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The residual stress-induced buckling of annular thin plates and its application in residual stress measurement of thin films
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Sensors and Actuators A 143 (2008) 409–414
The residual stress-induced buckling of annular thin plates and its application in residual stress measurement of thin films Da-Yong Qiao ∗ , Wei-Zheng Yuan, Yi-Ting Yu, Qing Liang, Zhi-Bo Ma, Xiao-Ying Li MEMS/NEMS Lab., The Northwestern Polytechnical Universtiy, Xi’an, PR China Received 5 May 2007; received in revised form 27 November 2007; accepted 28 November 2007 Available online 3 December 2007
Abstract The buckling method is presently one of the most commonly used methods in residual stress measurement, but still suffers from the problem that an array of structures occupying a large die area is required. In this paper, the buckling characteristics of annular thin plates were investigated and a new buckling method based on annular thin plates was proposed, implemented and verified for in situ measurement of both compressive and tensile stress with only a single structure but not an array. Annular thin plates with variable inner radius were realized by the sacrificial oxide etching of circular thin plates. The critical inner radius was measured by an optical microscope and was used to predict the residual stress by eigenvalue buckling analysis of ANSYS software. To measure both tensile and compressive stress with the same structure was proved to be feasible. Further measurements of compressive stress in thin polysilicon films have been carried out by this method and have shown reasonable agreement with results by micro-rotating gauge method. © 2007 Elsevier B.V. All rights reserved. Keywords: Residual stress; Eigenvalue buckling analysis; Annular thin plate
1. Introduction
2. The buckling characteristics of annular thin plates
Different techniques, such as deflections of the bilayer cantilevers [1], wafer curvatures [2], buckling microstructures [3,4], resonance frequency [5], pull-in voltages [6,7] and microrotating gauges [8,9] have been employed to determine residual stress according to different theories. Among these methods, the buckling method is widely used due to the readily detectable critical dimensions of buckling with an optical microscope. However, the buckling method suffers from the disadvantage that a family of similar structures with increasing flexibilities is required to detect the critical dimensions at which buckling occurs, and requires large die area. In this paper, the buckling characteristics of annular thin plates were investigated and a new buckling method based on annular thin plates was proposed, implemented and verified for in situ measurement of both compressive and tensile stress with only a single structure but not an array.
An annular thin plate with the outer radius of ro and the inner radius of ri is illustrated in Fig. 1. The residual stress-induced buckling of this kind of plates has been observed by Zhang [10]. Under given dimensions, there is a critical residual stress that causes the buckling of annular thin plates. In this paper, in order to investigate the relationship between the critical residual stress and the geometry of the annular thin plate, the finite element analysis (FEA) was performed using the eigenvalue buckling analysis of ANSYS software package. Eigenvalue buckling analysis, known as classical Euler buckling analysis, predicts buckling loads: critical loads at which an ideal elastic structure becomes unstable and buckled mode shapes: the characteristic shape associated with a structure’s buckled response. It computes the structural eigenvalues for the given system loading and constraints. Before a eigenvalue buckling analysis, a static analysis is needed with the prestress effects activated to calculate the stress stiffness matrix which is required in eigenvalue buckling analysis. In the static analysis, the structure is loaded with a unit load and the eigenvalue calculated by
∗
Corresponding author. Tel.: +86 29 88460353x8112; fax: +86 29 88495102. E-mail address: [email protected] (D.-Y. Qiao).
0924-4247/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2007.11.028
410
D.-Y. Qiao et al. / Sensors and Actuators A 143 (2008) 409–414
Fig. 1. The illustration of an annular thin plate: (a) 3D solid model and the (b) cross-section along the radial direction.
the eigenvalue solver will be the actual buckling load, since all loads are scaled during the analysis. The shell model of the annular thin plate was built and finely meshed using four-node isotropic 2D elements “SHELL63”. The annular thin plate was constrained by clamping on the inner edge, and was loaded with a biaxial unit residual stress via an equivalent fake thermal load (temperature difference) corresponding to fake thermal expansion coefficient (TEC). The temperature difference applied on the annular thin plate was determined such that it would cause the same stress as the residual stress if held constrained, and it was calculated by following equations: ε = αT σ=
(1)
E ε 1 − υ2
(2)
where T, ε, σ, α, υ and E are the temperature difference, residual strain, residual stress, thermal expansion coefficient, Poisson’s ratio and Young’s modulus, respectively. The mate-
Fig. 2. The relationship between the critical residual stress and δ (a) under compressive stress and (b) under tensile stress.
rial properties and dimensions used for this analysis are listed in Table 1. In order to facilitate the results illustration, the difference between ro and ri : δ, was used instead of ri in the FEA modeling. Fig. 2 demonstrates the critical residual stress as a function of δ for annular thin plates with various ro . Under given dimensions of the annular thin plate, this function can be used to predict the critical residual stress, and under given residual stress and ro , this function can be used to predict the critical δ or the critical ri .
