VIEWS: 18 PAGES: 6 CATEGORY: Technology POSTED ON: 3/4/2010
Combined Differential and Relative Pressure Sensor based on a Double-Bridged Structure. C. Pedersen∗ , S. T. Jespersen† , J. P. Krog∗ , C. Christensen∗ and E. V. Thomsen† ∗ Grundfos A/S, Poul Due Jensens Vej 7, DK-8850 Bjerringbro, Denmark, Email: capedersen@grundfos.com † Mikroelektronik Centret, Build. 345 East, DTU, DK-2800 Kgs. Lyngby, Denmark High Abstract— A combined differential and relative MEMS pres- Pressure sure sensor based on a double piezoresistive Wheatstone bridge Pa,high structure is presented. The developed sensor has a conventional (inner) bridge on a micro machined membrane and a sec- ondary (outer) bridge on the chip substrate. The double-bridge structure has previously been used e.g. in the compensation of Patm Patm temperature-induced errors in MEMS pressure sensors [1], [2], Pa [3]. A novel approach is demonstrated for a combined measure- Low ment of sensor output from inner and outer bridge, leading to Pressure the deduction of both differential and relative media pressure (with respect to atm. pressure), and a signiﬁcant improvement Fig. 1. A cross section sketch of an O-ring clamped double-bridged MEMS in differential pressure sensor accuracy. Output from both pressure sensor. bridges depends linearly on both differential and absolute media pressure. Furthermore, the sensor stress distributions involved are studied and supported by extensive 3D FEM stress analysis. O-ring contact area I. I NTRODUCTION O-ring clamping, as sketched in Fig. 1, has just recently shown great promise in the ﬁeld of MEMS pressure sensor packaging [4]. However, recent studies have shown that the output signal from the conventional inner bridge has a small dependency on the absolute media pressure, Pa , relative to atmospheric pressure, Patm [5]. The relative pressure is deﬁned as Prel = Pa − Patm . Based on this observation we have developed a MEMS pressure sensor with a secondary outer piezoresistive measurement bridge placed on the chip Piezoresistors substrate; see also Fig. 1. The conventional inner bridge Fig. 2. A top view sketch of the double-bridge sensor layout used in this mainly depends on differential pressure, Pd = Pa,high − Pa . work. However, the outer bridge has sensitivities to changes in differential and absolute pressures, which are of the same order of magnitude. By combining the outputs from inner process. The sensors were all based on piezoresistive read- and outer bridge using a microprocessor, we are able to out from piezoresistors interconnected in Wheatstone bridge deduce both differential and relative media pressure from structures. Furthermore, all sensor dies were encapsulated the sensor. Using this approach, a compensation for any using O-ring clamping as sketched in Fig. 1. Fig. 2 shows media pressure dependency can be achieved, leading to more a sketch of the double-bridged die layout used in this work. precise differential pressure sensors in combination with a Notice that the contact surface from the O-ring clamping on relative pressure sensor. the sensor die is indicated by a light gray circle in Fig. 2. Also notice that the two edges of the KOH-etched hole on the II. S ENSOR DESIGN backside of the sensor die are shown as two dashed squares All sensors used in this work were manufactured using and that the bonding pads to the outer Wheatstone bridge a conventional bulk silicon micro machining fabrication structure are divided in each corner. A collection of design Parameter Dimensions Diff. Pressure Abs. Pressure Die 4000×4000 µm Charact. Charact. Membrane 1000×1000 µm Membrane thickness 25 µm Vi Vi Inner piezores. distance Inner Sid(Pa) from die center 380-490 µm Bridge Oia(Pd) Sia(Pd) 1 1 Outer piezores. distance Oid(Pa) from die center 990-1040 µm 0 Pd 0 Pa TABLE I A LIST OF DESIGN PARAMETERS . Vo Vo Outer Soa(Pd) Bridge O (P ) Sod(Pa) Ooa(Pd) od a 1 1 0 Pd 0 Pa parameters are listed in Table I. Fig. 