sensors Article
Application and Optimization of Stiffness Abruption Structures for Pressure Sensors with High Sensitivity and Anti-Overload Ability Tingzhong Xu 1,2 , Dejiang Lu 1 , Libo Zhao 1, *, Zhuangde Jiang 1 , Hongyan Wang 3, *, Xin Guo 1 , Zhikang Li 1 , Xiangyang Zhou 4 and Yulong Zhao 1 1
2 3 4
*
State Key Laboratory for Manufacturing Systems Engineering, International Joint Laboratory for Micro/Nano Manufacturing and Measurement Technologies, Collaborative Innovation Center of SuzhouNano Science and Technology, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China;
[email protected] (T.X.);
[email protected] (D.L.);
[email protected] (Z.J.);
[email protected] (X.G.);
[email protected] (Z.L.);
[email protected] (Y.Z.) School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney, NSW 2052, Australia Shaanxi Institute of Metrology Science, Xi’an 710065, China School of Instrumentation Science & Optoelectronics Engineering, Beihang University, Beijing 100191, China;
[email protected] Correspondence:
[email protected] (L.Z.);
[email protected] (H.W.); Tel.: +86-29-8266-8616 (L.B.); +86-29-8872-8271 (H.W.)
Received: 4 July 2017; Accepted: 22 August 2017; Published: 26 August 2017
Abstract: The influence of diaphragm bending stiffness distribution on the stress concentration characteristics of a pressure sensing chip had been analyzed and discussed systematically. According to the analysis, a novel peninsula-island-based diaphragm structure was presented and applied to two differenet diaphragm shapes as sensing chips for pressure sensors. By well-designed bending stiffness distribution of the diaphragm, the elastic potential energy induced by diaphragm deformation was concentrated above the gap position, which remarkably increased the sensitivity of the sensing chip. An optimization method and the distribution pattern of the peninsula-island based diaphragm structure were also discussed. Two kinds of sensing chips combined with the peninsula-island structures distributing along the side edge and diagonal directions of rectangular diaphragm were fabricated and analyzed. By bonding the sensing chips with anti-overload glass bases, these two sensing chips were demonstrated by testing to achieve not only high sensitivity, but also good anti-overload ability. The experimental results showed that the proposed structures had the potential to measure ultra-low absolute pressures with high sensitivity and good anti-overload ability in an atmospheric environment. Keywords: bending stiffness distribution; peninsula-island structured diaphragm; stress concentration region; high sensitivity; high anti-overload ability
1. Introduction Attributed to their low-cost and simple fabrication process, micro electromechanical systems (MEMS) piezoresistive pressure sensors had been widely applied in industry for several decades. Sensors with high sensitivity are often needed in a wide variety of fields. In addition to automotive applications such as tire pressure monitoring, hydraulic system fluid pressure sensing and engine manifold monitoring [1–5], pressure is also one of the most important physical parameters for various biomedical applications, including measuring intrauterine pressure during birth, monitoring the Sensors 2017, 17, 1965; doi:10.3390/s17091965
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inlet and outlet pressures of blood in kidney dialysis and the cardiovascular system, measuring and controlling the vacuum level used to remove fluid from the eye during eye surgery [6–9], etc. One of the earliest research efforts in biomedical applications was a pressure sensor developed by Samaun et al. [10] for biomedical instrumentation applications. Based on a pressure detection mechanism classification, the previous studies can be divided into three kinds of detection methods: resonant detection, deformation detection and stress detection methods. The resonant detection method is based on the principle that the pressure load influences the resonant frequency of a diaphragm structure. For example, Cheng et al. [11] presented a micro-pressure sensor based on center frequency detection of a double-ended quartz tuning fork attached on a diaphragm. Although the sensor had a sensitivity of 299 kHz·kPa−1 and a nonlinearity of 0.0278% FS, the quartz tuning fork fabrication process was not compatible with the MEMS technology. Li et al. [12] presented a pressure detection model based on an electrostatically actuated resonant microplate, which had a working range within 100 Pa in theory. However, its parasitic capacitance and the low quality factor causd by the array design lower its real performance. The deformation detection method aims to detect the structure deflection induced by the pressure load, which is usually realized by a capacitive or optical sensing mechanism. For example, Chattopadhyay [13] presented a pressure sensor based on a capacitive sensing mechanism to detect the diaphragm deformation of the diaphragm, in which the sensor had a large non-linearity. Tang [14] presented an optical fiber grating-based pressure sensor with a sensitivity of −240 pm/MPa, however it had installation restrictions. In addition, strain gauge and piezoelectric sensor can be based on the stress detection method. Piezoresistive sensors have higher piezoresistance coefficients and good accuracy with simple signal transduction characteristics [15–28]. Besides, their fabrication process as compatible with the current MEMS technology so they can be mass produced. Thanks to the advantages presented above, MEMS piezoresistive pressure sensors are the most widely applied nowadays. As high sensitivity combined with low non-linearity are often very attractive performance features for a sensing chip, flat silicon diaphragms were generally modified with additional lump or boss structures to stiffen the diaphragm. These features improved the non-linearity by limiting the stretch deformation of the diaphragm, which is a significant cause of non-linearity [29]. However, the stiffened diaphragm also makes the diaphragm more constrained, lowering the measuring sensitivity of the sensors, so there is a contradiction between non-linearity and measuring sensitivity that cannot be solved easily. Previous studies usually focused on modifying the design of the lump or boss structures to resolve the contradiction [15–28]. For example, Hein et al. [26] used a structured diaphragm with four flexible beams and a rigid diaphragm centre to reduce nonlinearity effects. They presented piezoresistive micro sensors for the 300 Pa range with high sensitivity and excellent linearity. Bao et al. [18] presented a beam-diaphragm structure with a working range of 0–1 kPa. Although its non-linearity of 0.1% FS shown its good linearity performance, its sensitivity of 0.6901 µV/V/Pa was low. Yu et al. [23] introduced a high sensitive pressure sensor combined with a bossed diaphragm incorporated beam. It had a sensitivity of 11.098 µV/V/Pa, but its non-linearity of 3.046% FS was low. Huang et al. [22] introduced a peninsula structured diaphragm which remarkably lowered the non-linearity of a pressure sensor to 0.36% FS, but its sensitivity was only 3.68 µV/V/Pa. Besides the structures presented above for the measurement of low pressure, the low non-linearity and high measuring sensitivity of sensors was hardly improved at the same time in subsequent works [15–28]. In addition to the non-linearity and sensitivity performance, the anti-overload performance of a high sensitivity pressure sensor is also critical, especially in aerospace applications. Aircraft altitude can be determined by measuring pressure based on the relationship between absolute pressure and height. Because of the extremely low pressure at high altitude and a high overload caused by the atmosphere in the Earth environment, both high measuring sensitivity and good anti-overload ability are required. Hein [30] presented a capacitive pressure sensor for differential pressure with an overload capability without the need for an external overload protection. Johnson et al. [31] reported a ribbed
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and bossed structure. The incorporation of ribs into the diaphragm for stress concentration was proved to be effective in improving the sensitivity and non-linearity. However, the anti-overload ability was not good because of the thin bosses used. Yu et al. [25] proposed a beam-membrane-quad-island (BMQI) absolute pressure sensor with a sensitivity of 0.018 mV/V/Pa and non-linearity of 0.14%, but the quad-island structure necessary to withstand the overload severely impaired the 1st natural frequency of the sensing chip. In this paper, a systematic design method for a beam-boss structured diaphragm based on the relationship between the diaphragm bending stiffness distribution and diaphragm stress concentration condition is presented for the first time. Secondly, giuided by the design method a novel peninsula-island-based diaphragm structure is presented and applied to different diaphragm shapes to test its performance. Thirdly, a three-step optimization method with good accuracy and generalization performance is presented. Finally, the sensing chips were bonded on an anti-overload glass base with a stepped structure, which guaranteed the proposed sensor had a good anti-overload ability. 2. Sensing Chip Design A well designed diaphragm structure is critical to improve the performance of a sensing chip. The design of a diaphragm structure is closely related to its bending stiffness distribution on the diaphragm structure. In this part, a systematic analysis of the influence of diaphragm bending stiffness distribution on the stress concentration characteristics of a pressure sensing chip was conducted. Then, different diaphragms with peninsula-island structures were presented for further study. 2.1. Stiffness Distribution Characteristics of a Diaphragm Structure The measuring sensitivity of a silicon-based piezoresistive pressure sensor is mainly determined by the stress concentration conditions in the stress concentration region (SCR) of the sensing chip. The more elastic potential energy converted to an electrical output through piezoresistors, the higher the sensitivity of the sensing chip will be. High stress concentrations usually appear near a crack-like structure where the radius of curvature is the lowest. In an elliptical crack-like structure with length of 2a0 and width of 2b0 , under an applied external stress σ, the stress at the ends of major axes can be given by Inglis’ equation [32]:
σmax
a = σ 1+2 0 b0
= σ 1+2
r
a0 ρ0
(1)
where ρ0 is the curvature radius of the crack tip. As the radius of curvature approaches zero, the maximum stress approaches infinity. However, this could not be utilized in the design of a sensing chip because the sensing chip structure can fail via a propagating crack, when a concentrated stress exceeds the material's theoretical cohesive strength. Also the irregular shape of SCR makes it impossible to fabricate piezoresistors on it. In order to form a SCR with high stress concentration and good stress value uniformity to improve the non-linearity of sensing chips, researchers usually design structures such as bossed diaphragms and diaphragms with bulky islands to redistribute the stiffness in different parts of the diaphragm. According to the previous diaphragm structures, the key points of diaphragm stiffness design can be concluded as follows:
• •
The stiffened diaphragm had the ability to concentrate elastic potential energy in SCR. The stiffened area should not constrain the diaphragm deformation too much which would impair the stress concentration.
However, the stiffened structure will definitely constrain the diaphragm deformation which may impair the stress concentration at the SCR, so a balance between these two key points must be found and make a full use of the first key point to enhance the stress concentration. Here, the emphasis was put on the stiffened structure design around the SCR. Considering the maximum stress usually appears at a stationary stiffness point on the diaphragm surface and the
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structural symmetric characteristic of the diaphragm, the stiffened structure around the SCR should be be symmetric the SCR center should an intersection the stiffness stationary point symmetric andand the SCR center should be anbeintersection pointpoint of theof stiffness stationary point along along twodirections. main directions. With this infour mind four different distribution conditions around two main With this in mind different stiffnessstiffness distribution conditions around the SCR the SCR can be conceived, can be conceived, as shownasinshown Figurein 1. Figure 1.
