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Characterization of Young's modulus and residual stress gradient of MetalMUMPs electroplated nickel film
Sensors and Actuators A 154 (2009) 149–156
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Characterization of Young’s modulus and residual stress gradient of MetalMUMPs electroplated nickel film Siyuan He a,∗,1 , John S. Chang a , Lihua Li b , Hsu Ho c a b c
Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, Ontario, Canada M5B 2K3 MEMSCAP, Research Triangle Park, NC, USA Microelectronics Integration, CMC Microsystems, Kingston, Ontario, Canada K7L 3N6
a r t i c l e
i n f o
Article history: Received 3 December 2008 Received in revised form 18 February 2009 Accepted 18 June 2009 Available online 16 July 2009 Keywords: Electroplated nickel film Young’s modulus Residual stress gradient Free beam mechanism
a b s t r a c t Metal multi-user MEMS processes (MetalMUMPs) offered by MEMSCAP provide a 20 m thick electroplated nickel film suitable for constructing micro RF tunable capacitors, RF inductors, relays, switches, etc. Currently the Young’s modulus and the residual stress gradient of the MetalMUMPs nickel film have not been characterized. In this paper the resonance method is used to characterize the Young’s modulus of the MetalMUMPs nickel film. The characterization results show that the nickel film has a Young’s modulus of 155–164 GPa with an average of 159 GPa. A stress gradient induced free beam mechanism is proposed in this paper to characterize the residual stress gradient in the MetalMUMPs nickel film. Characterization results show that the residual stress in the electroplated nickel film has a gradient across the film thickness of −5.49 MPa/m to −4.30 MPa/m with the average of −4.72 MPa/m. The residual stress change from the bottom surface to the top surface of the nickel film is −97.7 MPa. The Young’s modulus and residual stress gradient of the MetalMUMPs nickel film obtained in this paper provide MetalMUMPs users an important reference for designing, optimizing and analyzing suspended nickel structures. The stress gradient induced free beam mechanism proposed in this paper provides a method of characterizing negative residual stress gradient in thin films without using trenches or through-wafer holes. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Metal multi-user MEMS processes (MetalMUMPs) provide a 20 m thick electroplated nickel layer for constructing micro devices [1]. MetalMUMPs has been used to fabricate micro RF tunable capacitors [2], RF inductors [3,4], relays [5,6] and switches [7]. Two important properties of the MetalMUMPs nickel film, i.e., the Young’s modulus and the residual stress gradient through the film thickness have not been characterized thus far. Consequently, various values such as 180 GPa [8] or 202 GPa [2] are assumed for the Young’s modulus of the nickel film by MetalMUMPs users. The residual stress gradient with even a small magnitude could cause significant undesired deformations of suspended MetalMUMPs nickel structures due to the high nickel film thickness and the large lateral dimension (∼1 mm) of MetalMUMPs nickel devices [2,5,6]. It has been reported that the residual stress gradient in the nickel film caused undesired deformation of the moving electrode of a MetalMUMPs tunable capacitor [2]. However the undesired defor-
∗ Corresponding author. E-mail addresses: [email protected] (S. He), [email protected] (J.S. Chang), [email protected] (L. Li), [email protected] (H. Ho). 1 Member IEEE. 0924-4247/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2009.06.014
mation and its effects on the performance of the tunable capacitor cannot be quantified due to the lack of the data of the residual stress gradient in the nickel film. In this paper, the Young’s modulus and the residual stress gradient of the MetalMUMPs nickel film are characterized. The paper is organized as follows. Section 1 is the introduction. The Young’s modulus of the nickel film is characterized in Section 2. The residual stress gradient of the nickel film is characterized in Section 3. Section 4 summarizes the conclusions. 2. Young’s modulus of MetalMUMPs nickel film 2.1. Preliminaries Characterizations of the Young’s modulus of electroplated nickel films have been reported [9–12], which have shown that the Young’s modulus of electroplated nickel films is heavily dependent on parameters of the electroplating process such as the temperature and current density. In MetalMUMPs, the electroplating process parameters (temperature of 30 ◦ C, current density of 20 mA/cm2 and pH level of 4) and the thickness of the electroplated nickel film are different from those characterized in the literatures [9–12]. Thus an accurate value of the Young’s modulus of the MetalMUMPs nickel film can only be obtained by characterizing the nickel films fabricated using the MetalMUMPs process, which has not been done
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Fig. 1. Nickel cantilever beams.
thus far. Two classes of methods are commonly used for characterizing the Young’s modulus of micro fabricated thin films. One is to extract the Young’s modulus based on the strain vs. stress behavior of the thin film or the displacement vs. load relation of micro structures (e.g., cantilever beams) made of the thin film under investigation [11,13–19]. The other class of methods extract the Young’s modulus based on the measured resonant frequency of a micro structure made of the thin film [10,11,20–24]. The resonance method is non-destructive and is chosen in this paper to characterize the Young’s modulus of the MetalMUMPs nickel film. 2.2. Prototypes and experimental measurements Nickel cantilever beams were fabricated using the MetalMUMPs process as shown in Fig. 1. Three MetalMUMPs loose dies (Loose die 1, Loose die 2 and Loose die 3) with 7 cantilever beams on each loose die were measured to characterize the Young’s modulus of the nickel film. All beams have the same width of 100 m. On each loose die, the beam length varies from 1000 m (Beam 1) to 700 m (Beam 7) with a step of −50 m. Each beam is composed of three layers [1], i.e., plating copper base (0.55 m), electroplated nickel (20 m) and top gold (0.5 m), as shown in Fig. 1(b). The thickness of each layer is the nominal value [1]. The Young’s modulus of the MetalMUMPs nickel film is characterized through the following steps: (1) measuring the beam thickness with the results used to build beam models for simulations; (2) measuring the beams’ first mode resonant frequencies; and (3) extracting the Young’s modulus of the nickel film. 2.2.1. Step (1) Beam thickness The thickness of each cantilever beam was measured using a 3D optical profiler (Zygo NewView 6300). The thickness was obtained by measuring the height difference from the top gold layer of the beam to the top silicon nitride layer on the substrate along the line B–B (Fig. 2) and then subtracting the gap (1.1 m), which is formed by the sacrificial oxide layer. Fig. 3 shows the thickness of all the nickel beams, which is obtained by subtracting the thickness of the copper and the gold layers from the total thickness of the beams. 2.2.2. Step (2) First mode resonant frequency Piezoelectric transducers were used to excite the cantilever beams to find their first mode resonant frequencies. The resonant frequencies were obtained by: (1) exciting the beam with the frequency scanned twice (the coarse and fine scans) and monitoring the oscillation magnitude of the beam tip under the 3D optical profiler; and (2) verification of the vibration mode. The frequency scanning step is 10 Hz for the fine scan. Fig. 4 shows the measured resonant frequencies of all 21 beams. The vibration mode is verified by measuring the deflection of the beam when it oscillates, which is obtained by subtracting the beam’s surface profile measured when it is at rest from the beam’s surface profile measured when it oscillates. Fig. 5 shows the deflection of one example nickel beam when it oscillates.
Fig. 2. SEM image of the cantilever beam.
2.2.3. Step (3) Extraction of the Young’s modulus The analytical equation relating the resonant frequency of a thin film cantilever beam to the Young’s modulus of the thin film material is available and has been used to extract the Young’s modulus of thin film materials [11,20,22,24]. Numerical simulations have also been used to extract the Young’s modulus of thin film materials based on the measured resonant frequencies of cantilevers beams [10,25,26]. In this paper numerical simulations are performed to extract the Young’s modulus of the MetalMUMPs nickel film because the analytical equation cannot account for the effects of the non-ideal support (Fig. 6(a)) of the MetalMUMPs nickel beams. As shown in Fig. 6, the non-ideal support provides a more flexible boundary condition than the ideal support, which is assumed by the analytical equation. The non-ideal support is formed due to the fabrication steps used in MetalMUMPs [1]. The
Fig. 3. Thickness of the nickel film of each beam.