3. A sketch deﬁning the sensitivities and offsets for a double bridged III. T HEORY MEMS pressure sensor with indicated indices. A. Output voltage versus differential pressure In the following we focus on the inner conventional bridge structure are deﬁned in a similar way replacing the Wheatstone bridge structure of the pressure sensor shown index i with an o. All above deﬁnitions are illustrated in in Fig. 2. When supplying the sensor bridge with a constant Fig. 3. Notice how a pressure dependency of the sensitivities current Ib and subjecting the sensor to a differential pressure and offsets are also indicated in this sketch. Pd , the bridge output voltage V is normally written as: Using the notation in Fig. 3, we write the output from the V = S Pd + O (1) inner and outer bridge as: Vi (Pd , Pa )= Sid (Pa )Pd + Oid (Pa ) (3) where we have introduced the differential pressure sensitivity S and the output offset O. The differential pressure sensitiv- = Sia (Pd )Pa + Oia (Pd ) (4) ity is deﬁned as: Vo (Pd , Pa ) = Sod (Pa )Pd + Ood (Pa ) (5) dV S= (2) = Soa (Pd )Pa + Ooa (Pd ) (6) dPd The temperature dependency of the sensitivity S and offset in which Eq. (3) and (5) corresponds to differential pressure O is characterized by the well known parameters TCS and characteristics on the two bridges and Eq. (4) and (6) TCO, respectively. For the sake of simplicity, this work does to absolute pressure characteristics. From the experimental not treat the temperature dependency of the used sensors. data later presented in Sec. IV, a close coupling between However, earlier unpublished studies have shown only a differential and absolute pressure characteristics are found moderate dependency on temperature. both on inner and outer sensor bridge. This coupled Pd -Pa dependency can be written as: B. Notation for double-bridged sensor Vi = α i Pd + β i Pa + γ i Pd Pa + δ i (7) In the following we expand the deﬁnitions reviewed in Sec. III-A. We use the indices i and o to indicate whether Vo = α o Pd + β o Pa + γ o Pd Pa + δ o (8) a parameter is measured or deduced on the inner or outer where the γx -term (x = i,o) in both equations is a coupling bridge, respectively. Furthermore we use the indices d and a term between the dependency on differential and absolute to indicate whether a parameter is deduced from a differential media pressure. Similarly the coefﬁcients αx and βx can be or an absolute pressure characteristic. By a differential and an interpreted as the differential and absolute pressure sensitiv- absolute pressure characteristic we mean the output voltage ity if ignoring the coupling term. Finally the parameters δx measured as function of differential and absolute pressure, corresponds to the conventional sensor offset at Pd = 0 bar respectively. In the rest of the text, the differential and and Pa = 0 bar. Using the proposed output dependency in absolute pressures are written as Pd and Pa . Eq. (7) and (8), the sensitivities introduced in Eq. (3-6) can Using the above indices, the output voltage from the inner be written as: and outer bridge will be written as Vi and Vo respectively. Similarly, the sensitivities to changes in differential and Sid (Pa ) = γi Pa + αi , Oid (Pa ) = βi Pa + δi (9) absolute pressure on the inner bridge will be written as Sid Sia (Pd ) = γi Pd + βi , Oia (Pd ) = αi Pd + δi (10) and Sia respectively. The notation for output offsets follows Sod (Pa ) = γo Pa + αo , Ood (Pa ) = βo Pa + δo (11) the same principle, Oid and Oia being the output offset on the Soa (Pd ) = γo Pd + βo , Ooa (Pd ) = αo Pd + δo (12) inner bridge, found from differential and absolute pressure characteristics respectively. The sensitivities Sod and Soa and These equations are later used to deduce the coefﬁcients αi , output offsets Ood and Ooa measured or deduced on the outer βi , γi , δi , αo , βo , γo and δo on each sensor bridge. Parameter Data Parameter Fitted value Unit Temperature 25◦ C αi 65.9 ± 0.3 mV/bar Constant current 1.0 mA βi 0.52 ± 0.03 mV/bar Pd interval 0-2 bar γi -0.17 ± 0.06 mV/bar2 Pa,high interval 2-9 bar δi 17.9 ± 0.5 mV Pa interval 2-7 bar TABLE III TABLE II PARAMETERS IN E Q . (9) AND (10) OBTAINED ON THE INNER BRIDGE . A LIST OF EXPERIMENTAL SETTINGS . 