Figure 1. 1. Stiffness distributions along along two two main main directions directions around around SCR SCR of of aa pressure pressure sensing sensing chip. chip. Figure Stiffness distributions
In condition I, the SCR had the lowest bending stiffness along the longitudinal direction and the In condition I, the SCR had the lowest bending stiffness along the longitudinal direction and the highest bending stiffness along the transversal direction. Then, the SCR was the most deformable highest bending stiffness along the transversal direction. Then, the SCR was the most deformable region along the longitudinal direction and the main role to resist the diaphragm deformation along region along the longitudinal direction and the main role to resist the diaphragm deformation along the transversal direction. the transversal direction. In condition II, the SCR had the lowest bending stiffness along both the longitudinal and In condition II, the SCR had the lowest bending stiffness along both the longitudinal and transversal directions, therefore, the SCR was the most deformable region along the two directions. transversal directions, therefore, the SCR was the most deformable region along the two directions. In condition III, the SCR had the highest bending stiffness along both the longitudinal and In condition III, the SCR had the highest bending stiffness along both the longitudinal and transversal directions. The SCR was a rigid body compared with the surrounding diaphragm transversal directions. The SCR was a rigid body compared with the surrounding diaphragm structure. structure. In condition IV, the SCR had the highest bending stiffness along the longitudinal direction and In condition IV, the SCR had the highest bending stiffness along the longitudinal direction and lowest bending stiffness along the transversal direction. Then, the position on both sides along the lowest bending stiffness along the transversal direction. Then, the position on both sides along the transversal direction of the SCR played the main role to resist the diaphragm deformation. transversal direction of the SCR played the main role to resist the diaphragm deformation. 2.1.1. Condition I 2.1.1. Condition I Most previously researched structures can be considered as belonging to condition I. However, Most previously researched structures can be considered as belonging to condition I. However, these structures usually strictly satisfy the bending stiffness distribution only in one direction, which these structures usually strictly satisfy the bending stiffness distribution only in one direction, which only has a maximum bending stiffness along the transversal direction, while the bending stiffness only has a maximum bending stiffness along the transversal direction, while the bending stiffness almost maintains a constant value along the other direction, and vice versa, like the structures shown almost maintains a constant value along the other direction, and vice versa, like the structures shown in Figure 2. P.K. Kinnell [21] created a bending stiffness valley along the longitudinal direction by in Figure 2. P.K. Kinnell [21] created a bending stiffness valley along the longitudinal direction by using n-type hollow silicon islands to stiffen the diaphragm. Huang [22] created a bending stiffness using n-type hollow silicon islands to stiffen the diaphragm. Huang [22] created a bending stiffness peak along the transversal direction by using a bossed peninsula structured diaphragm. Seo [33] peak along the transversal direction by using a bossed peninsula structured diaphragm. Seo [33] created a bending stiffness peak along the transversal direction by a combination of a silicon beam and created a bending stiffness peak along the transversal direction by a combination of a silicon beam a silicon rubber diaphragm based on the large Young modulus difference between these two materials. and a silicon rubber diaphragm based on the large Young modulus difference between these two For these structures, the elastic potential energy dissipation along the other direction without the materials. For these structures, the elastic potential energy dissipation along the other direction bending stiffness stationary point was large. The sensing chip structures presented in [25,34,35] had without the bending stiffness stationary point was large. The sensing chip structures presented in both bending stiffness valleys along the longitudinal direction and bending stiffness peaks along the [25,34,35] had both bending stiffness valleys along the longitudinal direction and bending stiffness transversal direction realized by bossed beams, islands and groove structures, as shown in Figure 3. peaks along the transversal direction realized by bossed beams, islands and groove structures, as shown in Figure 3. Compared with the structures presented in [21,22,33], the structures presented in [25,34,35] showed less elastic potential energy dissipation around the SCR boundary, so the stress
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Compared with the structures presented in [21,22,33], the structures presented in [25,34,35] showed less Sensors 2017, 17, 1965 5 of 25 elastic potential energy dissipation around the SCR boundary, so the stress concentration distribution Sensors 2017, 17, 1965 5 of 25 of condition I can confined in a region surrounded by the junctions of the low bending stiffness area concentration distribution of condition I can confined in a region surrounded by the junctions of the andconcentration high bending stiffness area. Also, onstiffness the principle ofsurrounded energy a higher of and condition I can confined in aarea. region junctions thestress low bending distribution stiffness area high based bending Also, based conservation, on by thethe principle of of energy low bending stiffness area and high bending stiffness area. Also, based on the principle of energy concentration can be obtained by shrinking the area of the SCR, by which means, the sensitivity of the conservation, a higher stress concentration can be obtained by shrinking the area of the SCR, by which conservation, a higher stress concentration can be obtained by shrinking the area of the SCR, by which sensing chipthe can be improved. means, sensitivity of the sensing chip can be improved. means, the sensitivity of the sensing chip can be improved.
(a) (a)
(b) (b)
(c) (c)
Figure 2. Diaphragm structure had either maximum bending stiffness along the transversal direction
Figure 2. Diaphragm structure had maximumbending bending stiffness along transversal direction Figure 2. Diaphragm had either either maximum stiffness along thethe transversal direction or minmum bendingstructure stiffness along the longitudinal direction: (a) Kinnell’s structure [21]; (b) Huang’s or minmum bending stiffness along the longitudinal direction: (a) Kinnell’s structure [21]; (b) Huang’s orstructure minmum[22]; bending stiffness along[33]. the longitudinal direction: (a) Kinnell’s structure [21]; (b) Huang’s (c) Seo’s structure structure [22]; (c) Seo’s structure [33]. structure [22]; (c) Seo’s structure [33].
(a) (a)
(b) (b)
(c) (c)
Figure 3. Diaphragm structures had both maximum bending stiffness along the transversal direction Figure 3. Diaphragm structures had boththe maximum bending stiffness the transversal direction and3.minmum bending stiffness along longitudinal direction: (a)along Yu’s structure [25]; (b) Yang’s Figure Diaphragm structures had both maximum bending stiffness along the transversal direction and minmum bending stiffness along the longitudinal direction: (a) Yu’s structure [25]; (b) structure [34]; (c) Xu’s structurealong [35]. the longitudinal direction: (a) Yu’s structure [25]; Yang’s and minmum bending stiffness (b) Yang’s structure [34]; (c) Xu’s structure [35]. structure [34]; (c) Xu’s structure [35]. 2.1.2. Condition II 2.1.2. Condition II Here a peninsula-island structured diaphragm with a pit at the SCR, as shown in Figure 4, was 2.1.2. Condition II Here a peninsula-island structured diaphragm with pitcondition at the SCR, shown in Figure 4, of was used to discuss the stress concentration characteristics ofathe II. as The pit plays the role the Here a peninsula-island structured diaphragm with a pit at the SCR, as shown in Figure 4, was used to discuss the stress concentration characteristics of the condition II. The pit plays the role of the SCR. Also, the influence from the SCR thickness on the stress concentration in both the stress used to discuss theinfluence stress concentration of the condition II. Theinpit plays role of SCR. Also, the from the discussed. SCRcharacteristics thickness on the stress concentration both the the stress dissipation area and SCR has been dissipation area and SCR has been discussed.
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the SCR. Also, the influence from the SCR thickness on the stress concentration in both the stress Sensors 2017, 17,and 1965 SCR has been discussed. 6 of 25 dissipation area Sensors 2017, 17, 1965
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Figure Diaphragmwith with peninsula-island peninsula-island structure and a pit. Figure 4. 4. Diaphragm structure and a pit. Figure 4. Diaphragm with peninsula-island structure and a pit.
As shown in Figure 5, by changing the SCR thickness, the stiffness difference between the SCR
As shown in Figure 5, byby changing the thickness, the stiffness difference between the SCR As remaining shown in Figure changing theSCR SCR thickness, difference between the SCR and the region5,along the transversal direction canthe be stiffness divided into three phases. and the region along thethe transversal canbe bedivided divided into three phases. andremaining the remaining region along transversaldirection direction can into three phases.
Figure 5. Stress concentration condition around the SCR influenced by the stiffness difference Figure 5.along Stresstheconcentration condition around the SCR influenced by the stiffness difference variation transversal direction. Figure 5. Stress concentration condition around the SCR influenced by the stiffness difference variation variation along the transversal direction.
along the transversal direction. In the first phase, the SCR thickness decrease lowered the bending stiffness of the diaphragm Inincreased the first phase, theconcentration SCR thicknessvalue decrease lowered the dissipation bending stiffness of the diaphragm which the stress in both the stress area and SCR. In the first phase, the SCR thickness decrease lowered the bending stiffness of the diaphragm which increased the stress concentration value in both the stress dissipation area and SCR. In the second phase, with the SCR thickness decreasing further, the bending stiffness difference In the second phase, with the SCR thickness decreasing further, the bending stiffness difference which increased the stress concentration value in both the stress dissipation area and SCR. between the SCR and the remaining part along the transversal direction became larger. The stress between thearea SCR and the the remaining part along the transversal direction became larger. The In the second phase, with the SCR thickness decreasing further, thepotential bending stiffness difference dissipation with higher bending stiffness acquired more elastic energy andstress this dissipation area with the higher bending stiffness acquired more elastic potential energy and this increased the stress concentration Considering the principle of energy conservation, thestress between the SCR and the remainingvalue part[26]. along the transversal direction became larger. The increased the stress concentration value [26]. Considering the principle of energy conservation, the stress concentration value at thebending SCR became lower.acquired more elastic potential energy and dissipation area with the higher stiffness this stressInconcentration value at the SCR became lower. the third phase, with the SCR becoming even thinner, the stress concentration value at the increased the stress concentration value [26]. Considering the principle of energy conservation, the thirdagain. phase, with SCR becoming thinner, the SCR stresswas concentration value at the the SCR In increased This is the because whole even structure at the getting away from the stress concentration value at the SCRthe became lower. SCR increased again. This is because the whole structure at the SCR was getting away from the neutral surface of the diaphragm, whereby the stress on the cross section of the SCR was dominated In the third phase, with the SCR becoming evenonthinner, stress the concentration value at the neutral surface of theThe diaphragm, whereby thecross stress themade crossthe section SCR was dominated by stretching forces. fast decrease in SCR section the stressofconcentration at the SCR SCR increase increased again. This is because the whole structure at the SCR was getting away from the by stretching again.forces. The fast decrease in SCR cross section made the stress concentration at the SCR neutral surface of the diaphragm, the stress on thestress cross and section of the SCR dominated increase again. However, according to thewhereby ratio between disspation maximum stresswas difference However, according to the ratio between disspation stress and maximum stress difference by stretching forces. The fast decrease in SCR cross section made the stress concentration at the SCR shown in Figure 5, the dissipation stress increased during all three phases, which causes a lot of elastic shown in Figure 5, the dissipation stress increased during all three phases, which causes a lot of elastic increase again.
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However, according to the ratio between disspation stress and maximum stress difference shown in Figure 5, the dissipation stress increased during all three phases, which causes a lot of elastic energy dissipation. Also it is hard to realize and control the etching thickness for the necessary multilevel Sensors 2017, 17, 1965 7 of 25 structure, so 2017, this17, kind Sensors 1965 of structure can hardly be used in pressure diaphragm structures. 7 of 25 energy dissipation. Also it is hard to realize and control the etching thickness for the necessary energy dissipation. Also is hard to realizecan and control etching thickness for the necessary 2.1.3. multilevel Condition III structure, so thisitkind of structure hardly be the used in pressure diaphragm structures. multilevel structure, so this kind of structure can hardly be used in pressure diaphragm structures.
