materials Article
Material Viscoelasticity-Induced Drift of Micro-Accelerometers Wu Zhou 1 1 2
*
ID
, Peng Peng 1, *, Huijun Yu 1 , Bei Peng 1, * and Xiaoping He 2
School of Mechatronics Engineering, University of Electronic Technology and Science of China, Chengdu 611731, China; [email protected] (W.Z.); [email protected] (H.Y.) Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621900, China; [email protected] Correspondence: [email protected] (P.P.); [email protected] (B.P.); Tel.: +86-28-6183-0227 (B.P.)
Received: 21 August 2017; Accepted: 12 September 2017; Published: 14 September 2017
Abstract: Polymer-based materials are commonly used as an adhesion layer for bonding die chip and substrate in micro-system packaging. Their properties exhibit significant impact on the stability and reliability of micro-devices. The viscoelasticity, one of most important attributes of adhesive materials, is investigated for the first time in this paper to evaluate the long-term drift of micro-accelerometers. The accelerometer was modeled by a finite element (FE) method to emulate the structure deformation and stress development induced by change of adhesive property. Furthermore, the viscoelastic property of the adhesive was obtained by a series of stress–relaxation experiments using dynamic mechanical analysis (DMA). The DMA curve was imported into the FE model to predict the drift of micro-accelerometers over time and temperature. The prediction results verified by experiments showed that the accelerometer experienced output drift due to the development of packaging stress induced by both the thermal mismatch and viscoelastic behaviors of the adhesive. The accelerometers stored at room temperature displayed a continuous drift of zero offset and sensitivity because of the material viscoelasticity. Moreover, the drift level of accelerometers experiencing high temperature load was relatively higher than those of lower temperature in the same period. Keywords: MEMS; adhesive; viscoelasticity; drift; accelerometer
1. Introduction In packaging of microelectromechanical systems (MEMS), polymer-based materials, such as epoxy and silicone, are widely used for mounting the die chip on the substrate because of their numerous advantages compared with other joining methods [1,2]. However, this type of adhesive packaging, like other packaging themes, involves residual thermal stress/packaging stress due to the mismatch of coefficients of thermal expansion (CTE) of different structural materials [3]. The stress existing in structures and interfaces forms a stable equilibrium of micro-devices based on deformation compatibility conditions [4]. The formed equilibrium, however, is prone to be upset by the temperature load and/or the shift of material properties, such as elastic module and Poisson’s ratio. The temperature aspects are always related to the thermal effects’ influence on device performance, which has been studied intensively, while the material properties of the polymer-based materials in current studies are often neglected or simply assumed to be linear–elastic [5–10]. This assumption could give a relatively accurate evaluation of device performance in the low- and medium-precision application fields, but could not be used to predict the long-term stability or drift in areas requiring high precision, because the polymers actually exhibit viscoelasticity presenting elastic and viscous characteristics simultaneously [11,12], and they also possess the features of time and temperature dependence. The viscoelasticity-related issue has become one of the most critical steps for assessing the packaging quality and output performance of highly precise MEMS sensors [13,14]. Applying the viscoelastic Materials 2017, 10, 1077; doi:10.3390/ma10091077
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the packaging quality and output performance of highly precise MEMS sensors [13,14]. Applying the property to property model thetoMEMS could give acould bettergive agreement the results in viscoelastic model devices the MEMS devices a betterwith agreement withobserved the results experiments than the previous elastic model [15]. The packaging stress in the MEMS was influenced observed in experiments than the previous elastic model [15]. The packaging stress in the MEMS was not only bynot theonly temperature change, but also bybut itsalso change rate due to thedue time-dependent property influenced by the temperature change, by its change rate to the time-dependent of polymer adhesives [16]. Besides, the viscoelastic behavior influenced by moisture was recognized property of polymer adhesives [16]. Besides, the viscoelastic behavior influenced by moisture was as the cause long-term stability of micro-sensors in storage CurrentCurrent works on the recognized asof thethe cause of the long-term stability of micro-sensors in [17,18]. storage [17,18]. works viscoelastic effects mainly focus onfocus the viscoelasticity-induced reliability issues ofissues MEMS on the viscoelastic effects mainly on the viscoelasticity-induced reliability of sensors, MEMS but the underlying mechanism of stress development over time and temperature is still open to sensors, but the underlying mechanism of stress development over time and temperature is still open further investigation. to further investigation. This study aims aims to to deeply deeply investigate investigate the the effects effects of of viscoelastic behavior of of epoxy-based epoxy-based This study viscoelastic behavior adhesive on the long-term stability of micro-capacitive accelerometers packaged in a ceramic shell adhesive on the long-term stability of micro-capacitive accelerometers packaged in a ceramic shell by by the adhesively bonding method. Section 2 gives introductiontotothe the working working principle principle of of the adhesively bonding method. Section 2 gives ananintroduction micro-accelerometers, and theoretically determines the zero offset and sensitivity by the deformation micro-accelerometers, and theoretically determines the zero offset and sensitivity by the deformation of the the sensitive sensitive structure structure of of the the accelerometer. accelerometer. In In Section Section 3, 3, the the accurate accurate viscoelastic viscoelastic property property of of the the of adhesive is is obtained obtained by by aa series series of of stress–relaxation stress–relaxation tests tests by by dynamic dynamic mechanical mechanical analysis analysis (DMA), (DMA), adhesive and the master curve is acquired by the proper shift function and fitted with the Prony function and the master curve is acquired by the proper shift function and fitted with the Prony function to to implement finite element analysis (FEA). Section4,4,the theobtained obtainedcurve curveisis introduced introduced into into the the implement finite element analysis (FEA). InIn Section physical model of the accelerometer to study the deformation law of sensitive components subjected to physical model of the accelerometer to study the deformation law of sensitive components subjected four different time and temperature cycles, and then the zero offset and sensitivity of the accelerometer to four different time and temperature cycles, and then the zero offset and sensitivity of the can be determined bydetermined the deformed structure. Thestructure. simulation and experiments are also givenare inalso this accelerometer can be by the deformed The simulation and experiments section. The discussion and conclusion are provided in Sections 5 and 6, respectively. given in this section. The discussion and conclusion are provided in Sections 5 and 6, respectively. 2. Structure Structure and and Principle Principle 2. The simplified model of the capacitive accelerometers is shown in Figure 1. The sensitive The simplified model of the capacitive accelerometers is shown in Figure 1. The sensitive component is a silicon-based structure supported elastically by four folded beams and bonded to component is a silicon-based structure supported elastically by four folded beams and bonded to a a Pyrex glasssubstrate. substrate.The Thewhole wholestructure structureisispackaged packagedonto ontoaaceramic ceramicshell shell with with an an epoxy-based epoxy-based Pyrex glass adhesive through a curing process. When an acceleration, a, is applied in the sensitive direction, adhesive through a curing process. When an acceleration, a, is applied in the sensitive direction, the the movement of the proof mass induced by inertial force generates a gap change of sensing capacitors movement of the proof mass induced by inertial force generates a gap change of sensing capacitors formed by byaafixed fixedfinger fingerononthe the silicon substrate a movable finger on proof the proof [19,20]. formed silicon substrate andand a movable finger on the massmass [19,20]. The The changed gap shifts the differential capacitance of capacitors, C and C , and the output of the 1 2, and the 2 changed gap shifts the differential capacitance of capacitors, C1 and C output of the micromicro-accelerometer be simply expressed as: accelerometer can be can simply expressed as: C1 C− CC22 Vout V=out G VVb G 1 C1C+ CC22 b 1
(1) (1)
where V accelerometer, G isGthe coefficient of theof sensing circuit out is is the theoutput outputvoltage voltageofof accelerometer, is amplification the amplification coefficient the sensing where Vout and V is the amptitude of carrier voltage. circuitband Vb is the amptitude of carrier voltage.
(a)
(b)
Figure 1. Structure of capacitive accelerometer. (a) Diagram of accelerometer; (b) SEM structure. Figure 1. Structure of capacitive accelerometer. (a) Diagram of accelerometer; (b) SEM structure.
