PIRANI PRESSURE SENSOR WITH DISTRIBUTED TEMPERATURE SENSING

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1 Proceedings of IMECE 2 ASME Internationa Mechanica Engineering Congress and Exposition November -6, 2, New York, NY, USA PIRANI PRESSURE SENSOR WITH DISTRIBUTED TEMPERATURE SENSING J.J. van Baar MESA + Research Institute University of Twente P.O. Box 27, 75 AE Enschede The Netherands E-mai: J.vanBaar@e.utwente.n Coauthors R.J. Wiegerink T.S.J. Lammerink G.J.M. Krijnen and M. Ewenspoek ABSTRACT A Pirani pressure sensor is based on the fact that the therma conductivity of a gas is dependent on the pressure. The structure presented in this paper consists of a heated microbeam, which is paced above a v-groove in a heat sink. The temperature distribution aong the microbeam is a measure for the therma conductivity of the surrounding gas. Measuring the temperature distribution instead of the average temperature of the beam has two advantages: the measurement becomes independent of the Temperature Coefficient of Resistance of the temperature sensing resistors and the heat oss to the substrate is impicity taken in account, which extends the ower pressure range. INTRODUCTION In the moecuar range the therma conductivity of a gas is proportiona to the pressure as found by M. von Pirani in 96 (vp6. This fact can be expoited in Pirani pressure sensors, where a heat source and heat sink are paced at cose distance from each other. The distance has to be smaer than the mean free path of the gas moecues. An important advantage of Pirani sensors is their robustness. They do not contain any moving parts (e.g. a bending membrane and are not damaged when an overpressure is appied. A disadvantage is that the output signa aso depends on the type of gas. Various impementations of Pirani sensors can be found in the iterature, e.g. using different heater shapes ike cantievers (vhs87, microbridges (BK94 or pates, using a v-groove cavity (WS94 or thin sacrificia ayer (Pau95 to reaize the narrow gap between heater and heat sink, having heat transfer atera (SN94 or perpendicuar to the wafer surface, using < > or < > (CCS99 wafers and using two bonded wafers (AJB95. The sensor presented in this paper consists of a heated microbridge, which is paced above a v-groove in the substrate. The difference with existing sensors is that the temperature distribution is measured instead of the average temperature of the microbeam. The shape of this temperature distribution depends on the pressure, which makes the absoute temperature rise unimportant. This has the advantage that the measurement becomes independent of the Temperature Coefficient of Resistance of the temperature sensing resistors. Figure shows a schematic drawing of the structure. A patinum heater is paced aong the center of a thin siicon nitride carrier. Additiona patinum eads are connected to the heater, dividing it into five segments. The votage drop across each of these segments can be measured individuay. The temperature dependent eectrica resistance can be cacuated from the votage drop and the current through the heater. The average temperature of each segment is cacuated from the change in eectrica resistance of the segment. A discretized mode for fitting the average temperatures of the five segments is used to extract the pressure. THEORY The pressure dependence of the therma conductivity can be spit up in three regions: moecuar, viscous sip and viscous, see figure 2. From microscopic considerations of kinetic theory the therma conductivity κ [W/Km] can be derived for an idea, Copyright 2 by ASME

