IEEE TRANSACTIONS ON ADVANCED PACKAGING, VOL. 28, NO. 4, NOVEMBER 2005 619

A Micromachined Pirani GaugeWith Dual Heat Sinks

Junseok Chae, Member, IEEE, Brian H. Stark, and Khalil Najafi, Fellow, IEEE

Abstract—This paper reports a micromachined Pirani gaugewith dual heat sinks that can be integrated with microelectrome-chanical systems (MEMS) devices inside a vacuum package tomonitor long-term pressure changes and stability inside thepackage. The Pirani gauge utilizes small gaps ( 1 m) betweenits heater and two thermal heat sinks to obtain large dynamic range(20 mtorr to 2 torr) and high sensitivity (3.5 105 (K/W) torr).The gauge is 2 2 mm2 in size, is fabricated using the dissolvedwafer process (DWP) on a glass substrate, and utilizes dielectricbridges for signal routing. Measurements show the low end ofthe dynamic range can be extended by reducing the gap distancebetween the heater and thermal sinks, which matches well withanalytical modeling. This gauge shows an uncertainty of 50 torrand a detectable leak rate of 3.1 10 16 cm3 s, assuming acommon micropackage volume of 1.6 10 5 cm3, which rep-resents at least four orders of magnitude improvement overtraditional leak testing.

Index Terms—Microelectromechanical systems (MEMS), Pack-aging, Pirani gauge, pressure sensor.

I. INTRODUCTION

CHARACTERIZATION of vacuum micropackages devel-oped for microelectromechanical systems (MEMS) de-

vices, such as resonant sensors and RF MEMS, has utilizedsuch techniques as Helium leak testing and factor extrac-tion [1], [2]. These methods are limited either by high cost (He-lium leak test) or sensor drift and lack of sufficient sensitivity atlow pressures ( factor extraction) and, thus, cannot preciselymeasure minute pressure changes inside a sealed microcavity.Pirani gauges address these limitations by offering a low-cost,easy to use, and high-sensitivity device. Since the Pirani gaugewas invented in 1906 [3], absolute pressure sensors that utilizethermal conductance changes, such as Pirani gauges, are widelyused in vacuum systems [4], [5]. By taking advantage of micro-machining technology, a number of miniaturized Pirani gaugeshave been reported [6], [7], which are sometimes integrated withreadout electronics on a single chip to achieve high resolution[8], [9]. In addition to these stand alone devices, micromachinedPirani gauges to test the environment inside a MEMS package

Manuscript received November 15, 2004; revised May 31, 2005. This workwas supported in part by the Engineering Research Centers Program of the Na-tional Science Foundation under Award EEC-9986866.

J. Chae was with the Department of Electrical Engineering and ComputerScience, Center for Wireless Integrated Microsystems, University of Michigan,Ann Arbor, MI 48109-2122 USA. He is now with the Electrical EngineeringDepartment, Arizona State University, Tempe, AZ 85044 USA (e-mail:junseok.chae@asu.edu).

B. H. Stark and K. Najafi are with the Department of Electrical Engineeringand Computer Science, Center for Wireless Integrated Microsystems, Univer-sity of Michigan, Ann Arbor, MI 48109-2122 USA.

Digital Object Identifier 10.1109/TADVP.2005.858316

have also been developed [9]–[11]. In order to detect small leakrates in a MEMS package, the gauge should not only be com-patible with the package fabrication technology but also shouldoffer high sensitivity and large dynamic range.

In this paper, we present a micromachined Pirani gauge fab-ricated using the dissolved wafer process (DWP) which usesheavily boron-doped (p++) silicon as its structural material. Thegauge can be integrated with a variety of sensors fabricated inthis technology [12], [13], and also with wafer-level vacuumpackages, and can, thus, be used for in situ vacuum testing.Furthermore, we have introduced a new structure with dualthermal heat sinks with small m gaps that provides largerdynamic range and higher sensitivity than traditional devices thatutilize only one thermal sink. In Sections II–IV, first we presentthe operating principle and analytical modeling of a Pirani gauge.Next, performance improvements, including increased dynamicrange and sensitivity by implementing the dual heat sink config-uration is introduced. Then, the fabrication process is describedin detail. Finally, measurement results such as dynamic range,sensitivity, the effect of air gap distance and effective heaterarea on gauge performance, and the minimum detectable leakrate are presented followed by concluding remarks.

