackets refer to the references listed herewith. The content of all of these references is incorporated herein by reference. 
     It is recognized that modifications and variations of the present invention will be apparent to those of ordinary skill in the art and it is intended that all such modifications and variations be included within the scope of the appended claims. 
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