In condition III, 2.1.3. Condition III the SCR had the highest bending stiffness along both the longitudinal and 2.1.3.directions. Condition IIIThe stress concentration value in this SCR can be derived by Euler-Bernoulli transversal In condition III, the SCR had the highest bending stiffness along both the longitudinal and beam theory According to the Euler-Bernoulli beam theory, the maximum stress and value was In [36]. condition III, the SCR the highest bending stiffness the longitudinal transversal directions. The stresshad concentration value in this SCR along can beboth derived by Euler-Bernoulli transversal directions. The stress concentration value inofthis SCR can be derived bySCR Euler-Bernoulli concentrated at the position around the SCR, instead concentrating on the with the highest beam theory [36]. According to the Euler-Bernoulli beam theory, the maximum stress value was beam theory [36].IIIAccording tostiffness the Euler-Bernoulli beam theory, the maximum stresspressure value was stiffness, so condition can’t be a distribution option for a piezoresistive sensor. concentrated at the position around the SCR, instead of concentrating on the SCR with the highest concentrated at the position around the SCR, instead of concentrating on the SCR with the highest
stiffness, so condition III can’t be a stiffness distribution option for a piezoresistive pressure sensor.
stiffness, soIV condition III can’t be a stiffness distribution option for a piezoresistive pressure sensor. 2.1.4. Condition
2.1.4. Condition 2.1.4. Condition IV SCR had highest bending stiffness along the longitudinal direction and lowest In condition IV, IV the In In condition the SCR bending stiffness along thelongitudinal longitudinal direction bending stiffness along the direction. This kind of bending stiffness direction distribution can be conditionIV, IV, thetransversal SCR had had highest highest bending stiffness along the andand lowest bending stiffness along the transversal direction. This kind of bending stiffness distribution realizedlowest by the structure shown Figure 6. According to the stress distribution in Figure 7, bending stiffness alonginthe transversal direction. This kind of bending stiffnessshown distribution cancan beboss realized byby the shown Figure 6. According the stress distribution shown be realized thestructure structurebending shown in Figure 6. According totothe stress distribution in in of the silicon region with higher stiffness plays the main role in resisting theshown deformation Figure 7, the silicon boss region with higher bending stiffness plays the main role in resisting the Figure 7, so thethe silicon bosspotential region with higher stiffness plays the main role in resisting thebending the diaphragm, elastic energy is bending mainly concentrated at the region with higher deformation potential energy energyisismainly mainlyconcentrated concentrated region deformationofofthe thediaphragm, diaphragm,so so the the elastic elastic potential at at thethe region stiffness along the transversal direction. Therefore, condition IV can’t be a stiffness distribution option with higherbending bendingstiffness stiffness along along the the transversal transversal direction. IV IV can’t be be a a with higher direction.Therefore, Therefore,condition condition can’t for a piezoresistive pressure sensor. stiffness distribution option for a piezoresistive pressure sensor. stiffness distribution option for a piezoresistive pressure sensor.
Figure 6. Stiffness distribution pattern for condition IV discussion.
Figure 6. Stiffness distribution pattern for condition IV discussion. Figure 6. Stiffness distribution pattern for condition IV discussion.
(a)
(b)
Figure 7. Stress distribution (a) in condition IV: (a) longitudinal stress Sy distribution (b) of the structure; (b) stress difference Sy−Sx distribution of the structure.
Figure 7. Stress distribution in condition IV: (a) longitudinal stress Sy distribution of the structure; (b)
Figure 7. Stress distribution in condition IV: (a) longitudinal stress Sy distribution of the structure; stress difference Sconditions y−Sx distribution In conclusion, I andofII the canstructure. be potential options for bending stiffness distribution for (b) stress difference Sy − Sx distribution of the structure.
a diaphragm structure. However, condition II always had a large elastic potential energy dissipation In conclusion, conditions and II limits can befurther potential options for stiffness distribution along the transversal directionI which improvement of bending the measuring sensitivity of the for sensing chip, soconditions condition I with the lowest stiffness along thefor longitudinal and the a diaphragm structure. However, condition II always had aoptions large elastic potentialdirection energy dissipation In conclusion, I and II can bending be potential bending stiffness distribution
the transversal direction which limits further improvement of the measuring sensitivity of the for a along diaphragm structure. However, condition II always had a large elastic potential energy sensing chip, so condition I with the lowest bending stiffness along the longitudinal direction and the
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dissipation along the transversal direction which limits further improvement of the measuring sensitivity of the sensing chip, so condition I with the lowest bending stiffness along the longitudinal direction and the highest bending stiffness along the transversal direction was the best Sensors 2017, 17, 1965 8 of 25stiffness distribution for a piezoresistive pressure sensing chip. Based on previously researched peninsula-island highest bending astiffness along the transversal was the distribution best stiffness patterns distribution forimproved a structures [35,37,38], peninsula-island structuredirection with different and piezoresistive pressure sensing chip. Based on previously researched peninsula-island structures optimization method is presented as follows. [35,37,38], a peninsula-island structure with different distribution patterns and improved optimization method is presented as follows.
2.2. Basic Design of the Sensing Chip
Basic Design of the Sensing Chip As2.2. shown in Figure 8, two representative distribution patterns of a peninsula-island structure As shown Figure 8, two representative distribution patterns of (Diaphragm a peninsula-island structure are presented, whichinare positioned along the side edge direction I) and the diagonal areof presented, which are positioned alongII). theAiming side edgefor direction (Diaphragm I) 500 and Pa the and diagonal direction square diaphragm (Diaphragm a working range of considering direction of square diaphragm (Diaphragm II). Aiming for a working range of 500 Pa and considering the limitations of current fabrication technology, the thickness of the peninsula-island structure was the limitations of current fabrication technology, the thickness of the peninsula-island structure was aroundaround 300 ±300 10 µm. TheThe effective dimension was as 3500 3500 µm2 . 2. ± 10 μm. effectivediaphragm diaphragm dimension was set set as 3500 × 3500×μm
(a)
(b)
Figure 8. Schematics of the peninsula-island based diaphragms structures: (a) diaphragm I with
Figure 8. Schematics of the peninsula-island based diaphragms structures: (a) diaphragm I with peninsula-island structure positioning along the side edge direction of diaphragm; (b) diaphragm II peninsula-island structurestructure positioning alongalong the side edge direction diaphragm; (b) diaphragm II with peninsula-island positioning the diagonal direction of of diaphragm. with peninsula-island structure positioning along the diagonal direction of diaphragm. 3. Finite Element Method Analysis and Designing Method
3. Finite Element Method Analysis and Designing Method
3.1. The Effect of Various Geometrical Parameters on Stress and Frequency
3.1. The Effect of Various on Stressparameters and Frequency In this part, theGeometrical influence of Parameters different geometrical on the stress difference value (σ = Sy−Sx) between the longitudinal and transversal stresses and 1st order natural frequency f are
Indiscussed, this part,asthe influence of different geometrical parameters on the stress difference value shown in Figure 9. (σ = Sy − SThe the longitudinal and transversal anddiaphragm 1st orderby natural frequency f are x ) between results indicate that the increasing stiffness ofstresses the whole thickening the discussed, as shown in Figure 9. diaphragm thickness h0 resulted in a decrease in Sy−Sx or an increase in f, as shown in Figure 9a. In Figure 9b, anindicate increasing width of the peninsula-island within adiaphragm small optimization range The results that thew increasing stiffness structure of the whole by thickening the can increase f by improving the partial stiffness of the diaphragm, while this can also increase diaphragm thickness h0 resulted in a decrease in Sy − Sx or an increase in f, as shown inthe Figure 9a. energy dissipation area to decrease the stress concentration at the SCR and Sy-Sx. The results In Figure 9b, an increasing width w of the peninsula-island structure within a small optimization mentioned above shown that the tradeoff between Sy−Sx and f can’t be solved by optimizing the range can increase f by improving the partial width stiffness diaphragm thickness h and peninsula-island w. of the diaphragm, while this can also increase the energy As dissipation area to decrease the stress concentration the SCR y − Snatural x . The results shown in Figure 9c, as the dimension of the gap size d at decreases theand 1st Sorder frequency and Sy−Sx increase at tradeoff the same time. Also,Sas in Figures 9d,e mentioned above shown that the between − Scoloured can’t beshown solved by optimizing the y the x and f regions show,thickness the variations of the island and peninsula lengths diaphragm h and peninsula-island width w. can also made Sy−Sx and f increase at the time within a certain optimization range. Compared with other structure sizes, the effects of d, Assame shown in Figure 9c, as the dimension of the gap size d decreases the 1st order natural frequency l1 and l2 on the relationship between Sy−Sx and f are very different. Generally, the increasing stiffness and Sy − Sx increase at the same time. Also, as the coloured regions shown in Figure 9d,e show, leads to a decrease in sensitivity, while, d and a certain optimization range of l1, l2 made the Sy−Sx and the variations andTherefore, peninsula alsothe made Sy − Ssensitivity at the same x and f increase f increaseofatthe the island same time. thelengths tradeoff can between measuring and dynamic time within a certain range. Compared structure sizes, effects of d, l1 and performance of optimization piezoresistive pressure sensing chipwith was other remarkably relieved. Asthe a result, these proposed diaphragm structures able to remarkably improve the measuring sensitivity of a l2 on the relationship between Sy − Swere f are very different. Generally, the increasing stiffness leads x and sensing in chip without impairing dynamic performance. to a decrease sensitivity, while, its d and a certain optimization range of l1 , l2 made the Sy − Sx and f increase at the same time. Therefore, the tradeoff between the measuring sensitivity and dynamic performance of piezoresistive pressure sensing chip was remarkably relieved. As a result, these proposed diaphragm structures were able to remarkably improve the measuring sensitivity of a sensing chip without impairing its dynamic performance.
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(a) (d)
(b)
(e)
(c) Figure 9. The effects of different geometrical parameters on Sy−Sx and f: (a) the effect of diaphragm thickness h0; Figure 9. The effects of different geometrical parameters on Sy − Sx and f : (a) the effect of diaphragm (b) the effect of peninsula-island structure width w; (c) the effect of gap size d; (d) the effect of l1; (e) the effect of thickness h0 ; (b) the effect of peninsula-island structure width w; (c) the effect of gap size d; (d) the l2. effect of l1 ; (e) the effect of l2 .