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Fig. 7. Beam model for simulations. Fig. 4. Measured first mode resonant frequencies of all beams.
and Poisson ratios (copper: 0.36, gold: 0.35 and nickel: 0.3) [8]. The beam is supported by a pad, whose dimensions are shown in Fig. 7. The depression area (Figs. 6(a) and 7) of the bottom surface of the pad is fixed. Each beam is simulated by varying the Young’s modulus of the nickel film until the simulation result of the first mode resonant frequency matches the measured result (as shown in Fig. 4) with an accuracy of ±10 Hz. The extracted Young’s modulus of the MetalMUMPs nickel film is shown in Fig. 8, which indicates that the Young’s modulus of the MetalMUMPs nickel film is 155–164 GPa with an average of 159 GPa. The extracted modulus is lower than the values currently assumed by MetalMUMPs users, e.g., 180 GPa [8] or 202 GPa [2]. The Young’s modulus of the nickel film obtained in this paper agrees with the results obtained in literatures. The nickel film obtained in a LIGA process was characterized to be 163 ± 14 GPa through tensile tests [27]. The nickel film’s Young’s modulus was found to be 148–159 GPa using AFM [28]. 2.3. Accuracy analysis
Fig. 5. Profiles of the beam when it oscillates at its first mode resonant frequency.
software CoventorWareTM [8] was used for the simulations. The simulation model is shown in Fig. 7 and includes the 0.55 m copper layer, the nickel layer and the 0.5 m gold layer. The nominal length and width and measured thickness are used to build the model for each beam. The following properties are used for the simulations, e.g., Young’s modulus (copper: 128 GPa and gold: 57 GPa)
Fig. 6. Non-ideal support of the MetalMUMPs nickel cantilever beam.
Finite air damping and squeeze film damping could affect the accuracy of the Young’s modulus of thin films characterized using the resonance method [22]. The quality factor of the beams measured in this paper is high and thus the finite air damping has an insignificant effect on the extracted modulus of the nickel film according to the calculation in [22]. The squeeze film damping,
Fig. 8. Extracted Young’s modulus of MetalMUMPs nickel film.
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which increases the resonant frequency of the beam due to the additional air-spring effect [22], leads to a higher Young’s modulus extracted using the resonance method. According to the analysis in [22], the squeeze film damping may not have significant effects on the Young’s modulus of the MetalMUMPs nickel film extracted in this paper due to the following reasons: (1) among all tested MetalMUMPs nickel beams, the smallest gap between the beam and the underneath substrate (the trench bottom) is greater than that in [22], which occurs at the tip of the longest beam (Beam 1 with a length of 1000 m); and (2) the highest first mode resonant frequency of the beams is lower than that in [22] with the measurements conducted at standard pressure and temperature. Even though the squeeze film damping does not play a significantly role, its effect on the extracted Young’s modulus of the nickel film is reflected as shown in Fig. 8, where the Young’s modulus extracted from beams longer than 800 m increases with the beam length. This is because the longer beams have a smaller gap between the beam tip and the trench bottom due to the negative residual stress gradient in the nickel film (see Section 3), which bends the beams downward. A smaller gap results in a stronger squeeze film damping effect, which increases the resonant frequency of the beam and then increases the extracted Young’s modulus of the nickel film. Another possible factor which may affect the extracted Young’s modulus is the geometric discrepancy between the actual cantilever beams and the beam models used for simulations. The cantilever beams are subject to the negative residual stress gradient (see Section 3) and thus the free tip of each beam bends downwards, while straight beams are assumed when building the beam models for simulations. However, the effect of this geometrical discrepancy should not be significant due to the small stress gradient induced deformation of the beams. Anticlastic effect is another possible factor affecting the extracted modulus [29]. However beams used in this paper have large length/width ratios, e.g., length of 700–1000 m, width of 100 m and thickness of 20 m (nominal value) and thus the anticlastic effect should not be significant. 3. Residual stress gradient of MetalMUMPs electroplated nickel film 3.1. Preliminaries The residual stress exists in microfabricated thin films [30], which can be approximated by superimposing a mean residual stress and a residual stress gradient [31]. The consequence of the residual mean stress in a thin film is to elongate (compressive stress) or shrink (tensile stress) the film along the lateral directions after the film is released. The consequence of the residual stress gradient through the film thickness is to bend a thin film structure, such as a cantilever, upward (positive stress gradient) or downward (negative stress gradient). The knowledge of both the residual mean stress and stress gradient in the thin film is important in order to fabricate high quality suspended thin film micro devices. The residual mean stress in the MetalMUMPs nickel film has been characterized [1]. However, there is no data of the residual stress gradient currently available. Consequently it is difficult to predict the performance and then optimize MetalMUMPs devices such as RF tunable capacitors and switches, which require flat moving electrode plates. In this section, the residual stress gradient of the MetalMUMPs electroplated nickel film is characterized. The most common technique of characterizing the residual stress gradient in thin films is to measure the deformation of a cantilever beam made of the thin film material under investigation [31–34]. It is convenient to use cantilever beams to extract the residual stress gradient if the residual stress gradient is positive [22,34–36]. However if the stress
gradient is negative, trenches or through-wafer holes underneath the beams are needed to accommodate the beams’ bending-down deflections [12,37]. Opening trenches or throughwafer holes is either impossible for some microfabrication processes or would significantly increase the process complexity. 3.2. Stress gradient induced free beam mechanism In this paper, a stress gradient induced free beam mechanism is proposed for characterizing negative residual stress gradient in thin films. The free beam mechanism consists of a bridge beam, a connecting beam and a free beam as shown in Fig. 9(a). The bridge beam is connected to two anchoring pads through two narrow support beams. The free beam is connected to the middle of the bridge beam through the connecting beam. Due to the negative residual stress gradient in the thin film, bending moments are induced in both the bridge beam and the free beam, which bends the bridge beam and the free beam into a convex shape after being released (Fig. 9(b)). The two ends of the free beam bend downwards relative to the middle of the free beam. Since the free beam is connected to the middle of the convexed bridge beam, it is raised by the bridge beam. Thus the two ends of the free beam can be lifted to be above the substrate if the bridge beam is long enough and therefore the free beam is raised high enough. The connecting beam should be much shorter than the bridge beam to ensure it will not bend the free beam down. The free beam mechanism could be used in two scenarios. (1) Trenches are unavailable. When trenches are unavailable, the free beam mechanism can be used to obtain a free beam, which is deformed by the negative stress gradient but is lifted above the substrate by the bridge beam. Thus the residual stress in the free beam is completely relieved and the residual stress gradient can be extracted by measuring the curvature of the deformed free beam. (2) Trenches are available. When trenches are available, the free beam mechanism can still be used to improve the accuracy of the calibration of the negative residual stress gradient in thin films. This is explained as follows. When using a beam (cantilever or free beam) to calibrate the negative residual stress gradient, the longer the beam is, the more accurate the extracted residual stress gradient will be. This is because a longer beam renders a more accurate calculation of the curvature of the deformed beam based on the measured beam surface profile using circle fitting techniques [38,39]. Since the residual stress gradient is extracted from the beam curvature, a more accurate beam curvature means a more accurate characterization of the residual stress gradient. However, a longer beam, which is under negative residual stress gradient, leads to more bending-downward displacement. Consequently, a deeper trench is needed to accommodate the bending-downward displacement. But the depth of the trench in an established process is normally fixed and limited. Then the amount of the bending-downward displacement, which can be accommodated by the trench, is fixed and limited. As a result, the beam used for calibrating the stress gradient can only have a limited length, which leads to a limited accuracy of the extracted residual stress gradient. If the free beam mechanism can be used along with the available trenches, the total amount of the stress gradient induced bending-down displacement, which can be accommodated, becomes the sum of the trench depth and the height, by which the free beam is raised by the bridge beam (see Fig. 9). Because more bendingdownward displacement can be accommodated through using both the trench and the free beam mechanism, a longer beam can be used for the calibration of the stress gradient. Therefore, a more accurate calibration of the negative stress gradient can be achieved.
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Fig. 9. Residual stress induced free beam mechanism.
Fig. 10. SEM images of the MetalMUMPs free beam mechanism.
3.3. Characterization of the residual stress gradient in MetalMUMPs nickel film 3.3.1. Prototype of the MetalMUMPs stress gradient induced free beam mechanism From previous MetalMUMPs prototypes, it has been known that the residual stress in the nickel film has a negative gradient. Thus the stress gradient induced free beam mechanism, along with trenches available in the MetalMUMPs process, is used to characterize the negative residual stress gradient in the nickel film. Fig. 10 shows one prototype of the free beam mechanism. Compared with the design in Fig. 9, finger structures are added to the bridge beam for observing the deflection of the bridge beam without significantly affecting the bending stiffness of the bridge beam. A wide bridge beam (200 m) and a wide free beam (100 m) are used for convenience in measuring their surface profiles using the 3D optical profiler. In addition, a wide bridge beam is needed to obtain a large residual stress gradient induced bending moment to pull its two ends against the support beams to form a high convex shape, such that the free beam can be lifted as high as possible. The trenches underneath the bridge beam and the connecting beam are for facilitating the release of the beams. The trench underneath the free beam is for accommodating more bending-down deflection of the free beam. Dimensions of the MetalMUMPs free beam mechanism are listed in Table 1. Fig. 10(a) shows the con-
Table 1 Dimensions of the MetalMUMPs stress gradient induced free beam mechanism.