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Half of the sensitive component is selected to derive the analytical expressions of performance, zero offset and sensitivity of the micro-accelerometer. The folded beams anchored to separated sides are represented Materials 2017,by 10, two 1077 springs with different stiffness constants, k1 and k2 , due to fabrication errors 3 of 11 [21] (Figure 2). The output of the accelerometer, according to Equation (1), is directly proportional to the Half of the sensitive component is selected the analytical expressions offixed performance, differential capacitance, which is dependent on to thederive relative position between the fingers and zero offset and sensitivity of the micro-accelerometer. The folded beams anchored to separated sides the movable fingers. Therefore, the positions of finger anchors (3, 4) and the proof mass determine are represented by two springs with different stiffness constants, k 1 and k2, due to fabrication errors [21] performance parameters of the micro-accelerometer, and are influenced by the stress state of the (Figure 2). The output of the accelerometer, according to Equation (1), is directly proportional to the whole structure. Ideally, the free state of packaged accelerometers should show no internal stress, differential capacitance, which is dependent on the relative position between the fixed fingers and but the packaging process with a fluctuating temperature leads to thermal stress in the chip due to movable fingers. Therefore, the positions of finger anchors (3, 4) and the proof mass determine the different thermo–mechanical properties of the structural materials. Thus, by thethe zero offset or bias performance parameters of the micro-accelerometer, and are influenced stress state of theof the micro-accelerometer be expressed as of [22]: whole structure. can Ideally, the free state packaged accelerometers should show no internal stress, but the packaging process with a fluctuating temperature leads to thermal stress in the chip due to Kum different thermo–mechanical properties ofBias the structural materials. Thus, the zero offset or bias of the =− m micro-accelerometer can be expressed as [22]:
(2)
where K denotes the total stiffness of the folded beams,Ku K = k1 + k2 , m is the proof mass and um is the (2) Bias m displacement of the proof mass center. Furthermore, m where K denotes the total stiffness of the k1 folded − k2 beams, K = k1 + k2, m is the proof mass and um is the ( P1x − l1 ∆Tαsilicon ) umcenter. = Furthermore, displacement of the proof mass k + k 1
(3)
2
k1 k2
silicon ) connecting the folded beams um ( P1 x the l1 Tpoint (3) and where P1x denotes the longitudinal displacements k1 k2 of the anchors; l1 is half the length of the proof mass; ∆T is the temperature change between curing x denotes the longitudinal displacements of the point connecting the folded beams and the where P1and temperature room temperature; and αsilicon is the CTE of silicon. anchors; l1 is half the length of the proof mass; ∆T is the temperature change between curing The sensitivity of the micro-accelerometer can be expressed as:
temperature and room temperature; and αsilicon is the CTE of silicon. The sensitivity of the micro-accelerometer can be as: 1 expressed 1 Gm
Sensitivity = (
− ) d 1 d12 GmK
Sensitivity 1(
d1
d2
)
K
(4) (4)
where d1 and d2 denote narrow and wide gaps once the curing process is completed, respectively. The whereisd1mainly and d2 denote narrow gapsgap, oncebecause the curing completed, much issmaller thanrespectively. d2 . sensitivity determined byand thewide narrow d1 isprocess The sensitivity is mainly determined by the narrow gap, because d 1 is much smaller than d2. The Equations (3) and (4) represent the zero offset and sensitivity of the packaged The Equations (3) and (4) represent the zero offset and sensitivity of the packaged micromicro-accelerometer, respectively. Both parameters are constant when the structure has no deformation accelerometer, respectively. Both parameters are constant when the structure has no deformation or or movement, because the silicon, glass, circuit and internal environment are almost invariant. The movement, because the silicon, glass, circuit and internal environment are almost invariant. micro-accelerometer after storage, exhibited an obvious drift of performance parameters. The micro-accelerometer after however, storage, however, exhibited an obvious drift of performance That is to say, theThat structural equilibrium sustained by the residual stress was upset parameters. is to say, the structural equilibrium sustained by thermal the residual thermal stress by wassome factors related to the structural material properties. upset by some factors related to the structural material properties.
Figure 2. Half-structure of sensitive components.
Figure 2. Half-structure of sensitive components.
3. Material Property
3. Material Property
The sensor of the micro-accelerometer consists of four different materials including silicon,
The of the micro-accelerometer four Pyrex different including silicon, Pyrexsensor glass, ceramic material and packaging consists adhesive.of Silicon, glassmaterials and the ceramic material Pyrexwere glass, ceramic material and packaging adhesive. Silicon, and the material used broadly and have very stable material properties withPyrex linearglass elasticity. The ceramic Poisson ratio
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were used broadly and have very stable material properties with linear elasticity. The Poisson ratio and CTE of the adhesive were assumed as constant values, because they have little impact on the packaging stress [23]. The material properties are listed in Table 1. Table 1. Material properties for the sensor. Material
Young’s Modulus (Gpa)
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Silicon 160 0.22 2.6 and Glass CTE of the adhesive were assumed on the 62.7 as constant values, because 0.2 they have little impact 3.25 packaging properties are listed in Table0.22 1. Ceramicstress [23]. The material360 6.5 Adhesive Table 2 0.37 60 Table 1. Material properties for the sensor.
Material
Young’s Modulus (Gpa)
Poisson Ratio
CTE (ppm/°C)
The packaging adhesive, a typical epoxy-based polymer, however, exhibits both elastic and viscous Silicon 160 0.22 2.6 behaviors, that is, viscoelasticity. The elasticity responding to while the viscous Glass 62.7 0.2stress is instantaneous, 3.25 Ceramic 360temperature, which 0.22 consequently 6.5 has significant impact on response is time-dependent and varies with Adhesive Table 2 0.37the viscoelastic 60 characteristics, therefore, the stress distribution in the micro-accelerometer. To measure is one of most The critical steps adhesive, before evaluating the stability of micro-accelerometers of the timepackaging a typical epoxy-based polymer, however, exhibits both because elastic and and temperature-dependent of the adhesive. Theresponding common to measuring method is while through stress viscous behaviors, thatfeature is, viscoelasticity. The elasticity stress is instantaneous, viscoustests response time-dependent andstress–relaxation varies with temperature, whichperformed consequently has dynamic relaxation the or creep [24]. isHence, a series of tests were using significant impact on the stress distribution in the micro-accelerometer. To measure the viscoelastic mechanical analysis (TA instrument DMA Q800, New Castle, DE, USA). A rectangular specimen characteristics, therefore, is one of most critical steps before evaluating the stability of micro(35 mm × accelerometers 10 mm × 2 mm) was prepared cured by the same process in theThe accelerometers, and because of the time- andand temperature-dependent feature of the as adhesive. common then mounted on the instrument operating in a single cantilever mode.a series The experimental temperature measuring method is through stress relaxation or creep tests [24]. Hence, of stress–relaxation ◦ C with were performed dynamic mechanical analysis instrument DMA Q800, New range wastests set from 25 to 125using an increment of 10 ◦(TA C and an increase rate of 5 ◦Castle, C/min, and at DE, USA). A rectangular specimen (35 mm × 10 mm × 2 mm) was prepared and cured by the same each test point, 5 min was allowed for temperature stabilization and 0.1% strain was applied on the process as in the accelerometers, and then mounted on the instrument operating in a single cantilever specimen for 20The min, followedtemperature by a 10 min recovery. The25test results are inofFigure 3. mode. experimental range was set from to 125 °C with an shown increment 10 °C and The relaxation data, normalization, were modeled the master curve, which translates the an increase rate of 5for °C/min, and at each test point, 5 min wasby allowed for temperature stabilization and 0.1% was applied on the specimen for 20 min, temperature followed by a 10with min recovery. The test curve segments atstrain different temperatures to a reference logarithmic coordinates results are shown in Figure 3. according to a time–temperature superposition [25]. The master curve can be fitted by a third-order The relaxation data, for normalization, were modeled by the master curve, which translates the polynomial function, such as: curve segments at different temperatures to a reference temperature with logarithmic coordinates according to a time–temperature superposition [25]. The master curve can be fitted by a third-order loga T ( Tsuch ) =as:C1 ( T − T0 ) + C2 ( T − T0 )2 + C3 ( T − T0 )3 polynomial function, l o g aT (T ) C 1 (T T0 ) C 2 (T T0 ) 2 C 3 (T T0 ) 3
(5)
(5)
where aT are the offset values at different temperatures (T1 ) and C1 , C2 and C3 are constants. where aT are the offset values at different temperatures (T1) and C1, C2 and C3 are constants. The reference temperature was set at 25 ◦ C, and then the three coefficients of the polynomial The reference temperature was set at 25 °C, and then the three coefficients of the polynomial function were determined to be toC1be=C0.223439, −0.00211 C3 = 5.31163 × 104).−6 (Figure 4). function were determined 1 = 0.223439,C C22 ==−0.00211 and and C3 = 5.31163 × 10−6 (Figure 3000
130 120 110 100
2000
90 80 70
1500
60 50
1000
40 30
500
20 10
0
0 0
100
200
300
400
Time (min)
Figure 3. Stress–relaxation test results.
Figure 3. Stress–relaxation test results.
500
Temperature (℃)
Relaxation modulus (MPa)
2500
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Polynomial fit
log (aT)
-2 -3 -4 -5 -6 -7 -8 20
40
60
80
100
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Temperature (℃ ) Figure of 25 25 ◦°C. Figure 4. 4. Master Master curve curve with with reference reference temperature temperature of C.
