Monte Carlo simulations of gas flow and heat transfer in vacuum packaged MEMS devices
Introduction
MEMS technique has been greatly developed since the late of 1980s, and was ever expected as emerging technologies with significant potential for future growth [1]. Micro systems based on MEMS are capable of sensing and controlling physical processes with length scales on the order of 1 μm, or even sub-micron [2], [3], [4]. Despite the growing number of realized applications of MEMS in scientific and engineering devices, there is only a minimum level of understanding of the fluid dynamics and heat transfer processes in fluidic MEMS. It was pointed that the technology was progressing at a rate that far exceeded that of our understanding of the unconventional physics involved in the operation as well as the manufacturing of those minute devices [5]. Performance of MEMS often defies predictions made using scaling laws developed for large systems. Therefore, there is a pressing need for reliable computational capabilities for understanding of the thermal and fluid dynamic processes in micro systems [6].
As well known, most MEMS devices have to be packaged before usage. To get a stable performance, a vacuum environment is generally needed when packaging. Although filling with a special gas is an alternative to reduce the cost remarkably, the vacuum package is a necessary requirement for some important applications [7], [8]. The MEMS packages build up a closed system, including the chip, the gas (rarefied or not), and the package walls. The gas plays the role of transporting energies between the chip and the environment, so its flow and heat transfer characteristics are very important to the temperature-sensitive performance of the chip [9].
Rarefied or not, the gas in MEMS devices might have different behavior from the macroscopic gas due to the small characteristic length in MEMS. When the mean free path of gas is at the same order of or even much larger than the system characteristic length, the continuum assumption will break down, and the traditional CFD techniques will therefore lead to large errors [10]. Such flows should be described using a molecular point of view [11], [12]. The direct simulation Monte Carlo (DSMC) method, proposed by Bird [13], [14] is the most successful numerical method for high Knudsen number gas flows. The DSMC method was validated by comparing with experimental data of rarefied gas flows in the last century [15], [16]. In the past ten years, it has been used to predict the high Knudsen gas flow and heat transfer in microchannels [17], [18], [19], [20], [21]. Specially, the DSMC was recently extended to high Knudsen number non-ideal gas flow and heat transfer in micro- and nanochannels [22], [23].
Though the rarefied gas flow behaviors in an enclosure have been studied much in the past years [24], [25], [26], [27], [28], the present paper focuses on the gas flow and heat transfer mechanism above a hot chip in micro square enclosures by using the DSMC method. The effects of wall temperature distributions on the gas flow and heat transfer will be concerned. The results are compared with continuum-based results. The factors influencing chip cooling in vacuum packaged MEMS devices are then summarized.
Section snippets
DSMC procedure
DSMC is a molecular-based statistical simulation method for rarefied gas flow introduced by Bird [13], [14]. The method numerically solves the dynamic equations for gas flow using thousands of simulated molecules. Each simulated molecule represents a large number of real molecules. With the assumption of molecular chaos and a rarefied gas, only the binary collisions are considered, so the molecular motion and their collisions are uncoupled if the computational time step is smaller than the
Results and discussion
Here, we focus on the rarefied gas flow and heat transfer in a 2D micro square enclosure with a hot chip at the bottom by two cases. Firstly, assuming the whole bottom was a hot chip surface and the other sides were at an environment temperature, we simulate the flow and heat transfer in the enclosure by DSMC and compare with the continuum-based results. At the same time, the gravity effect on such flows and heat transfer are also checked. Secondly, we consider the hot chip is only at the
Conclusions
The flow and heat transfer in vacuum packaged MEMS devices is numerically investigated by the direct simulation Monte Carlo method. The results show that: when the bottom is a completely uniform hot chip, flow would be induced by the thermal stress difference of discontinuous temperature distribution effect. Compared with the non-slip continuum-based solution, the gas temperature gradient near the surfaces is much less when considering the rarefied gas effect. The heat transfer enhanced by the
Acknowledgement
The present work was supported by the National Natural Science Foundation of China (Grant No. 59995550-2).
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