Diaphragm thickness is usually determined by the fabrication capacity and working range of a Diaphragm thickness is usually determined the capacity and working range of a sensing chip; here the diaphragm thickness h0 wasbyset asfabrication 10 μm. In order to improve the measuring sensing chip;ofhere the diaphragm h0 was be setsmall as 10enough µm. In to order to improve the potential measuring sensitivity the sensing chip, thethickness SCR area should diminish the elastic 2 to elastic sensitivity of the sensing SCRwas area be small enough diminish potential energy dissipation, so thechip, SCRthe region setshould as a rectangular region ofto160 × 35 μmthe spare enough 2 spacedissipation, for arranging Theset l1 as and l2 values are region critical of to 160 optimize the sensitivity and energy sothe thepiezoresistors. SCR region was a rectangular × 35 µm to spare enough dynamic performance of the sensing chip, in the part. space for arranging the piezoresistors. Theas l1 discussed and l2 values arefollowing critical to optimize the sensitivity and dynamic performance of the sensing chip, as discussed in the following part. 3.2. Optimization Method for the Peninsula-Island Based Structure 3.2. Optimization Method for the Peninsula-Island Based Structure For the proposed structures, the lengths of the peninsula and island structures are key parameters to optimize the measuring sensitivity. Based on and the island double-step optimization method For the proposed structures, the lengths of the peninsula structures are key parameters previous sensitivity. research [38],Based a three-step had been presentedmethod to improve the to presented optimize in theour measuring on the method double-step optimization presented measuring sensitivity of sensing chips, as shown in Figure 10. The first step was to optimize the in our previous research [38], a three-step method had been presented to improve the measuring
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sensitivity of shownthe in island Figurestructure 10. The first step was to optimize thefrom position of the Sensors 17, 1965 chips, 10 of 25 position of2017, thesensing peninsula tip as without to relieve constraints arising the silicon peninsula tip without the island structure to relieve constraints arising from the silicon pedestal of pedestal of the SCR. This was determined by the distance l1 between the peninsula tip and the position of the peninsula tip without the island structure to relieve constraints arising from the silicon the SCR. This was determined thewas distance l1 between the peninsula diaphragm center. diaphragm center. The secondby step to optimize the distance l2 fromtip theand tipthe of island structure to pedestal of was the SCR. This was determined by the the distance lisland 1 between the peninsula tip and the The second step to optimize the distance l from tip of structure to the diaphragm center. the diaphragm center. This step maximizes 2 the elastic potential energy transferred from the diaphragm center. The second step was to optimize the distance l2 from the tip of island structure to This step maximizes the elastic potential energy transferred the remainder the step diaphragm remainder of the diaphragm to the peninsula-island part of from the diaphragm. The of third was to the diaphragm center. This step maximizes the elastic potential energy transferred from the to the peninsula-island part ofredistributing the diaphragm. The third step was to optimize the to SCR position by optimize the SCR position by the elastic potential energy transferred the peninsularemainder of the diaphragm to the peninsula-island part of the diaphragm. The third step was to redistributing the elastic potential energy transferred to the peninsula-island by the second step. In the island by thethe second step. Inbythe third step, the theelastic lengths of theenergy peninsula and island structures had optimize SCR position redistributing potential transferred to the peninsulathird step, the lengths of step. the peninsula and island structures had been adjusted by in lstructures to guarantee beenisland adjusted by second l1 to guarantee thethird most elastic is concentrated SCR.had the 1 the by the In the step, the potential lengths of energy the peninsula and island mostbeen elastic potential is concentrated in the SCR. energy is concentrated in the SCR. adjusted by l1energy to guarantee the most elastic potential
Figure 10. Optimization processofofthe thepeninsula-island peninsula-island structure different distribution patterns. Figure 10. Optimization process structureforfor different distribution patterns. Figure 10. Optimization process of the peninsula-island structure for different distribution patterns.
Figure 11 shown the results of the first optimization step. At two sides of the optimized range,
Figure 11 thedifference results of step. Atshrinkage two sidesofof optimized range, 11ofshown shown ofatthe the first optimization the value the stress the first SCR optimization was constrained by the thethe effective loaded the value of the stress at the SCR constrained by shrinkage of areas, the loaded stress difference difference at the the silicon SCR was was constrained by the theIn the effective effective loaded area and constraint force from pedestal, respectively. these two the stress area force from the silicon pedestal, In these two areas, the stress difference decreased linearly with change of l1 respectively. value. respectively. In this step, theIn SCR was set in aareas, regiondifference withstress area and andconstraint constraint force from thethesilicon pedestal, these two the a lower constraint from the silicon pedestal. Also, an optimized range for the SCR position had been decreased linearly with the change l1 value. In thisInstep, the SCR was was set in with a difference decreased linearly with theofchange of l1 value. this step, the SCR setainregion a region with determined tofrom provide asilicon reference for l1 optimization in the third range step. lower constraint Also, a lower constraint fromthe the siliconpedestal. pedestal. Also,an anoptimized optimized rangefor forthe theSCR SCR position position had had been been determined determined to to provide provide aa reference reference for for ll11 optimization optimization in in the the third third step. step.
Figure 11. The relationship between maximum stress difference (σ = Sy−Sx) and l1 for two diaphragm structures.
In 11. Figure 12, the traversing method was carried out to verify(σthe results derived two from the threeFigure The between maximum stress difference y−S Figure Therelationship relationship between maximum stress difference= S(σ =x)Sand l1 for two y −l1Sfor x ) and diaphragm step method for both diaphragm structures. In the three-step method, the length l2 was determined structures. structures. diaphragm by the second step and the length l1 was determind by the third step. As shown in Figures 11 and 12, the values of l1 for both structures deduced by the first step of In Figure 12, the traversing method was carried out to verify the results derived from the threethree-step method were shorter than those deduced from the traversing method. The reason is that
step method for both diaphragm structures. In the three-step method, the length l2 was determined by the second step and the length l1 was determind by the third step. As shown in Figures 11 and 12, the values of l1 for both structures deduced by the first step of three-step method were shorter than those deduced from the traversing method. The reason is that
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In Figure 12, the traversing method was carried out to verify the results derived from the three-step method for both diaphragm structures. In the three-step method, the length l2 was determined by the second step and the length l1 was determind by the third step. As shown in Figures 11 and 12, the values of l1 for both structures deduced by the first step Sensors 2017, 17, 1965 11 of 25 of three-step method were shorter than those deduced from the traversing method. The reason is that the in the thefirst firststep stepwas wasoptimized optimized a condition without an island structure. thepeninsula peninsula length length in in in a condition without an island structure. Then Then the the stiffness stiffnessofofthe thestructure structurewithout without island structure was lower than that of structure with island structure was lower than that of structure with both both peninsula peninsula and and island island structures. structures. Compared Compared with with the the diaphragm diaphragm with with higher higher stiffness, stiffness, the thestress stress concentration condition in theinSCR waswas more likely to be byby thethe constraint concentration condition the SCR more likely to influenced be influenced constraintfrom fromthe thesilicon silicon pedestal. In order to relieve the constraint from silicon pedestal, SCR needstotobebeset setfurther further pedestal. In order to relieve the constraint from thethe silicon pedestal, thethe SCR needs away from the silicon pedestal. If the length l 1 deduced from the first step were applied to the sensing away from the silicon pedestal. If the length l1 deduced from the first step were applied to the sensing the stress difference at SCR the SCR would be decreased 2.33% diaphragmI Iand and4.40% 4.40%for for chips,chips, the stress difference at the would be decreased by by 2.33% forfor diaphragm diaphragm II, when compared to their optimized stress difference values with the lengthl1l1deduced deduced diaphragm II, when compared to their optimized stress difference values with the length the transversing method. by theby transversing method.
FigureFigure 12. The between stressstress difference (σ = S(σ l1 lfor two 12.relationship The relationship between difference = SSy−S ) and 1 for twodiaphragm diaphragmstructures. structures. y− x ) xand
onsecond the second by relocating SCR position third step, thestress stressdifference difference BasedBased on the step,step, by relocating the the SCR position in in thethe third step, the and optimized values of l 1 and l2 agreed well with the results of the transversing method. The and optimized values of l1 and l2 agreed well with the results of the transversing method. traversingmethod methodproved provedthe thefeasibility feasibilityofofthe thethree-step three-stepmethod methodwhich whichwould wouldgreatly greatlyreduce reducethe the The traversing optimization workload. optimization workload. Figure 12 also indicated that the optimized positions of the peninsula tip and island tip for the Figure 12 also indicated that the optimized positions of the peninsula tip and island tip for the diaphragm I and diaphragm II were very close and the optimized stress difference values were not diaphragm I and diaphragm II were very close and the optimized stress difference values were not very very sensitive to the size variation. Therefore, the optimized l1 and l2 for a diaphragm with certain sensitive to the size variation. Therefore, the optimized l1 and l2 for a diaphragm with certain dimensions dimensions could be determined, regardless of the distribution pattern of the peninsula-island could be determined, regardless of the distribution pattern of the peninsula-island structure. structure. However, the maximum valuevalue of stress difference was was associated withwith the distribution patterns of However, the maximum of stress difference associated the distribution patterns the peninsula-island structure. The stress difference of diaphragm I was larger than that of diaphragm of the peninsula-island structure. The stress difference of diaphragm I was larger than that II. of This can be explained bycan simplifing the deformation ofthe a square diaphragm into the model shown in diaphragm II. This be explained by simplifing deformation of a square diaphragm into the Figuremodel 13 and giveninby Equations shown Figure 13 and(2)–(4). given by Equations (2)–(4).
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p α = arcsin 2h/ 4h2 + a2 β = arcsin a = β
√
s a2
2h/
p
2h2 + a2
a2 +1 > 1 + 4h2
(2) (3) (4)
where, a was the edge size of simplified model, h was the displacement at the center of simplfied model. Equations (2) and (3) shown the values of angles α and β. Equation (4) indicates that the valueFigure of β was definitly smaller than stress that of α. The (σ stress value thetwo SCR was mainly caused by 13. The relationship between difference = Sy−S x) andin l1 for diaphragm structures. the bending moment which was directly propotional to the rotation angle of the diaphragm along the corresponding direction. This also indicated that the sensing chip with diaphragm I had a better 2 2 arcsin 2 h / 4 h a Sensors 2017, 17, to 1965 12 of(2) 25 performance enhance the measuring sensitivity.
arcsin 2h / a
2h a 2
2
a2 1 1 a 4h 2
(3) (4)
2
where, a was the edge size of simplified model, h was the displacement at the center of simplfied model. Equations (2) and (3) shown the values of angles α and β. Equation (4) indicates that the value of β was definitly smaller than that of α. The stress value in the SCR was mainly caused by the bending moment which was directly propotional to the rotation angle of the diaphragm along the corresponding direction. This also indicated that the sensing chip with diaphragm I had a better performance enhance the measuring sensitivity. Figure 13. The relationship between difference andll11for fortwo twodiaphragm diaphragm structures. 13.to The relationship betweenstress stress difference(σ(σ= =SySy− −SSxx) )and 3.3. Stress Stress Distribution Distribution Analysis Analysis of of the the Diaphragm Diaphragm 3.3. arcsin 2h / 4h2 a 2 (2) Based of aa sensing chip can be predicted Based on on the the former former optimization optimization process, process, the the performance performance of sensing chip can be predicted 2 through arcsin the 2h /ANSYS 2h2 asoftware. using (3) using static static analysis analysis and and modal modal analysis analysis through the ANSYS software. Figures Figures 14 14 and and 15 15 show show the the stress − xS)xdistributions ) distributionsofofthe thediaphragms diaphragms under 500 500 Pa Pa uniform stress difference difference (σ (σ==SSyy−S under uniform loading. loading. These These a a2 figures indicated that the region above the gap had the largest stress difference value, which was (4) 1 1 figures indicated that the region above the gap had the 2 2 largest stress difference value, which was a a 4h agood good verification stiffness distribution pattern presented in condition I. Apart from the verification forfor thethe stiffness distribution pattern presented in condition I. Apart from the region region above the gap, there was no such stiffness abruption and no such elastic potential energy where, a was edge size of simplified model, h was the displacement at the center of simplfied above the gap, there was no such stiffness abruption and no such elastic potential energy concentration characteristics. model. Equations (2) and (3) shown the values of angles α and β. Equation (4) indicates that the value concentration characteristics. of β was definitly smaller than that of α. The stress value in the SCR was mainly caused by the bending moment which was directly propotional to the rotation angle of the diaphragm along the corresponding direction. This also indicated that the sensing chip with diaphragm I had a better performance to enhance the measuring sensitivity.