4. 4. Simulation Simulation and and Experiments Experiments The The master master curve curve in in Figure Figure 44 shows shows the the relaxation relaxation behaviors behaviors of of polymer polymer adhesives adhesives under under certain certain strain loads. This relaxed strain or stress results from the effective modulus of viscoelasticity, strain loads. This relaxed strain or stress results from the effective modulus of viscoelasticity, which which can series [26]: [26]: can be be described described as as aa Prony Prony series N (t ) t E +N Ei exp( t) , i i η (6) i 1 E(t) = (6) = 0 E∞ + ∑ Ei exp(− i ), τi =Ei i ε0 τi Ei i =1 where E(t) is the relaxation modulus; σ(t) is the stress; ε0 is the imposed constant strain; and E∞ is the fully modulus. Ei and τi are referred to as a Prony Ei is theconstant elastic modulus; ηi is whererelaxed E(t) is the relaxation modulus; σ(t) is the stress; ε0 is pair; the imposed strain; and E∞the is viscosity; and τi ismodulus. the relaxation of referred ith Prony N is the number of Prony the fully relaxed Ei andtime τ i are topair. as a Prony pair; Ei is the elasticpairs. modulus; η i is the For this therelaxation master curve needs to be pair. transformed into Prony seriespairs. for modeling and viscosity; andstudy, τ i is the time of ith Prony N is the number of Prony experiments 5). The coefficients of Equation (6) with nine Prony pairs arefor listed in Table 2, For this (Figure study, the master curve needs to be transformed into Prony series modeling and where E0 is the instantaneous modulus when time is zero. experiments (Figure 5). The coefficients of Equation (6) with nine Prony pairs are listed in Table 2, The introduced the Prony series modulus where E0 simulation is the instantaneous modulus when time is zero. into the whole finite element model (FEM) in ABAQUS softwareintroduced to acquirethe theProny outputseries of the micro-accelerometers and temperature. The simulation modulus into the wholeover finitetime element model (FEM) The thermal experiment was carried out in an incubator with an accurate temperature controller. in ABAQUS software to acquire the output of the micro-accelerometers over time and temperature. Each thermal experiment test involvedwas three micro-accelerometers mounted at aaccurate cube fixture (Figure 6). The full The thermal carried out in an incubator with an temperature controller. loading history used in boththree simulation and experimentmounted is shownat inaFigure 7. The (Figure red-marked points Each thermal test involved micro-accelerometers cube fixture 6). The full represent the starting or ending points a loadingisstep. The analysis started at the curing loading history used in both simulation andofexperiment shown in Figure 7. The red-marked points temperature °C, 0)or atending which the internal stress of the structure is zero. Then, thecuring modeltemperature was cooled represent the(60 starting points of a loading step. The analysis started at the ◦ C, 0) to temperature (25internal °C, 1) with rate ofstructure −5 °C/minisand at that for 60 to min (2), (60room at which the stressa of the zero.kept Then, the temperature model was cooled room ◦ ◦ and then the(25 temperature raised a higher temperature 60 min holding, followed a temperature C, 1) withwas a rate of −5to C/min and kept at thatwith temperature for 60 min (2), and by then temperature decrease to room (3) with with the same change ratefollowed and holding The high the temperature was raised to atemperature higher temperature 60 min holding, by a(4). temperature temperature points were 50, (3) 75 with and the 125same °C change for the rate three tests, The decrease to room temperature andgroups holdingof(4). The respectively. high temperature ◦ accelerometers subjected to three temperature The devices kept points were 50,in 75each and group 125 Cwere for the three groups of high–low tests, respectively. The steps. accelerometers in each at room temperature curing and cooling were also simulated andkept tested. group were subjected after to three high–low temperature steps. The devices at room temperature after Toand investigate the time and temperature dependence of device performance, 40 FEM and curing cooling were also simulated and tested. packaged accelerometers wereand simulated and tested over the of loading history of Figure 40 7, where the To investigate the time temperature dependence device performance, FEM and high temperature points were to 50, 70 125 over °C. Each thermalhistory cycle was applied to ten packaged accelerometers were set simulated andand tested the loading of Figure 7, where accelerometers, and the remaining tento were °CEach for comparison. offsettoand the high temperature points were set 50, 70kept and at 12525◦ C. thermal cycleThe waszero applied ten ◦ sensitivity of the arewere shown Figure This showsThe great between accelerometers, andaccelerometers the remaining ten kept in at 25 C for8.comparison. zero agreement offset and sensitivity experimental and simulation datainwith small deviation, is mainly caused by experimental fabrication errors of the accelerometers are shown Figure 8. This showswhich great agreement between and and temperature fluctuation, because the experimental areby thefabrication average value of and eachtemperature ten sensors’ simulation data with small deviation, which is mainly data caused errors results. Bothbecause the zerothe offset and sensitivity of the average micro-accelerometers stored at room temperature fluctuation, experimental data are value of each ten sensors’ results. Both the decreased gradually over time, due to the thermal stress relaxation induced by the viscoelasticity of the polymer adhesive. For the 50 and 75 °C thermal cycles, higher temperature led to a higher offset
Eσ((t )t)
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Materials 2017, 10, 1077 6 of 11 zero offset and sensitivity of the micro-accelerometers stored at room temperature decreased gradually over time, due toand thethe thermal stress relaxation induced by the viscoelasticity polymer adhesive. and sensitivity, data of room temperature in each cycle also showedofa the decrease of offset and and sensitivity, and the data of room temperature in each cycle also showed a decrease of offset and ◦ For the 50 and 75 C thermal higher temperature to a higher offsetand andsensitivity sensitivity,tested and the sensitivity. However, the 125cycles, °C condition exhibited anled increase of offset at sensitivity. However, the 125 °C condition exhibited an increase of offset and sensitivity tested at data of room temperature in each cycle also showed a decrease of offset and sensitivity. However, room temperature. room temperature. the 125 ◦ C condition exhibited an increase of offset and sensitivity tested at room temperature.
Table 2. Prony pairs of the die attach adhesive. Table 2. Prony pairs of the die attach adhesive. Table 2. Prony pairs of the die attach adhesive.
Ei/E0 1 τi Ei/E0 1 1 τ iτi Ei /E0 0.08510 3041.87694 0.08510 3041.87694 0.08510 3041.87694 0.14589 981,765.85865 0.14589 0.14589 981,765.85865 981,765.85865 0.22654 243.32699 0.22654 243.32699 243.32699 0.22654 0.11248 2083.25650 0.11248 2083.25650 0.11248 2083.25650 0.15906 48,993.21024 48,993.21024 0.15906 0.15906 48,993.21024 0.21617 31.16988 0.21617 31.16988 0.21617 31.16988 0.03923 5052.23180 0.03923 5052.23180 0.00025 5052.23180 6992.77554 0.03923 0.00025 6992.77554 0.00676 3321.33054 0.00025 6992.77554 0.00676 3321.33054 1 E = 2744.76252 MPa. 0 0.00676 3321.33054
i i 1 11 2 2 3 33 4 44 55 5 66 76 7 87 8 98 9 9 i
1 1
E0 = 2744.76252 MPa. E0 = 2744.76252 MPa.
Relaxation Relaxationmodulus modulus(MPa) (MPa)
3000 3000 2500 2500
Modulus Modulus Prony fit Prony fit
2000 2000 1500 1500 1000 1000 500 500 0 0
0 0
2 2
4 4
6 6 Log t (s) Log t (s)
8 8
10 10
Figure 5. Prony series fitted fitted to master master curve. Figure Prony series series Figure 5. 5. Prony fitted to to master curve. curve.
Figure 6. Mounted accelerometers in the test. Figure 6. 6. Mounted accelerometers in in the the test. test. Figure Mounted accelerometers
12 12
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Figure Figure 7. 7. Loading Loading history history for for the the analysis. analysis. Figure 7. Loading history for the analysis. 87.5 87.5 87 87
Bias(mg) (mg) Bias
86.5 86.5 86 86 85.5 85.5 85 85 84.5 84.5 84 84 1 1
2 2
Sensitivity (mV/g) Sensitivity (mV/g)
25°C simulation 25°C experiment simulation 25°C 25°C experiment
3 3
4
5
4 5 Loading history Loading history
50°C simulation 50°C experiment simulation 50°C 50°C experiment (a)
6 6
7 7
75°C simulation 75°C experiment simulation 75°C 75°C experiment
8 8
125°C simulation 125°C experiment simulation 125°C 125°C experiment
(a)
258.06 258.06 258.05 258.05 258.04 258.04 258.03 258.03 258.02 258.02 258.01 258.01 258 258 257.99 257.99 257.98 257.98 257.97 257.97 1 1
2 2
25°C simulation 25°C simulation 25°C experiment 25°C experiment
3 3
4 4
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Loading history Loading history 50°C simulation 75°C simulation 50°C simulation 75°C simulation 50°C experiment 75°C experiment 50°C experiment 75°C experiment
7 7
8 8
125°C simulation 125°C simulation 125°C experiment 125°C experiment
(b) (b) Figure 8. Results comparison. (a) Bias; (b) sensitivity. Figure Figure 8. 8. Results Results comparison. comparison. (a) (a) Bias; Bias; (b) (b) sensitivity. sensitivity.