Table 1 List of material properties and dimensions Parameter
Value
Material Young’s modulus (MPa) Poisson’s ratio TEC (10−6 /T) ro (m)
163,000 0.22 2.6 150, 300
Geometry δ (m) Thickness (m)
20–30 0.25
Load Residual stress (MPa)
1
Fig. 3. The buckled mode shapes of the annular thin plate under (a) tensile stress and (b) compressive stress.
D.-Y. Qiao et al. / Sensors and Actuators A 143 (2008) 409–414
Fig. 4. The realization process of the annular thin plate with variable ri .
As shown in Fig. 2(a), when under constant compressive residual stress (negative) and constant ro , there is a critical δ at which the buckling of the annular thin plate occurs, and the increasing in ro will decrease the critical δ, i.e., increase the critical ri . As shown in Fig. 2(b), when under constant tensile residual stress (positive) and constant ro , there is a critical δ at which the buckling of the annular thin plate occurs and the increasing in ro will increase the critical δ, i.e., decrease the critical ri . Fig. 3(a) and (b) illustrate the scaled contour plot of buckled mode shapes under residual tensile stress and residual compressive stress, respectively. Fig. 3 indicates that the buckled mode shapes of annular thin plates are different depending on the stress
411
Fig. 6. The buckling sequence of annular thin plates with various ro under compressive stress. (a) Buckling of the annular thin plate of larger ro occurred ahead of (b) that of smaller one.
state. When under tensile stress, the buckled mode shape is of bowl-like pattern, while under compressive stress, the buckled mode shape is of scalloping-like pattern. This kind of difference can be used to distinguish between tensile or compressive stress under optical microscopes. It should be noticed that the root stiffness [11] was not taken into consideration in the 2D finite element model with inner edge clamping boundary condition. Finite element simulations using full 3D model have also been performed involving the effect of the not released polysilicon and the remained sacrificial oxide. The simulation results revealed that only an error about 1% will be introduced into the predicted residual stress without root effect. Since the 2D inner edge clamping model can achieve almost the same simulation results but with less computational time, it was chosen as the finite element model in this research. 3. The application in residual stress measurement For a buckled annular thin plate, there is a critical residual stress under given ro and ri . On the other hand, under given Table 2 List of critical inner radius and the corresponding residual strain/stress predicted by FEA
Fig. 5. Experimental setup for in situ observation of buckling.
Deposition
ro (m)
Critical ri (m)
Strain (10−4 )
Stress (MPa)
580 ◦ C No annealing 580 ◦ C With annealing
150 300 150 300
128.5 279.5 125.5 277.0
−1.77 −1.82 −1.39 −1.46
−30.3 −31.3 −23.8 −25.0
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Table 3 List of tip movements and the corresponding residual strain/stress determined by FEA Deposition 580 ◦ C No annealing 580 ◦ C With annealing
Tip movement (m)
Strain (10−4 )
Stress (MPa)
0.8
−1.56
−32.7
0.6
−1.17
−24.5
residual stress and ro , there is a critical ri at which the residual stress-induced buckling occurs. Hence, an annular thin plate with fixed ro and variable ri can be used to predict the residual stress in thin films by gradually decreasing ri to find its critical value. An annular thin plate with variable ri can be achieved by releasing an circular thin plate as shown in Fig. 4. The circular thin plate was fabricated using surface micromachining technology. First, 600 nm LPCVD SiO2 was deposited as sacrificial layer and patterned by RIE using CHF3 to form the anchor structure. Second, a 250 nm polysilicon layer was deposited by LPCVD and patterned by RIE using SF6 to define the circular thin plate. During BOE releasing process of the circular thin plate, with the removal of the sacrificial oxide, an annular thin plate with decreasing ri can be realized. When buckling of the released annular region occurs, the radial distance from the circular plate center to the etch front is the critical ri . A 250 nm polysilicon layer is thick enough to prevent BOE from diffusing through to etch the underlying sacrificial oxide [12], while semitransparent to enable the measurement