3.3. Stress Distribution Analysis of the Diaphragm Based on the former optimization process, the performance of a sensing chip can be predicted using static analysis and modal analysis through the ANSYS software. Figures 14 and 15 show the stress difference (σ = Sy−Sx) distributions of the diaphragms under 500 Pa uniform loading. These figures indicated that the region above the gap had the largest stress difference value, which was a good verification for the stiffness distribution pattern presented in condition I. Apart from the region above the gap, there was no such stiffness abruption and no such elastic potential energy concentration characteristics. (a) (b) Figure 14. 14. Stress Stressdifference difference(σ(σ= =S S− y−Sx) distribution of diaphragm I: (a) stress difference (σ = Sy−Sx) Figure Sx ) distribution of diaphragm I: (a) stress difference (σ = Sy − Sx ) y distribution of a 1/4 model; (b) detailed of 1/2 SCR. distribution of a 1/4 model; (b) detailed stress stress difference difference (σ (σ == SSyy−S−x)Sdistribution x ) distribution of 1/2 SCR.
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(a) (a)
(b) (b)
Figure 15. 15. Stressdifference difference (σ= =SyS− y−Sx) distribution of diaphragm II: (a) stress difference (σ = Sy−Sx) Figure distribution of difference (σ (σ = S=y S−y−S Sxx)) Figure 15.Stress Stress difference(σ(σ = Sy−SSxx)) distribution of diaphragm diaphragmII:II:(a) (a)stress stress difference distribution of of aa 1/4 1/4 model; (b) detailed stress difference (σ == SSyy−S−x)Sdistribution of 1/2 SCR. distribution model; (b) detailed stress difference (σ ) distribution of 1/2 SCR. x distribution of a 1/4 model; (b) detailed stress difference (σ = Sy−Sx) distribution of 1/2 SCR.
4. Improved Improved Diaphragm Structures Structures 4. 4. Improved Diaphragm Diaphragm Structures 4.1. Structure Structure Design 4.1. 4.1. Structure Design Design Based on the order create a stiffness peak along thethe transversal direction, the Based the basic basicdesign, design,in orderto create a stiffness peak along transversal direction, Based on on the basic design, ininorder totocreate a stiffness peak along the transversal direction, the front side of diaphragm was designed as a bossed structure with four grooves. Here, considering the front of diaphragm was designed bossedstructure structurewith withfour fourgrooves. grooves. Here, Here, considering considering aaa front sideside of diaphragm was designed asasa abossed silicon on on insulator(SOI) (SOI) wafer (top silicon: 10 +μm + buried 2: 1 μm) was used totherealize the silicon wafer (top silicon: 10 µm buried SiO2 : SiO 1SiO µm) was used to realize proposed silicon oninsulator insulator (SOI) wafer (top silicon: 10 μm + buried 2: 1 μm) was used to realize the proposed structure, the grooves were set 5 μm deep and 109 μm wide. Four ridges were formed structure, grooves the weregrooves set 5 µmwere deepset and5 109 wide. wereFour formed between two proposedthe structure, μmµm deep andFour 109 ridges μm wide. ridges wereeach formed between as each two in grooves, as shown in Figure of 16.the Thediaphragm dimensions ofpeninsula-island the diaphragm and peninsulagrooves, shown Figure 16. The dimensions and structure were between each two grooves, as shown in Figure 16. The dimensions of the diaphragm and peninsulaisland structureaccording were bothtooptimized to Section 3.2. both optimized Section 3.2.according island structure were both optimized according to Section 3.2.
(a) (a)
(b) (b)
Figure 16. Schematics of the peninsula-island based bossed diaphragm structure: (a) improved Figure 16. 16. Schematics Schematics of of the the peninsula-island peninsula-island based based bossed bossed diaphragm diaphragm structure: structure: (a) (a) improved improved Figure diaphragm I with peninsula-island structure along the side edge direction; (b) improved diaphragm diaphragmIIwith withpeninsula-island peninsula-islandstructure structurealong alongthe theside sideedge edgedirection; direction; improved diaphragm diaphragm (b)(b) improved diaphragm II II with peninsula-island structure along the diagonal direction. II with peninsula-island structure along the diagonal direction. with peninsula-island structure along the diagonal direction.
4.2. Finite Element Analysis 4.2. Finite Element Analysis 4.2. Finite Element Analysis Based on the longitudinal stiffness valley introduced by the peninsula-island structure discussed Based on the longitudinal stiffness valley introduced by the peninsula-island structure discussed Based 2.1.1. on thethe longitudinal stiffness valley introduced theeased peninsula-island structure discussed in Section evenly distributed grooves here not by only the constraint from the silicon in Section 2.1.1. the evenly distributed grooves here not only eased the constraint from the silicon in Sectionon 2.1.1. the evenlyofdistributed grooves only aeased the constraint the silicon pedestal the deflection the diaphragm, buthere alsonot created stiffness peak alongfrom the transversal pedestal on the deflection of the diaphragm, but also created a stiffness peak along the transversal pedestal the gap deflection ofshown the diaphragm, butThe alsoridge created stiffness peak along the transversal directionon at the position in Figure 17. hadathe strongest stiffness compared with direction at the gap position shown in Figure 17. The ridge had the strongest stiffness compared with direction the gap shown in Figure 17. The ridge had the stiffness compared the grooveatregion onposition both sides, and played a main role in resisting the strongest diaphragm deformation. The the groove region on both sides, and played a main role in resisting the diaphragm deformation. The with the groove region on both sides, and played a main would role in mainly resistingconcentrate the diaphragm longitudinal stress created by the diaphragm deflection at thedeformation. SCR which longitudinal stress created by the diaphragm deflection would mainly concentrate at the SCR which was the top surface of the ridge. At the same time, the ridge formed a clear boundary between the was the top surface of the ridge. At the same time, the ridge formed a clear boundary between the SCR and other regions of the diaphragm along the transversal direction of the peninsula structure. SCR and other regions of the diaphragm along the transversal direction of the peninsula structure.
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The longitudinal stress created by the diaphragm deflection would mainly concentrate at the SCR The value stress difference thesame peninsula-island structure were further enhancedbetween on which was theof top surface of thegenerated ridge. Atby the time, the ridge formed a clear boundary Sensors 2017, 17, 1965 14 of 25 the ridge and the elastic potential energy was strictly confined in the SCR, as shown in Figure 17. the SCR and other regions of the diaphragm along the transversal direction of the peninsula structure. The value of stress difference generatedby bythe thepeninsula-island peninsula-island structure were further enhanced on on The value of stress difference generated structure were further enhanced the ridge and elastic the elastic potential energywas wasstrictly strictly confined confined in asas shown in Figure 17. 17. the ridge and the potential energy inthe theSCR, SCR, shown in Figure
(a)
(b)
Figure 17. Stress difference (σ = Sy−Sx) distributions of the improved diaphragms: (a) improved diaphragm I with peninsula-island structure along the side edge direction; (b) (a) (b)improved diaphragm II with peninsula-island structure along the diagonal direction. Figure 17. Stress difference (σ = Sy−Sx) distributions of the improved diaphragms: (a) improved Figure 17. Stress difference (σ = Sy − Sx ) distributions of the improved diaphragms: (a) improved diaphragm I with peninsula-island structure along the side edge direction; (b) improved diaphragm The curves Figure 18a represent andalong compare the stress difference(b) distributions of differentII diaphragm I withinpeninsula-island structure the side edge direction; improved diaphragm II with peninsula-island structure along the diagonal direction.
diaphragms from center to edge.along The different diaphragms with peninsula-island structure the diagonal direction.included the diaphragm I, diaphragm II, improved diaphragm I, improved diaphragm II and a flat diaphragm (C-cup diaphragm) with the The curves in Figure 18a represent and compare the stress difference distributions of different same dimensions. It was evident that the stress differences of these proposed diaphragms reached diaphragms from center18a to edge. The different diaphragms included the diaphragm I, diaphragm II, The curves in Figure represent and compare the stress difference distributions of different their maximum values at the position above the gap. The improved diaphragm I had the maximum improved diaphragm I, improved diaphragm II and a flat diaphragm (C-cup diaphragm) with the diaphragms from center edge.was Theincreased differentby diaphragms included I, diaphragm II, stress difference value,towhich 381% compared with the the diaphragm flat diaphragm without same dimensions. It was evident that the stress differences of these proposed diaphragms reached improved diaphragm I, improved diaphragm and flat diaphragm with the peninsula-island structure. As shown in Figure II 18b, theastress difference (σ(C-cup = Sy−Sx) diaphragm) of flat diaphragm their maximum values at the position above the gap. The improved diaphragm I had the maximum samewithout dimensions. It was evident that the stress differences these proposed peninsula-island structure changed slightly along the of transversal direction.diaphragms Remarkably, reached for stress difference value, which was increased by 381% compared with the flat diaphragm without peninsula-island based bossed diaphragms structure, the stress differences (σ I= had Sy−Sthe x) inmaximum their their the maximum values at the position above the gap. The improved diaphragm peninsula-island structure. As shown in Figure 18b, the stress difference (σ = Sy−Sx) of flat diaphragm were much largerwhich than those any otherby diaphragms. stressSCR difference value, was of increased 381% compared with direction. the flat diaphragm without peninsula-island structure changed slightly along the transversal Remarkably,without for For the proposed diaphragm structures, the stress distribution characteristics at )the SCRdiaphragm were − peninsula-island structure. As shown in Figure 18b, the stress difference (σ = S S flat y the peninsula-island based bossed diaphragms structure, the stress differences (σ x= Sof y−S x) in their studied in detail. Considering the symmetry of structure, the stress distributions of only half SCR without peninsula-island changed slightly along the transversal direction. Remarkably, for the SCR were much largerstructure than those of any other diaphragms. were shown in Figure 18c,d, which indicate that the center region of the ridge is the best region to For the proposed diaphragm structures, the stress characteristics were SCR peninsula-island based bossed diaphragms structure, thedistribution stress differences (σ = Syat−the SxSCR ) in their arrange the piezoresistor, where the stress difference is not only very uniform but also large enough. in detail. theother symmetry of structure, the stress distributions of only half SCR were studied much larger thanConsidering those of any diaphragms. were shown in Figure 18c,d, which indicate that the center region of the ridge is the best region to arrange the piezoresistor, where the stress difference is not only very uniform but also large enough.
(a) (a)
(b) Figure 18. Cont.
(b)
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Figure 18. Cont. Sensors 2017, 17, 1965
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Figure 18. Cont.
