Thin square membranes including a deep circular corrugation are realized and tested for application in a strain-based pressure sensor. Package-induced stresses are reduced and relief of the residual stress is obtained, resulting in a large pressure sensitivity and a reduced temperature sensitivity. Finite element method simulations were carried out, showing that the pressure-deflection behaviour of the structure is close to that of a circular membrane with clamped edge but free radial motion

Bouwstra, S.

Burger, J.F.

Elwenspoek, M.

Spiering, V.L.

English

Thin square membranes including a deep circular corrugation are realized and tested for application in a strain-based pressure sensor. Package-induced stresses are reduced and relief of the residual stress is obtained, resulting in a larger pressure sensitivity and a reduced temperature sensitivity. Finite element method simulations were carried out, showing that the pressure-deflection behaviour of the structure is close to that of a circular membrane with clamped edge but free radial motion

Elwenspoek, M.C.

University of Twente Research Information

J. Micromech. Mioroeng. 3 (1993) 243-246. hinted in the UK Membranes fabricated with a deep single corrugation for package stress reduction and residual stress relief V L Spieringt, S Bouwstre, J F Burgart and M Elwenspoekt t MESA Research Institute. University d Twente, Po Box 217, 7500 A€ Enschede, The Netherlands t Miuoelectronic Centre (MIC), Technical University of Denmark (DTH), Lyngby, Denmark Abstract. Tnin square membranes including a deep circular cwrugation are realized and tested fw application In a strain-based pressure sensor. Package- induced stresses are reduced and relief of the residual stress is obtained, resuning In a larger pressure sensitivity and e reduced temperature sensitivlty. Finite element method simulations were carried out, shewing that the pressura- deflection behaviour of the structure is close lo that of a circular membrane with clamped edge but free radial motion. 1. lntroductlon Packaging-induced stress is usually an unwanted phenomenon in micromechanical devices [l]. Especially in high sensitivity micromechanical sensors package- stresses can jam the sensor output. These stresses can be reduced by the application of a mechanical decoupling zone (2-41. In [2] a theoretical model was presented for the mechanical behaviour of a deep circular V- groove as the decoupling zone and it was shown that a very high reduction of stresses is reached for deep, thin zones. Spiering d a1 [4] report on the fabrication of a membrane with an on-chip decoupling zone. In this paper thin square silicon nitride membranes are compared with the same membranes including a deep circular corrugation. The residual stress as well as thermally induced centre deflections are measured. Figure 1 shows the structures considered (a)  a thin square membrane and (b) the same membrane containing a thin corrugated circular zone. The grooves (front side) were etched into the bulk silicon by reactive ion etching with a SF&* plasma and afterwards covered with 1 pm low-pressure chemical vapour deposited (LPCVD) silicon nitride. The backside etching was done in a KOH solution. Figure 2 shows a photograph of the resulting structure. 2. Model For a flat clamped quare membrane with thickness t, length 2a, Young’s modulus E, Poisson’s ratio 21 and initial stress uo the relation between the pressure 09601317/93/040243+W07.50 @ 1993 IOP Publishing Ud Flgure 1. 3~ view d the structures considered (a) flat membrane, (b) membrane wth a deep drcular corrugation for package stress reduction and low residual stress. difference P over the membrane and the corresponding centre deflection y is [5,6]: ( 1) P = -  C d U u  Czf(v)tEy3 The first term shows the stiffness due to residual stress. The second term shows a flattening out in y for larger pressures as a result of stretching of the membrane. For square membrane C1 = 3.41, C, = 1.98, and f( v )  = 1-0.2%v [6]. The membranes including the circular mne were modelled with the finite element method 243 a2 ’+ a 4 ( 1 - v )  . V L Spiering et al Figure 2 Photograph d a square silicon nitride membrane containing a 100 pm deep