II. SENSOR DESIGN

A. Operating Principle

The operation of a Pirani gauge is based on heat transfer froma suspended heater to a heat sink through a gas. The thermal con-ductance through the gas is a function of its pressure. Dependingon the Knudsen number ( , is mean free path of agas, is the dimension of the domain), the gas can be modeledas in a continuum regime at high pressure or can bein a molecular regime at low pressure [Fig. 1(a)][14], [15]. With reasonable assumptions and approximations,heat flux, which is a function of ambient pressure forall , can be modeled as [16]

(1)

where is an empirical transition pressure. This has alinear dependence on at low pressure and limits to a constant

at high pressure, which determines the upper limit of thedynamic range.

From the simple heater and heat sink model shown in Fig. 2,can be found as [8]

(2)

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620 IEEE TRANSACTIONS ON ADVANCED PACKAGING, VOL. 28, NO. 4, NOVEMBER 2005

Fig. 1. Heat flux and thermal conductance versus pressure. (Color versionavailable online at http://ieeexplore.ieee.org.)

Fig. 2. Simplified schematics of Pirani gauge. (Color version available onlineat http://ieeexplore.ieee.org.)

where , , and are the width, thickness, and the perimeterof the heater, and is the distance between the heater and heatsink. Reducing the gap between the heater and heat sink is themost effective method of increasing the high-pressure limit ofthe dynamic range since typically is much smaller than 1.

The lower limit of the dynamic range is determined by heattransfer through the solid support anchors (solid conduction,

). Assuming the heater is a lossless thermal conductor, thetotal thermal conductance of the heater is the sum of conduc-tances due to solid conduction, gaseous conduction, gaseousconvection, and radiation. Radiation can be ignored at lowtemperature, and gaseous convection can be neglected becausethe Pirani gauge is usually placed inside a package where noexternal forced gas convection exists [17]. Modeling constantsolid conduction over pressure, the total thermal conductanceat low pressure is dominated by solid conduction. Therefore,in order to obtain large dynamic range, a Pirani gauge needsto be designed to have a small gap distance and minimal solidconduction.

Fig. 3. Effects of dual heat sinks on the sensitivity and the dynamic range (SHSand DHS stand for single heat sink and dual heat sinks, respectively.Gis ignored). (Color version available online at http://ieeexplore.ieee.org.)

The sensitivity of the Pirani gauge is the slope of the totalthermal conduction versus pressure as shown inFig. 1(b). Gaseous thermal conductivity can be modeled as [16]

(3)

where is gaseous thermal conductivity, is thermal con-ductance of the gas, and is the area of the heater. The sensi-tivity can be obtained as

(4)

This parameter can be modeled with a simpli-fied heater and heat sink model (Fig. 2) [16]

Sensitivity

(5)

where is the length of the heater. Typically, the width of theheater is much larger than its thickness ; thus, the sensi-tivity is proportional to the area of the heater.

In order to increase the sensitivity and the dynamic rangeof the Pirani gauge, we have implemented dual heat sinks in-stead of the conventional single heat sink. By doing so, bothgaseous conduction and effective heater area are increased toobtain high sensitivity and large dynamic range; gaseous con-duction increases because heat flux can be absorbed by twoheat sinks. Fig. 3 shows the effects of the dual heat sink configu-ration on the sensitivity and the dynamic range of a Pirani gauge.The dual heat sink configuration offers a high-performance Pi-rani gauge. However, implementing the dual heat sink configu-ration is technically challenging because it is necessary to haveboth heat sinks located evenly from the heater with minimal gapspacing.

III. FABRICATION

Two types of Pirani gauges have been developed: one is atraditional vertical heat transfer configuration, and the other

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CHAE et al.: MICROMACHINED PIRANI GAUGE WITH DUAL HEAT SINKS 621

Fig. 4. Proposed Pirani gauges with dual heat sinks. (Color version availableonline at http://ieeexplore.ieee.org.)

TABLE IDESIGN SPECIFICATIONS OF THE PROPOSING PIRANI GAUGES

is a lateral configuration (Fig. 4). The vertical configurationhas a thin metal resister (Cr/Pt, 200/300 ) on a dielectricmembrane anchored to p++ silicon. P++ silicon and a glasssubstrate form the top and bottom heat sinks. Each p++ siliconisland is electrically isolated and is defined by deep reactiveion etch (DRIE). The p++ silicon can be utilized as a structuralmaterial for a variety of MEMS devices that need vacuumenvironment for their operation. Thus, the proposed Piranigauges can be integrated with these MEMS devices to monitorpressure changes. A metal layer on a dielectric bridge transferssignals from the substrate to the bond pads. To ensure electricalcontact to p++ silicon, a contact metal is deposited over thethin resister. The distance between the heater and heat sinks isonly 0.4 m. The lateral gauge employs p++ silicon as bothheater and heat sinks. The two heat sinks are separated from theheater by 1 m which is defined by DRIE. The vertical gaugeis made in a six-mask process, while the lateral gauge requiresonly two masks. Table I shows the design specifications of theproposed Pirani gauges [18].