(c)
(d)
Figure 18. Stress distributions of different diaphragms: (a) stress differences (σ = Sy−Sx) of different
Figure 18. Stress distributions of different diaphragms: (a) stress differences (σ = Sy − Sx ) of different diaphragms from the central point to diaphragm edge; (b) stress differences (σ = Sy−Sx) of different diaphragms from the central point to diaphragm edge; (b) stress differences (σ = Sy − Sx ) of different diaphragms in the SCR along the X direction; (c) stress difference (σ = Sy−Sx) distribution of improved diaphragms in the SCR along the X direction; (c) stress difference (σ = Sy − Sx ) distribution of improved diaphragm I in the SCR; (d) stress difference (σ = Sy−Sx) distribution of improved diaphragm II in the (c) (d) diaphragm SCR. I in the SCR; (d) stress difference (σ = Sy − Sx ) distribution of improved diaphragm II in the SCR. Figure 18. Stress distributions of different diaphragms: (a) stress differences (σ = Sy−Sx) of different Besides from the sensitivity and linearity performance, the(b) mechanical stability (σ of =a diaphragm is also diaphragms the central point to diaphragm edge; stress differences Sy−Sx) of different important for high sensitivity pressure sensors used in high accuracy measurements. The mechanical For the proposed diaphragm thestress stress distribution SCR were diaphragms in the SCR along the structures, X direction; (c) difference (σ = Sycharacteristics −Sx) distributionat of the improved stability of the diaphragm is closely related to its 1st order natural frequency. In order to improve diaphragm the SCR; (d)the stress differenceof(σstructure, = Sy−Sx) distribution of improved diaphragm II in thewere studied in detail.I in Considering symmetry the stress distributions of only half SCR robustness of the diaphragm, a higher 1st order natural frequency is preferred. Compared with the SCR. shown in Figure 18c,d, which indicate that the center region of the ridge is the best region to arrange flat diaphragm, the 1st order natural frequencies of the proposed diaphragms almost remained the the piezoresistor, where the stress is not uniform but also large enough. same, as shown in Figure 19, anddifference much higher thanonly thosevery of beams-membrane-mono-island (BMMI) Besides the the sensitivity sensitivity and and linearity linearity performance, performance, the the mechanical mechanical stability stability of aa diaphragm diaphragm is is also also Besides [23] and beam-membrane-quad-island (BMQI) [25] with the same working range of of 500 Pa.
important for for high high sensitivity sensitivity pressure pressure sensors sensors used used in in high high accuracy accuracy measurements. measurements. The The mechanical mechanical important stability of the diaphragm is closely related to its 1st order natural frequency. In order to improve improve stability of the diaphragm is closely related to its 1st order natural frequency. In order to robustness of ofthe thediaphragm, diaphragm,a ahigher higher1st 1st order natural frequency is preferred. Compared the robustness order natural frequency is preferred. Compared withwith the flat flat diaphragm, the 1st order natural frequencies of the proposed diaphragms almost remained the diaphragm, the 1st order natural frequencies of the proposed diaphragms almost remained the same, same, as shown in Figure 19,much and much than those of beams-membrane-mono-island (BMMI) as shown in Figure 19, and higherhigher than those of beams-membrane-mono-island (BMMI) [23] [23] beam-membrane-quad-island and beam-membrane-quad-island (BMQI) [25] with the same working ofPa. 500 Pa. and (BMQI) [25] with the same working rangerange of 500
Figure 19. Dynamic behaviors of flat diaphragm, improved diaphragm I and improved diaphragm II.
5. Anti-Overload Design Conventionally, anti-overload structures were usually based on the properly designed space between the glass base and the mass block attached to the back side of a diaphragm [23,25]. However, the mass block may stick to the glass base and be unable to return to its working status, because there exists intermolecular attraction and electrostatic attraction between the large area contact surfaces, and even an anti-absorption electrode is fabricated on thediaphragm contact surface the glassdiaphragm base this can Figure 19.ifDynamic I andof II. behaviors of flat diaphragm, improved improved hardly prevent the mass block from adhereing to the glass base. Besides, the conventionally designed anti-overload structures 5. Anti-Overload Design may cause a huge shear stress in the SCR under 1 atm loading condition, which would destroy the structure, as shown in Figure 20. Based on the conventional anti-overload Conventionally, anti-overload structures were usually based on be the properly designed designed properly structure, the maximum tension stress and maximum shear stress would concentrated in the SCR.space between mass block attached to the in back aa diaphragm However, Eventhe worse, values of the maximum shear stresses theside SCRofboth exceed the[23,25]. silicon shear between glassthe base and the diaphragm [23,25]. However, strength (1.3may GPa) [39].to the glass base and be unable to return to its working status, because there the mass block stick
exists intermolecular attraction and electrostatic attraction attraction between between the the large area contact surfaces, and even if an anti-absorption electrode is fabricated on the contact surface of the glass base this can hardly prevent prevent the the mass mass block from from adhereing adhereing to to the glass base. Besides, the conventionally designed hardly anti-overload structures may cause a huge shear stress in the SCR under 1 atm loading condition, the structure, structure, as as shown shown in in Figure Figure 20. 20. Based Based on on the the conventional conventional anti-overload anti-overload which would destroy the structure, the maximum tension stress and maximum shear stress would be concentrated in the SCR. Even worse, the values of the maximum shear stresses in the SCR both exceed the silicon shear strength (1.3 GPa) [39].
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structure, the maximum tension stress and maximum shear stress would be concentrated in the SCR. Even worse, the values of the maximum shear stresses in the SCR both exceed the silicon shear strength (1.3 GPa) Sensors [39]. 2017, 17, 1965 16 of 25 Sensors 2017, 17, 1965
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(a)
(a)
(c)
(b)
(b)
(d)
Figure 20. Stress distributions under overload condition based on conventionally designed anti(d)
(c) under overload condition based on conventionally designed anti-overload Figure 20. Stress distributions overload glass base under 1 atm: (a) shear stress γ of improved diaphragm I; (b) tension stress Sy of glass base under 1diaphragm atm:distributions (a) I;shear stress γoverload ofofimproved diaphragm I;conventionally (b) tension Sy of improved Figure 20. Stress under condition based II; on(d) antiimproved (c) shear stress γ improved diaphragm tension stress stress Sdesigned y of improved overload under atm: (a) shear stress γ ofII; improved diaphragm I; y(b) stressdiaphragm Sy of diaphragm I; (c)glass shear stress γ of1 improved diaphragm (d) tension stress S oftension improved II. diaphragm II.base improved diaphragm I; (c) shear stress γ of improved diaphragm II; (d) tension stress Sy of improved diaphragm In order II. to avoid the over-critical shear stress and adhesion problem between the mass block
In order to avoid over-critical shear stress adhesion problem thestructure mass block and and glass base, athe stepped structure is proposed forand the anti-overload glass base.between The stepped In order avoid the over-critical stress and adhesion problem the mass block glass base, a stepped structure istoproposed for thestate anti-overload glass base. The stepped enables the to island structure remainshear a sloping when undergoing anbetween overload condition, asstructure glass base, a stepped is proposed for the anti-overload glasscondition base. Theto stepped structure shown in Figure 21. By this means, convertsstate a shear stress dominating a tension stressas shown enablesand the island structure tostructure remain a itsloping when undergoing an overload condition, dominating condition, which isremain mainlyacaused bending moment in the SCR. Alsocondition, the steppedas enables structure slopingbystate when undergoing an overload in Figure 21. the Byisland this means, itto converts a shearthe stress dominating condition to a tension stress structure of the21. anti-overload glass face to facecondition contact form to the line to shown in Figure By this means, it converts converts aa conventionally shear stress dominating to a tension stress dominating condition, which is mainly caused by the bending moment in the SCR. Also the stepped face contact form, which remarkably reducesby thethe contact area and solves theSCR. absorption dominating condition, which is mainly caused bending moment in the Also theproblem stepped structure of theof anti-overload glass conventionally face contact form during overloading conditions. structure the anti-overload glassconverts converts aaconventionally face face to facetocontact form to the lineto to the line to face face contact form, which reducesthe the contact solves the absorption contact form, whichremarkably remarkably reduces contact areaarea and and solves the absorption problemproblem overloading conditions. during during overloading conditions.
(a)
(b)
Figure 21. Working mechanism comparison between the conventional and stepped structures of antioverload glass bases: anti-overload design. (a)(a) conventional anti-overloading design; (b) improved(b)
Figure 21. Working mechanism comparison between the conventional and stepped structures of anti-
22 indicates that the stepped structure of the anti-overload glass base was very effective Figure 21.Figure Working mechanism comparison between the conventional and stepped structures of bases: (a) conventional design; (b) improved anti-overload design. with in overload reducingglass the maximum stress in the anti-overloading SCR when exposed to overloading conditions. Compared anti-overload glass bases: (a) conventional anti-overloading design; (b) improved anti-overload design.
the conventional one, the maximum values of shear stress of both bossed diaphragms were reduced Figure 22 indicates that the steppedsafety structure offor thethe anti-overload glass base was very effective below 1 GPa. This reserves a sufficient factor proposed diaphragms. in reducing the maximum stress in the SCR when exposed to overloading conditions. Compared with Figure 22 indicates that the stepped structure of the anti-overload glass base was very effective in the conventional one, the maximum values of shear stress of both bossed diaphragms were reduced reducing the maximum stress in the SCR when exposed to overloading conditions. Compared with below 1 GPa. This reserves a sufficient safety factor for the proposed diaphragms.
the conventional one, the maximum values of shear stress of both bossed diaphragms were reduced below 1 GPa. This reserves a sufficient safety factor for the proposed diaphragms.
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Figure 22. Stress distributions under overload condition based on anti-overload glass base with
Figure 22. Stress distributions (c) under overload condition based on anti-overload (d) glass base with stepped stepped structure under 1 atm: (a) shear stress γ distribution of improved diaphragm I; (b) tension structure under 1 atm: (a) shear stress γ distribution of improved diaphragm I; (b) tension stress Sy of stress S22. y of Stress improved diaphragm I; (c) shear stress γ of improved II; (d) Tension stress Sy Figure distributions under overload condition based diaphragm on anti-overload glass base with improved diaphragm I; (c) shear stress γ of improved diaphragm II; (d) Tension stress Sy of improved of improved diaphragm stepped structure under II. 1 atm: (a) shear stress γ distribution of improved diaphragm I; (b) tension diaphragm II. stress Sy of improved diaphragm I; (c) shear stress γ of improved diaphragm II; (d) Tension stress Sy
6. Performance of improved Experiments diaphragm II.
6. Performance Experiments Here the pressure sensors using different sensing chips with peninsula-island bossed 6. Performance Experiments diaphragms as shown in Figure 16 were sensing fabricated to verify the design theory. The detailed Here the pressure sensors using different chips with peninsula-island bossed diaphragms fabrication process of the sensing chip was described in the Appendix [35]. The schematic packaging Here the pressure sensors using different sensing chips with peninsula-island bossed as shown in Figure 16 were fabricated to verify the design theory. The detailed fabrication process structure of the sensor is shown in Figure 23. The was attached a Kovar base. diaphragms as pressure shown in Figure 16 were fabricated to sensing verify chip the design theory.to The detailed of the sensing chip was described in the Appendix [35]. The schematic packaging structure of the The electrodes on the sensing chip were connected by gold[35]. wireThe bonding. Thepackaging pins were fabrication process of the sensing chip was describedtointhe thepins Appendix schematic pressure sensor is shown in Figure 23. The sensing chip was attached to a Kovar base. The electrodes connectedoftothe thepressure signal wire from backside of the base. Then, basetowas assembled structure sensor is the shown in Figure 23.Kovar The sensing chip the wasKovar attached a Kovar base. on theThe chipon were connected towere the connected pins by gold wire bonding. The pins wereThe connected insensing a electrodes metal shell to testsensing the sensor performance. the chip to the pins by gold wire bonding. pins wereto the signalconnected wire from thesignal backside thethe Kovar base.ofThen, the base. Kovar basethe was assembled a metal shell to the wireof from backside the Kovar Then, Kovar base wasin assembled to testinthe sensor performance. a metal shell to test the sensor performance.