86 −22 P = 2.0 bar 200 P = 1.0bar d V (mV) d 85 1.5 bar −24 150 84 i Vo (mV) 83 1.0 bar −26 Vi (mV) 0 2 4 6 8 100 P (bar) 0.5 bar a −28 0.0 bar 50 −30 Pa = 2.0bar 0 0 2 4 6 8 0 0.5 1 1.5 2 Pa (bar) Pd (bar) Fig. 5. Output versus absolute media pressure measured on outer bridge Fig. 4. Output versus differential and absolute media pressure on the inner at different differential pressures. bridge at Pa = 2 bar and Pd = 1 bar, respectively. The inner bridge coefﬁcients αi , βi , γi and δi deﬁned in IV. E XPERIMENTAL R ESULTS Eq. (7) were found from an analysis of Sid (Pa ), Sia (Pd ), In the following sections, data measured on inner and outer Oid (Pa ) and Oia (Pd ) deﬁned in Sec. III-B. From differential sensor bridge are presented separately. and absolute pressure characteristics as in Fig. 4 an analysis of the inner bridge sensitivities and offsets showed approxi- A. Experiments mate linear relations as the proposed ﬁrst order approxima- A compressor supplied compressed air to each side of the tion in Eq. (9) and (10). The inner bridge coefﬁcients αi , βi , mounted sensor in Fig. 1. The absolute pressure, Pa,high and γi and δi ﬁnally obtained are listed in Table III. Pa , of the compressed air on each side of the sensor were measured by two high precision reference absolute pressure C. Outer bridge results sensors. Similarly, the differential pressure Pd between the two pressure lines were measured by a high precision refer- In Fig. 5 is shown a Vo -Pa -plot measured on the outer ence differential pressure sensor. During measurements, both bridge in Fig. 2. During measurement the sensor bridge was inner and outer sensor bridge in Fig. 2 were supplied with closed by externally connected pads. As on the inner sensor a constant current Ib , while a high precision multimeter was bridge in Fig. 4, the sensor output depends linearly on Pa used to measure sensor outputs. A selection of experimental but with a sensitivity Soa of the opposite sign at all applied settings are listed in Table II. differential pressures. However, the sensor output also has a dependency on Pd of the same order of magnitude and B. Inner bridge results with a sensitivity Sod of the same sign as on the inner sensor Fig. 4 shows a Vi -Pd and a Vi -Pa plot measured on the bridge; see Fig. 4. inner bridge in Fig. 2 at Pa = 2 bar and Pd = 1 bar, As on the inner bridge, the outer bridge coefﬁcients αo , respectively. As expected, the output depends linearly on βo , γo and δo deﬁned in Eq. (8) were found from an the primary pressure parameter, Pd , but also has a small analysis of Sod (Pa ), Soa (Pd ), Ood (Pa ) and Ooa (Pd ). From (max. 1.5% of Full Span, FS) linear dependency on Pa differential and absolute pressure characteristics as in Fig. 5 (inserted plot). This dependency on absolute media pressure an analysis of the outer bridge sensitivities and offsets also has been presented and discussed elsewhere [5]. Similar showed approximate linear relations as the proposed ﬁrst linear relations as in Fig. 4 were found at other Pd and Pa order approximation in Eq. (11) and (12). The resulting outer values. bridge coefﬁcients αo , βo , γo and δo are listed in Table IV. Parameter Fitted value Unit αo 3.42 ± 0.01 mV/bar 35 Inner bridge -0.226 ± 0.005 mV/bar (MPa) βo 1.0 Pd = 1.0bar Stress σxx (MPa) γo 0.005 ± 0.002 mV/bar2 δo -28.93 ± 0.05 mV xx σ TABLE IV 0.9 34 PARAMETERS IN E Q . (11) AND (12) OBTAINED ON THE OUTER BRIDGE . 0 2 4 6 8 P (bar) a y (mm ) 0.8 Outer bridge P = 1.0bar d 0 2 4 6 8 ) P (bar) x (mm a Fig. 7. Longitudinal stress at the piezoresistor position of inner (inserted) and outer bridge piezoresistors. 