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5. Discussion The observed output drift in the simulation and experiments indicates that the viscoelasticity of adhesive was the main cause of the deviation of zero offset and sensitivity. The underlying mechanism can be attributed to the time- and temperature-dependent stress and deformation states of the sensitive components of the micro-accelerometers. The residual compressive stress and tensile stress existed in the glass and the ceramic substrate, respectively, and because the CTE of ceramic material is larger than glass, the top and bottom interfaces of the adhesive layer exhibit different stress statuses. When the sensors were stored at room temperature, the residual stress in the adhesive gradually changed due to its relaxation induced by the viscoelastic property, and the stress in the chip experienced a corresponding shift to influence the deformation of sensitive components. The stress relaxation of the adhesive at room temperature resulted in an expansion of the glass layer because of the compressive stress in it, so the distance of points P1 and P2 was extended (Figure 2), which led to a broadened gap d1 and a reduced displacement of proof mass based on Equation (3). The sensitivity and zero offset, therefore, decreased over time. In the thermal cycle experiments, the stress state in the chip changes with the loading process, including time and temperature effects. Take the experiment at 125 ◦ C as an example; the key points of temperature change are marked in Figure 9. The displacement of point P1 is selected to explain the structural deformation of the sensitive components over time, and the temperature during heating and cooling processes (Figure 10). The detailed information can be concluded in the following steps:
• •
•
•
•
•
•
Step 1—curing process: The initial state or stress-free state of the sensor appeared at 60 ◦ C where the curing process started, and the P1 was located at position 0 in Figure 10a. Step 2—cooling to room temperature: The point P1 moved to the center, the proof mass generated a positive movement along x direction and gap d1 decreased (Figure 10b). Thus, the offset and sensitivity both increased at this stage compared with those in Figure 10a. Step 3—room temperature retention: The compression of glass decreased due to stress relaxation, and P1 slightly moved in the negative x direction, which led to the decrease of um and increase of d1 (Figure 10c). The offset and sensitivity decreased. Step 4—starting point of high temperature: The model expanded, and the point P1 moved in the negative x direction substantially, which caused the decrease of um and increase of d1 (Figure 10d). Therefore, the offset and sensitivity continued to decrease. Step 5—ending point of high temperature: During the thermal treatment process, the tension on the glass decreased due to stress relaxation, and P1 slightly moved in the positive x direction to result in a higher offset and sensitivity (Figure 10e). Step 6—cooling to room temperature again: The model shrank, and the shrinkage included both the thermal part in step 4 and additional shrinkage value generated by strong viscoelasticity at 125 ◦ C. Hence, the point P1 moved to the right position 1 (Figure 10f). Consequently, the offset and sensitivity at this stage were larger than those of Figure 10b. Step 7—room temperature retention again: The offset and sensitivity decreased, due to stress relaxation, but they were still larger than those in Figure 10c. This indicated that the offset level is influenced by thermal treatment, so higher-temperature dwells lead to greater offset and sensitivity (Figure 10g).
For the accelerometers exposed to thermal cycles of 50 and 75 ◦ C, the displacement pattern of point P1 is the same as that of 125 ◦ C, but with a smaller value, because of the smaller expansion of structures.
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E E
°C/min 55 °C/min 60 60
60 60 11
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Time (min) (min) Time ◦°C. 9. The The first first thermal cycle process process at at 125 125 °C. Figure Figure 9. thermal cycle C.
0
00
1
(a)
S
00 2 11
(b) SS E 00 22 11
00 22 11
(d)
(c) SS EE 00 22 113
(e)
SS EE00 22411 33
(f)
zz xx
(g)
◦°C. Figure 10. 10. The The moving trail of point P111 at at each step in the first thermal thermal cycle cycle at at 125 125 °C. (a) Curing Curing Figure Figure 10. The moving moving trail trail of of point point PP at each each step step in in the the first first thermal cycle at 125 C. (a) (a) Curing process; (b) cooling to room temperature; (c) room temperature retention; (d) starting point of high process; (b) cooling to room temperature; (c) room temperature retention; (d) starting point of process; (b) cooling to room temperature; (c) room temperature retention; (d) starting point of high high temperature; (e) ending point of high temperature; (f) cooling to room temperature again; (g) room temperature; (e) ending point of high temperature; (f) cooling to room temperature again; (g) room temperature; (e) ending point of high temperature; (f) cooling to room temperature again; (g) room temperature retention retention again. again. temperature temperature retention again.
6. Conclusions Conclusions 6. 6. Conclusions The viscoelasticity viscoelasticity effects of the epoxy-based die attach adhesive onon the output performance of The adhesive on the output performance of The viscoelasticityeffects effectsof ofthe theepoxy-based epoxy-baseddie dieattach attach adhesive the output performance MEMS capacitive accelerometers over time and temperature were studied by simulation and MEMS capacitive accelerometers over time and temperature were studied by simulation and of MEMS capacitive accelerometers over time and temperature were studied by simulation and experimental methods. methods. The zero offset and sensitivity gradually gradually decreased due to stress relaxation relaxation experimental experimental methods. The The zero zero offset offset and and sensitivity sensitivity gradually decreased decreased due due to to stress stress relaxation when accelerometers accelerometers were were kept kept at at room room temperature temperature after after adhesive adhesive packaging. packaging. In In the same period, when when accelerometers were kept at room temperature after adhesive packaging. In the the same same period, period, the high-temperature load slowed down the process of stress relaxation, and was not advantageous the high-temperature load slowed down the process of stress relaxation, and was not advantageous the high-temperature load slowed down the process of stress relaxation, and was not advantageous in in improving improving the long-term stabilityrelated relatedtoto toviscoelasticity viscoelasticityof ofpackaging packagingadhesives. adhesives. Furthermore, Furthermore, in long-term stability related viscoelasticity of packaging adhesives. improving thethe long-term stability Furthermore, the drift of bias and sensitivity can be attributed to the residual stress development induced by the the the drift of bias and sensitivity can be attributed to the residual stress development induced by the drift of bias and sensitivity can be attributed to the residual stress development induced viscoelastic behavior of adhesion materials. To aid in an in-depth understanding of the viscoelastic viscoelastic behavior of adhesion materials. To aid in an in-depth understanding of the viscoelastic by the viscoelastic behavior of adhesion materials. To aid in an in-depth understanding of the behavior of ofbehavior materials, future work work will concentrate on developing developing the theoretical theoretical model of behavior materials, future will concentrate on the model of viscoelastic of materials, future work will concentrate on developing the theoretical model viscoelasticity of materials in the tri-layered assembly. Furthermore, the viscoelasticity difference viscoelasticity of materials in the tri-layered assembly. Furthermore, the viscoelasticity difference of viscoelasticity of materials in the tri-layered assembly. Furthermore, the viscoelasticity difference induced by by preparation preparation and process will be studied to find out the solution to the drift of micro-devices. induced induced by preparation and and process process will will be be studied studied to tofind findout outthe thesolution solutionto tothe thedrift driftof ofmicro-devices. micro-devices. Acknowledgments: This This work work was was supported supported in in part part by by NSAF NSAF (No. (No. U1530132), U1530132), National National Natural Natural Science Science Acknowledgments: by NSAF (No. Foundation of China (No. 51505068) and Fundamental Research Funds for the Central Universities (Grant Nos. Fundamental Research Research Funds Funds for for the the Central Central Universities Universities (Grant (Grant Nos. Nos. Foundation of China (No. 51505068) and Fundamental ZYGX2015J085 and ZYGX2016J112). ZYGX2015J085 and and ZYGX2016J112). ZYGX2016J112). ZYGX2015J085
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Author Contributions: Wu Zhou, Peng Peng and Xiaoping He conceived and designed the idea and experiments; Peng Peng performed the experiments; Huijun Yu and Bei Peng analyzed the data; Wu Zhou and Peng Peng wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
References 1. 2. 3. 4.
