Nanoporous membrane device for ultra high heat flux thermal management

High power density electronics are severely limited by current thermal management solutions which are unable to dissipate the necessary heat flux while maintaining safe junction temperatures for reliable operation. We designed, fabricated, and experimentally characterized a microfluidic device for ultra-high heat flux dissipation using evaporation from a nanoporous silicon membrane. With ~100 nm diameter pores, the membrane can generate high capillary pressure even with low surface tension fluids such as pentane and R245fa. The suspended ultra-thin membrane structure facilitates efficient liquid transport with minimal viscous pressure losses. We fabricated the membrane in silicon using interference lithography and reactive ion etching and then bonded it to a high permeability silicon microchannel array to create a biporous wick which achieves high capillary pressure with enhanced permeability. The back side consisted of a thin film platinum heater and resistive temperature sensors to emulate the heat dissipation in transistors and measure the temperature, respectively. We experimentally characterized the devices in pure vapor-ambient conditions in an environmental chamber. Accordingly, we demonstrated heat fluxes of 665 ± 74 W/cm2 using pentane over an area of 0.172 mm × 10 mm with a temperature rise of 28.5 ± 1.8 K from the heated substrate to ambient vapor. This heat flux, which is normalized by the evaporation area, is the highest reported to date in the pure evaporation regime, that is, without nucleate boiling. The experimental results are in good agreement with a high fidelity model which captures heat conduction in the suspended membrane structure as well as non-equilibrium and sub-continuum effects at the liquid–vapor interface. This work suggests that evaporative membrane-based approaches can be promising towards realizing an efficient, high flux thermal management strategy over large areas for high-performance electronics.


I. Measurement Uncertainty
First, the uncertainty in temperature measurement was accounted for based on a combination of four factors: 1) error in the reference thermocouple, 2) error in measurement of RTD resistance using the data acquisition, 3) resistance of wire traces on the sample, and 4) temperature non-uniformity during RTD calibration. The reference thermocouple has an uncertainty of ±0.5 K as specified by the thermocouple manufacturer (Omega). The error in measurement of resistance was ±0.02 K as specified by the data acquisition manufacturer National Instruments). The wire traces on the sample, which extend from spring-loaded pins to the RTD, accounted for 4% of the total RTD circuit resistance. However, the temperature of the wire traces increase by half as much as the RTD, so the maximum deviation is ±0.02 K per degree temperature rise. Finally, temperature gradients during calibration resulted in ±0.022 K per degree temperature rise. In summary, the measurement uncertainty of the custom RTD was ± (0.5+0.042×ΔT) or ±1.8 K at ΔT=30 K. Figure S-1 shows an example calibration curve for the RTD, which fits the data to within ±0.1 K.
Figure S-1: Example calibration of the RTD using a thermocouple as a reference thermometer. The linear fit has a good correlation with less than 0.1 K deviation from the measured temperature as shown in the insert. However, the data have a temperature uncertainty up to ±1.8 K due to temperature gradients during calibration, wire trace resistance and measurement error of the DAQ.

II. Calculation of Evaporative Heat Fluxes
An energy balance for the sample during evaporation experiments is shown in Figure S-2. The timedependent parasitic heat loss to the sample holder was estimated by heating the sample in a dry ambient. A step rise in heat flux was applied to the sample at time t=0. At short time scales, the cold sample holder absorbed heat the fastest. As the sample holder saturated with heat, it absorbed heat more slowly. During evaporation experiments, the parasitic heat loss was assumed to be only a function of the sample temperature and time. The heat loss due to sensible cooling was calculated using the flow rate and temperature change of the liquid flowing through the sample. The remaining thermal energy was dissipated by evaporation. The evaporative heat flux can be calculated by normalizing to either the heater area (0.2 mm × 10 mm) or to the membrane area (0.172 mm x 9.7 mm). The evaporative heat flux accounts for between 72-91% of the applied heat flux depending on the substrate temperature, duration of experiment and flow conditions.

III. Experimental Setup
Samples were tested in an experimental chamber which is shown in Figure S-3. Air inside the chamber was evacuated to an absolute pressure of 3 mTorr and then the chamber was filled with vapor of the working fluid from the reservoir until the vapor pressure reached saturation conditions at room temperature or 1.4 bar in the case of R245fa. The chamber was designed and tested up to 250 psi or 17 bar for higher pressure refrigerants. The sample was visually inspected for flooding or boiling during experiments through a sapphire viewport. The sample holder, made from Ultem, a high temperature plastic, facilitated electrical and fluidic connections. Heaters and RTDs on the sample were connected to the power supply and DAQ, respectively, via spring loaded, gold plated pogo pins (HPA-1H, Everett Charles). Liquid inlet and outlet ports were connected to the sample via custom gaskets made from indium wire, which is non-porous unlike traditional gaskets made from silicone, Buna-N, or Viton.

IV. Finite Element Model
The domain used to model evaporation from the nanoporous membrane samples is shown in Figure  S-4, which is not drawn to scale. Heat flux is applied to the serpentine heater, which lies within a rectangular area 0.2 mm wide and 10 mm long, while a heat tranfer coefficient for evaporation is applied to the membrane area which is 0.172 mm × 9.7 mm. The membrane area and heater area were designed to be the same size to demonstrate scalability of the suspended membrane device for high heat flux dissipation across areas larger than 10 mm × 10 mm. An adiabatic boundary condition was applied to all other surfaces. Heat in the silicon substrate spreads in all three dimensions since the heated area is narrow compared to the thickness of the substrate. Whereas GaN devices are typically fabricated on substrates only 100 µm thick, the finite element model demonstrates that the majority of temperature drop occurs in the substrate of the tested samples (650 µm thick). temperature drop occurs in the substrate of the tested samples, which are 650 µm thick.

V. Clogging Issue
With a high surface-to-volume ratio, contamination is common in microfluidic devices. There are two types of contamination that can potentially clog membranes during evaporation: particles that are insoluble in the working fluid and nonvolatile molecular compounds that are soluble in the working fluid (e.g., hydrocarbons or salts). Solid particles can be separated from the working fluid using a filter. However, evidence during and after experiments affirms that the contamination issue observed during these experiments was with nonvolatile soluble contaminants. As contaminants were built up in the membrane, they restricted the working fluid from accessing evaporation sites, thus the heat transfer coefficient decreased and the substrate temperature increased. After the sample was flushed with fresh liquid, contaminants were removed. When the evaporation resumed, the substrate returned to the same temperature. Figure S-5 shows images of membranes after evaporation with nonvolatile residue inside the nanopores. Post-evaporation analysis with X-ray photoelectron spectroscopy (XPS) and electron discharge spectroscopy (EDS) confirmed the existance of carbon-based compounds on the surface of the membranes.