1200 500 2 0 P =7bar a Fig. 6. Sketch of FE model used to simulate the media pressure dependency Compressive 1.5 Pa=4bar (MPa) of O-ring clamped MEMS pressure sensors. P =1bar a xx V. S IMULATION RESULTS 1 Stress σ A series of FEM simulations were carried out to support the experimental ﬁndings in Sec. IV. 0.5 A. 3D FE model Tensile 0 In Fig. 6 is shown a picture of the developed ﬁnite element 0 200 400 600 800 1000 1200 model (FEM) used to investigate the stress distribution in O- Position x (µm) ring clamped sensors, resulting from variations in absolute Fig. 8. Stress versus position for a selection of absolute media pressures media pressure. The model was developed using the com- at Pd = 0 bar. mercial FE program ANSYSTM and used roughly 120.000 elements in a mapped mesh conﬁguration. An anisotropic material model of silicon [8] was used in the calculations, Pd and Pa on both inner and outer piezoresistor positions. showing a difference of approximately 9% compared with Similar linear relations were found at other Pd and Pa values calculations normally based on isotropic material models. on both inner and outer piezoresistor positions. As illustrated in Fig. 6, calculations were performed only on one quarter of the die using symmetry constraints around C. Stress proﬁles the symmetry planes of the die. The model was ﬁnally Fig. 8 shows calculated stress proﬁles along the x-axis clamped in the z-direction of the bottom O-ring mounting in Fig. 6 at Pa = 1, 4 and 7 bar, all calculated at Pd = and symmetry was added to the symmetry-planes locking the 0 bar. From the proﬁle calculated at Pa = 1 bar and model in the x- and y-directions. These boundary conditions Pd = 0 bar (atmospheric pressure all around the sensor) we proved to be sufﬁcient for an analysis of the media pressure notice that the O-ring clamping induces a tensile stress in the dependency investigated in this work. whole region inside the O-ring contact area. Furthermore, the induced stress close to the O-ring contact area around x = B. Stress versus pressure 1200 µm seems to drop exponentially towards the membrane. The stress distribution in the top surface of the die was However, because of the much smaller dimensions, the stress calculated for a number of differential and absolute pressures concentration in the membrane region is relatively high for comparison with the experimental data in Fig. 4 and 5. compared to the stress concentration around x = 800 µm. Fig. 7 shows calculated longitudinal stress, σxx , as function of Pa and Pd , respectively. Results from both inner (inserted Fig. 8 further shows, how an increase in absolute media plot) and outer piezoresistor positions at Pd = 1 bar and pressure Pa induces an additional tensile stress in the region Pa = 1 bar are shown. As seen from the output data in Fig. 4 x = 0−650 µm. This corresponds to the increase in stress as and 5, the stress σxx follows a similar linear dependency on plotted for the inner piezoresistor position in the inserted plot Pa : Com- Com- pressive Tensile pressive Com- Pd : Tensile pressive Tensile Pa,high Media Pressure Patm M Compressive Stress (sxx<0) Pa Fig. 10. The distribution in induced stress in the top surface of the sensor Fig. 9. A FEM contour plot of the stress component σxx induced by a die, resulting from an increase in differential and absolute media pressure. high absolute media pressure of Pa = 7 bar (zoom of membrane region in Fig. 6). B. Pressure Characteristics in Fig. 7. Fig. 8 further illustrates how an increase in absolute The experimental data presented in Fig. 4 and 5 showed media pressure results in an additional compressive stress in a close coupling between differential and absolute pressure the region x > 650 µm. This corresponds to the decrease in characteristics on both inner and outer sensor bridge. As stress plotted for the outer piezoresistor positions in Fig. 7. proposed in Sec. III-B, this coupling between differential and absolute media pressure is well approximated by the