Analysis of laminar convective heat transfer in micro heat exchanger for stacked multi-chip module

Transcription

1 Microsyst Technol (2005) 11: DOI /s TECHNICAL PAPER Moon Koo Kang Æ Joong Han Shin Æ Hae-Hyung Lee Kukjin Chun Analysis of laminar convective heat transfer in micro heat exchanger for stacked multi-chip module Received: 7 June 2004 / Accepted: 20 November 2004 / Published online: 21 July 2005 Ó Springer-Verlag 2005 Abstract This article presents a numerical and experimental investigation for the single-phase forced laminar convective heat transfer through arrays of microchannels in micro heat exchangers to be used for cooling power-intensive semiconductor packages, especially the stacked multi-chip modules (MCMs). In the numerical analysis, a parametric study was carried out for the factors affecting the efficiency of heat transfer in the flow of coolants through parallel rectangular microchannels. In the experimental study, the cooling performance of the micro heat exchanger was tested on the prototypes of stacked MCMs with different channel dimensions. The simulation result and the experiment data were acceptably accordant within a wide range of design variations, suggesting the numerical procedure as a useful method for designing the cooling mechanism in stacked multichip packages and similar electronic applications. Keywords Multi-chip module (MCM) Æ Micro heat exchanger Æ Channel aspect ratio Æ Entry length effect Nomenclature A Bottom area C p Specific heat D h Hydraulic diameter g Acceleration of gravity H Height of microchannel h Mean convective heat transfer coefficient k f, k s Thermal conductivities of fluid, solid L Length of microchannels Nu Nusselt number M. K. Kang (&) Æ H.-H. Lee Æ K. Chun School of Electrical Engineering and Computer Science, Seoul National University, Seoul, , Korea moonkang@ee.snu.ac.kr Tel.: Fax: J. H. Shin School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, , Korea Pe Pr p Q q Re u S T DT m DT i, DT o W W c x i Greek letters l Viscosity q Density Subscripts i,j f s 1 Introduction Peclet number Prandtl number Pressure Heat Heat flux Reynolds number Velocity Volume metric heat source Temperature Log mean temperature Temperature difference between solid and liquid at inlet and outlet Width of microchannel Center-to-center distance of microchannels Coordinates Direction indices Fluid Solid With the increasing power density of the semiconductor chips used in many electronic devices, the cooling problem has become a subject of prime interest. The durability of an electronic device is seriously influenced by the maximum operating temperature, and hence lowering the maximum operating temperature via pertinent cooling systems is crucial, especially for highly power-intensive semiconductor chips. In modern electronic devices, a rapid reduction of the circuit board size is underway, necessitating space-efficient chip designs