Length (m) Width (m)
Bridge beam
Connecting beam
Free beam
Support beam
Finger structure
5240 200
1000 200
3970 100
600 8
550 30
vexed bridge beam and the convexed free beam. Fig. 10(b) and (c) show that the two ends of the free beam are free (not touching the trench bottom) because the free beam is lifted by the bridge beam. The residual stress gradient in the nickel film is characterized through the following steps: (1) measuring the surface profiles of the free beams; (2) calculation of the free beam curvatures based on measured beam surface profiles using circle fitting techniques; and (3) extraction of the residual stress gradient from the calculated curvatures. 3.3.2. Measurement of free beam surface profile Six prototypes (Prototype 1 to Prototype 6) of the free beam mechanism were measured. Measurement results show that the bridge beam and the free beam are both in a convex shape after being released. For example, the bridge beam and the free beam of Prototype 1 have convex heights of 21 m (excluding the contribution of the two support beams) and 40 m respectively, which confirms a negative residual stress gradient in the nickel film. In Prototype 1 the middle of the bridge beam is raised by 24.7 m (including the contribution of the two support beams) from its unreleased position and the free beam is lifted by 27.8 m from its unreleased position. The difference between these two raised heights is attributed to the deflection of the connecting beam and the out-of-plane rotation of the whole free beam mechanism about the two support beams. The out-of-plane rotation of the whole free beam mechanism could be caused by the inertial moment generated during the drying process, which induces plastic deformation in the two support beams. The measurement results also verify that the two ends of the free beam do not touch the trench bottom. For example, in Prototype 1 the two ends of the free beam are about 10 m above the trench bottom even though the free beam bends downward by 40 m
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Fig. 11. MetalMUMPs nickel beam without using the free beam mechanism.
Fig. 13. 3-layer composite free beam.
failed prototypes the bridge beams were not completely released and then the free beams were not raised. Fig. 12. Circle fitting of the surface profile.
from its middle to its two ends while the trench is only 22.5 m deep (measured depth). Using the free beam mechanism proposed in this paper, a long (unreleased length of 3970 m) free beam (free ends and free of residual stress after being released) is achieved, which can be used for extracting the residual stress gradient in the MetalMUMPs nickel film. Such a long free beam would be impossible without using the free beam mechanism. Due to its long length, the curvature of the free beam can be accurately calculated based on the measured beam surface profile, which leads to an accurate extraction of the residual stress gradient of the nickel film. Fig. 11 shows a beam of the same length (3970 m) and width (100 m) touching the trench bottom at its two ends because the free beam mechanism is not used. Even though the bridge beam of the free beam mechanism is much wider (200 m) than the nominal maximum width (100 m) of MetalMUMPS nickel beams (which could be completely released according to MetalMUMPs process [1]), almost half of the prototypes were completely released. This should be attributed to the trench etching process and residual stress gradient induced bending moment which helped releasing the wide bridge beams. In the
3.3.3. Calculation of curvature The curvatures of the convexed free beams can be calculated from their measured surface profiles. Before calculating the curvature, the noise in the measured surface profile data is filtered out. Various algorithms are available for fitting circles to discrete points [38–40]. In this paper the curvatures of the free beams are calculated using the Maple code for circle fitting developed in [41]. Fig. 12 shows the fitted arc of Prototype 1. The curvatures of all free beams are listed in Table 2. 3.3.4. Extracting residual stress gradient The MetalMUMPs free beam is a 3-layer composite beam as shown in Fig. 13 [1]. The bending moment in the beam is expressed as [30]: M=
E¯ Ni INi + E¯ Cu ICu + E¯ Au IAu
(1)
where M is the bending moment. INi , ICu , IAu are the moments of inertia of the nickel layer, the copper layer and the gold layer about the neutral axis, which is assumed to be located on the mid plane of the nickel layer. 1/ is the curvature. E¯ Ni , E¯ Cu , E¯ Au are the equivalent Young’s modulus of nickel, copper and gold layers respectively,
Table 2 Measured results of the prototypes of the free beam mechanism. Prototype
Thickness of nickel film (m)
Curvature of free beam (m−1 )
Stress gradient (MPa/m)
Stress change through thickness (MPa)
1 2 3 4 5 6
17.94 21.62 22.75 22.30 19.00 21.70
1/46316 1/55365 1/57321 1/57828 1/50292 1/53867
−5.49 −4.51 −4.33 −4.30 −5.03 −4.63
−98.53 −97.44 −98.57 −95.95 −95.50 −100.48
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Fig. 14. Residual stress gradient of the nickel film.
which can be calculated as follows [33,36,42,43]. E¯ =
E 1−
(2)
The 3-layer composite beam is asymmetrical because the copper layer and the gold layer have different Young’s modulus and thicknesses. The bending moment caused by the mean residual stress (100 MPa tensile [1]) in the nickel layer due to the asymmetrical structure of the composite beam is neglected. The residual stresses in both the gold and the copper layers are neglected due to their small thickness in comparison to the nickel layer. Thus the bending moment is only induced by the residual stress gradient in the nickel layer, i.e., M = · INi
(3)
Substituting Eq. (3) into Eq. (1) results in =
E¯ Ni INi + E¯ Cu ICu + E¯ Au IAu INi
(4)
Eq. (4) relates the residual stress gradient in the MetalMUMPs nickel film to the curvature of the free beam. Lateral dimensions of the free beam can be found in Table 1. The Young’s modulus of the nickel film is obtained in Section 2 of this paper, which is 159 GPa. Other parameters of the copper layer, the gold layer and the nickel film are from [8] as described in Section 2.2.3. The nickel film thick-
155
ness of the free beam mechanism is obtained by measuring the height from the top surface of the anchoring pad (Fig. 10) to the top surface of the nitride layer and then subtracting the thickness of the copper, gold, chromium (10 nm) and platinum (25 nm) layers. The measured results are listed in Table 2. Substituting the above parameters and the curvatures of the free beams (Table 2) into Eq. (4) results in the residual stress gradient of the MetalMUMPs nickel film as shown in Table 2 and depicted in Fig. 14. The characterized residual stress gradient is −5.49 MPa/m to −4.30 MPa/m with the average of −4.72 MPa/m. The total residual stress change across the nickel film thickness is also shown in Table 2 and depicted in Fig. 15, which has an average stress change of −97.7 MPa. The characterized stress gradient is verified using numerical simulations by applying the stress gradient characterized using Eq. (4) to the free beam structure and then obtaining its curvature. The simulated curvatures closely match the measured results. Fig. 14 shows that the magnitude of the residual stress gradient is inversely proportional to the nickel film thickness. This might be caused by some factors, which contribute to the bending moment in the beam but were not considered when extracting the residual stress gradient in the nickel film. Those factors include the mean residual stress in the nickel layer, which generates a bending moment due to the asymmetric structure of the beam, and the residual stresses in the gold and the copper layers, which could also generate a bending moment in the beam. The obtained residual stress gradient would have non-negligible error if the residual stresses in the copper and gold layers cause non-negligible bending moment because the above calculations assume they do not cause significant bending moment. 4. Conclusions In this paper the Young’s modulus of the MetalMUMPs nickel film is characterized to be 155–164 GPa with an average of 159 GPa. A stress gradient induced free beam mechanism is proposed, which can be used to characterize the negative residual stress gradient in thin films when trenches and through-wafer holes are not available. When trenches are available, the free beam mechanism can still be used to improve the accuracy of the characterization of the negative stress gradient in thin films by allowing a long free beam to be used. The characterized residual stress gradient of the MetalMUMPs nickel film is −5.49 MPa/m to −4.30 MPa/m with the average of −4.72 MPa/m. The Young’s modulus and residual stress gradient of the MetalMUMPs nickel film obtained in this paper provide MetalMUMPs users an important reference for designing, optimizing and analyzing suspended nickel structures.
References
Fig. 15. Change in residual stress across the nickel film.