of the critical ri through an optical microscope (X1000) by using the attached ruler. In order to observe the buckling, sacrificial layer releasing experiments were carried out under an in situ monitoring system, which is schematically shown in Fig. 5. This monitoring system consists of an optical microscope, a video camera and a computer. Etching of the sample was performed in a specially designed teflon container with a transparent plastic cover slide. The whole process can be video-recorded by the computer. As soon as buckling observed, the BOE etchant was drained and deionized (DI) water was fed into the container to stop the etching. Following the sacrificial layer releasing, samples were immersed in a large volume of continuously flowing DI water for 5 min and dried inside a 150 ◦ C oven for 15 min. Later on, data of the critical ri was read out by inspecting the samples under an optical microscope. Two groups of examples were fabricated under different conditions. In the first group, the 250 nm polysilicon was deposited at 580 ◦ C without annealing, and in the second group, the 250 nm polysilicon was deposited at 580 ◦ C followed by an annealing at 1050 ◦ C in tube furnace for 30 min. Scalloping-like bucklings were observed in releasing of both the two groups of samples and indicate the presence of compressive residual stress. Micro-photos in Fig. 6 demonstrate the phenomenon as indicated by the FEA results that the annular
Fig. 7. SEM photos of micro-rotating gauges. (a) Overview of the micro-rotating gauge without annealing, (b) enlarged view of the indicator without annealing, (c) overview of the micro-rotating gauge with annealing and (d) enlarged view of the indicator with annealing.
thin plate of larger ro leads to larger critical ri compared with that of smaller one when under compressive residual stress. When buckling occurs, the measured critical ri and the eigenvalue buckling analysis predicted residual strains and stresses of different annular thin plates with various ro are listed in Table 2.
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413
Acknowledgements This work has been sponsored by Program for New Century Excellent Talents in University (05-0869), the Doctorate Foundation of Northwestern Polytechnical University and Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No. 706055). References
Fig. 8. The buckling of the annular thin plate with smaller ro occurs ahead of that with large ro under tensile stress.
The residual stresses were evaluated when 163 GPa was used as the Young’s modulus of the polysilicon. 4. Verification by the micro-rotating gauge method In order to verify measurement results of the annular thin plate buckling method, the micro-rotating gauges were fabricated within the same die. It can be easily observed that the indicators have moved to the left, which means a compressive strain occurred. The enlarged views of the indicators are shown in Fig. 7(b) and (d), which illustrate the tip movements of indicators. The residual strain/stress were then calculated according to the ANSYS simulation determined relationship between the stress and the tip movement and were listed in Table 3. It is found that measurement results of annular thin plates show reasonable agreement with results of micro-rotating gauges. To investigate the buckling under tensile stress, 300 nm LPCVD silicon nitride has been used as the structural layer instead of polysilicon, and the bowl-like buckling of the annular thin plate with smaller ro has been observed as shown in Fig. 8. Because the micro-rotating gauges got fractured due to the excessive tensile stress in silicon nitride layer and failed to measure the residual stress, the measurement comparison between these two methods has not been carried out. 5. Conclusions The buckling behavior of annular thin plates was investigated and employed to predict the residual stress of thin films. The buckling pattern was used to distinguish between tensile and compressive stress, and the critical inner radius determined during the structure releasing was used to predict the residual stress value via the eigenvalue buckling analysis of ANSYS software package. The measurements of compressive stress in thin polysilicon films have been carried out by this method and have shown reasonable agreement with results from micro-rotating gauge method.