The fabrication process for these Pirani gauges is shown inFig. 5. The vertical gauge process starts with blanket high-con-centration boron doping of a silicon wafer. Then, LPCVD

Fig. 5. Fabrication process. (Color version available online athttp://ieeexplore.ieee.org.)

Si N , which forms a boron diffusion barrier, and sacrifi-cial polysilicon layers are deposited and patterned. Next, a750-nm-thick LPCVD SiO Si N SiO membrane and me-andering Cr/Pt (200/300 ) resister are formed. The Cr/Pt layeralso forms electrical connections between the mechanicallyisolated p++ islands. This is followed by DRIE to form fluidicaccess to the sacrificial polysilicon layer and to isolate p++islands for subsequent anisotropic wet etch such as ethylene–di-amine pyrocatechol (EDP). The silicon device wafer is thenbonded to a recessed glass wafer, and EDP etching releases themembrane. The lateral devices, which have minimal processcomplexity and reasonable performance, are manufactured ina two-mask process. Fabrication begins with a blanket borondoping followed by DRIE to isolate the heater and heat sink.Fabrication is completed after the silicon wafer is bonded to arecessed glass support wafer and etched in EDP. Fig. 6 showsfabricated Pirani gauges.

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622 IEEE TRANSACTIONS ON ADVANCED PACKAGING, VOL. 28, NO. 4, NOVEMBER 2005

Fig. 6. Photograph of the fabricated Pirani gauges. (Color version available online at http://ieeexplore.ieee.org.)

IV. TEST RESULTS

A. Pirani Gauge Characterization

The sensors are characterized inside a vacuum chamber usinga standard four-point probe measurement to extract the pres-sure-dependent thermal impedance [10]. A current source with10-nA resolution (Keithley 225 A) forces a constant current tothe gauge, and the voltage drop across the gauge is measuredusing a standard four-point probe configuration. Temperatureis determined from the measured resistance of the gauge withgiven temperature coefficient of resistance (TCR) while poweris measured from the current and voltage product. Current is in-creased until the gauge reaches a preset temperature C ,and then a linear curve fit is applied to the power versus tem-perature data to extract thermal impedance that is a slope ofthe linear curve. As pressure decreases, the slope of the curve(thermal impedance) increases; thus, we can extract the pres-sure dependent thermal impedance of the device. Fig. 7 showsthermal impedance of a lateral device versus ambient pressure.

Fig. 8 shows the thermal impedance versus ambient pressurefor vertical and lateral gauges. The vertical device shows highersensitivity and larger dynamic range due to larger heater areaand smaller gap distance between the heater and heat sinks.Fig. 9 shows the variance in thermal impedance measurements.This presents an uncertainty of 4 mtorr and 50 absolutepressure at 100 mtorr for lateral and vertical devices, respec-tively. The uncertainty of 4 mtorr and 50 indicates the Pi-rani gauges can measure leak rates as low as 2.3 10 cm sand 3.1 10 cm s, respectively, assuming a common mi-cropackage volume of 1.6 10 cm . Measured specificationsof the Pirani gauges are summarized in Table II.

B. Effect of Air Gap Distance to Performance of Pirani Gauges

According to (2) in Section II, (empirical transitionpressure) is inversely proportional to (distance between heaterand heat sink). When the distance decreases, increases aschanging Knudsen number ( , ), whichresults in small thermal impedance at high pressure and large

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CHAE et al.: MICROMACHINED PIRANI GAUGE WITH DUAL HEAT SINKS 623

Fig. 7. Thermal impedance (slope) of a lateral device versus ambient pressure. (Color version available online at http://ieeexplore.ieee.org.)

Fig. 8. Extracted thermal impedance of the Pirani gauges versus pressure.(Color version available online at http://ieeexplore.ieee.org.)

Fig. 9. Variance of thermal impedance measurements. (Color version availableonline at http://ieeexplore.ieee.org.)

dynamic range. We have tested identical lateral Pirani gaugesexcept for their different gap distance to see if the gap distancechanges the thermal impedance at high pressure. Table III showsthermal impedance data of the gauges with 1.1- and 2.1- mgap distances. As the gap decreases, the thermal impedancedecreases by 5.1%, which matches well with calculated valuesbased on a simple two-dimensional analytical model [8], [19].