Figure 23. Schematic of the packaged pressure sensor. Figure Schematic of of the the packaged sensor. Figure 23.23.Schematic packagedpressure pressure sensor.
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6.1. Anti-Overload Anti-Overload Experiment Experiment 6.1. Anti-Overload Experiment 6.1. In this this test, test, the the anti-overload anti-overload ability ability of of the the improved improved diaphragm diaphragm III was was tested tested using using aaa piston piston In this test, the anti-overload ability of the improved diaphragm was tested using piston In pressure gauge gauge (CWZ-4T) (CWZ-4T) which which can can apply apply aaa maximum maximum standard standard pressure pressure with with the the value value of of 400 kPa, pressure gauge (CWZ-4T) which can apply maximum standard pressure with the value of 400 400 kPa, kPa, pressure as shown in Figure 24. Firstly, a highly-compressive gas was used to apply an initial pressure of as shown shown in in Figure Figure 24. Firstly, aa highly-compressive highly-compressive gas gas was was used used to to apply apply an an initial initial pressure pressure of of as 24. Firstly, around 500 kPa to the piston pressure gauge. Secondly, pressure balance weights were used to set around 500 500 kPa kPa to to the the piston pressure gauge. Secondly, pressure pressure balance balance weights weights were were used used to to set set around piston pressure gauge. Secondly, the test pressure. Thirdly, the decompression valve and fine adjustment valve were used to balance the test pressure. Thirdly, the decompression valve and fine adjustment valve were used to balance the test pressure. Thirdly, the decompression valve and fine adjustment valve were used to balance the applied applied pressure, pressure, and and then then applied applied the the standard standard pressure to the the calibrated calibrated sensor. In this process, the applied pressure, and then applied the standard pressure pressure to to the calibrated sensor. sensor. In In this this process, process, the the applied pressure was increased gradually at a pressure interval of 10 kPa until it increased to 105 105 the applied pressure was increased gradually at a pressure interval of 10 kPa until it increased to 105 the applied pressure was increased gradually at a pressure interval of 10 kPa until it increased to kPa, which meant the sensor had an overload ability of 21000%FS. The output voltage is shown in kPa, which meant the sensor had an overload ability of 21,000% FS. The output voltage is shown kPa, which meant the sensor had an overload ability of 21000%FS. The output voltage is shown in Figure 25 when the applied pressure was up to 105 kPa. Based on the output voltage, the island in Figure when applied pressure wasup uptoto105 105kPa. kPa.Based Basedon onthe the output output voltage, voltage, the the island island Figure 25 25 when thethe applied pressure was structure contacted the anti-overload glass base when the pressure reached to be around 2200 Pa. structure contacted the anti-overload glass base when the pressure reached to be around 2200 Pa. structure contacted the anti-overload glass base when the pressure reached to be around 2200 Pa. After several test rounds, the sensing chip was continued to be validated in the following sensitivity After several several test test rounds, rounds, the the sensing sensing chip chip was was continued continued to to be be validated validated in in the the following following sensitivity sensitivity After experiments, which demonstrated the sensing chip was safe and sound after overloading. experiments, which demonstrated the sensing chip was safe and sound after overloading. experiments, which demonstrated the sensing chip was safe and sound after overloading.
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(b) (b)
Figure 24. 24. Experiment Experiment facilities for the anti-overload test: test: (a) (a) the photo of whole set; set; (b) (b) piston piston Figure Experiment facilities facilities for for the the anti-overload anti-overload test: (a) the the photo photo of of whole whole set; (b) piston Figure 24. pressure gauge. gauge. pressure pressure gauge.
Figure 25. 25. Output voltage voltage versus overloading overloading pressures up up to to 105 105 kPa kPa for for improved improved diaphragm diaphragm I.I. Figure Figure 25. Output Output voltage versus versus overloading pressures pressures
6.2. Sensitivity Sensitivity Experiment Experiment 6.2. The sensitivities sensitivities of of the the pressure pressure sensors sensors were were tested tested by by the the experimental experimental facilities facilities shown shown in in The Figure 26. 26. The The pressure pressure was was loaded loaded onto onto the the sensing sensing chip chip from from the the PVC PVC hose hose using using aa pressure pressure Figure
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6.2. Sensitivity Experiment The sensitivities of the pressure sensors were tested by the experimental facilities shown in Figure 26. Sensors 2017, 17, 1965 19 of 25 The pressure was loaded onto the sensing chip from the PVC hose using a pressure controller (FLUKE PPC4). The temperature performance of the pressure sensors testedsensors in a constant temperature controller (FLUKE PPC4). The temperature performance of thewas pressure was tested in a ◦ to 60 ◦ C. oven (ESPEC PG-2J) from 20 constant temperature ovenC(ESPEC PG-2J) from 20 °C to 60 °C.
26. The pressure calibrationfacilities facilities used sensitivity experiment. FigureFigure 26. The pressure calibration usedinin sensitivity experiment.
The calibrated data of three cycles of loading and unloading pressure for two developed sensors,
Theascalibrated data 1ofand three cycles of loading and pressure foras two developed shown in Tables 2, were plotted and fitted by unloading the least squares method, shown in Figuresensors, 27. as shown in Tables 1 and 2, were plotted and fitted by the least squares method, as shown in Figure 27. Table 1. Calibration data for the improved diaphragm I. Table 1. Calibration data for the improved diaphragm I. Pressure (Pa)
Pressure (Pa) 0
100
0 200 100 300 200 400 300 500 400 500 Pressure (Pa) 0
Pressure 100 (Pa)200 300
0 400 100 500 200 300 400 500
1st Round
Voltage Output (mV) 2nd Round 3rd Round Voltage Output (mV)
Forward Backward Forward Backward 1st Round 2nd Round 14.10 14.40 14.10 14.50 Forward Forward Backward 47.87 Backward 48.13 47.48 47.22 80.91 81.12 80.5 80.21 14.10 14.40 14.10 14.50 113.22 113.32 112.9 112.74 47.87 48.13 47.48 47.22 80.91 81.12 80.5 80.21 145.03 145.27 145.1 144.9 113.22 113.32 112.9 112.74 176.73 176.73 177 177
145.03 176.73
Forward Backward 3rd Round 14.10 14.40 Forward Backward 47.75 47.93 80.75 80.95 14.10 14.40 113.33 113.46 47.75 47.93 80.75 80.95 145.52 145.74 113.33 113.46 177.57 177.57
Mean Value Forward Backward Mean Value 14.10 14.43 Forward 47.76 Backward 47.70 80.72 80.76 14.10 14.43 113.15 113.17 47.70 47.76 80.72 80.76 145.21 145.30 113.15 113.17 177.10 177.10
145.27 145.1 144.9 145.52 145.74 176.73 177 177 177.57 177.57 Table 2. Calibration data for the improved diaphragm II.
145.21 177.10
Voltage Output (mV) Table 2. Calibration2nd data for the improved II. 1st Round Round 3rddiaphragm Round Forward Backward Forward Backward Forward Backward Voltage (mV) 14.80 14.90 14.85 14.97 Output14.8 14.84 45.53 45.98 46.10 46.05 45.87 1st Round 45.56 2nd Round 3rd Round 75.94 76.03 76.54 76.61 76.59 76.32 Forward Backward Forward Backward Forward Backward 106.02 106.12 106.55 106.56 106.5 106.33 14.80 14.90 14.85 14.97 14.8 14.84 135.91 136.00 136.22 136.36 136.24 135.97 45.53 45.56 45.98 46.10 46.05 45.87 165.90 165.85 165.91 165.90 166.00 166.00
75.94 106.02 135.91 165.90
76.03 106.12 136.00 165.85
76.54 106.55 136.22 165.91
76.61 106.56 136.36 165.90
76.59 106.5 136.24 166.00
76.32 106.33 135.97 166.00
145.30 177.10
Mean Value
Forward Backward 14.82 14.90 45.85Mean Value 45.84 76.36 76.32 Forward Backward 106.36 106.34 14.82 14.90 136.12 136.11 45.85 45.84 165.94 165.92
76.36 106.36 136.12 165.94
76.32 106.34 136.11 165.92
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Figure 27. 27. Output Output voltage voltage versus versus applied applied pressure pressure with Figure with aa range range from from 00 to to 500 500 Pa. Pa.
6.3. Zero Drift Experiment Zero caused by by the the piezoresistor fabrication quality and residual stress caused Zero output outputwas wasmainly mainly caused piezoresistor fabrication quality and residual stress by the sensing chip packaging process.process. The equation for zerofor drift candrift be presented as: caused by the sensing chip packaging The equation zero can be presented as:
V0 max ∆V0max Z =Z ×100% 100% V VFSFS
(5)
minimum ∆V0max where ∆V thedifference difference between between the the initial initial voltage voltage output output and and the maximum or minimum 0maxisisthe during the the testing testing time; time; V VFS FS was voltage out during was full full scale output of the sensing chip. The sensing chip with two twodifferent differentdiaphragm diaphragm shapes were powered 5 Vvoltage. DC voltage. The sensing chipsplaced were with shapes were powered by 5by V DC The sensing chips were ◦ placed 20 °Ctemperature. room temperature. Thelasted tests lasted an hour anddata-collection the data-collection interval in 20 Cinroom The tests for anfor hour and the interval was was one one second. drift results two different diaphragms are plottedininFigure Figure28. 28.The The zero zero drift second. TheThe zerozero drift results forfor two different diaphragms are plotted for the the improved improved diaphragm diaphragm II and and II II were were 0.064% 0.064%FS values for FS and 0.024%FS, 0.024% FS,respectively. respectively.
Figure 28. Zero drift data for two proposed sensing chips.
The performance performance of of the the proposed proposed sensor sensor chips chips is is presented presented in in Table Table 3.3. The The performance performance The comparision with some other typical low pressure sensing chips is presented in Table 4. According comparision with some other typical low pressure sensing chips is presented in Table 4. According to to the comparision data listed in Table 4, the proposed sensing chip had the best sensitivity and good good the comparision data listed in Table 4, the proposed sensing chip had the best sensitivity and nonlinearity performance. were the the nonlinearity performance. Also Also the the 1st 1st natural natural frequencies frequencies of of the the proposed proposed sensing sensing chips chips were highest among the compared 500 Pa working range sensing chips. highest among the compared 500 Pa working range sensing chips.