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Dai, G.; Li, M.; He, X.; Du, L.; Shao, B.; Su, W. Thermal drift analysis using a multiphysics model of bulk silicon MEMS capacitive accelerometer. Sens. Actuators A Phys. 2011, 172, 369–378. [CrossRef] He, J.; Xie, J.; He, X.; Du, L.; Zhou, W. Analytical study and compensation for temperature drifts of a bulk silicon MEMS capacitive accelerometer. Sens. Actuators A Phys. 2016, 239, 174–184. [CrossRef] Suhir, E. Predictive analytical thermal stress modeling in electronics and photonics. Appl. Mech. Rev. 2009, 62, 933–944. [CrossRef] Chae, S.H.; Zhao, J.H.; Edwards, D.R.; Ho, P.S. Characterization of the viscoelasticity of molding compounds in the time domain. J. Electron. Mater. 2010, 39, 419–425. [CrossRef] Hu, M.; Xia, Y.; Daeffler, C.S.; Wang, J.; McKenna, G.B.; Kornfield, J.A.; Grubbs, R.H. The linear rheological responses of wedge-type polymers. J. Polym. Sci. Part B Polym. Phys. 2015, 53, 899–906. [CrossRef] Kim, Y.K.; White, S.R. Stress relaxation behavior of 3501-6 epoxy resin during cure. Polym. Eng. Sci. 2010, 36, 2852–2862. [CrossRef] © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Material Viscoelasticity-Induced Drift of Micro-Accelerometers Wu Zhou 1 1 2
*
ID
, Peng Peng 1, *, Huijun Yu 1 , Bei Peng 1, * and Xiaoping He 2
School of Mechatronics Engineering, University of Electronic Technology and Science of China, Chengdu 611731, China; [email protected] (W.Z.); [email protected] (H.Y.) Institute of Electronic Engineering, China Academy of Engineering Physics, Mianyang 621900, China; [email protected] Correspondence: [email protected] (P.P.); [email protected] (B.P.); Tel.: +86-28-6183-0227 (B.P.)
Received: 21 August 2017; Accepted: 12 September 2017; Published: 14 September 2017
Abstract: Polymer-based materials are commonly used as an adhesion layer for bonding die chip and substrate in micro-system packaging. Their properties exhibit significant impact on the stability and reliability of micro-devices. The viscoelasticity, one of most important attributes of adhesive materials, is investigated for the first time in this paper to evaluate the long-term drift of micro-accelerometers. The accelerometer was modeled by a finite element (FE) method to emulate the structure deformation and stress development induced by change of adhesive property. Furthermore, the viscoelastic property of the adhesive was obtained by a series of stress–relaxation experiments using dynamic mechanical analysis (DMA). The DMA curve was imported into the FE model to predict the drift of micro-accelerometers over time and temperature. The prediction results verified by experiments showed that the accelerometer experienced output drift due to the development of packaging stress induced by both the thermal mismatch and viscoelastic behaviors of the adhesive. The accelerometers stored at room temperature displayed a continuous drift of zero offset and sensitivity because of the material viscoelasticity. Moreover, the drift level of accelerometers experiencing high temperature load was relatively higher than those of lower temperature in the same period. Keywords: MEMS; adhesive; viscoelasticity; drift; accelerometer
1. Introduction In packaging of microelectromechanical systems (MEMS), polymer-based materials, such as epoxy and silicone, are widely used for mounting the die chip on the substrate because of their numerous advantages compared with other joining methods [1,2]. However, this type of adhesive packaging, like other packaging themes, involves residual thermal stress/packaging stress due to the mismatch of coefficients of thermal expansion (CTE) of different structural materials [3]. The stress existing in structures and interfaces forms a stable equilibrium of micro-devices based on deformation compatibility conditions [4]. The formed equilibrium, however, is prone to be upset by the temperature load and/or the shift of material properties, such as elastic module and Poisson’s ratio. The temperature aspects are always related to the thermal effects’ influence on device performance, which has been studied intensively, while the material properties of the polymer-based materials in current studies are often neglected or simply assumed to be linear–elastic [5–10]. This assumption could give a relatively accurate evaluation of device performance in the low- and medium-precision application fields, but could not be used to predict the long-term stability or drift in areas requiring high precision, because the polymers actually exhibit viscoelasticity presenting elastic and viscous characteristics simultaneously [11,12], and they also possess the features of time and temperature dependence. The viscoelasticity-related issue has become one of the most critical steps for assessing the packaging quality and output performance of highly precise MEMS sensors [13,14]. Applying the viscoelastic Materials 2017, 10, 1077; doi:10.3390/ma10091077
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the packaging quality and output performance of highly precise MEMS sensors [13,14]. Applying the property to property model thetoMEMS could give acould bettergive agreement the results in viscoelastic model devices the MEMS devices a betterwith agreement withobserved the results experiments than the previous elastic model [15]. The packaging stress in the MEMS was influenced observed in experiments than the previous elastic model [15]. The packaging stress in the MEMS was not only bynot theonly temperature change, but also bybut itsalso change rate due to thedue time-dependent property influenced by the temperature change, by its change rate to the time-dependent of polymer adhesives [16]. Besides, the viscoelastic behavior influenced by moisture was recognized property of polymer adhesives [16]. Besides, the viscoelastic behavior influenced by moisture was as the cause long-term stability of micro-sensors in storage CurrentCurrent works on the recognized asof thethe cause of the long-term stability of micro-sensors in [17,18]. storage [17,18]. works viscoelastic effects mainly focus onfocus the viscoelasticity-induced reliability issues ofissues MEMS on the viscoelastic effects mainly on the viscoelasticity-induced reliability of sensors, MEMS but the underlying mechanism of stress development over time and temperature is still open to sensors, but the underlying mechanism of stress development over time and temperature is still open further investigation. to further investigation. This study aims aims to to deeply deeply investigate investigate the the effects effects of of viscoelastic behavior of of epoxy-based epoxy-based This study viscoelastic behavior adhesive on the long-term stability of micro-capacitive accelerometers packaged in a ceramic shell adhesive on the long-term stability of micro-capacitive accelerometers packaged in a ceramic shell by by the adhesively bonding method. Section 2 gives introductiontotothe the working working principle principle of of the adhesively bonding method. Section 2 gives ananintroduction micro-accelerometers, and theoretically determines the zero offset and sensitivity by the deformation micro-accelerometers, and theoretically determines the zero offset and sensitivity by the deformation of the the sensitive sensitive structure structure of of the the accelerometer. accelerometer. In In Section Section 3, 3, the the accurate accurate viscoelastic viscoelastic property property of of the the of adhesive is is obtained obtained by by aa series series of of stress–relaxation stress–relaxation tests tests by by dynamic dynamic mechanical mechanical analysis analysis (DMA), (DMA), adhesive and the master curve is acquired by the proper shift function and fitted with the Prony function and the master curve is acquired by the proper shift function and fitted with the Prony function to to implement finite element analysis (FEA). Section4,4,the theobtained obtainedcurve curveisis introduced introduced into into the the implement finite element analysis (FEA). InIn Section physical model of the accelerometer to study the deformation law of sensitive components subjected to physical model of the accelerometer to study the deformation law of sensitive components subjected four different time and temperature cycles, and then the zero offset and sensitivity of the accelerometer to four different time and temperature cycles, and then the zero offset and sensitivity of the can be determined bydetermined the deformed structure. Thestructure. simulation and experiments are also givenare inalso this accelerometer can be by the deformed The simulation and experiments section. The discussion and conclusion are provided in Sections 5 and 6, respectively. given in this section. The discussion and conclusion are provided in Sections 5 and 6, respectively. 2. Structure Structure and and Principle Principle 2. The simplified model of the capacitive accelerometers is shown in Figure 1. The sensitive The simplified model of the capacitive accelerometers is shown in Figure 1. The sensitive component is a silicon-based structure supported elastically by four folded beams and bonded to component is a silicon-based structure supported elastically by four folded beams and bonded to a a Pyrex glasssubstrate. substrate.The Thewhole wholestructure structureisispackaged packagedonto ontoaaceramic ceramicshell shell with with an an epoxy-based epoxy-based Pyrex glass adhesive through a curing process. When an acceleration, a, is applied in the sensitive direction, adhesive through a curing process. When an acceleration, a, is applied in the sensitive direction, the the movement of the proof mass induced by inertial force generates a gap change of sensing capacitors movement of the proof mass induced by inertial force generates a gap change of sensing capacitors formed by byaafixed fixedfinger fingerononthe the silicon substrate a movable finger on proof the proof [19,20]. formed silicon substrate andand a movable finger on the massmass [19,20]. The The changed gap shifts the differential capacitance of capacitors, C and C , and the output of the 1 2, and the 2 changed gap shifts the differential capacitance of capacitors, C1 and C output of the micromicro-accelerometer be simply expressed as: accelerometer can be can simply expressed as: C1 C− CC22 Vout V=out G VVb G 1 C1C+ CC22 b 1
(1) (1)
where V accelerometer, G isGthe coefficient of theof sensing circuit out is is the theoutput outputvoltage voltageofof accelerometer, is amplification the amplification coefficient the sensing where Vout and V is the amptitude of carrier voltage. circuitband Vb is the amptitude of carrier voltage.
(a)
(b)
Figure 1. Structure of capacitive accelerometer. (a) Diagram of accelerometer; (b) SEM structure. Figure 1. Structure of capacitive accelerometer. (a) Diagram of accelerometer; (b) SEM structure.