TABLE IIMEASURED PIRANI GAUGES SPECIFICATIONS

We also compared the measured data at low pressure (10 mtorr).The measured data are a bit lower than what we expect. Thismight be due to nonuniform temperature distribution of theheater. For bridge-type Pirani gauges, the center of the heateris at a higher temperature than the edges due to proximityto anchor points. This nonuniform temperature distributionmight result in the smaller thermal impedance at low pressurethan that calculated using a simple analytical model whichassumes that the temperature of the heater is constant. Thesmall thermal impedance also could be from parasitic heat lossto the glass substrate. Although the gap between the heater andthe substrate is larger (3 m) than between the heater and p++silicon (1.1 m), some heat dissipates to the glass substrate.

C. Effective Area to Performance of the Gauges

The sensitivity of the Pirani gauge is approximately propor-tional to the area of the heater and heat sinks as shown in (5).It should be noted that the sensitivity is a strong function of thearea, not the area to volume ratio. Obviously, microscale de-vices, including the micro-Pirani gauge developed in this work,generally have very large surface area to volume ratio compared

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624 IEEE TRANSACTIONS ON ADVANCED PACKAGING, VOL. 28, NO. 4, NOVEMBER 2005

TABLE IIIDEPENDENCE OF THE THERMAL IMPEDANCE TO THE GAP DISTANCE

Fig. 10. Effective area versus sensitivity of the Pirani gauge. (Color versionavailable online at http://ieeexplore.ieee.org.)

to macroscale devices. However, the operating principle of thegauge is dependent on heat flux from the heater to heat sinks.This is the amount of heat that is transferred per unit area in aunit of time. Therefore, volume does not play a significant rolefor heat flux. The volume of the gauge contributes to the thermalcapacitance and thermal mass of the heater, and these in turn af-fect the thermal time constant.

We have tested two types of lateral design Pirani gaugeswhich have the same gap distance but have different heaterand heat sink areas. The large device (L19) has a larger heaterarea (not heat sink) by a factor of 2.67 than the small device(L15). However, the small device has heat sinks surrounding itsentire heater, while only 80 of the large device’s heater issurrounded by heat sinks. Therefore, the effective heater area ofthe large device decreases, and the ratio of the effective heaterarea becomes 2.14. Fig. 10 shows thermal conductanceversus pressure for these two devices. We took four deviceseach for both types on a wafer to check the uniformity of deviceperformance characteristics. As error bars show, except at verylow pressure the measurements demonstrate less than 3% de-viation for most of the pressure range. Sensitivity, the slope inthe figure, is proportional to the effective heater area. The largedevice has higher sensitivity than the small device by a factorof 1.85 which is less than what is expected from analyticalmodeling. This is because of parasitic heat loss to the glasssubstrate. Heat flux from the heater of lateral design devices

can be dissipated either to p++ silicon or glass substrate. Thisundesirable parasitic heat loss can be minimized by simplyincreasing the distance to the substrate.

V. CONCLUSION

Micromachined Pirani gauges with dual heat sinks have beendeveloped to monitor long-term pressure changes and stabilityinside the package. The gauges can be integrated with MEMSdevices using the dissolved wafer process inside a small vacuumpackage. Two thermal sinks have been implemented in order toobtain high sensitivity and large dynamic range. We have devel-oped two different designs of Pirani gauges: vertical and lateralconfiguration. Vertical devices requiring six masks show higherperformance than lateral devices which only need two masks.The vertical device has large dynamic range (20 mtorr–2 torr)and high sensitivity (3.5 10 K/W torr) with uncertaintyof 50 . Assuming a common micropackage volume of1.6 10 cm , the gauge can resolve leak rates inside a smallsealed cavity as low as 3.1 10 cm s, which representsat least four orders of magnitude improvement over traditionalhelium leak testing with a substantially reduced cost.

ACKNOWLEDGMENT

The authors would like to thank Dr. H. Kulah, B. Casey, andS. Kim for wire bonding, device packaging, and device char-acterization. They also thank the staff at Wireless IntegratedMicro-Systems (WIMS), the University of Michigan.

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[8] C. H. Mastrangelo and R. S. Muller, “Microfabricated thermal absolute-pressure sensor with on-chip digital front-end processor,” IEEE J. Solid-State Circuits, vol. 26, no. 12, pp. 1998–2007, Dec. 1991.