2 1177 such as stacked multi-chip modules (MCMs) along with the compatible cooling systems. To increase the maximum power handling of electronic devices, micro-sized heat exchangers incorporating liquid coolants are becoming more important. In the early 1980s, Tuckerman and Pease showed that the electronic chips could be effectively cooled down by water flow in microchannels fabricated inside the packages or on the circuit board where the chips were mounted (Tuckerman and Pease 1982, 1991). The dissipated heat per area was about W/m 2 for a surface temperature maintained below 130 C, confirming this technology as a potential cooling option. In the later works by Peng and Wang (1998), Choi et al. (1991), Weisberg et al. (1992) and Bower and Mudawar (1994), the heat transfer and liquid flow through microchannels was investigated in more detail. Peng et al. (1995) and Peng and Peterson (1995) considered the convective heat transfer with or without phase change of the cooling fluid in microchannel structures. Recently, convective heat transfer including phasechange in microchannels has been investigated experimentally and numerically. Zhang et al. (2002) conducted an experimental measurement and developed a model for two-phase flow in microchannels. Hetsroni et al. (2001) observed the patterns of two-phase flow of vapor and water in parallel microchannels using a microscope and a high-speed video camera. According to their observation, flow boiling in parallel microchannels was found to considerably enhance the heat transfer rate, although the boiling water in microchannels became hydraulically unstable. Peterson and Ortega (1990) reviewed preceding researches and developments in the thermal control of electronic devices that have high power densities, and concluded that the best way to decrease the temperature is to locate the heat sink as close to the device junction as possible. In this study, the laminar convective heat transfer through parallel rectangular microchannels was simulated numerically, and the resulting numerical data was summarized in a table, or a formula, so that it can be used to determine the design parameters and to predict the cooling performance of parallel microchannels of different configurations. The numerical results were compared with the experimental data for verification. To illustrate a sample usage of this formula, the laminar convective heat transfer in micro heat exchangers for stacked MCMs was predicted by the suggested formula and then compared with the numerical results and experimental results. þ i i þ u i þ qg 2 j ð1þ For steady flows of small flow rates and micro-scale dimensions, the transient, the inertial and the gravitational terms can be neglected such that Eq. 1 is reduced to Eq þ u 2 ð2þ j Convection heat transfer in an array of microchannels is significantly different from the flow in a single channel. The channel width and depth, as well as the spacing between channels, are also important factors to affect the overall cooling performance. Since a general analytic relation can hardly be found for such a configuration, the flow through arrays of channels with different dimensions should be determined either experimentally or numerically. From the work of Peng and Peterson (1996), an empirical model was suggested for the Nusselt number for the convective laminar heat transfer through an array of parallel rectangular microchannels as follows. Nu ¼ 0:1165 D 0:81 h H 0:79 Re 0:62 Pr 1=3 ð3þ W c W q 00 ¼ Q A h ¼ q00 DT m ; DT m ¼ DT i DT o lnðdt i =DT o Þ ð4þ ð5þ Nu ¼ hd h ; D h ¼ 2HW ð6þ k f H þ W where Q is the total heat and A is the area of the bottom surface, and subscripts i and o denote the inlet and the outlet, respectively. As shown in Fig. 1, W is the width of the channel, H is the height of the wall, and W c is the length between channel centers. D h is the hydraulic diameter. They designed twelve different arrays of microchannels and evaluated the effects of channel width, depth and wall thickness on the heat transfer performance. In this case, they fixed the channel length to 45 mm and the flow was assumed to be fully developed. For many real micro devices, however, the channel length is much shorter, and it is unreasonable to use this 2 Laminar convective heat transfer in parallel rectangular microchannels 2.1 Conventional modeling The Navier Stokes equation to describe the momentum balance in fluids is given as follows. Fig. 1 Cross-section of the microchannels

3 1178 formula to predict the flow through short channels because the entrance effect becomes significant. In Sect. 2.2, we suggest engaging a correction factor L/D h which is the ratio of the channel length to the hydraulic diameter, so that the modified formula can be used for developing flows of shorter lengths. Fig. 2 Array of parallel rectangular microchannels 2.2 Modification of the empirical formula A modification was made to Eq. 3 to account for different total lengths of the micro channels. An Eq. 7 shows the modified formula to consider the channel length effect, in which the ratio of channel length to hydraulic diameter (L/D h ) is introduced. m 0:81 L Dh H 0:79 Nu ¼ a Re n Pr 1=3 ð7þ W D h W c Fig. 3 Coordinate system Using the definition of Reynolds number and Prandtl number, Eq. 7 can be rewritten as follows. m 0:81 L Dh H 0:79 qud n h m 1=3 Nu ¼ a ð8þ W l a D h W c By using Eq. 8 with proper model constants, the convective heat transfer rate can be obtained for laminar flows through parallel rectangular microchannels of short length. For simplicity, the powers 0.81, 0.79 and 1/3 were kept the same as in the empirical formula of Peng and Peterson (1996). 2.3 Determination of the model constants To determine the model constants in Eq. 8, we performed numerical simulation for 18 different sample arrays of microchannels. One typical example is shown in Fig. 2. The coordinate system for a channel is given in Fig. 3. First, the experimental result by Peng and Fig. 4 Nusselt number as a function of pressure drop. a Channel length: 45 mm. b Channel length: 10 mm Fig. 5 Nusselt number as a function of the channel width and the center-to-center distance of channels