2 .5 y n.5 with the constant K depending on the type of gas and the accommodation coefficient, the pressure P t depending on the characteristic ength of the system, i.e. the distance between heater and heat sink and A s is the effective surface area of the sensor.. x z y x Si 3 N 4 Si Pt y MODEL The temperature profie T (y n aong the ength of the beam is dependent on the ratio between heat transport through the gas and through the beam. It can be cacuated using the foowing second order differentia equation (Bru94. Figure. Schematic drawing of the structure R b 2 T (y n y 2 n + G f T (y n = P (3 therma conductivity κ moecuar viscous sip viscous pressure p Figure 2. Therma conductivity as function of pressure (ogog-pot where y n is the aong the beam and P is the eectrica ine power in [W/m]. The temperature profie is dependent on the therma ine resistance of the beam R b [K/(Wm], the therma ine conductance through the gas G f [W/(Km] and the ength of the beam [m]. The soution of equation 3 is given by (Bru94 T (y n = P G f ( cosh y n 2 (4 diute gas in (Rei65 κ = n v c λ ( 3 with c the pressure independent specific heat per moecue and v the mean moecuar veocity. In the viscous region κ is pressure independent, because the number of partices in a voume, n, and the mean free path λ of the moecues are directy and inversey proportiona to the gas pressure, respectivey. In the moecuar range the therma conductivity is proportiona to the number of moecues, because the mean-free-path is imited by the characteristic ength of the system. The therma conductance G g measured between the heater and heat sink in a Pirani sensor depends on the pressure in the same way as the therma conductivity. This dependence can be described by the foowing equation (vs: P t G g = A s KP( (2 P + P t Normaizing the temperature distribution of equation 4 to the temperature rise at the center of the beam resuts in: ( T n (y n = T (y cosh 2 R n T ( = b G f 2 ( cosh y n (5 Figure 3 shows a pot of this normaized temperature distribution for severa vaues of the term ranging from to 2. The advantage of normaizing in this manner is the canceing out of the Temperature Coefficient of Resistance, which is otherwise needed to know the temperature. In a practica sensor the temperature cannot be measured in a singe point. Instead the average temperature over a segment is measured. Integration of equation 4 and dividing by the ength of the segment resuts in the foowing expression for the average segment temperature per unit appied ine power [W/(Km] for a segment with ower boundary a and upper boundary b, which both are normaized to : 2 Copyright 2 by ASME

3 T Tmax increasing increasing increasing increasing 2 G f R R R b paraboic, G f = y n on beam.5 normaized temperature without underetch with underetch Figure 3. Normaized temperature distribution aong the beam Figure 4. Average of the normaized temperature of the segments and the normaized temperature distribution versus the aong a segments with and without underetch. T (a,b P = G f ( sinh b (b a ( sinh 2 a (6 Averaging the normaized temperature distribution of equation 5 over the ength of the resistor segment gives: 2 T n (a,b = 2 ( sinh b (b a sinh (cosh ( 2 ( a (7 d w d e f f d e f f = effective depth w = width d = depth Figure 5. Cross section of the v- groove, with underetched support, which has an effective depth d e f f taken haf of the depth of the groove. P P 2 P 3 G G p Figure 4 shows a pot of the normaized temperature distribution (equation 5 together with the average temperature per segment indicated by boxes (equation 7. Due to underetch the beam ength wi be somewhat arger than designed. The dashed curve in figure 4 iustrates the infuence of this underetch. Equation 7 is used for interpretation of the measurement resuts using a reaistic vaue for incuding the underetch. A rough estimate for the ine conductance G f in equations 3 to 7 can be obtained using a parae pate approximation, as indicated in figure 5. G f = κ w/d e f f with the width w [m] and the effective depth d e f f [m]. Using an effective depth equa to haf of the groove depth d [m] gives a vaue for G f around W/(Km in the case the therma conductivity of the fuid is 26 3 W/(Km, the depth 4 µm and the width of the beam 25 µm. The underetching of the support has been drawn. A better estimate for the ine conductance G f can be obtained using the umped eement mode shown in figure 6. In = G p Figure 6. = G = heat sink = beam Lumped eement mode with nine nodes drawn this mode ony the heat transfer in the direction perpendicuar to the beam is considered: no heat transfer through the beam to its edges is assumed. The ight gray eements respresent the therma conductances in horizonta direction and the dark gray eements represent the conductances in vertica direction. For each node in the umped eement mode Kirchhoffs current aw can be appied (VS83 resuting in the therma conductance matrix G. Inverting 3 Copyright 2 by ASME

temperature [K] 25 2 5 5 25 -.6 -.4 -.2 normaised position.2.4.2.6.4.6.8 normaised depth Figure 7.