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Half of the sensitive component is selected to derive the analytical expressions of performance, zero offset and sensitivity of the micro-accelerometer. The folded beams anchored to separated sides are represented Materials 2017,by 10, two 1077 springs with different stiffness constants, k1 and k2 , due to fabrication errors 3 of 11 [21] (Figure 2). The output of the accelerometer, according to Equation (1), is directly proportional to the Half of the sensitive component is selected the analytical expressions offixed performance, differential capacitance, which is dependent on to thederive relative position between the fingers and zero offset and sensitivity of the micro-accelerometer. The folded beams anchored to separated sides the movable fingers. Therefore, the positions of finger anchors (3, 4) and the proof mass determine are represented by two springs with different stiffness constants, k 1 and k2, due to fabrication errors [21] performance parameters of the micro-accelerometer, and are influenced by the stress state of the (Figure 2). The output of the accelerometer, according to Equation (1), is directly proportional to the whole structure. Ideally, the free state of packaged accelerometers should show no internal stress, differential capacitance, which is dependent on the relative position between the fixed fingers and but the packaging process with a fluctuating temperature leads to thermal stress in the chip due to movable fingers. Therefore, the positions of finger anchors (3, 4) and the proof mass determine the different thermo–mechanical properties of the structural materials. Thus, by thethe zero offset or bias performance parameters of the micro-accelerometer, and are influenced stress state of theof the micro-accelerometer be expressed as of [22]: whole structure. can Ideally, the free state packaged accelerometers should show no internal stress, but the packaging process with a fluctuating temperature leads to thermal stress in the chip due to Kum different thermo–mechanical properties ofBias the structural materials. Thus, the zero offset or bias of the =− m micro-accelerometer can be expressed as [22]:
(2)
where K denotes the total stiffness of the folded beams,Ku K = k1 + k2 , m is the proof mass and um is the (2) Bias m displacement of the proof mass center. Furthermore, m where K denotes the total stiffness of the k1 folded − k2 beams, K = k1 + k2, m is the proof mass and um is the ( P1x − l1 ∆Tαsilicon ) umcenter. = Furthermore, displacement of the proof mass k + k 1
(3)
2
k1 k2
silicon ) connecting the folded beams um ( P1 x the l1 Tpoint (3) and where P1x denotes the longitudinal displacements k1 k2 of the anchors; l1 is half the length of the proof mass; ∆T is the temperature change between curing x denotes the longitudinal displacements of the point connecting the folded beams and the where P1and temperature room temperature; and αsilicon is the CTE of silicon. anchors; l1 is half the length of the proof mass; ∆T is the temperature change between curing The sensitivity of the micro-accelerometer can be expressed as:
temperature and room temperature; and αsilicon is the CTE of silicon. The sensitivity of the micro-accelerometer can be as: 1 expressed 1 Gm
Sensitivity = (
− ) d 1 d12 GmK
Sensitivity 1(
d1
d2
)
K
(4) (4)
where d1 and d2 denote narrow and wide gaps once the curing process is completed, respectively. The whereisd1mainly and d2 denote narrow gapsgap, oncebecause the curing completed, much issmaller thanrespectively. d2 . sensitivity determined byand thewide narrow d1 isprocess The sensitivity is mainly determined by the narrow gap, because d 1 is much smaller than d2. The Equations (3) and (4) represent the zero offset and sensitivity of the packaged The Equations (3) and (4) represent the zero offset and sensitivity of the packaged micromicro-accelerometer, respectively. Both parameters are constant when the structure has no deformation accelerometer, respectively. Both parameters are constant when the structure has no deformation or or movement, because the silicon, glass, circuit and internal environment are almost invariant. The movement, because the silicon, glass, circuit and internal environment are almost invariant. micro-accelerometer after storage, exhibited an obvious drift of performance parameters. The micro-accelerometer after however, storage, however, exhibited an obvious drift of performance That is to say, theThat structural equilibrium sustained by the residual stress was upset parameters. is to say, the structural equilibrium sustained by thermal the residual thermal stress by wassome factors related to the structural material properties. upset by some factors related to the structural material properties.
Figure 2. Half-structure of sensitive components.
Figure 2. Half-structure of sensitive components.
3. Material Property
3. Material Property
The sensor of the micro-accelerometer consists of four different materials including silicon,
The of the micro-accelerometer four Pyrex different including silicon, Pyrexsensor glass, ceramic material and packaging consists adhesive.of Silicon, glassmaterials and the ceramic material Pyrexwere glass, ceramic material and packaging adhesive. Silicon, and the material used broadly and have very stable material properties withPyrex linearglass elasticity. The ceramic Poisson ratio
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were used broadly and have very stable material properties with linear elasticity. The Poisson ratio and CTE of the adhesive were assumed as constant values, because they have little impact on the packaging stress [23]. The material properties are listed in Table 1. Table 1. Material properties for the sensor. Material
Young’s Modulus (Gpa)
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Poisson Ratio
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Silicon 160 0.22 2.6 and Glass CTE of the adhesive were assumed on the 62.7 as constant values, because 0.2 they have little impact 3.25 packaging properties are listed in Table0.22 1. Ceramicstress [23]. The material360 6.5 Adhesive Table 2 0.37 60 Table 1. Material properties for the sensor.
Material
Young’s Modulus (Gpa)
Poisson Ratio
CTE (ppm/°C)
The packaging adhesive, a typical epoxy-based polymer, however, exhibits both elastic and viscous Silicon 160 0.22 2.6 behaviors, that is, viscoelasticity. The elasticity responding to while the viscous Glass 62.7 0.2stress is instantaneous, 3.25 Ceramic 360temperature, which 0.22 consequently 6.5 has significant impact on response is time-dependent and varies with Adhesive Table 2 0.37the viscoelastic 60 characteristics, therefore, the stress distribution in the micro-accelerometer. To measure is one of most The critical steps adhesive, before evaluating the stability of micro-accelerometers of the timepackaging a typical epoxy-based polymer, however, exhibits both because elastic and and temperature-dependent of the adhesive. Theresponding common to measuring method is while through stress viscous behaviors, thatfeature is, viscoelasticity. The elasticity stress is instantaneous, viscoustests response time-dependent andstress–relaxation varies with temperature, whichperformed consequently has dynamic relaxation the or creep [24]. isHence, a series of tests were using significant impact on the stress distribution in the micro-accelerometer. To measure the viscoelastic mechanical analysis (TA instrument DMA Q800, New Castle, DE, USA). A rectangular specimen characteristics, therefore, is one of most critical steps before evaluating the stability of micro(35 mm × accelerometers 10 mm × 2 mm) was prepared cured by the same process in theThe accelerometers, and because of the time- andand temperature-dependent feature of the as adhesive. common then mounted on the instrument operating in a single cantilever mode.a series The experimental temperature measuring method is through stress relaxation or creep tests [24]. Hence, of stress–relaxation ◦ C with were performed dynamic mechanical analysis instrument DMA Q800, New range wastests set from 25 to 125using an increment of 10 ◦(TA C and an increase rate of 5 ◦Castle, C/min, and at DE, USA). A rectangular specimen (35 mm × 10 mm × 2 mm) was prepared and cured by the same each test point, 5 min was allowed for temperature stabilization and 0.1% strain was applied on the process as in the accelerometers, and then mounted on the instrument operating in a single cantilever specimen for 20The min, followedtemperature by a 10 min recovery. The25test results are inofFigure 3. mode. experimental range was set from to 125 °C with an shown increment 10 °C and The relaxation data, normalization, were modeled the master curve, which translates the an increase rate of 5for °C/min, and at each test point, 5 min wasby allowed for temperature stabilization and 0.1% was applied on the specimen for 20 min, temperature followed by a 10with min recovery. The test curve segments atstrain different temperatures to a reference logarithmic coordinates results are shown in Figure 3. according to a time–temperature superposition [25]. The master curve can be fitted by a third-order The relaxation data, for normalization, were modeled by the master curve, which translates the polynomial function, such as: curve segments at different temperatures to a reference temperature with logarithmic coordinates according to a time–temperature superposition [25]. The master curve can be fitted by a third-order loga T ( Tsuch ) =as:C1 ( T − T0 ) + C2 ( T − T0 )2 + C3 ( T − T0 )3 polynomial function, l o g aT (T ) C 1 (T T0 ) C 2 (T T0 ) 2 C 3 (T T0 ) 3
(5)
(5)
where aT are the offset values at different temperatures (T1 ) and C1 , C2 and C3 are constants. where aT are the offset values at different temperatures (T1) and C1, C2 and C3 are constants. The reference temperature was set at 25 ◦ C, and then the three coefficients of the polynomial The reference temperature was set at 25 °C, and then the three coefficients of the polynomial function were determined to be toC1be=C0.223439, −0.00211 C3 = 5.31163 × 104).−6 (Figure 4). function were determined 1 = 0.223439,C C22 ==−0.00211 and and C3 = 5.31163 × 10−6 (Figure 3000
130 120 110 100
2000
90 80 70
1500
60 50
1000
40 30
500
20 10
0
0 0
100
200
300
400
Time (min)
Figure 3. Stress–relaxation test results.