4 1179 Fig. 6 Stacked multi-chip module (MCM) Peterson (1996) for the array of sufficiently long rectangular channels was compared to the numerical simulation. Figure 4 shows the values of the Nusselt number from the experimental and numerical results as a function of pressure drop between the inlet and outlet. For the total channel length of 45 mm, the values of Nusselt number from the experiment and the numerical simulation are in good agreement. Next, the channel length was reduced to 10 mm, and the result of Eq. 3 was compared to the new simulation output. As was expected, the result for 10 mm of total length was quite different for the case of 45 mm length. This is because Eq. 3 is suited for long channels that can be considered as fully developed and the length effect is neglected, while the numerical simulation can handle arbitrary channel lengths. This result confirms that short channel Fig. 7 The boundary conditions and the geometry. a Boundary condition. b Cross section of A-A. c Top view. d Front view. e Side view arrays require a modified formula such as Eq. 8 to account for the channel length effect. For this, we conducted 18 numerical simulations for different channel lengths of 10 mm, 25 m and 45 mm, and the channel widths and lengths were varied from 50 to 1000 lm. The model constants a,m and n were then found by curve fitting the numerical simulation data to Eq. 8. The other constants 0.81, 0.79 and 1/3 were simply taken from Eq. 3. Using the model constants obtained by curve fitting, sensitivity test was carried out for the channel widths and distances. In Fig. 5, Nusselt number predicted by Eq. 8 was plotted as a function of channel width (W) and center-to-center distance (W c ). As can be seen from Fig. 5, the heat transfer rate improves with increasing W and decreasing W c, showing the same tendency as the results from Peng and Peterson (1996). In real cases, however, the actual channel width and center-to-center distance will be structurally limited such as too thin channel bulkheads being collapsible, etc. 3 Investigation for stacked multi-chip modules 3.1 Stacked multi-chip module (MCM) The proposed formula was applied to a stacked multichip module (MCM), which is an emerging packaging technology to reduce the size of semiconductor chips

5 i ¼ 0 qu i þ u 2 j ð9þ ð10þ Fig. 8 Schematic of the heat exchanger and electronic devices. As shown in Fig. 6, two chips are stacked on the same footprint on the circuit board and wire bonded. When a micro heat exchanger is inserted between these two chips, the heat generated from the two chips should be removed by the heat exchanger so that the chips become thermally safe. In this study, both numerical simulation and experimentation were carried out for the stacked MCMs with various channel dimensions. 3.2 Numerical analysis for stacked multi-chip module Governing equations The governing equations for the flow analysis and thermal analysis of the stacked MCM are to be considered. For the cooling fluid, the conservations of mass, momentum and energy can be written as qc p u k f i For solid regions including two chips and channel walls, the following conduction equation can k s þ S ¼ 0 i In Eq. 12, S stands for the heat generation from the semiconductor chips. The phase change of water was not taken into consideration FVM model The geometry and the boundary conditions for the micro heat exchanger are shown in Figs. 7 and 8. The external surface of the whole domain was considered to be adiabatic. At the inlet of the heat exchanger, the pressure was varied from 500 to 10,000 Pa. The pressure at the outlet was set to 0 Pa. Chips 1 and 2 were appointed as uniform volumetric heat sources. Nine different channel dimensions were considered as shown in Table 1. The material properties were assumed to be constants as in Table 2. Figure 9 shows the numerical mesh for the calculation domain. The fournode tetrahedral elements were used. The total number of elements ranged between 500,000 and 800,000, depending on the channel width. The simulation was conducted by using Table 1 Geometric parameters of the channel arrays Number of channels W (mm) W c (mm) L (mm) H (mm) D h (mm) H/W D h /W c L/D h Table 2 Material properties used in the calculation Density (kg/m 3 ) Thermal conductivity (w/m-k) Viscosity (kg/m-s) Specific heat (kj/kg-k) Water Silicon PDMS (Polydimethylsiloxane)

6 1181 Fig. 11 Maximum temperature of the chip as a function of channel width at the pressure drop of 5000 Pa between inlet and outlet the commercial software FLUENT with the following options. Steady state Incompressible fluid Laminar viscous model Segregated solution algorithm The flowchart of the numerical simulation is given in Fig Numerical results Fig. 9 Numerical mesh. a Entire domain. b Heat exchanger. c Fluid zone Simulation was carried out for the convection heat transfer in the micro heat exchanger. Based on the simulation data, we could locate an optimal window of dimensional parameters such as the channel width, Fig. 10 Flowchart of the numerical simulation Fig. 12 Flow rate as a function of channel width at the pressure drop of 5000 Pa between inlet and outlet