4 temperature [K] normaised position normaised depth Figure 7. 2D Temperature distribution of the v-groove (a (b (c bare Si < > wafer crysta orientation known deposition and patterned poysiicon nm LPCVD of Si 3 N 4 ( µm this matrix and mutipying it with the power P gives the temperature distribution T in the v-groove under the beam. The sum of the ratios between the appied power P i and the temperature difference T j between the beam and the heat sink gives the vaue of the effective therma conductance G f, with in the case of figure 6 i=,2,3 and j=2,3,4. This gives a vaue around 5 2 W/(Km in the case the width of the v-groove is 6 µm. This vaue is somewhat arger than the previousy cacuated vaue using the very rough parae pate approximation. Figure 7 shows a pot of the cacuated temperature distribution in the v-groove. (d (e (f paterned Si 3 N 4 sputtering Cr nm Pt 2 nm KOH etching REALIZATION Figure 8 shows the process sequence used for fabrication of the sensor chips. The first step of the process is the deposition of a µm thick Si 3 N 4 ayer on a siicon ( wafer, with a thickness of approximatey 38 µm. A specia mask structure is used in combination with KOH-etching for precisey finding the crystaographic orientation (VB96. This step is necessary because of the arge ength to width ratio of the v-groove. A sight misaignment resuts in a arge underetch, which widens the v-groove. The next steps are seectivey stripping of the Si 3 N 4 and the deposition of a nm thick sacrificia poysiicon ayer. The atter is needed for underetching of the beam. After patterning the poy-si ayer a Si 3 N 4 ayer is deposited and patterned. A nm chromium primary ayer and a 2 nm patinum ayer are sputtered and after ift-off, KOH etching is used for reeasing the beam. The KOH etching woud normay stop at a depth of about 2 µm. However, due to a very ong etching time (required for some other structures on the same chip, see (vbwl + a significant underetch occurs, resuting in a v-groove with a depth of about 4 µm. Figure 9 shows a photograph of the first two segments of a beam (with a tota of five segments. The underetch is ceary visibe. The beam itsef has a ength of mm, a width of 25 µm Figure 9. Photograph of part of the beam with heater divided in five segments Figure 8. Process steps 2 µm width of v-groove and thickness of µm. The patinum heater and votage eads have a width of 5 µm and a thickness of 2 nm. 4 Copyright 2 by ASME

5 resistance [Ω] µa.3 ma T /P [Km/W] e+ 3.6e+ 4.e+2 4.e+3.e y n on beam.4 Figure. Resistances of the segments for currents of 3 µa and.3 ma at 3.5 Pa. Figure 2. Measured temperature per unit ine power versus the normaized position on the beam for severa pressures normaized resistance.99 resistor segment st 4th 2nd 5th.98 3rd fit 2e 8 4e 8 6e 8 8e 8 I 2 [A 2 ] e 7 P /T [W/(Km]... segment position Figure. Resistances of the segments normaized to the resistance at.3 ma for currents from 3 µa to.3 ma. The fit is ineair and gives us the extrapoated resistance at I= A. The temperature rise is proportiona to the appied power. MEASUREMENTS As mentioned before, the votage drop across each segment can be measured individuay. To measure the resistance of a segment a current is appied to the heater and the resuting votage drop is measured, corresponding to a four point measurement. Figure shows a pot of the resistance vaues for two different heating currents, 3 µa and.3 ma. The spread in resistance vaues is due to random variations of the patinum ine-width due to the ift-off process. The dependence on the appied current is due to the resuting change in temperature. The reative change in resistance is a measure for the temperature. We see that this change is argest for the center segment, which has the highest temperature. Figure 3. Line power per unit temperature versus pressure for each resistor segment. The owest curve is from the center segment. To obtain the temperature of a segment we first need to know the resistance when there is no heating current appied. This is done by measuring the resistance at severa current eves as shown in figure. The resistance is ineary dependent on the temperature and, therefore, on the heating power. A curves are normaized to the vaue at a current of.3 ma. Extrapoation of the curves resuts in the resistance vaue at zero heating current. Measurements have been performed using nitrogen with the pressure ranging from 3.5 Pa up to atmospheric pressure. For the different pressures care is taken to keep the maximum temperature rise between 5 and K. To eiminate the variation of the required appied power the temperature distribution aong the beam has been divided by the ine power, see figure 2. Measurements from the same data set are potted in a different way in figure 3. The ratio of ine power and temperature rise is potted as a func- 5 Copyright 2 by ASME