Figure 3. Stress–relaxation test results.
500
Temperature (℃)
Relaxation modulus (MPa)
2500
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-1
Polynomial fit
log (aT)
-2 -3 -4 -5 -6 -7 -8 20
40
60
80
100
120
Temperature (℃ ) Figure of 25 25 ◦°C. Figure 4. 4. Master Master curve curve with with reference reference temperature temperature of C.
4. 4. Simulation Simulation and and Experiments Experiments The The master master curve curve in in Figure Figure 44 shows shows the the relaxation relaxation behaviors behaviors of of polymer polymer adhesives adhesives under under certain certain strain loads. This relaxed strain or stress results from the effective modulus of viscoelasticity, strain loads. This relaxed strain or stress results from the effective modulus of viscoelasticity, which which can series [26]: [26]: can be be described described as as aa Prony Prony series N (t ) t E +N Ei exp( t) , i i η (6) i 1 E(t) = (6) = 0 E∞ + ∑ Ei exp(− i ), τi =Ei i ε0 τi Ei i =1 where E(t) is the relaxation modulus; σ(t) is the stress; ε0 is the imposed constant strain; and E∞ is the fully modulus. Ei and τi are referred to as a Prony Ei is theconstant elastic modulus; ηi is whererelaxed E(t) is the relaxation modulus; σ(t) is the stress; ε0 is pair; the imposed strain; and E∞the is viscosity; and τi ismodulus. the relaxation of referred ith Prony N is the number of Prony the fully relaxed Ei andtime τ i are topair. as a Prony pair; Ei is the elasticpairs. modulus; η i is the For this therelaxation master curve needs to be pair. transformed into Prony seriespairs. for modeling and viscosity; andstudy, τ i is the time of ith Prony N is the number of Prony experiments 5). The coefficients of Equation (6) with nine Prony pairs arefor listed in Table 2, For this (Figure study, the master curve needs to be transformed into Prony series modeling and where E0 is the instantaneous modulus when time is zero. experiments (Figure 5). The coefficients of Equation (6) with nine Prony pairs are listed in Table 2, The introduced the Prony series modulus where E0 simulation is the instantaneous modulus when time is zero. into the whole finite element model (FEM) in ABAQUS softwareintroduced to acquirethe theProny outputseries of the micro-accelerometers and temperature. The simulation modulus into the wholeover finitetime element model (FEM) The thermal experiment was carried out in an incubator with an accurate temperature controller. in ABAQUS software to acquire the output of the micro-accelerometers over time and temperature. Each thermal experiment test involvedwas three micro-accelerometers mounted at aaccurate cube fixture (Figure 6). The full The thermal carried out in an incubator with an temperature controller. loading history used in boththree simulation and experimentmounted is shownat inaFigure 7. The (Figure red-marked points Each thermal test involved micro-accelerometers cube fixture 6). The full represent the starting or ending points a loadingisstep. The analysis started at the curing loading history used in both simulation andofexperiment shown in Figure 7. The red-marked points temperature °C, 0)or atending which the internal stress of the structure is zero. Then, thecuring modeltemperature was cooled represent the(60 starting points of a loading step. The analysis started at the ◦ C, 0) to temperature (25internal °C, 1) with rate ofstructure −5 °C/minisand at that for 60 to min (2), (60room at which the stressa of the zero.kept Then, the temperature model was cooled room ◦ ◦ and then the(25 temperature raised a higher temperature 60 min holding, followed a temperature C, 1) withwas a rate of −5to C/min and kept at thatwith temperature for 60 min (2), and by then temperature decrease to room (3) with with the same change ratefollowed and holding The high the temperature was raised to atemperature higher temperature 60 min holding, by a(4). temperature temperature points were 50, (3) 75 with and the 125same °C change for the rate three tests, The decrease to room temperature andgroups holdingof(4). The respectively. high temperature ◦ accelerometers subjected to three temperature The devices kept points were 50,in 75each and group 125 Cwere for the three groups of high–low tests, respectively. The steps. accelerometers in each at room temperature curing and cooling were also simulated andkept tested. group were subjected after to three high–low temperature steps. The devices at room temperature after Toand investigate the time and temperature dependence of device performance, 40 FEM and curing cooling were also simulated and tested. packaged accelerometers wereand simulated and tested over the of loading history of Figure 40 7, where the To investigate the time temperature dependence device performance, FEM and high temperature points were to 50, 70 125 over °C. Each thermalhistory cycle was applied to ten packaged accelerometers were set simulated andand tested the loading of Figure 7, where accelerometers, and the remaining tento were °CEach for comparison. offsettoand the high temperature points were set 50, 70kept and at 12525◦ C. thermal cycleThe waszero applied ten ◦ sensitivity of the arewere shown Figure This showsThe great between accelerometers, andaccelerometers the remaining ten kept in at 25 C for8.comparison. zero agreement offset and sensitivity experimental and simulation datainwith small deviation, is mainly caused by experimental fabrication errors of the accelerometers are shown Figure 8. This showswhich great agreement between and and temperature fluctuation, because the experimental areby thefabrication average value of and eachtemperature ten sensors’ simulation data with small deviation, which is mainly data caused errors results. Bothbecause the zerothe offset and sensitivity of the average micro-accelerometers stored at room temperature fluctuation, experimental data are value of each ten sensors’ results. Both the decreased gradually over time, due to the thermal stress relaxation induced by the viscoelasticity of the polymer adhesive. For the 50 and 75 °C thermal cycles, higher temperature led to a higher offset
Eσ((t )t)
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Materials 2017, 10, 1077 6 of 11 zero offset and sensitivity of the micro-accelerometers stored at room temperature decreased gradually over time, due toand thethe thermal stress relaxation induced by the viscoelasticity polymer adhesive. and sensitivity, data of room temperature in each cycle also showedofa the decrease of offset and and sensitivity, and the data of room temperature in each cycle also showed a decrease of offset and ◦ For the 50 and 75 C thermal higher temperature to a higher offsetand andsensitivity sensitivity,tested and the sensitivity. However, the 125cycles, °C condition exhibited anled increase of offset at sensitivity. However, the 125 °C condition exhibited an increase of offset and sensitivity tested at data of room temperature in each cycle also showed a decrease of offset and sensitivity. However, room temperature. room temperature. the 125 ◦ C condition exhibited an increase of offset and sensitivity tested at room temperature.
Table 2. Prony pairs of the die attach adhesive. Table 2. Prony pairs of the die attach adhesive. Table 2. Prony pairs of the die attach adhesive.
Ei/E0 1 τi Ei/E0 1 1 τ iτi Ei /E0 0.08510 3041.87694 0.08510 3041.87694 0.08510 3041.87694 0.14589 981,765.85865 0.14589 0.14589 981,765.85865 981,765.85865 0.22654 243.32699 0.22654 243.32699 243.32699 0.22654 0.11248 2083.25650 0.11248 2083.25650 0.11248 2083.25650 0.15906 48,993.21024 48,993.21024 0.15906 0.15906 48,993.21024 0.21617 31.16988 0.21617 31.16988 0.21617 31.16988 0.03923 5052.23180 0.03923 5052.23180 0.00025 5052.23180 6992.77554 0.03923 0.00025 6992.77554 0.00676 3321.33054 0.00025 6992.77554 0.00676 3321.33054 1 E = 2744.76252 MPa. 0 0.00676 3321.33054
i i 1 11 2 2 3 33 4 44 55 5 66 76 7 87 8 98 9 9 i
1 1
E0 = 2744.76252 MPa. E0 = 2744.76252 MPa.
Relaxation Relaxationmodulus modulus(MPa) (MPa)
3000 3000 2500 2500
Modulus Modulus Prony fit Prony fit
2000 2000 1500 1500 1000 1000 500 500 0 0
0 0
2 2
4 4
6 6 Log t (s) Log t (s)
8 8
10 10
Figure 5. Prony series fitted fitted to master master curve. Figure Prony series series Figure 5. 5. Prony fitted to to master curve. curve.