7 1182 number of channels and the distance between channels. For a given channel configuration, the key factor was the total flow rate through microchannels. To lower the maximum operation temperature, it was necessary to increase the flow rate by raising the inlet pressure. Figure 11 shows the maximum temperature of the chips as a function of the channel width under constant inlet pressure. The rise of maximum temperature becomes more severe for smaller channel widths, because the flow rate is reduced significantly. Figure 12 shows the plot of flow rate through microchannels as a function of the channel width. Figure 13 shows the maximum temperature of the chip as a function of the channel width for different dissipated powers and different inlet pressures. In Fig. 13, the maximum temperature rises drastically for decreasing channel widths under 1 lm. The rise of maximum temperature for small channel width is related to the change of convective heat transfer coefficient with flow rate. For high flow rates, the rise of maximum Fig. 13 Maximum temperature of the chip as a function of channel width at various pressure drop between inlet and outlet. a Chip power: 2 W. b Chip power: 4 W. c Chip power: 6 W. d Chip power: 8W Fig. 14 Maximum temperature of the chip as a function of the pressure drop between inlet and outlet (number of channels = 15) temperature is moderate because the heat transfer coefficient is sufficiently large. For small flow rates, however, the heat transfer coefficient decrease considerably and the maximum temperature increases rapidly.

8 1183 Fig. 15 Pressure distribution in microchannels. a Number of channels = 5. b Number of channels = 10. c Number of channels = 20. d Number of channels = 40. e Number of channels = 50. f Number of channels = 60 Figure 14 shows the maximum temperature of the chip as a function of the pressure drop between the inlet and the outlet. According to Fig. 14, raising the inlet pressure above a certain level does not seriously help in reducing the maximum temperature. For high flow rates, the conduction resistance of the micro heat exchanger becomes the bottleneck for cooling, and the maximum cooling rate is limited. The uniformity of temperature can be another important factor to be considered when designing the heat exchangers. Figure 15 shows the pressure distribution in the microchannels. The pressure gradient and the flow rate in microchannels become nearly constant with increasing number of channels, the temperature becomes more uniform, and the hot spots at the corners are tempered for larger number of channels. 3.3 Experimental results Fabrication of the heat exchanger The Su-8 50 photo resist molds on a silicon wafer of different sizes were fabricated by two-layer lithography method (Zhang et al. 2001). Figure 16 shows the sim-

9 1184 Fig. 16 The SU-8 mold fabrication process plified mold fabrication process. In the first step, Su-8 50 mold was spin coated on a silicon wafer of 200 lm thickness at a spin rate of 850 rpm for 30 s. This mold was pre-baked at 65 C for 30 min and at 135 C for 30 min. After this, the soft-baked wafer was lithographed at 720 mj/cm 2. The second layer of Su-8 50 mold was spin coated on the wafer of 250 lm thickness at a spin rate of 750 rpm for 30 s. The coated Su-8 50 mold was pre-baked at 65 C for 30 min and at 95 C for 120 min and lithographed at 840 mj/cm 2. After this, the post-exposure baking process was carried out at 95 C for 30 min. The bottom mold is shown in Fig. 16 (g). To fabricate the top mold, a silicon wafer on a glass (SOG) wafer was used. The SOG wafer was patterned and overetched by using the deep silicon etcher. To make the PDMS heat exchanger, raw PDMS resin was mixed with the hardener at 10:1 ratio and degassed in a vacuum chamber. The PDMS mixture was cast on the bottom mold and the top mold is stacked on it. The PDMS mixture was cured at 75 C for 30 min. The cured Fig. 18 The MCM assembly PDMS layer was then peeled off from the mold. The patterned device was bonded to a flat, 50 lm-thick PDMS film via O 2 plasma surface treatment. Figure 17 shows the fabricated PDMS heat exchanger and the Su-8 mold Integration of the cooler with the chips Figure 18 shows the stacked MCM assembly. To emulate the function of real chips as the heat sources, the thermo-chips were used. Each thermo-chip includes two polysilicon thermo-resistors (heater) and five thermal diodes (temperature sensor). The size of a thermo-chip Fig. 17 Fabrication of PDMS heat exchanger (left) and SU-8 mold (right) Fig. 19 Packaging of MCM assembly by using epoxy mold compound (EMC)