6 T /P [Km/W] pressure 3 Pa measurement fitted curve averaged therma conductance [W/(Km]... p p+p t fitted from temperature distribution per ine power Figure 4. Temperature distribution per unit ine power versus the normaized position at 3.5 Pa. Figure 6. Therma conductance versus pressure obtained from the temperature distribution per ine power for the fuid nitrogen. T /P [Km/W] Figure Temperature distribution per unit ine power versus the normaized position at bar. pressure Pa measurement fitted curve averaged tion of pressure for each segment. The bottom curve corresponds to the center segment and the top curves correspond to the outer segments of the beam. The two upper curves are not identica as woud be expected. This is due to the fact that a cap was paced over the chip, which was needed for other structures on the same chip. Misaignment of this cap causes a sighty asymmetrica temperature profie. We see that for ow pressures the sensitivity decreases because the heat transfer through the beam dominates the heat transfer through the gas. Figures 4 and 5 show the measured temperature distribution of figure 2 for 3.5 Pa and 5 Pa, respectivey. These measurements are fitted using function 6, which gives the therma conductance. The dashed curve is the temperature distribution predicted by the mode. The average temperature over each segment (indicated by the boxes is fitted to the measure- ment data. An impementation of the noninear east-squares Marquardt-Levenberg agorithm has been used. For the therma resistance of the beam a vaue of R b = 4.7e + 9K/(Wm was taken for a pressures. Theoreticay this vaue shoud be 4e + 8K/(Wm, however the difference corresponds very we to earier resuts with fow sensors (vbwl +. Using equation 6 resuts in the fitted therma conductances of figure 6. The transition pressure P t is Pa. For the therma conductance to the fuid at atmosperic pressure.28k/(w m was found. The theoretica vaue obtained from the rough umped eement mode was 5 2. The deviation can be expained by the fact that severa factors have been negected. In the mode the heat transfer through the beam (for a homogeneous temperature, the Si 3 N 4 faps due to underetch, the therma conductance to the cap and free convection were not taken in account. An effective enargement of the beam due to underetch is taken 2.5 µm, whie the underetch was 4 µm. In this effective enargement can be taken in account that the width of the support is much arger than the width of the beam, which wi resut in a ower therma ine resistance. The normaized temperature distribution is the measured temperature distribution divided by the temperature rise in the center. Measurements from the same data set as used in figure 2 can be appied to obtain figure 7. In this figure it can be seen ceary that the shape changes with the pressure. The normaized temperature has been fitted with equation 7 for severa pressures, see figures 8 and 9. The product has been fitted and the therma conductivity of the fuid has been normaized to the vaue at atmospheric pressure, see figure 2. Note that for the temperature distribution per ine power the R b and G f are fitted and for the temperature distribution normaized to the temperature rise of the center segment ony the 6 Copyright 2 by ASME