VI. D ISCUSSION following expressions: In the following section we take a deeper look into Vi = α i Pd + β i Pa + γ i Pd Pa + δ i (13) the mechanisms behind the observed effects of changes in absolute media pressure and furthermore discuss promising Vo = α o Pd + β o Pa + γ o Pd Pa + δ o (14) applications of the double-bridged pressure sensor. From the experimentally obtained coefﬁcients in Table III and IV, we notice that the ratio αi /βi between differential A. The stress distribution and absolute pressure sensitivity the inner bridge (ignoring The main contributor to the observed absolute media the coupling term with coefﬁcient γi ) is of the order 100. In pressure dependency in Fig. 4 results from the changes in the full span of absolute media pressures this means, that the the absolute media pressure supported by the KOH etched absolute media pressure contributes with less than 1.5%FS sidewalls of the sensor die [5]. In Fig. 9 is shown a FEM to the output on the inner sensor bridge. However, on the contour plot of the stress component σxx for a relatively high outer sensor bridge the ratio αo /βo is of the order 10 and the absolute media pressure Pa = 7 bar (axis direction corre- coupling coefﬁcient γo almost negligible. Also visible from spond to Fig. 6). We notice the relatively high compressive the data in Fig. 5 this means, that in the full span of absolute stress amplitude (σxx < 0) in the region around the KOH media pressures, the output contribution from changes in etched sidewalls resulting from the effect mentioned above. differential and absolute media pressures are comparable in As illustrated in Fig. 8 the media pressure on the sidewalls size on the outer bridge structure. induces an additional tensile and compressive stress at the position of the inner and outer piezoresistors, respectively. C. Algorithm for combined pressure measurement This distribution in induced stress is sketched in Fig. 10 We now propose a simple but efﬁcient approach on how to both for an increase in absolute and differential pressure. The deduce both differential and relative media pressure (relative sketched effect fully explains the absolute media pressure to atm. pressure) from the sensor based on the double-bridge dependency observed on both the inner and outer sensor pressure characteristics in Eq. (13) and (14) above. bridge in Fig. 4 and 5, respectively. We assume having characterized the double-bridged pres- The differential pressure dependency of the outer sensor sure sensor both as function of Pd and Pa including having bridge is a simple consequence of the moment M acting found the parameters αi , βi , γi , δi , αo , βo , γo and δo deﬁned on the die substrate for Pd > 0 bar; see Fig. 10. A in Eq. (13) and (14). For outputs Vi and Vo measured on differential pressure Pd > 0 bar slightly bends the die the inner and outer sensor bridge, respectively, the goal is substrate downwards and induces an additional tensile stress to convert these into the unknown differential and absolute in the top surface of the die including at the outer bridge pressure values, Pd and Pa . Since Pd and Pa are the only position. This explains the increase in outer bridge output unknowns in Eq. (13) and (14), we are left with two non- for an increase in differential pressure; see Fig. 5. A sketch linear equations with two unknown parameters - Pd and Pa . of the overall stress distributions resulting from an increase These can easily be found by an iterative loop as proposed in absolute and differential pressure is included in Fig. 10. below: 1) From Eq. (13) we use the approximation Vi (Pd , Pa ) relative pressure could be deduced with an accuracy of order Vi (Pd ) = αi Pd +δi . Using Vi (Pd , Pa ), αi , δi as input in ±10% of full relative media pressure span. Finally, the media this equation, we ﬁnd Pd (approximate value for Pd ). ∗ pressure induced stress distribution in the sensor was studied 2) Now using Vo (Pd , Pa ), αo , βo , γo , δo and Pd as input ∗ and fully conﬁrmed by 3D FEM simulations. in Eq. (14), we ﬁnd Pa∗ (approximate value for Pa ). R EFERENCES 3) Next we use the full version of Eq. (13). By using Vi (Pd , Pa ), αi , βi , γi , δi and Pa∗ as input, we ﬁnd Pd ∗∗ [1] M. Akbar and M. A. Shanblatt, Temperature compensation of piezore- sistive pressure sensors, Sensors and Actuators A, 33 (1992), p. 155 (new approximate value for Pd ). [2] J. J.Dziuban, A. Grecka-Drzazga, U. Lipowicz and W. Indyka, Self- 4) Either the loop in step 2)+3) proceeds a given period or compensating piezoresistive pressure sensor, Sensors and Actuators A, until the step-by-step change in Pd and Pa are smaller 41-42 (1994), p. 368 [3] Young-Tae Lee and Hee-Don Seo, Compensation method of offset than a preset value. and its temperature drift in silicon piezoresistive pressure sensor using In a double-bridged pressure application, a microprocessor double Wheatstone-bridge conﬁguration, Proc. of Transducers‘95, Vol.2, 1995, p. 570 could be programmed with the above algorithm, making it [4] Grundfos. Pressure sensor or differential pressure sensor. Patent possible to deduce both the the differential and absolute EP00801293B1. media pressure based on measured outputs Vi and Vo . From [5] C. Pedersen, S. T. Jespersen, J. P. Krog, K. W. Jacobsen, C. Christensen and E. V. Thomsen, Characterization of MEMS Pressure Sensor these results, the relative pressure is found by Prel = Pa − Packaging Concept using O-rings as Hermetic Sealing, Eurosensors Patm . XVII, Portugal, 2003 [6] C. Christensen, R. de Reus and S. Bouwstra, Tantalum oxide thin ﬁlms D. Sensor calibration and applications as protective coating for sensors, MEMS’99, USA, 1999, p. 267 [7] R. de Reus, C. Christensen, S. Weichel, S. Bouwstra, J. Janting, As noted in Sec. I, use of the O-ring packaging concept G. Friis Eriksen, K. Dyrbye, T. Romedahl Brown, J. P. Krog, O. Snder- in Fig. 1 results in a small dependency on absolute media grd Jensen and P. Graversen, Reliability of industrial packaging for microsystems, Microelectronics Reliability, 38 (1998) p. 1251 pressure; see Fig. 4. However, using the double-bridge output [8] ”Properties of silicon”, Inspec., ISBN: 0852964757, 1988, p. 3 model established in Sec. VI-B and VI-C a compensation technique for this small media pressure dependency is also achieved. By implementing this technique, the error induced by the absolute media pressure dependency can be reduced by more than a factor of 10. For future applications, this will allow a fabrication of more precise piezoresistive differential pressure sensors based on the O-ring packaging principle sketched in Fig. 1. Furthermore, since the inclusion of an outer bridge structure on the chip substrate does not involve additional processing steps, the double-bridge concept also has certain economical advantageous. From the sensor parameters listed in Table IV we note, that the sensitivity to changes in absolute media pressure are somewhat limited on the outer sensor bridge in the current design. However, in certain applications there are no need for a high precision absolute media pressure measurement but only an estimate on the overall pressure level. In such applications, a combined differential and absolute pressure measurement (Prel = Pa − Patm ) based on the double-bridged pressure sensor is an interesting sensor candidate. Further- more, new improved designs of double bridged MEMS devices are already under development. VII. C ONCLUSION A combined differential and relative MEMS pressure sensor was developed, based on novel use of a double- bridged structure. By utilizing linear pressure dependencies on the two bridges, both Pd and Prel = Pa − Patm could be deduced by an iterative process. By use of this process, small measurement errors induced by variations in absolute media pressure could be reduced by more than a factor of 10. Furthermore, using the double-bridge technique the