corrugation. Flgure 3. Definitions of parameters of the mrrugated structure. (SYSTUS Framatome software) using axisymmetrical shell elements. Thichess, depth and shape of the corrugation were varied as well as the length of the flat part at the outer edge of the zone. Figure 3 shows the definition of the applied parameters. Note that y ( P )  denotes the centre deflection minus the (offset) deflection yo of the inner edge of the corrugation. Figure 4 shows the non-linear deflection-pressure curve y( P) for the corrugated structure as well as for several circular membranes with radius a under different edge conditions: clamped edge, clamped with free radial motion of the edge, simply supported, and the latter with free radial motion of the edge. All simulations and calculations were done with a zero initial stress, which is close to the real situation for a deep corrugation [Z]. A Young’s modulus E = 245 GPa, Poisson’s ratio IJ = 0.3 and standard dimensions: t = 1 pm, H = 100 pm, a = 0.35 mm, ZOut = 50 pm and y = 60° were applied. The best description of the mechanical behaviour of the membrane with a corrugated zone is given by the membrane with clamped edges with free radial motion: the zone is weak for radial loads but relatively stiff for the lateral pressure load. Therefore the rotation of the 244 Figure 4. EM resuits for the centre-edge deflection as a function d pressure difference for membranes with different edge conditions: damped, damped but radially free to m e ,  simply supported. simply supported and radiaity free to move, and the corrugated structure. Anawicai resuits for a membrane with damped edge but free radial motion are plotted as weii. edge at the inner radius of the zone can be ignored. The analytical description of this circular membrane with radius a is given by: p=- (2) C3Et3 C4 Et Y + Y3 a 4 ( 1  - IJ) a4 with a bending coefficient C3 = 5.85 and the non-linear coefficient C, = 0.598 for U = 0.3 [7]. A non-linear term is still present, not because of stretching but because of increased stiffness due to the shell shape. This model could be further refined by including a rotational stiffness at the edge, rather than the clamped condition. Detailed investigation of linear FEM results (P = 1 Pa) shows that the flat rim outside the corrugation with length IWt results in an increasing ofEet displacement yo for increasing Zmt. This is caused by changes of the deflection and the rotation at the outer radius of the zone. However, the values of deflections and rotations of the actual membrane are not affected. Moreover the effect can be suppressed by choosing I,, as small as possible: for IWt + 0 the offset displacement yo + 0. Also for corrugation depths above 25 pm and mne- angles above XIo the deformation of the membrane is not affected by the actual dimensions of the cormgation, see figure 5. The increase of the deflections and rotations for a mne depth H = 10 pm, is explained by the fact that the membrane now approaches the structure of the Oarger) square membrane. 3. Experimental results ’Ib test the reduction of stresses, samples were mounted on a steel backplate with a pressure inlet, which was placed on a Peltier element to control the temperature, see figure 6 The temperature was measured with a Membranes with a deep single corrugation Figure 5. Displacements and rotations d the structure as a function d (a) zone depth H (7 = W O ) ,  and (b) zone angle (H = 100 pm). Y zone denotes the vertical displacement between Inner and cuter edge of the zone. Figure 6. Ewperimental set-up. thermocouple located close to the membrane. The pressure was adjusted and measured by a pressure regulator and deflections were recorded by a DEKTAK mechanical profile scanner. mble 1. Experimental results for (I) a flat membrane and membranes with a corrugation of (2) 25 pm and (3) 100 pm. Sample Zone ZMe Zone El (1  - v) lnfilal Stress ao d((Yp,T/Yp,To) - l)/dT da/dT inner radius depth width bm)  bm) bm) W a )  (Mpa) ( 1 0 - 4 l o ~ )  (MPWC) 1 0 )  - 350 85 -100 5.5 2 386 25 75 375. < 10 - 3.38 < 0.05 3 355 100 150 375' < 10 - 2.53 < 0.05 E Measured from a square membrane on the same wafer. 