[1] Y.H. Min, Y.K. Kim, In situ measurement of residual stress in micromachined thin films using a specimen with composite-layered cantilevers, J. Micromech. Microeng. 10 (2000) 314–321. [2] G.G. Stoney, The tension of metallic films deposited by electrolysis, Proc. R. Soc. 82 (1909) 172–175. [3] H. Guckel, et al., A simple technique for the determination of mechanical strain in thin films with applications to polysilicon, J. Appl. Phys. 57 (1985) 1671–1675. [4] H. Guckel, et al., Diagnostic microstructures for the measurement of intrinsic strain in thin films, J. Micromech. Microeng. 2 (1992) 86– 95. [5] L.M. Zhang, et al., Measurement of the mechanical properties of silicon microresonators, Sens. Actuators A 29 (1991) 79–84. [6] P.M. Osterberg, S.D. Senturia, M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures, J. Microelectromech. Syst. 6 (1997) 107–118. [7] H. Guckel, et al., Fine-grained polysilicon films with built-in tensile strain, IEEE Trans. Electron Devices 35 (1988) 800–801. [8] L.-W. Lin, et al., A micro strain gauge with mechanical amplifier, J. Microelectromech. Syst. 6 (1997) 313–321. [9] C.S. Pan, W. Hsu, A microstructure for in situ determination of residual strain, J. Microelectromech. Syst. 8 (1999) 200–207. [10] X. Zhang, Residual stresses in MEMS thin films, Ph.D thesis. Hong Kong University of Science and Technology, 1998. [11] W. Fang, J.A. Wicket, Determination mean and gradient residual stresses in thin films using micromachined cantilever, J. Micromech. Microeng. 6 (1996) 301–309. [12] K.R. Williams, R.S. Muller, Etch rates for micromachining processing, J. Microelectromech. Syst. 5 (1996) 256–269.
Biographies Da-Yong Qiao (1977) received the BS degree in mechanical engineering from TsingDao University, China in 2000, the MS degree in MicroElectroMechanical Systems from Northwestern Polytechnical University, China in 2003. He is currently working toward the PhD degree in Micro/Nano System Laboratory in Northwestern Polytechnical University, China. His research interests include micromachined actuators and microfabrication technologies. Wei-Zheng Yuan (1961) received his MS and PhD degrees from Northwestern Polytechnical University in 1986 and 1996, respectively. He is the director of Micro/Nano System Laboratory in Northwestern Polytechnical University. He was a visiting scholar with ENSMM in France, MEEM Department at City University of Hong Kong in HKSARS of China, and with NRC in Canada. His research fields are microfabrication technologies, modeling and simulation of MEMS, and intelligent sensors. He authored a book entitled Micromachine and Micromachining Fabrication Technology that was published by Northwestern Polytechnical University Press, 2000. Yu-Ting Yu (1980) received his BS and MS degrees in mechanical engineering from Northwestern Polytechnical University in 2003 and 2006, respectively. He is now pursuing his PhD degree in Micro/Nano System Laboratory in Northwestern Polytechnical University. His research interests are optical MEMS, microactuators and microfabrication technologies. Qing Liang (1982) received his BS degree in biomedical engineering from Northwestern Polytechnical University, China in 2001. He
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D.-Y. Qiao et al. / Sensors and Actuators A 143 (2008) 409–414
is currently working toward the MS degree in Micro/Nano System Laboratory in Northwestern Polytechnical University, China. His research interests include microsystem control and microfabrication technologies. Zhi-Bo Ma (1978) received the BS degree in mechanical engineering from TsingDao University, China in 2004, the MS degree in MicroElectroMechanical Systems from Northwestern Polytechnical University, China in 2007. His
research interests include micromachined sensors, actuators and microfabrication technologies. Xiao-ying li (1968) received her BS and MS degrees from Northwestern Polytechnical University in 1989 and 1992, respectively. She is working in Micro/Nano System Laboratory in Northwestern Polytechnical University. Her research fields are microfabrication technologies, micro-sensors and measurement technique.