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Junseok Chae (M’03) received the B.S. degree inmetallurgical engineering from Korea University,Seoul, in 1998, and the M.S. and Ph.D. degrees inelectrical engineering and computer science fromthe University of Michigan, Ann Arbor, in 2000 and2003, respectively.

From 2000 to 2005, he was a Postdoctoral Re-search Fellow at Wireless Integrated MicroSystems(WIMS), University of Michigan. He joined the fac-ulty of Arizona State University, Tempe, in August2005, where he is currently an Assistant Professor in

electrical engineering. His areas of interests are MEMS sensors, mixed-signalinterface electronics, MEMS packaging, ultrafast pulse (femto-second) laserfor micro-/nanostructures, and cell-on-a-chip bio-MEMS. He had an invitedtalk at Microsoft, Inc. regarding “MEMS technology for consumer electronicapplications” and holds a couple of U.S. patents.

Dr. Chae received the first place prize and the Best Paper Award at the DesignAutomation Conference (DAC) student design contest in 2001 with the paperentitled “Two-dimensional position detection system with MEMS accelerom-eter for mouse application.”

Brian H. Stark was born in Boston, MA, in 1977.He received the B.S. degree in electrical engineering(cum laude) from Cornell University, Ithaca, NY, in1999 and the M.S. and Ph.D. degrees in electricalengineering with a major in solid-state theory and aminor in circuits and microsystems from the Univer-sity of Michigan, Ann Arbor, in 2002 and 2004, re-spectively.

During his undergraduate career, he interned at theJet Propulsion Laboratory, where he worked on pro-cesses related to MEMS reliability. His work there

culminated with his authorship of a MEMS reliability guideline, which remainsthe only published book on MEMS reliability. From 1997 to the present, he hasalso presided as the CEO of Stark Software, a small company that has createdsoftware packages for the medical community. He has had over 20 refereed pub-lications since 1997.

Khalil Najafi (S’84–M’86–SM’97–F’00) receivedthe B.S., M.S., and Ph.D. degrees in electricalengineering from the Department of ElectricalEngineering and Computer Science, University ofMichigan, Ann Arbor, in 1980, 1981, and 1986respectively.

From 1986 to 1988, he was a Research Fellow,from 1988 to 1990 as an Assistant Research Scientist,from 1990 to 1993 as an Assistant Professor, from1993 to 1998 as an Associate Professor, and sinceSeptember 1998 as a Professor and the Director of

the Solid-State Electronics Laboratory, Department of Electrical Engineeringand Computer Science, University of Michigan. His research interests include:micromachining technologies, micromachined sensors, actuators, and MEMS;analog integrated circuits; implantable biomedical microsystems; micropack-aging; and low-power wireless sensing/actuating systems.

Dr. Najafi was awarded a National Science Foundation Young InvestigatorAward from 1992 to 1997, was the recipient of the Beatrice Winner Award forEditorial Excellence at the 1986 International Solid-State Circuits Conference,of the Paul Rappaport Award for coauthoring the Best Paper published in theIEEE TRANSACTIONS ON ELECTRON DEVICES, and of the Best Paper Award atISSCC 1999. In 2003, he received the EECS Outstanding Achievement Award,in 2001 he received the Faculty recognition Award, and in 1994 the Universityof Michigan’s “Henry Russel Award” for outstanding achievement and schol-arship, and was selected as the “Professor of the Year” in 1993. In 1998, hewas named the Arhtur F. Thurnau Professor for outstanding contributions toteaching and research, and received the College of Engineering’s Research Ex-cellence Award. He has been active in the field of solid-state sensors and actu-ators for more than 20 years, and has been involved in several conferences andworkshops dealing with solid-state sensors and actuators, including the Interna-tional Conference on Solid-State Sensors and Actuators, the Hilton-Head Solid-State Sensors and Actuators Workshop, and the IEEE/ASME Microelectrome-chanical Systems (MEMS) Conference. He is the Editor for Solid-State Sen-sors for the IEEE TRANSACTIONS ON ELECTRON DEVICES, an Associate Editorfor the Journal of Micromechanics and Microengineering, Institute of PhysicsPublishing, and an Editor for the Journal of Sensors and Materials. He alsoserved as the Associate Editor for the IEEE JOURNAL OF SOLID-STATE CIRCUITS

from 2000 to 2004, and the Associate Editor for the IEEE TRANSACTIONS ON

BIOMEDICAL ENGINEERING from 1999 to 2000.

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