245 Figure 7. (a) Pressuredeflection measurements and least squares ft to model both membrane structures at room temperature, and (b) the relative change d deflection at constant pressure (33 kPe) as a function d temperature elevation for the membrane structures. Figure 7(a) shows the pressure-deflection measure- ments of a 1x1  mm silicon-nitride membrane with thickness of 1 pm as well as a membrane with the same dimensions containing a zone with dimensions as given in table 1. The bi-axial elasticity modulus E/(1- v) differed a little between the samples and an initial stress U" = 85 MPa was found for the flat membrane. Due to the very low initial stress the pressure-deflection curve of the membrane with zone has a very small linear part over the pressure range considered. Although this makes a reliable fitting of the measured c u m  difficult, it a n  be concluded that the residual stress U" was at least reduced to 10 m a .  V L Spiering et Heating the sample with a Peltier element results in an additional thermal (package) stress. The centre deflection y was monitored at constant pressure as a function of the temperature, see figure 7(b). The deflections y p , ~  were normalized with respect to the deflection y p , ~ ~  at room temperature. For the flat membrane a thermal sensitivity of the total residual stress d u / d T  = 5.5 MPaPC was determined, using the pressuredeflection test. The measurements on membranes containing a decoupling mne show a large reduction of the thermal influence. The results are summarized in table 1. 4. Conclusions Thin membranes including a deep single circular corrugation have been realized and characterized by means of their pressuredeflection behaviour. Package- induced and thermal stresses are reduced while a relief of the residual stress is obtained in the inner circular membrane. FEM simulations showed that the deformation of the inner membrane is hardly affected by the actual dimensions of the cormgation. A good estimate of this deformation is given by a circular membrane with clamped edge but free motion in the radial direction. The increasing pressure sensitivity and the decreas- ing temperature sensitivity make the membranes includ- ing the circular corrugation very attractive for applica- tion in strain based pressure sensors. Acknowledgments These investigations in the programme of the Foundation for Fundamental Research on Matter (FOM) have been supported by the Netherlands Txhnology Foundation (Snv). References [l] Seuturia S D and Smith R L 1988 Microsensor packaging and system partitioning Sens. Actuators 15 221-34 [2] Spiering V Elwenspoek M 1991 On-chip dewupling mne for packagestress reduction Sens. Actuators A39 149-56 [3] Offereins HI, Sandmaier Folkner B, Steger U and Iang W I991 Stress-free assembly technique for a silicon based pressure sensor Roc. 6th In& Con{ SolS-S!ate Sensors and Actuators (San Francisco. C4. Bouwstra S, Spiering R M E J and 1991) (New York: BEE) pp 98529 141 Soierine V L Bouwstra S and Fluitman J H J 1993 L 1 -r Reafzati& of dewupling zones for package-stress reduction Sens. Actuators A3738 800-4 [SI Dbata 0, Kawahata K, Sugiyama S and Igarashi I 1989 Mechanical property measurements of thin films using loaddeflection of mmposite rectangular membranes Sens. Acfuators 20 135-41 [6] Pan J Y, Lin P, Maseeh F and Senturia S D 1990 Verification of FEM analysis of loaddeflection methods for measuring mechanical properties of thin Nms IEEE Solid-State Sensor and Actuator Workshop (Hiton SC, 1990) (New York IEEE) Technical digest pp 70-3 %ory of Plates and Shells 2nd edn (New York McGraw-Hill) pp 396-412 c7] Timoshenko S and Minowsky-Krieger S 1970 246 

Membranes fabricated with a deep single corrugation for package stress reduction and residual stress relief

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L 1 -r Reafzati& of dewupling zones for package-stress reduction Sens. Actuators A3738 800-4 [SI Dbata 0, Kawahata K, Sugiyama S and Igarashi I

Microsensor packaging and system partitioning Sens. Actuators 15 221-34 [2] Spiering V Elwenspoek M

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Membranes fabricated with a deep single corrugation for package stress reduction and residual stress relief

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