[1] A. Cowen, R. Mahadevan, S. Johnson, B. Hardy, MetalMUMPs Design Handbook, Revision 2.0, MEMSCAP Inc., 2002. [2] M. Bakri-Kassem, R.R. Mansour, Two movable-plate nitride-loaded MEMS variable capacitor, IEEE Transaction on Microwave Theory and Techniques 52 (2004) 831–837. [3] L. Li, D. Uttamchandani, Monolithic RF MEMS inductor using silicon MEMS foundry process, Micro & Nano Letters 1 (2006) 5–8. [4] Imed Zine-El-Abidine, Michal Okoniewski, A tunable radio frequency MEMS inductor using MetalMUMPs, Journal of Micromechanics and Microengineering 17 (2007) 2280–2287. [5] L. Almeida, R. Ramadoss, R. Jackson, K. Ishikawa, Q. Yu, Study of the electrical contact resistance of multi-contact MEMS relays fabricated using the MetalMUMPs process, Journal of Micromechanics and Microengineering 16 (2006) 1189–1194. [6] A. Cao, P. Yuen, L. Lin, Microrelays with bidirectional electrothermal electromagnetic actuators and liquid metal wetted contacts, IEEE/ASME Journal of Microelectromechanical Systems 16 (2007) 700–708. [7] D. Girbau, L. Pradell, A. Lazaro, A. Nebot, Electrothermally actuated RF MEMS switches suspended on a low-resistivity substrate, IEEE/ASME Journal of Microelectromechanical Systems 16 (2007) 1061–1070. [8] CoventorWareTM , 2008, Coventor Inc.
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[9] E. Mazza, S. Abel, J. Dual, Experimental determination of mechanical properties of Ni-Fe microbars, Microsystem Technologies 2 (1996) 197–202. [10] H. Majjad, et al., Dynamic determination of Young’s modulus of electroplated nickel used in LIGA technique, Sensors and Actuators A: Physical 74 (1999) 148–151. [11] T. Fritz, M. Griepentrog, W. Mokwa, U. Schnakenberg, Determination of Young’s modulus of electroplated nickel, Electrochimica Acta (2003) 3029–3035. [12] J.K. Luo, A.J. Flewitt, S.M. Spearing, N.A. Fleck, W.I. Milne, Young’s modulus of electroplated Ni thin film for MEMS applications, Materials Letters 58 (2004) 2306–2309. [13] W.N. Sharpe Jr., B. Yuan, R.L. Edwards, A new technique for measuring the mechanical properties of thin films, IEEE/ASME Journal of Microelectromechanical Systems 6 (1997) 193–199. [14] T.P. Weihs, et al., Mechanical deflection of cantilever microbeams: a new technique for testing the mechanical properties of thin films, Journal of Materials Research 3 (1988) 931–942. [15] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments, Journal of Materials Research 7 (1992) 1564–1583. [16] R. Yokokawa, J. Paik, B. Dunn, N. Kitazawa, H. Kotera, C. Kim, Mechanical properties of aerogel-like thin films used for MEMS, Journal of Micromechanics and Microengineering 14 (2004) 681–686. [17] Z. Zhou, Y. Zhou, C. Yang, J. Chen, G. Ding, W. Ding, M. Wang, Y. Zhang, The evaluation of Young’s modulus and residual stress of nickel films by microbridge testings, Measurement Science and Technology 15 (2004) 2389–2394. [18] B. Comella, M. Scanlon, The determination of the elastic modulus of microcantilever beams using atomic force microscopy, Journal of Materials Science 35 (2000) 567–0572. [19] B.D. Jensen, M.P. de Boer, N.D. Masters, F. Bitsie, D.A. La Van, Interferometry of actuated microcantilevers to determine material properties and test structure nonidealities in MEMS, IEEE/ASME Journal of Microelectromechanical Systems 10 (2001) 336–346. [20] L. Kiesewetter, et al., Determination of Young’s moduli of micromechanical thin films using the resonance method, Sensors and Actuators A: Physical 35 (1992) 153–159. [21] J. Jeong, S. Chung, S. Lee, D. Kwon, Evaluation of elastic properties and temperature effects in Si thin films using an electrostatic microresonator, IEEE/ASME Journal of Microelectromechanical Systems 12 (2003) 524–530. [22] C.-W. Baek, Y.-K. Kim, Y. Ahn, Y.-H. Kim, Measurement of the mechanical properties of electroplated gold thin films using micromachined beam structures, Sensors and Actuators A: Physical 117 (2005) 17–27. [23] C. Yu, C. Hsu, W. Fang, Comments on determining the elastic modulus of a thin film using the micromachined free–free beam, Journal of Micromechanics and Microengineering 15 (2005) 351–357. [24] R. Wiser, M. Tabib-Azar, M. Mehregany, C. Zorman, Polycrystalline siliconcarbide surface-micromachined vertical resonators–Part II: Electrical testing and material property extraction, IEEE/ASME Journal of Microelectromechanical Systems 14 (2005) 579–589. [25] I. Voiculescu, M. Zaghloul, R. McGill, E. Houser, G. Fedder, Electrostatically actuated resonant microcantilever beam in CMOS technology for the detection of chemical weapons, IEEE Journal of Sensors 5 (2005) 641–647.
[26] G. McShane, M. Boutchich, A. Phani, D. Moore, T. Lu, Young’s modulus measurement of thin-film materials using micro-cantilevers, Journal of Micromechanics and Microengineering 16 (2006) 1926–1934. [27] H.S. Cho, K.J. Hemker, K. Lian, J. Goettert, G. Dirras, Measured mechanical properties of LIGA Ni structures, Sensors and Actuators A: Physical 103 (2003) 59–63. [28] S.H. Kim, J.G. Boyd, A new technique for measuring Young’s modulus of electroplated nickel using AFM, Measurement Science and Technology 17 (2006) 2343–2348. [29] J.H. He, J.K. Luo, H.R. Le, D.F. Moore, Mechanical characterization of biocompatible thin film materials by scanning along micro-machined cantilevers for micro-/nano-system, Materials Science and Engineering A 423 (2006) 134–142. [30] K-S. Chen, MEMS/NEMS Handbook Techniques and Applications, Chapter 9: Techniques in residual stress measurement for MEMS and their applications, pp.1252-1328, Springer: US, 2006. [31] W. Fang, A.J. Wickert, Determining mean and gradient residual stresses in thin films using micromachined cantilevers, Journal of Micromechanics and Microengineering 6 (1996) 301–309. [32] W.-H. Chu, M. Mehregany, A study of residual stress distribution through the thickness of p+ silicon films, IEEE Transactions on Electron Devices 40 (1993) 1245–1250. [33] F. Ericson, et al., High-sensitivity surface micromachined structures for internal stress and stress gradient evaluation, Journal of Micromechanics and Microengineering 7 (1997) 30–36. [34] A.B. Yu, et al., Characterization and optimization of dry releasing for the fabrication of RF MEMS capacitive switches, Journal of Micromechanics and Microengineering 17 (2007) 2024–2030. [35] H. Huang, K. Winchester, Y. Liu, X.Z. Hu, C.A. Musca, J.M. Dell, L. Faraone, Determination of mechanical properties of PECVD silicon nitride thin films for tunable MEMS Fabry–Pérot optical filters, Journal of Micromechanics and Microengineering 15 (2005) 608–614. [36] Y. Zhang, Y. Zhao, An effective method of determining the residual stress gradients in a micro-cantilever, Microsystem Technologies 12 (2006) 357–364. [37] S.S. Yang, E.H. Yang, The quantitative determination of the residual stress profile in oxidized p+ silicon films, Sensors and Actuators A: Physical 54 (1996) 684–689. [38] G. Vosselman, R.M. Haralick, Performance analysis of line and circle fitting in digital images, in: Proceedings of the Workshop on Performance Characteristics of Vision Algorithms, Cambridge, 1996. [39] C. Rusu, M. Tico, P. Kuosmanen, E.J. Delp, Classical geometrical approach to circle fitting – review and new developments, Journal of Electronic Imaging 12 (2003) 179–193. [40] N. Chernov, C. Lesort, Least squares fitting of circles, Journal of Mathematical Imaging and Vision 23 (2005) 239–252. [41] T. Schramm, Fitting a circle to data using a linear model, http://www.maplesoft. com/Applications/app center view.aspx?AID=372, 2001. [42] W. Fang, Determination of the elastic modulus of thin film materials using self-deformed micromachined cantilevers, Journal of Micromechanics and Microengineering 9 (1999) 230–235. [43] P. Krulevitch, G.C. Johnson, Curvature of a cantilever beam subject to an equibiaxial bending moment, Materials Research Society Symposium Proceedings 518 (1998) 67–72.