7 normaized temperature e+5 4.e+3 4.e+2 3.6e+ 3.5e y n on beam.4 normaized temperature pressure Pa measurement fitted curve averaged Figure 7. Measured temperature distribution normaized to the temperature rise of the center segment versus the on the beam for severa pressures. Figure 9. Temperature distribution normaized to the temperature rise of the center segment versus the at bar with fit normaized temperature pressure 3 Pa measurement fitted curve averaged normaized therma conductivity κn... fitted from temperature distribution normaized to temperature p p+p t at center of beam Figure 8. Temperature distribution normaized to the temperature rise of the center segment versus the at 3.5 Pa with fit Figure 2. Normaized therma conductivity versus pressure obtained from normaized temperature distribution for the fuid nitrogen. product is fitted. CONCLUSIONS A Pirani pressure sensor with distributed temperature sensing above a v-grooved heat sink has been reaized. Compared to a sensor which measures ony the average temperature of the beam, the advantages are the increased working range and the independence of the Temperature Coefficient of Resistance of the sensors on the beam. The first advantage is due to the abiity to take in account the heat transfer through the beam to its support, which extends the ower pressure range. The second advantage is due to the normaization of the temperature distribution to the temperature rise at the center, which cances out the TCR. The temperature measurements are not measured in a singe point, but are averaged over each resistor segment. This has been taken in account in the used mode to fit the measurement data. For pressures from 3.5 Pa up to bar the therma conductance to the buk is extracted from the temperature distribution. A first order behaviour fits we through the therma conductance-pressure pot. ACKNOWLEDGMENT The authors woud ike to thank Erwin Berenschot and Meint de Boer for their advice on the technoogica part and Remco Sanders for his advice on the measurement part. This research is supported by the Dutch technoogy foundation STW. 7 Copyright 2 by ASME

8 REFERENCES [AJB95] W.J. Avesteffer, D.C Jacobs, and D.H. Baker. Miniaturized thin fim therma vacuum sensor. J. Vac. Sci. Techno., A 3(6: , 995. [BK94] Urich Bonne and Dave Kubisiak. Burstproof, therma pressure sensor for gases. Soid-State Sensor and Actuator Workshop Hiton Head, pages 78 8, 994. [Bru94] H.H. Bruun. Hot-Wire Anemometry. Oxford University Press, 994. [CCS99] Bruce C.S. Chou, Chung-Nan Chen, and Jin- Shown Shie. Micromachining on -oriented siicon. Sensors and Actuators 75, pages , 999. [Pau95] O. Pau. Vacuum gauging with compementary meta-oxide semiconductor microsensors. J. Vac. Sci. Techno., A 3(3:53 58, 995. [Rei65] Frederick Reif. Fundamentas of statistica and therma physics. McGraw-Hi, 965. [SN94] Nichoas R. Swart and Arokia Nathan. An integrated cmos poysiicon coi-based micro-pirani gauge with high heat transfer efficiency. IEEE, pages 35 38, 994. [VB96] Mattias Vangbo and Yva Bäckund. Terracing of ( si with one mask and one etching step using misaigned v-grooves. Journa of Micromechanics and Microengineering, 6(:39 4, 996. [vbwl + ] J.J. van Baar, R.J. Wiegerink, T.S.J. Lammerink, G.J.M. Krijnen, and M. Ewenspoek. Micromachined structures for therma measurements of fuid and fow parameters. JMM, voume, issue 4 (Juy:3 38, 2. [vhs87] A.W. van Herwaarden and P.M. Sarro. Doubebeam integrated therma vacuum sensor. J.Vac.Sci.Techno., A Vo. 5 No. 4: , 987. [vp6] M. von Pirani. Sebszeigendes vakuummefsinstrument. Verhandungen der Deutschen Physikaischen Geseschaft, pages , 96. [vs] M. von Smouchowski. Zur theorie der warmteeitung in verdunnten gasen und der dabei auftretenden druckkrafte. Annaen der Physik, 35:983 4, 9. [VS83] Jiri Vach and Kishore Singha. Computer methods for circuit anaysis and design. van nostrand reinhod, 983. [WS94] Ping Kuo Weng and Jin-Shown Shie. Micro-pirani vacuum gauge. Rev. Sci. Instrum. 65 (2, pages , Copyright 2 by ASME

Pirani pressure sensor with distributed temperature measurement

Pirani pressure sensor with distributed temperature measurement B.R. de Jong, W.P.Bula, D. Zalewski, J.J. van Baar and R.J. Wiegerink MESA' Research Institute, University of Twente P.O. Box 217, NL-7500