Sensors and Actuators A 143 (2008) 409–414
The residual stress-induced buckling of annular thin plates and its application in residual stress measurement of thin films Da-Yong Qiao ∗ , Wei-Zheng Yuan, Yi-Ting Yu, Qing Liang, Zhi-Bo Ma, Xiao-Ying Li MEMS/NEMS Lab., The Northwestern Polytechnical Universtiy, Xi’an, PR China Received 5 May 2007; received in revised form 27 November 2007; accepted 28 November 2007 Available online 3 December 2007
Abstract The buckling method is presently one of the most commonly used methods in residual stress measurement, but still suffers from the problem that an array of structures occupying a large die area is required. In this paper, the buckling characteristics of annular thin plates were investigated and a new buckling method based on annular thin plates was proposed, implemented and verified for in situ measurement of both compressive and tensile stress with only a single structure but not an array. Annular thin plates with variable inner radius were realized by the sacrificial oxide etching of circular thin plates. The critical inner radius was measured by an optical microscope and was used to predict the residual stress by eigenvalue buckling analysis of ANSYS software. To measure both tensile and compressive stress with the same structure was proved to be feasible. Further measurements of compressive stress in thin polysilicon films have been carried out by this method and have shown reasonable agreement with results by micro-rotating gauge method. © 2007 Elsevier B.V. All rights reserved. Keywords: Residual stress; Eigenvalue buckling analysis; Annular thin plate
1. Introduction
2. The buckling characteristics of annular thin plates
Different techniques, such as deflections of the bilayer cantilevers [1], wafer curvatures [2], buckling microstructures [3,4], resonance frequency [5], pull-in voltages [6,7] and microrotating gauges [8,9] have been employed to determine residual stress according to different theories. Among these methods, the buckling method is widely used due to the readily detectable critical dimensions of buckling with an optical microscope. However, the buckling method suffers from the disadvantage that a family of similar structures with increasing flexibilities is required to detect the critical dimensions at which buckling occurs, and requires large die area. In this paper, the buckling characteristics of annular thin plates were investigated and a new buckling method based on annular thin plates was proposed, implemented and verified for in situ measurement of both compressive and tensile stress with only a single structure but not an array.
An annular thin plate with the outer radius of ro and the inner radius of ri is illustrated in Fig. 1. The residual stress-induced buckling of this kind of plates has been observed by Zhang [10]. Under given dimensions, there is a critical residual stress that causes the buckling of annular thin plates. In this paper, in order to investigate the relationship between the critical residual stress and the geometry of the annular thin plate, the finite element analysis (FEA) was performed using the eigenvalue buckling analysis of ANSYS software package. Eigenvalue buckling analysis, known as classical Euler buckling analysis, predicts buckling loads: critical loads at which an ideal elastic structure becomes unstable and buckled mode shapes: the characteristic shape associated with a structure’s buckled response. It computes the structural eigenvalues for the given system loading and constraints. Before a eigenvalue buckling analysis, a static analysis is needed with the prestress effects activated to calculate the stress stiffness matrix which is required in eigenvalue buckling analysis. In the static analysis, the structure is loaded with a unit load and the eigenvalue calculated by
∗
Corresponding author. Tel.: +86 29 88460353x8112; fax: +86 29 88495102. E-mail address: [email protected] (D.-Y. Qiao).
0924-4247/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2007.11.028
410
D.-Y. Qiao et al. / Sensors and Actuators A 143 (2008) 409–414
Fig. 1. The illustration of an annular thin plate: (a) 3D solid model and the (b) cross-section along the radial direction.
the eigenvalue solver will be the actual buckling load, since all loads are scaled during the analysis. The shell model of the annular thin plate was built and finely meshed using four-node isotropic 2D elements “SHELL63”. The annular thin plate was constrained by clamping on the inner edge, and was loaded with a biaxial unit residual stress via an equivalent fake thermal load (temperature difference) corresponding to fake thermal expansion coefficient (TEC). The temperature difference applied on the annular thin plate was determined such that it would cause the same stress as the residual stress if held constrained, and it was calculated by following equations: ε = αT σ=
(1)
E ε 1 − υ2
(2)
where T, ε, σ, α, υ and E are the temperature difference, residual strain, residual stress, thermal expansion coefficient, Poisson’s ratio and Young’s modulus, respectively. The mate-
Fig. 2. The relationship between the critical residual stress and δ (a) under compressive stress and (b) under tensile stress.
rial properties and dimensions used for this analysis are listed in Table 1. In order to facilitate the results illustration, the difference between ro and ri : δ, was used instead of ri in the FEA modeling. Fig. 2 demonstrates the critical residual stress as a function of δ for annular thin plates with various ro . Under given dimensions of the annular thin plate, this function can be used to predict the critical residual stress, and under given residual stress and ro , this function can be used to predict the critical δ or the critical ri .
Table 1 List of material properties and dimensions Parameter
Value
Material Young’s modulus (MPa) Poisson’s ratio TEC (10−6 /T) ro (m)
163,000 0.22 2.6 150, 300
Geometry δ (m) Thickness (m)
20–30 0.25
Load Residual stress (MPa)
1
Fig. 3. The buckled mode shapes of the annular thin plate under (a) tensile stress and (b) compressive stress.