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Characterization of Young’s modulus and residual stress gradient of MetalMUMPs electroplated nickel film Siyuan He a,∗,1 , John S. Chang a , Lihua Li b , Hsu Ho c a b c
Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, Ontario, Canada M5B 2K3 MEMSCAP, Research Triangle Park, NC, USA Microelectronics Integration, CMC Microsystems, Kingston, Ontario, Canada K7L 3N6
a r t i c l e
i n f o
Article history: Received 3 December 2008 Received in revised form 18 February 2009 Accepted 18 June 2009 Available online 16 July 2009 Keywords: Electroplated nickel film Young’s modulus Residual stress gradient Free beam mechanism
a b s t r a c t Metal multi-user MEMS processes (MetalMUMPs) offered by MEMSCAP provide a 20 m thick electroplated nickel film suitable for constructing micro RF tunable capacitors, RF inductors, relays, switches, etc. Currently the Young’s modulus and the residual stress gradient of the MetalMUMPs nickel film have not been characterized. In this paper the resonance method is used to characterize the Young’s modulus of the MetalMUMPs nickel film. The characterization results show that the nickel film has a Young’s modulus of 155–164 GPa with an average of 159 GPa. A stress gradient induced free beam mechanism is proposed in this paper to characterize the residual stress gradient in the MetalMUMPs nickel film. Characterization results show that the residual stress in the electroplated nickel film has a gradient across the film thickness of −5.49 MPa/m to −4.30 MPa/m with the average of −4.72 MPa/m. The residual stress change from the bottom surface to the top surface of the nickel film is −97.7 MPa. The Young’s modulus and residual stress gradient of the MetalMUMPs nickel film obtained in this paper provide MetalMUMPs users an important reference for designing, optimizing and analyzing suspended nickel structures. The stress gradient induced free beam mechanism proposed in this paper provides a method of characterizing negative residual stress gradient in thin films without using trenches or through-wafer holes. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Metal multi-user MEMS processes (MetalMUMPs) provide a 20 m thick electroplated nickel layer for constructing micro devices [1]. MetalMUMPs has been used to fabricate micro RF tunable capacitors [2], RF inductors [3,4], relays [5,6] and switches [7]. Two important properties of the MetalMUMPs nickel film, i.e., the Young’s modulus and the residual stress gradient through the film thickness have not been characterized thus far. Consequently, various values such as 180 GPa [8] or 202 GPa [2] are assumed for the Young’s modulus of the nickel film by MetalMUMPs users. The residual stress gradient with even a small magnitude could cause significant undesired deformations of suspended MetalMUMPs nickel structures due to the high nickel film thickness and the large lateral dimension (∼1 mm) of MetalMUMPs nickel devices [2,5,6]. It has been reported that the residual stress gradient in the nickel film caused undesired deformation of the moving electrode of a MetalMUMPs tunable capacitor [2]. However the undesired defor-
∗ Corresponding author. E-mail addresses: [email protected] (S. He), [email protected] (J.S. Chang), [email protected] (L. Li), [email protected] (H. Ho). 1 Member IEEE. 0924-4247/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2009.06.014
mation and its effects on the performance of the tunable capacitor cannot be quantified due to the lack of the data of the residual stress gradient in the nickel film. In this paper, the Young’s modulus and the residual stress gradient of the MetalMUMPs nickel film are characterized. The paper is organized as follows. Section 1 is the introduction. The Young’s modulus of the nickel film is characterized in Section 2. The residual stress gradient of the nickel film is characterized in Section 3. Section 4 summarizes the conclusions. 2. Young’s modulus of MetalMUMPs nickel film 2.1. Preliminaries Characterizations of the Young’s modulus of electroplated nickel films have been reported [9–12], which have shown that the Young’s modulus of electroplated nickel films is heavily dependent on parameters of the electroplating process such as the temperature and current density. In MetalMUMPs, the electroplating process parameters (temperature of 30 ◦ C, current density of 20 mA/cm2 and pH level of 4) and the thickness of the electroplated nickel film are different from those characterized in the literatures [9–12]. Thus an accurate value of the Young’s modulus of the MetalMUMPs nickel film can only be obtained by characterizing the nickel films fabricated using the MetalMUMPs process, which has not been done
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Fig. 1. Nickel cantilever beams.
thus far. Two classes of methods are commonly used for characterizing the Young’s modulus of micro fabricated thin films. One is to extract the Young’s modulus based on the strain vs. stress behavior of the thin film or the displacement vs. load relation of micro structures (e.g., cantilever beams) made of the thin film under investigation [11,13–19]. The other class of methods extract the Young’s modulus based on the measured resonant frequency of a micro structure made of the thin film [10,11,20–24]. The resonance method is non-destructive and is chosen in this paper to characterize the Young’s modulus of the MetalMUMPs nickel film. 2.2. Prototypes and experimental measurements Nickel cantilever beams were fabricated using the MetalMUMPs process as shown in Fig. 1. Three MetalMUMPs loose dies (Loose die 1, Loose die 2 and Loose die 3) with 7 cantilever beams on each loose die were measured to characterize the Young’s modulus of the nickel film. All beams have the same width of 100 m. On each loose die, the beam length varies from 1000 m (Beam 1) to 700 m (Beam 7) with a step of −50 m. Each beam is composed of three layers [1], i.e., plating copper base (0.55 m), electroplated nickel (20 m) and top gold (0.5 m), as shown in Fig. 1(b). The thickness of each layer is the nominal value [1]. The Young’s modulus of the MetalMUMPs nickel film is characterized through the following steps: (1) measuring the beam thickness with the results used to build beam models for simulations; (2) measuring the beams’ first mode resonant frequencies; and (3) extracting the Young’s modulus of the nickel film. 2.2.1. Step (1) Beam thickness The thickness of each cantilever beam was measured using a 3D optical profiler (Zygo NewView 6300). The thickness was obtained by measuring the height difference from the top gold layer of the beam to the top silicon nitride layer on the substrate along the line B–B (Fig. 2) and then subtracting the gap (1.1 m), which is formed by the sacrificial oxide layer. Fig. 3 shows the thickness of all the nickel beams, which is obtained by subtracting the thickness of the copper and the gold layers from the total thickness of the beams. 2.2.2. Step (2) First mode resonant frequency Piezoelectric transducers were used to excite the cantilever beams to find their first mode resonant frequencies. The resonant frequencies were obtained by: (1) exciting the beam with the frequency scanned twice (the coarse and fine scans) and monitoring the oscillation magnitude of the beam tip under the 3D optical profiler; and (2) verification of the vibration mode. The frequency scanning step is 10 Hz for the fine scan. Fig. 4 shows the measured resonant frequencies of all 21 beams. The vibration mode is verified by measuring the deflection of the beam when it oscillates, which is obtained by subtracting the beam’s surface profile measured when it is at rest from the beam’s surface profile measured when it oscillates. Fig. 5 shows the deflection of one example nickel beam when it oscillates.
Fig. 2. SEM image of the cantilever beam.
2.2.3. Step (3) Extraction of the Young’s modulus The analytical equation relating the resonant frequency of a thin film cantilever beam to the Young’s modulus of the thin film material is available and has been used to extract the Young’s modulus of thin film materials [11,20,22,24]. Numerical simulations have also been used to extract the Young’s modulus of thin film materials based on the measured resonant frequencies of cantilevers beams [10,25,26]. In this paper numerical simulations are performed to extract the Young’s modulus of the MetalMUMPs nickel film because the analytical equation cannot account for the effects of the non-ideal support (Fig. 6(a)) of the MetalMUMPs nickel beams. As shown in Fig. 6, the non-ideal support provides a more flexible boundary condition than the ideal support, which is assumed by the analytical equation. The non-ideal support is formed due to the fabrication steps used in MetalMUMPs [1]. The
Fig. 3. Thickness of the nickel film of each beam.