10 Experimental results Fig. 20 Schematic of the experimental apparatus was 8 8 mm 2. The first thermo-chip was attached on the PCB, and the micro heat exchanger and the second thermo-chip were stacked on it. Au-wire was bonded to the chips. The assembly was finally packaged in epoxy molding compound (EMC) by injection molding. Figure 19 shows the MCM packaged in EMC. Fig. 21 Experimental data and simulation results for the maximum temperature as a function of the channel width. a Chip power: 2 W. b Chip power: 4 W. c Chip power: 6 W. d Chip power: 8 W Figure 20 shows the schematic of the experimental apparatus. The water flow rate was controlled by a syringe pump and two pressure transducers were located at the inlet and outlet to detect the pressure drop between the inlet and outlet. The temperature was measured using five thermal diodes installed in the thermo-chip. The voltages measured from thermal diodes were translated into temperature by using the following calibration curve. T ¼ 505:2 611:8V ð CÞ ð12þ (at diode sensing current of 1 ma) The simulation output and the experimental data were plotted in the same graphs to compare the results. As can be seen in Figs. 21 and 22, the experimental data are in a good match with the simulation results. 4 Conclusions A numerical and experimental investigation was conducted for the single-phase forced laminar convective

11 1186 References Fig. 22 Experimental data and simulation results for the maximum temperature as function of the pressure drop between inlet and outlet (number of channels = 15) heat transfer in the arrays of micro channels. The output from the numerical simulation was curve fitted to a suggested formula. The formula after curve fitting was used to predict the heat transfer efficiency in parallel rectangular microchannels with different channel dimensions. The simulation procedure was also applied to a micro heat exchanger inserted between two heatgenerating semiconductors stacked vertically MCM, and the cooling performance of the heat exchanger was analyzed. The numerical result was then verified experimentally for a few prototypes of stacked MCMs. A close agreement was found between the simulation result and the experimental data. Acknowledgment The authors wish to acknowledge the financial support and cooperation from Samsung Electronics Inc., Korea, in the course of this study. Bowers MB, Mudawar I (1994) High flux boiling in low flow rate, low pressure drop mini-channel and microchannel heat sinks. Int J Heat Mass Transfer 37(2): Choi SB, Barron RF, Warrington RO (1991) Liquid flow and heat transfer in microtubes. In: Cho D et al (eds) Micromechanical sensors, actuators and systems, vol 32. ASME DSC, pp Hetsroni G, Mosyak A, Segal Z (2001) Non-uniform temperature distribution in electronic devices cooled by flow in parallel microchannels. IEEE Trans Components Packaging Technol 24(1):16 23 Peng XF, Peterson GP (1995) The effect of thermo-fluid and geometric parameters on convection of liquid through rectangular microchannels. Int J Heat Mass Transfer 38(4): Peng XF, Peterson GP (1996) Convective heat transfer and flow friction for water flow in microchannel structures. Int J Heat Mass Transfer 39(12): Peng XF, Wang BX (1998) Forced convection and boiling characteristics in microchannels. In: Proceedings of the heat transfer 11th IHTC 98, vol 1. Kyongiu, Korea, August 23 28, pp Peng XF, Wang BX, Peterson GP, Ma HB (1995) Experimental investigation on forced-flow convection of liquid flow through microchannel. Int J Heat Mass Transfer 38(1): Peterson GP, Ortega A (1990) Thermal control of electronic equipment and devices. In: Advances in heat transfer, vol 17. Pergamon Press, Oxford, pp Tuckermann DB, Pease RFW (1982) Optimized convective cooling using micromachined structure. J Electrochem Soc 129(3):C98 Tuckermann DB, Pease RFW (1991) High-performance heat sinking for VLSI. IEEE Electron Device Lett EDL 2(5): Weisberg A, Bau HH, Zemel J (1992) Analysis of microchannels for integrated cooling. Int J Heat Mass Transfer 35(10): Zhang L, Koo JM, Jiang L, Asheghi M, Goodson KE, Santiago JG, Kenny TW (2002) Measurements and modeling two-phase flow in microchannels with constant heat flux boundary conditions. J Micro-electromech Syst 11(1):12 19 Zhnag J, Tan KL, Hong GD, Yang LJ, Gong HQ (2001) Polymerization optimization of SU-8 photoresist and its applications in microfluidic system and MEMS. J Micromech Microeng 11(1):20 26