Figure 6. Mounted accelerometers in the test. Figure 6. 6. Mounted accelerometers in in the the test. test. Figure Mounted accelerometers
12 12
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Figure Figure 7. 7. Loading Loading history history for for the the analysis. analysis. Figure 7. Loading history for the analysis. 87.5 87.5 87 87
Bias(mg) (mg) Bias
86.5 86.5 86 86 85.5 85.5 85 85 84.5 84.5 84 84 1 1
2 2
Sensitivity (mV/g) Sensitivity (mV/g)
25°C simulation 25°C experiment simulation 25°C 25°C experiment
3 3
4
5
4 5 Loading history Loading history
50°C simulation 50°C experiment simulation 50°C 50°C experiment (a)
6 6
7 7
75°C simulation 75°C experiment simulation 75°C 75°C experiment
8 8
125°C simulation 125°C experiment simulation 125°C 125°C experiment
(a)
258.06 258.06 258.05 258.05 258.04 258.04 258.03 258.03 258.02 258.02 258.01 258.01 258 258 257.99 257.99 257.98 257.98 257.97 257.97 1 1
2 2
25°C simulation 25°C simulation 25°C experiment 25°C experiment
3 3
4 4
5 5
6 6
Loading history Loading history 50°C simulation 75°C simulation 50°C simulation 75°C simulation 50°C experiment 75°C experiment 50°C experiment 75°C experiment
7 7
8 8
125°C simulation 125°C simulation 125°C experiment 125°C experiment
(b) (b) Figure 8. Results comparison. (a) Bias; (b) sensitivity. Figure Figure 8. 8. Results Results comparison. comparison. (a) (a) Bias; Bias; (b) (b) sensitivity. sensitivity.
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5. Discussion The observed output drift in the simulation and experiments indicates that the viscoelasticity of adhesive was the main cause of the deviation of zero offset and sensitivity. The underlying mechanism can be attributed to the time- and temperature-dependent stress and deformation states of the sensitive components of the micro-accelerometers. The residual compressive stress and tensile stress existed in the glass and the ceramic substrate, respectively, and because the CTE of ceramic material is larger than glass, the top and bottom interfaces of the adhesive layer exhibit different stress statuses. When the sensors were stored at room temperature, the residual stress in the adhesive gradually changed due to its relaxation induced by the viscoelastic property, and the stress in the chip experienced a corresponding shift to influence the deformation of sensitive components. The stress relaxation of the adhesive at room temperature resulted in an expansion of the glass layer because of the compressive stress in it, so the distance of points P1 and P2 was extended (Figure 2), which led to a broadened gap d1 and a reduced displacement of proof mass based on Equation (3). The sensitivity and zero offset, therefore, decreased over time. In the thermal cycle experiments, the stress state in the chip changes with the loading process, including time and temperature effects. Take the experiment at 125 ◦ C as an example; the key points of temperature change are marked in Figure 9. The displacement of point P1 is selected to explain the structural deformation of the sensitive components over time, and the temperature during heating and cooling processes (Figure 10). The detailed information can be concluded in the following steps:
• •
•
•
•
•
•
Step 1—curing process: The initial state or stress-free state of the sensor appeared at 60 ◦ C where the curing process started, and the P1 was located at position 0 in Figure 10a. Step 2—cooling to room temperature: The point P1 moved to the center, the proof mass generated a positive movement along x direction and gap d1 decreased (Figure 10b). Thus, the offset and sensitivity both increased at this stage compared with those in Figure 10a. Step 3—room temperature retention: The compression of glass decreased due to stress relaxation, and P1 slightly moved in the negative x direction, which led to the decrease of um and increase of d1 (Figure 10c). The offset and sensitivity decreased. Step 4—starting point of high temperature: The model expanded, and the point P1 moved in the negative x direction substantially, which caused the decrease of um and increase of d1 (Figure 10d). Therefore, the offset and sensitivity continued to decrease. Step 5—ending point of high temperature: During the thermal treatment process, the tension on the glass decreased due to stress relaxation, and P1 slightly moved in the positive x direction to result in a higher offset and sensitivity (Figure 10e). Step 6—cooling to room temperature again: The model shrank, and the shrinkage included both the thermal part in step 4 and additional shrinkage value generated by strong viscoelasticity at 125 ◦ C. Hence, the point P1 moved to the right position 1 (Figure 10f). Consequently, the offset and sensitivity at this stage were larger than those of Figure 10b. Step 7—room temperature retention again: The offset and sensitivity decreased, due to stress relaxation, but they were still larger than those in Figure 10c. This indicated that the offset level is influenced by thermal treatment, so higher-temperature dwells lead to greater offset and sensitivity (Figure 10g).
For the accelerometers exposed to thermal cycles of 50 and 75 ◦ C, the displacement pattern of point P1 is the same as that of 125 ◦ C, but with a smaller value, because of the smaller expansion of structures.
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60 60
125 125 SS 60 00 60
25 25
E E
°C/min 55 °C/min 60 60
60 60 11
22
33
44
Time (min) (min) Time ◦°C. 9. The The first first thermal cycle process process at at 125 125 °C. Figure Figure 9. thermal cycle C.
0
00
1
(a)
S
00 2 11
(b) SS E 00 22 11
00 22 11
(d)
(c) SS EE 00 22 113
(e)
SS EE00 22411 33
(f)
zz xx
(g)
◦°C. Figure 10. 10. The The moving trail of point P111 at at each step in the first thermal thermal cycle cycle at at 125 125 °C. (a) Curing Curing Figure Figure 10. The moving moving trail trail of of point point PP at each each step step in in the the first first thermal cycle at 125 C. (a) (a) Curing process; (b) cooling to room temperature; (c) room temperature retention; (d) starting point of high process; (b) cooling to room temperature; (c) room temperature retention; (d) starting point of process; (b) cooling to room temperature; (c) room temperature retention; (d) starting point of high high temperature; (e) ending point of high temperature; (f) cooling to room temperature again; (g) room temperature; (e) ending point of high temperature; (f) cooling to room temperature again; (g) room temperature; (e) ending point of high temperature; (f) cooling to room temperature again; (g) room temperature retention retention again. again. temperature temperature retention again.
6. Conclusions Conclusions 6. 6. Conclusions The viscoelasticity viscoelasticity effects of the epoxy-based die attach adhesive onon the output performance of The adhesive on the output performance of The viscoelasticityeffects effectsof ofthe theepoxy-based epoxy-baseddie dieattach attach adhesive the output performance MEMS capacitive accelerometers over time and temperature were studied by simulation and MEMS capacitive accelerometers over time and temperature were studied by simulation and of MEMS capacitive accelerometers over time and temperature were studied by simulation and experimental methods. methods. The zero offset and sensitivity gradually gradually decreased due to stress relaxation relaxation experimental experimental methods. The The zero zero offset offset and and sensitivity sensitivity gradually decreased decreased due due to to stress stress relaxation when accelerometers accelerometers were were kept kept at at room room temperature temperature after after adhesive adhesive packaging. packaging. In In the same period, when when accelerometers were kept at room temperature after adhesive packaging. In the the same same period, period, the high-temperature load slowed down the process of stress relaxation, and was not advantageous the high-temperature load slowed down the process of stress relaxation, and was not advantageous the high-temperature load slowed down the process of stress relaxation, and was not advantageous in in improving improving the long-term stabilityrelated relatedtoto toviscoelasticity viscoelasticityof ofpackaging packagingadhesives. adhesives. Furthermore, Furthermore, in long-term stability related viscoelasticity of packaging adhesives. improving thethe long-term stability Furthermore, the drift of bias and sensitivity can be attributed to the residual stress development induced by the the the drift of bias and sensitivity can be attributed to the residual stress development induced by the drift of bias and sensitivity can be attributed to the residual stress development induced viscoelastic behavior of adhesion materials. To aid in an in-depth understanding of the viscoelastic viscoelastic behavior of adhesion materials. To aid in an in-depth understanding of the viscoelastic by the viscoelastic behavior of adhesion materials. To aid in an in-depth understanding of the behavior of ofbehavior materials, future work work will concentrate on developing developing the theoretical theoretical model of behavior materials, future will concentrate on the model of viscoelastic of materials, future work will concentrate on developing the theoretical model viscoelasticity of materials in the tri-layered assembly. Furthermore, the viscoelasticity difference viscoelasticity of materials in the tri-layered assembly. Furthermore, the viscoelasticity difference of viscoelasticity of materials in the tri-layered assembly. Furthermore, the viscoelasticity difference induced by by preparation preparation and process will be studied to find out the solution to the drift of micro-devices. induced induced by preparation and and process process will will be be studied studied to tofind findout outthe thesolution solutionto tothe thedrift driftof ofmicro-devices. micro-devices. Acknowledgments: This This work work was was supported supported in in part part by by NSAF NSAF (No. (No. U1530132), U1530132), National National Natural Natural Science Science Acknowledgments: by NSAF (No. Foundation of China (No. 51505068) and Fundamental Research Funds for the Central Universities (Grant Nos. Fundamental Research Research Funds Funds for for the the Central Central Universities Universities (Grant (Grant Nos. Nos. Foundation of China (No. 51505068) and Fundamental ZYGX2015J085 and ZYGX2016J112). ZYGX2015J085 and and ZYGX2016J112). ZYGX2016J112). ZYGX2015J085
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Author Contributions: Wu Zhou, Peng Peng and Xiaoping He conceived and designed the idea and experiments; Peng Peng performed the experiments; Huijun Yu and Bei Peng analyzed the data; Wu Zhou and Peng Peng wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
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