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Fig. 7. Beam model for simulations. Fig. 4. Measured first mode resonant frequencies of all beams.
and Poisson ratios (copper: 0.36, gold: 0.35 and nickel: 0.3) [8]. The beam is supported by a pad, whose dimensions are shown in Fig. 7. The depression area (Figs. 6(a) and 7) of the bottom surface of the pad is fixed. Each beam is simulated by varying the Young’s modulus of the nickel film until the simulation result of the first mode resonant frequency matches the measured result (as shown in Fig. 4) with an accuracy of ±10 Hz. The extracted Young’s modulus of the MetalMUMPs nickel film is shown in Fig. 8, which indicates that the Young’s modulus of the MetalMUMPs nickel film is 155–164 GPa with an average of 159 GPa. The extracted modulus is lower than the values currently assumed by MetalMUMPs users, e.g., 180 GPa [8] or 202 GPa [2]. The Young’s modulus of the nickel film obtained in this paper agrees with the results obtained in literatures. The nickel film obtained in a LIGA process was characterized to be 163 ± 14 GPa through tensile tests [27]. The nickel film’s Young’s modulus was found to be 148–159 GPa using AFM [28]. 2.3. Accuracy analysis
Fig. 5. Profiles of the beam when it oscillates at its first mode resonant frequency.
software CoventorWareTM [8] was used for the simulations. The simulation model is shown in Fig. 7 and includes the 0.55 m copper layer, the nickel layer and the 0.5 m gold layer. The nominal length and width and measured thickness are used to build the model for each beam. The following properties are used for the simulations, e.g., Young’s modulus (copper: 128 GPa and gold: 57 GPa)
Fig. 6. Non-ideal support of the MetalMUMPs nickel cantilever beam.
Finite air damping and squeeze film damping could affect the accuracy of the Young’s modulus of thin films characterized using the resonance method [22]. The quality factor of the beams measured in this paper is high and thus the finite air damping has an insignificant effect on the extracted modulus of the nickel film according to the calculation in [22]. The squeeze film damping,
Fig. 8. Extracted Young’s modulus of MetalMUMPs nickel film.
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which increases the resonant frequency of the beam due to the additional air-spring effect [22], leads to a higher Young’s modulus extracted using the resonance method. According to the analysis in [22], the squeeze film damping may not have significant effects on the Young’s modulus of the MetalMUMPs nickel film extracted in this paper due to the following reasons: (1) among all tested MetalMUMPs nickel beams, the smallest gap between the beam and the underneath substrate (the trench bottom) is greater than that in [22], which occurs at the tip of the longest beam (Beam 1 with a length of 1000 m); and (2) the highest first mode resonant frequency of the beams is lower than that in [22] with the measurements conducted at standard pressure and temperature. Even though the squeeze film damping does not play a significantly role, its effect on the extracted Young’s modulus of the nickel film is reflected as shown in Fig. 8, where the Young’s modulus extracted from beams longer than 800 m increases with the beam length. This is because the longer beams have a smaller gap between the beam tip and the trench bottom due to the negative residual stress gradient in the nickel film (see Section 3), which bends the beams downward. A smaller gap results in a stronger squeeze film damping effect, which increases the resonant frequency of the beam and then increases the extracted Young’s modulus of the nickel film. Another possible factor which may affect the extracted Young’s modulus is the geometric discrepancy between the actual cantilever beams and the beam models used for simulations. The cantilever beams are subject to the negative residual stress gradient (see Section 3) and thus the free tip of each beam bends downwards, while straight beams are assumed when building the beam models for simulations. However, the effect of this geometrical discrepancy should not be significant due to the small stress gradient induced deformation of the beams. Anticlastic effect is another possible factor affecting the extracted modulus [29]. However beams used in this paper have large length/width ratios, e.g., length of 700–1000 m, width of 100 m and thickness of 20 m (nominal value) and thus the anticlastic effect should not be significant. 3. Residual stress gradient of MetalMUMPs electroplated nickel film 3.1. Preliminaries The residual stress exists in microfabricated thin films [30], which can be approximated by superimposing a mean residual stress and a residual stress gradient [31]. The consequence of the residual mean stress in a thin film is to elongate (compressive stress) or shrink (tensile stress) the film along the lateral directions after the film is released. The consequence of the residual stress gradient through the film thickness is to bend a thin film structure, such as a cantilever, upward (positive stress gradient) or downward (negative stress gradient). The knowledge of both the residual mean stress and stress gradient in the thin film is important in order to fabricate high quality suspended thin film micro devices. The residual mean stress in the MetalMUMPs nickel film has been characterized [1]. However, there is no data of the residual stress gradient currently available. Consequently it is difficult to predict the performance and then optimize MetalMUMPs devices such as RF tunable capacitors and switches, which require flat moving electrode plates. In this section, the residual stress gradient of the MetalMUMPs electroplated nickel film is characterized. The most common technique of characterizing the residual stress gradient in thin films is to measure the deformation of a cantilever beam made of the thin film material under investigation [31–34]. It is convenient to use cantilever beams to extract the residual stress gradient if the residual stress gradient is positive [22,34–36]. However if the stress
gradient is negative, trenches or through-wafer holes underneath the beams are needed to accommodate the beams’ bending-down deflections [12,37]. Opening trenches or throughwafer holes is either impossible for some microfabrication processes or would significantly increase the process complexity. 3.2. Stress gradient induced free beam mechanism In this paper, a stress gradient induced free beam mechanism is proposed for characterizing negative residual stress gradient in thin films. The free beam mechanism consists of a bridge beam, a connecting beam and a free beam as shown in Fig. 9(a). The bridge beam is connected to two anchoring pads through two narrow support beams. The free beam is connected to the middle of the bridge beam through the connecting beam. Due to the negative residual stress gradient in the thin film, bending moments are induced in both the bridge beam and the free beam, which bends the bridge beam and the free beam into a convex shape after being released (Fig. 9(b)). The two ends of the free beam bend downwards relative to the middle of the free beam. Since the free beam is connected to the middle of the convexed bridge beam, it is raised by the bridge beam. Thus the two ends of the free beam can be lifted to be above the substrate if the bridge beam is long enough and therefore the free beam is raised high enough. The connecting beam should be much shorter than the bridge beam to ensure it will not bend the free beam down. The free beam mechanism could be used in two scenarios. (1) Trenches are unavailable. When trenches are unavailable, the free beam mechanism can be used to obtain a free beam, which is deformed by the negative stress gradient but is lifted above the substrate by the bridge beam. Thus the residual stress in the free beam is completely relieved and the residual stress gradient can be extracted by measuring the curvature of the deformed free beam. (2) Trenches are available. When trenches are available, the free beam mechanism can still be used to improve the accuracy of the calibration of the negative residual stress gradient in thin films. This is explained as follows. When using a beam (cantilever or free beam) to calibrate the negative residual stress gradient, the longer the beam is, the more accurate the extracted residual stress gradient will be. This is because a longer beam renders a more accurate calculation of the curvature of the deformed beam based on the measured beam surface profile using circle fitting techniques [38,39]. Since the residual stress gradient is extracted from the beam curvature, a more accurate beam curvature means a more accurate characterization of the residual stress gradient. However, a longer beam, which is under negative residual stress gradient, leads to more bending-downward displacement. Consequently, a deeper trench is needed to accommodate the bending-downward displacement. But the depth of the trench in an established process is normally fixed and limited. Then the amount of the bending-downward displacement, which can be accommodated by the trench, is fixed and limited. As a result, the beam used for calibrating the stress gradient can only have a limited length, which leads to a limited accuracy of the extracted residual stress gradient. If the free beam mechanism can be used along with the available trenches, the total amount of the stress gradient induced bending-down displacement, which can be accommodated, becomes the sum of the trench depth and the height, by which the free beam is raised by the bridge beam (see Fig. 9). Because more bendingdownward displacement can be accommodated through using both the trench and the free beam mechanism, a longer beam can be used for the calibration of the stress gradient. Therefore, a more accurate calibration of the negative stress gradient can be achieved.
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Fig. 9. Residual stress induced free beam mechanism.
Fig. 10. SEM images of the MetalMUMPs free beam mechanism.
3.3. Characterization of the residual stress gradient in MetalMUMPs nickel film 3.3.1. Prototype of the MetalMUMPs stress gradient induced free beam mechanism From previous MetalMUMPs prototypes, it has been known that the residual stress in the nickel film has a negative gradient. Thus the stress gradient induced free beam mechanism, along with trenches available in the MetalMUMPs process, is used to characterize the negative residual stress gradient in the nickel film. Fig. 10 shows one prototype of the free beam mechanism. Compared with the design in Fig. 9, finger structures are added to the bridge beam for observing the deflection of the bridge beam without significantly affecting the bending stiffness of the bridge beam. A wide bridge beam (200 m) and a wide free beam (100 m) are used for convenience in measuring their surface profiles using the 3D optical profiler. In addition, a wide bridge beam is needed to obtain a large residual stress gradient induced bending moment to pull its two ends against the support beams to form a high convex shape, such that the free beam can be lifted as high as possible. The trenches underneath the bridge beam and the connecting beam are for facilitating the release of the beams. The trench underneath the free beam is for accommodating more bending-down deflection of the free beam. Dimensions of the MetalMUMPs free beam mechanism are listed in Table 1. Fig. 10(a) shows the con-
Table 1 Dimensions of the MetalMUMPs stress gradient induced free beam mechanism.