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Table 3. The sensor performance of proposed sensing chips. Parameter
Improved Diaphragm I
Improved Diaphragm II
Reference temperature (◦ C) Supply voltage (V) Full scale output (mV) Sensitivity (mV/V/Pa) Nonlinearity (% FS) Hysteresis (% FS) Repeatability (% FS) Accuracy (% FS) Zero drift (% FS)
20 5 165 0.065 0.33 0.36 0.67 0.94 0.064
20 5 151 0.060 0.30 0.16 0.26 0.55 0.024
Table 4. The sensor performance comparisons among the proposed bossed diaphragms and previously researched sensing chips. Diaphragm Structure
Sensitivity (mV/V/Pa)
Nonlinearity (% FS)
1st Natural Frequency (kHz)
Working Range (Pa)
Improved diaphragm I Improved diaphragm II BMMI [23] BMQI [25] C-cup with the same dimension Beam-diaphragm structure [18] Peninsula structured diaphragm [22] CBM [24] Hollow stiffening structure [21]
0.065 0.060 0.011 0.018 0.013 0.00069 0.00368 0.00154 0.0116
0.33 0.3 3.05 0.124 0.8 0.1 0.36 0.19 0.4
11.6 11.7 7.0 10.2 11.6 / 44.2 44.5 /
500 500 500 500 500 1000 5000 5000 3000
7. Conclusions This paper provided a systematic analysis of the influence of the diaphragm stiffness distribution on the stress concentration characteristics of a pressure sensing chip, which provides a guideline for diaphragm design for piezoresistive pressure sensing chips. Based on our systematic analysis, the optimization method and distribution patterns of peninsula-island structure were also discussed to improve the performance of sensing chips. An anti-overload glass base with stepped structure guaranteed a sensor with a high anti-overload ability of 21,000% FS. In accordance with the FEM results, the experimental results showed that the fabricated pressure sensors using bossed diaphragms combined with side edge and diagonal directional positioned peninsula-islands had sensitivities of 0.065 mV/V/Pa and 0.060 mV/V/Pa, respectively, and nonlinearity errors of 0.33% FS and 0.30% FS, respectively, within the pressure range of 0–500 Pa. It was concluded that pressure sensors with the proposed bossed diaphragms had excellent sensitivity, linearity and stability. The pressure sensors with the proposed diaphragm are potentially a better choice to measure ultra-low pressures in the fields of biomedical instruments, smart homes and aerodynamics Acknowledgments: This work was supported in part by the National Natural Science Foundation of China (51375378, 91323303, 51421004), National Key R&D Program of China (2016YFB0501604-02, 2016YFB1200103-04), the 973 Program (2015CB057402), the 111 Program (B12016) and 2016 Years of Scientific and Technological Activities of Overseas Scholars Preferred Funding. Author Contributions: Tingzhong Xu and Libo Zhao conceived and designed the sensing chip; Yulong Zhao performed the fabrication of the sensing chip; Tingzhong Xu performed the calibration experiment; Hongyan Wang and Xin Guo performed the anti-overload experiment; Zhikang Li analyzed the data; Tingzhong Xu and Hongyan Wang wrote the paper; Zhuangde Jiang and Xiangyang Zhou checked the English gramma. Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations The following abbreviations are used in this manuscript: MEMS SCR
Micro-electromechanical Systems Stress Concentration Region
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MEMS Systems SensorsMicro-electromechanical 2017, 17, 1965 SCR Stress Concentration Region
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Sensors 2017, 17, 1965 MEMS Micro-electromechanical Systems
SCR Appendix
A
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Stress Concentration Region
MEMS are employed to fabricate the sensing chip. The main processes were listed Appendix A Appendix Atechnologies as follows, as shown in Figure A1. MEMS technologies employed fabricatethe thesensing sensing chip. chip. The listed MEMS technologies are are employed to to fabricate Themain mainprocesses processeswere were listed as as follows, as shown in Figure A1. follows, as shown in Figure A1.
Figure A1.Main Mainfabrication fabrication process chip. Figure A1. processofofsensing sensing chip. Figure A1. Main fabrication process of sensing chip.
Step 1. The starting material is a n-type (100) double-sided polished single-crystal silicon on
Step 1. The starting material is a n-type double-sided polished single-crystal silicon on Step 1. The n-type (100) (100) double-sided polished single-crystal insulator (SOI)starting materialmaterial fabricatedisbyaseparation by implantation of oxygen (SIMOX) technology.silicon The on insulator (SOI) material fabricated by separation by implantation of oxygen (SIMOX) technology. insulator (SOI) material fabricated by separation by implantation of oxygen (SIMOX) technology. The thicknesses of top silicon layer, buried SiO2 layer and bottom silicon layer are 10 μm, 1 μm, 300 μm, The thicknesses top silicon SiO2and layer and bottom silicon are110 µm, µm, respectively. thicknesses of topofsilicon layer,layer, buriedburied SiO2 layer bottom silicon layer arelayer 10 μm, μm, 3001 μm, 300 µm, respectively. Step 2. Considering high piezoresistive coefficient and low temperature coefficient of p-type respectively. silicon, implantationhigh and diffusion of B (boron) is performed from a B2O3 constant source into Step Considering high piezoresistive coefficient and low temperature coefficient of p-type Step 2. 2.the Considering piezoresistive coefficient and low temperature coefficient ofthe p-type top Si layer followed by annealing process to eliminate some crystal lattice defects and improve the silicon, the implantation and diffusion of B (boron) is performed from a B O constant source 3 silicon, the implantation and diffusion of B (boron) is performed from a B2O23 constant source intointo the conducting power of by topannealing Si layer. After the to thermal activation process,lattice four piezoresistors are the Si layer followed process eliminate some crystal defects improve top top Si layer followed by annealing process to eliminate some crystal lattice defects andand improve the achieved with sheet resistance of 220 Ω/Υ, as shown in Figure A2. The initial resistance values of four the conducting power of top layer.After Afterthe thethermal thermalactivation activationprocess, process, four four piezoresistors piezoresistors are conducting power of top Si Si layer. are piezoresistors are all around 3.8 kΩ. achieved /Υ, as The initial initial resistance resistance values achieved with with sheet sheet resistance resistance of of 220 220 Ω Ω/Υ, as shown shown in in Figure Figure A2. A2. The values of of four four piezoresistors Ω. piezoresistors are are all all around around 3.8 3.8 kkΩ.
(a)
(b)
Figure A2. Microscopic photos of piezoresistors in two patterns: (a) piezoresistor in position 1 shown in Figure 16; (b) piezoresistor in position 2 shown in Figure 16.
(a)
(b)
Figure A2. A2. Microscopic Microscopic photos photos of of piezoresistors piezoresistors in in two two patterns: patterns: (a) (a) piezoresistor piezoresistor in in position position 11 shown shown Figure in Figure Figure 16; 16; (b) (b) piezoresistor piezoresistor in in position position 22 shown shown in in Figure Figure16. 16. in
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Step The SiO SiO22 layers layers are are formed formed onto onto top top Si Si layer layer and Step 3. 3. The and bottom bottom of of substrate substrate with with oxidation oxidation process in O . The resistor holes are etched by reactive ion etching (RIE). Gold is sputtered the top top process in O22. The resistor holes are etched by reactive ion etching (RIE). Gold is sputtered on on the of to17,connect four for 22 layer of SiO SiO layer connect four piezoresistors piezoresistors into into aa Wheatstone Wheatstone bridge. bridge. Then, Then, thermal thermal treatment treatment Sensors 2017,to 1965 23 of 25 for ohmic connection and metallization is carried out in vacuum. ohmic connection and metallization is carried out in vacuum. 3. The SiO2 layers are silicon formed structure onto top Siare layer and bottom substrate oxidation Step 4. Four grooves on top top silicon structure are fabricated by of RIE. Then, with is Step Step 4. Four grooves on fabricated by RIE. Then, aa ridge ridge is formed formed process in O 2 . The resistor holes are etched by reactive ion etching (RIE). Gold is sputtered on the top between between each each two two grooves. grooves. of SiO2 layer to connect piezoresistors into a Wheatstone bridge. Then, thermal treatment for Step The back back cavityfour of structure structure is etched etched by deep Step 5. 5. The cavity of is by deep reactive reactive ion ion etching etching (DRIE) (DRIE) to to form form the the ohmic connection and metallization is carried out in vacuum. center membrane and the peninsula-island structure. center effective effective membrane and the peninsula-island structure. Step 4. Four grooves on top silicon structure are fabricated by RIE. Then, a ridge is formed Step 6. Finally, the wafer Step 6. Finally, the wafer is is packaged packaged on on the the steped steped glass glass with with the the thickness thickness of of 0.4 0.4 mm mm by by anodic anodic between each two grooves. bonding technology in vacuum, and then diced into single sensing chips with bonded glass by scribing bonding technology in vacuum, and then diced into single sensing chips with bonded glass Step 5. The back cavity of structure is etched by deep reactive ion etching (DRIE) to form the by technology. Figure A3 showsA3 the fabricated piezoresistive sensing chips. scribing technology. Figure shows the fabricated piezoresistive sensing chips. center effective membrane and the peninsula-island structure. Step 6. Finally, the wafer is packaged on the steped glass with the thickness of 0.4 mm by anodic bonding technology in vacuum, and then diced into single sensing chips with bonded glass by scribing technology. Figure A3 shows the fabricated piezoresistive sensing chips.
(a)
(b)
Figure A3. A3. SEM of fabricated fabricated sensing sensing chips chips with with different different bossed bossed(b) diaphragms: (a) (a) improved improved Figure SEM pictures pictures (a) of diaphragms: diaphragm I; (b) improved diaphragm II. diaphragm (b)SEM improved Figure I; A3. picturesdiaphragm of fabricatedII. sensing chips with different bossed diaphragms: (a) improved diaphragm I; (b) improved diaphragm II.
And the stpped glass base was fabricated by isotropic etching by HF. First, use the HF to etch a And the stpped glass base was fabricated by isotropic etching by HF. First, use the HF to etch a cavity with 10–11 μm depth, for the pattern dimension ±3 μm, shown intoFigure And the stpped glass and baseerror was fabricated by isotropic etchingwas by HF. First,asuse the HF etch a A4a. cavity with 10–11 µm depth, and error for the pattern dimension was ±3 µm, as shown in Figure A4a. cavity with 10–11 μm depth, and error for the pattern dimension was ±3 μm, as shown in Figure Then, use the HF to etch the step with 1.5–2.5 μm depth; and error for the pattern dimensionA4a. was ±0.5 Then,Then, use the HFHF to to etch the step with 1.5–2.5μm µm depth; and error for the pattern dimension was use the etch the step withthe 1.5–2.5 depth; and error for dimension was ±0.5 by μm, as shown in Figure A4b. Finally, via hole at the center of the the pattern glass base was fabricated ±0.5 µ m, as inFigure FigureA4b. A4b.Finally, Finally,the the hole center of the glass fabricated as shown shown in viavia hole at at thethe center of the glass basebase was was fabricated by by liquidμm, blasting method. liquidliquid blasting method. blasting method.
(a)
(a)
(b)
(b)
Figure A4. Fabrication process steppedglass glass base: base: (a) glass base etching; (b) 2nd Figure A4. Fabrication process forfor stepped (a)1st 1ststep stepfor for glass base etching; (b) step 2nd step forA4. glass etching. process for stepped glass base: (a) 1st step for glass base etching; (b) 2nd step Figure Fabrication for glass etching. for glass etching. References
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