Length (m) Width (m)
Bridge beam
Connecting beam
Free beam
Support beam
Finger structure
5240 200
1000 200
3970 100
600 8
550 30
vexed bridge beam and the convexed free beam. Fig. 10(b) and (c) show that the two ends of the free beam are free (not touching the trench bottom) because the free beam is lifted by the bridge beam. The residual stress gradient in the nickel film is characterized through the following steps: (1) measuring the surface profiles of the free beams; (2) calculation of the free beam curvatures based on measured beam surface profiles using circle fitting techniques; and (3) extraction of the residual stress gradient from the calculated curvatures. 3.3.2. Measurement of free beam surface profile Six prototypes (Prototype 1 to Prototype 6) of the free beam mechanism were measured. Measurement results show that the bridge beam and the free beam are both in a convex shape after being released. For example, the bridge beam and the free beam of Prototype 1 have convex heights of 21 m (excluding the contribution of the two support beams) and 40 m respectively, which confirms a negative residual stress gradient in the nickel film. In Prototype 1 the middle of the bridge beam is raised by 24.7 m (including the contribution of the two support beams) from its unreleased position and the free beam is lifted by 27.8 m from its unreleased position. The difference between these two raised heights is attributed to the deflection of the connecting beam and the out-of-plane rotation of the whole free beam mechanism about the two support beams. The out-of-plane rotation of the whole free beam mechanism could be caused by the inertial moment generated during the drying process, which induces plastic deformation in the two support beams. The measurement results also verify that the two ends of the free beam do not touch the trench bottom. For example, in Prototype 1 the two ends of the free beam are about 10 m above the trench bottom even though the free beam bends downward by 40 m
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Fig. 11. MetalMUMPs nickel beam without using the free beam mechanism.
Fig. 13. 3-layer composite free beam.
failed prototypes the bridge beams were not completely released and then the free beams were not raised. Fig. 12. Circle fitting of the surface profile.
from its middle to its two ends while the trench is only 22.5 m deep (measured depth). Using the free beam mechanism proposed in this paper, a long (unreleased length of 3970 m) free beam (free ends and free of residual stress after being released) is achieved, which can be used for extracting the residual stress gradient in the MetalMUMPs nickel film. Such a long free beam would be impossible without using the free beam mechanism. Due to its long length, the curvature of the free beam can be accurately calculated based on the measured beam surface profile, which leads to an accurate extraction of the residual stress gradient of the nickel film. Fig. 11 shows a beam of the same length (3970 m) and width (100 m) touching the trench bottom at its two ends because the free beam mechanism is not used. Even though the bridge beam of the free beam mechanism is much wider (200 m) than the nominal maximum width (100 m) of MetalMUMPS nickel beams (which could be completely released according to MetalMUMPs process [1]), almost half of the prototypes were completely released. This should be attributed to the trench etching process and residual stress gradient induced bending moment which helped releasing the wide bridge beams. In the
3.3.3. Calculation of curvature The curvatures of the convexed free beams can be calculated from their measured surface profiles. Before calculating the curvature, the noise in the measured surface profile data is filtered out. Various algorithms are available for fitting circles to discrete points [38–40]. In this paper the curvatures of the free beams are calculated using the Maple code for circle fitting developed in [41]. Fig. 12 shows the fitted arc of Prototype 1. The curvatures of all free beams are listed in Table 2. 3.3.4. Extracting residual stress gradient The MetalMUMPs free beam is a 3-layer composite beam as shown in Fig. 13 [1]. The bending moment in the beam is expressed as [30]: M=
E¯ Ni INi + E¯ Cu ICu + E¯ Au IAu
(1)
where M is the bending moment. INi , ICu , IAu are the moments of inertia of the nickel layer, the copper layer and the gold layer about the neutral axis, which is assumed to be located on the mid plane of the nickel layer. 1/ is the curvature. E¯ Ni , E¯ Cu , E¯ Au are the equivalent Young’s modulus of nickel, copper and gold layers respectively,
Table 2 Measured results of the prototypes of the free beam mechanism. Prototype
Thickness of nickel film (m)
Curvature of free beam (m−1 )
Stress gradient (MPa/m)
Stress change through thickness (MPa)
1 2 3 4 5 6
17.94 21.62 22.75 22.30 19.00 21.70
1/46316 1/55365 1/57321 1/57828 1/50292 1/53867
−5.49 −4.51 −4.33 −4.30 −5.03 −4.63
−98.53 −97.44 −98.57 −95.95 −95.50 −100.48
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Fig. 14. Residual stress gradient of the nickel film.
which can be calculated as follows [33,36,42,43]. E¯ =
E 1−
(2)
The 3-layer composite beam is asymmetrical because the copper layer and the gold layer have different Young’s modulus and thicknesses. The bending moment caused by the mean residual stress (100 MPa tensile [1]) in the nickel layer due to the asymmetrical structure of the composite beam is neglected. The residual stresses in both the gold and the copper layers are neglected due to their small thickness in comparison to the nickel layer. Thus the bending moment is only induced by the residual stress gradient in the nickel layer, i.e., M = · INi
(3)
Substituting Eq. (3) into Eq. (1) results in =
E¯ Ni INi + E¯ Cu ICu + E¯ Au IAu INi
(4)
Eq. (4) relates the residual stress gradient in the MetalMUMPs nickel film to the curvature of the free beam. Lateral dimensions of the free beam can be found in Table 1. The Young’s modulus of the nickel film is obtained in Section 2 of this paper, which is 159 GPa. Other parameters of the copper layer, the gold layer and the nickel film are from [8] as described in Section 2.2.3. The nickel film thick-
155
ness of the free beam mechanism is obtained by measuring the height from the top surface of the anchoring pad (Fig. 10) to the top surface of the nitride layer and then subtracting the thickness of the copper, gold, chromium (10 nm) and platinum (25 nm) layers. The measured results are listed in Table 2. Substituting the above parameters and the curvatures of the free beams (Table 2) into Eq. (4) results in the residual stress gradient of the MetalMUMPs nickel film as shown in Table 2 and depicted in Fig. 14. The characterized residual stress gradient is −5.49 MPa/m to −4.30 MPa/m with the average of −4.72 MPa/m. The total residual stress change across the nickel film thickness is also shown in Table 2 and depicted in Fig. 15, which has an average stress change of −97.7 MPa. The characterized stress gradient is verified using numerical simulations by applying the stress gradient characterized using Eq. (4) to the free beam structure and then obtaining its curvature. The simulated curvatures closely match the measured results. Fig. 14 shows that the magnitude of the residual stress gradient is inversely proportional to the nickel film thickness. This might be caused by some factors, which contribute to the bending moment in the beam but were not considered when extracting the residual stress gradient in the nickel film. Those factors include the mean residual stress in the nickel layer, which generates a bending moment due to the asymmetric structure of the beam, and the residual stresses in the gold and the copper layers, which could also generate a bending moment in the beam. The obtained residual stress gradient would have non-negligible error if the residual stresses in the copper and gold layers cause non-negligible bending moment because the above calculations assume they do not cause significant bending moment. 4. Conclusions In this paper the Young’s modulus of the MetalMUMPs nickel film is characterized to be 155–164 GPa with an average of 159 GPa. A stress gradient induced free beam mechanism is proposed, which can be used to characterize the negative residual stress gradient in thin films when trenches and through-wafer holes are not available. When trenches are available, the free beam mechanism can still be used to improve the accuracy of the characterization of the negative stress gradient in thin films by allowing a long free beam to be used. The characterized residual stress gradient of the MetalMUMPs nickel film is −5.49 MPa/m to −4.30 MPa/m with the average of −4.72 MPa/m. The Young’s modulus and residual stress gradient of the MetalMUMPs nickel film obtained in this paper provide MetalMUMPs users an important reference for designing, optimizing and analyzing suspended nickel structures.
References
Fig. 15. Change in residual stress across the nickel film.
[1] A. Cowen, R. Mahadevan, S. Johnson, B. Hardy, MetalMUMPs Design Handbook, Revision 2.0, MEMSCAP Inc., 2002. [2] M. Bakri-Kassem, R.R. Mansour, Two movable-plate nitride-loaded MEMS variable capacitor, IEEE Transaction on Microwave Theory and Techniques 52 (2004) 831–837. [3] L. Li, D. Uttamchandani, Monolithic RF MEMS inductor using silicon MEMS foundry process, Micro & Nano Letters 1 (2006) 5–8. [4] Imed Zine-El-Abidine, Michal Okoniewski, A tunable radio frequency MEMS inductor using MetalMUMPs, Journal of Micromechanics and Microengineering 17 (2007) 2280–2287. [5] L. Almeida, R. Ramadoss, R. Jackson, K. Ishikawa, Q. Yu, Study of the electrical contact resistance of multi-contact MEMS relays fabricated using the MetalMUMPs process, Journal of Micromechanics and Microengineering 16 (2006) 1189–1194. [6] A. Cao, P. Yuen, L. Lin, Microrelays with bidirectional electrothermal electromagnetic actuators and liquid metal wetted contacts, IEEE/ASME Journal of Microelectromechanical Systems 16 (2007) 700–708. [7] D. Girbau, L. Pradell, A. Lazaro, A. Nebot, Electrothermally actuated RF MEMS switches suspended on a low-resistivity substrate, IEEE/ASME Journal of Microelectromechanical Systems 16 (2007) 1061–1070. [8] CoventorWareTM , 2008, Coventor Inc.
156
S. He et al. / Sensors and Actuators A 154 (2009) 149–156
[9] E. Mazza, S. Abel, J. Dual, Experimental determination of mechanical properties of Ni-Fe microbars, Microsystem Technologies 2 (1996) 197–202. [10] H. Majjad, et al., Dynamic determination of Young’s modulus of electroplated nickel used in LIGA technique, Sensors and Actuators A: Physical 74 (1999) 148–151. [11] T. Fritz, M. Griepentrog, W. Mokwa, U. Schnakenberg, Determination of Young’s modulus of electroplated nickel, Electrochimica Acta (2003) 3029–3035. [12] J.K. Luo, A.J. Flewitt, S.M. Spearing, N.A. Fleck, W.I. Milne, Young’s modulus of electroplated Ni thin film for MEMS applications, Materials Letters 58 (2004) 2306–2309. [13] W.N. Sharpe Jr., B. Yuan, R.L. Edwards, A new technique for measuring the mechanical properties of thin films, IEEE/ASME Journal of Microelectromechanical Systems 6 (1997) 193–199. [14] T.P. Weihs, et al., Mechanical deflection of cantilever microbeams: a new technique for testing the mechanical properties of thin films, Journal of Materials Research 3 (1988) 931–942. [15] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments, Journal of Materials Research 7 (1992) 1564–1583. [16] R. Yokokawa, J. Paik, B. Dunn, N. Kitazawa, H. Kotera, C. Kim, Mechanical properties of aerogel-like thin films used for MEMS, Journal of Micromechanics and Microengineering 14 (2004) 681–686. [17] Z. Zhou, Y. Zhou, C. Yang, J. Chen, G. Ding, W. Ding, M. Wang, Y. Zhang, The evaluation of Young’s modulus and residual stress of nickel films by microbridge testings, Measurement Science and Technology 15 (2004) 2389–2394. [18] B. Comella, M. Scanlon, The determination of the elastic modulus of microcantilever beams using atomic force microscopy, Journal of Materials Science 35 (2000) 567–0572. [19] B.D. Jensen, M.P. de Boer, N.D. Masters, F. Bitsie, D.A. La Van, Interferometry of actuated microcantilevers to determine material properties and test structure nonidealities in MEMS, IEEE/ASME Journal of Microelectromechanical Systems 10 (2001) 336–346. [20] L. Kiesewetter, et al., Determination of Young’s moduli of micromechanical thin films using the resonance method, Sensors and Actuators A: Physical 35 (1992) 153–159. [21] J. Jeong, S. Chung, S. Lee, D. Kwon, Evaluation of elastic properties and temperature effects in Si thin films using an electrostatic microresonator, IEEE/ASME Journal of Microelectromechanical Systems 12 (2003) 524–530. [22] C.-W. Baek, Y.-K. Kim, Y. Ahn, Y.-H. Kim, Measurement of the mechanical properties of electroplated gold thin films using micromachined beam structures, Sensors and Actuators A: Physical 117 (2005) 17–27. [23] C. Yu, C. Hsu, W. Fang, Comments on determining the elastic modulus of a thin film using the micromachined free–free beam, Journal of Micromechanics and Microengineering 15 (2005) 351–357. [24] R. Wiser, M. Tabib-Azar, M. Mehregany, C. Zorman, Polycrystalline siliconcarbide surface-micromachined vertical resonators–Part II: Electrical testing and material property extraction, IEEE/ASME Journal of Microelectromechanical Systems 14 (2005) 579–589. [25] I. Voiculescu, M. Zaghloul, R. McGill, E. Houser, G. Fedder, Electrostatically actuated resonant microcantilever beam in CMOS technology for the detection of chemical weapons, IEEE Journal of Sensors 5 (2005) 641–647.
[26] G. McShane, M. Boutchich, A. Phani, D. Moore, T. Lu, Young’s modulus measurement of thin-film materials using micro-cantilevers, Journal of Micromechanics and Microengineering 16 (2006) 1926–1934. [27] H.S. Cho, K.J. Hemker, K. Lian, J. Goettert, G. Dirras, Measured mechanical properties of LIGA Ni structures, Sensors and Actuators A: Physical 103 (2003) 59–63. [28] S.H. Kim, J.G. Boyd, A new technique for measuring Young’s modulus of electroplated nickel using AFM, Measurement Science and Technology 17 (2006) 2343–2348. [29] J.H. He, J.K. Luo, H.R. Le, D.F. Moore, Mechanical characterization of biocompatible thin film materials by scanning along micro-machined cantilevers for micro-/nano-system, Materials Science and Engineering A 423 (2006) 134–142. [30] K-S. Chen, MEMS/NEMS Handbook Techniques and Applications, Chapter 9: Techniques in residual stress measurement for MEMS and their applications, pp.1252-1328, Springer: US, 2006. [31] W. Fang, A.J. Wickert, Determining mean and gradient residual stresses in thin films using micromachined cantilevers, Journal of Micromechanics and Microengineering 6 (1996) 301–309. [32] W.-H. Chu, M. Mehregany, A study of residual stress distribution through the thickness of p+ silicon films, IEEE Transactions on Electron Devices 40 (1993) 1245–1250. [33] F. Ericson, et al., High-sensitivity surface micromachined structures for internal stress and stress gradient evaluation, Journal of Micromechanics and Microengineering 7 (1997) 30–36. [34] A.B. Yu, et al., Characterization and optimization of dry releasing for the fabrication of RF MEMS capacitive switches, Journal of Micromechanics and Microengineering 17 (2007) 2024–2030. [35] H. Huang, K. Winchester, Y. Liu, X.Z. Hu, C.A. Musca, J.M. Dell, L. Faraone, Determination of mechanical properties of PECVD silicon nitride thin films for tunable MEMS Fabry–Pérot optical filters, Journal of Micromechanics and Microengineering 15 (2005) 608–614. [36] Y. Zhang, Y. Zhao, An effective method of determining the residual stress gradients in a micro-cantilever, Microsystem Technologies 12 (2006) 357–364. [37] S.S. Yang, E.H. Yang, The quantitative determination of the residual stress profile in oxidized p+ silicon films, Sensors and Actuators A: Physical 54 (1996) 684–689. [38] G. Vosselman, R.M. Haralick, Performance analysis of line and circle fitting in digital images, in: Proceedings of the Workshop on Performance Characteristics of Vision Algorithms, Cambridge, 1996. [39] C. Rusu, M. Tico, P. Kuosmanen, E.J. Delp, Classical geometrical approach to circle fitting – review and new developments, Journal of Electronic Imaging 12 (2003) 179–193. [40] N. Chernov, C. Lesort, Least squares fitting of circles, Journal of Mathematical Imaging and Vision 23 (2005) 239–252. [41] T. Schramm, Fitting a circle to data using a linear model, http://www.maplesoft. com/Applications/app center view.aspx?AID=372, 2001. [42] W. Fang, Determination of the elastic modulus of thin film materials using self-deformed micromachined cantilevers, Journal of Micromechanics and Microengineering 9 (1999) 230–235. [43] P. Krulevitch, G.C. Johnson, Curvature of a cantilever beam subject to an equibiaxial bending moment, Materials Research Society Symposium Proceedings 518 (1998) 67–72.