D.-Y. Qiao et al. / Sensors and Actuators A 143 (2008) 409–414
Fig. 4. The realization process of the annular thin plate with variable ri .
As shown in Fig. 2(a), when under constant compressive residual stress (negative) and constant ro , there is a critical δ at which the buckling of the annular thin plate occurs, and the increasing in ro will decrease the critical δ, i.e., increase the critical ri . As shown in Fig. 2(b), when under constant tensile residual stress (positive) and constant ro , there is a critical δ at which the buckling of the annular thin plate occurs and the increasing in ro will increase the critical δ, i.e., decrease the critical ri . Fig. 3(a) and (b) illustrate the scaled contour plot of buckled mode shapes under residual tensile stress and residual compressive stress, respectively. Fig. 3 indicates that the buckled mode shapes of annular thin plates are different depending on the stress
411
Fig. 6. The buckling sequence of annular thin plates with various ro under compressive stress. (a) Buckling of the annular thin plate of larger ro occurred ahead of (b) that of smaller one.
state. When under tensile stress, the buckled mode shape is of bowl-like pattern, while under compressive stress, the buckled mode shape is of scalloping-like pattern. This kind of difference can be used to distinguish between tensile or compressive stress under optical microscopes. It should be noticed that the root stiffness [11] was not taken into consideration in the 2D finite element model with inner edge clamping boundary condition. Finite element simulations using full 3D model have also been performed involving the effect of the not released polysilicon and the remained sacrificial oxide. The simulation results revealed that only an error about 1% will be introduced into the predicted residual stress without root effect. Since the 2D inner edge clamping model can achieve almost the same simulation results but with less computational time, it was chosen as the finite element model in this research. 3. The application in residual stress measurement For a buckled annular thin plate, there is a critical residual stress under given ro and ri . On the other hand, under given Table 2 List of critical inner radius and the corresponding residual strain/stress predicted by FEA
Fig. 5. Experimental setup for in situ observation of buckling.
Deposition
ro (m)
Critical ri (m)
Strain (10−4 )
Stress (MPa)
580 ◦ C No annealing 580 ◦ C With annealing
150 300 150 300
128.5 279.5 125.5 277.0
−1.77 −1.82 −1.39 −1.46
−30.3 −31.3 −23.8 −25.0
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Table 3 List of tip movements and the corresponding residual strain/stress determined by FEA Deposition 580 ◦ C No annealing 580 ◦ C With annealing
Tip movement (m)
Strain (10−4 )
Stress (MPa)
0.8
−1.56
−32.7
0.6
−1.17
−24.5
residual stress and ro , there is a critical ri at which the residual stress-induced buckling occurs. Hence, an annular thin plate with fixed ro and variable ri can be used to predict the residual stress in thin films by gradually decreasing ri to find its critical value. An annular thin plate with variable ri can be achieved by releasing an circular thin plate as shown in Fig. 4. The circular thin plate was fabricated using surface micromachining technology. First, 600 nm LPCVD SiO2 was deposited as sacrificial layer and patterned by RIE using CHF3 to form the anchor structure. Second, a 250 nm polysilicon layer was deposited by LPCVD and patterned by RIE using SF6 to define the circular thin plate. During BOE releasing process of the circular thin plate, with the removal of the sacrificial oxide, an annular thin plate with decreasing ri can be realized. When buckling of the released annular region occurs, the radial distance from the circular plate center to the etch front is the critical ri . A 250 nm polysilicon layer is thick enough to prevent BOE from diffusing through to etch the underlying sacrificial oxide [12], while semitransparent to enable the measurement of the critical ri through an optical microscope (X1000) by using the attached ruler. In order to observe the buckling, sacrificial layer releasing experiments were carried out under an in situ monitoring system, which is schematically shown in Fig. 5. This monitoring system consists of an optical microscope, a video camera and a computer. Etching of the sample was performed in a specially designed teflon container with a transparent plastic cover slide. The whole process can be video-recorded by the computer. As soon as buckling observed, the BOE etchant was drained and deionized (DI) water was fed into the container to stop the etching. Following the sacrificial layer releasing, samples were immersed in a large volume of continuously flowing DI water for 5 min and dried inside a 150 ◦ C oven for 15 min. Later on, data of the critical ri was read out by inspecting the samples under an optical microscope. Two groups of examples were fabricated under different conditions. In the first group, the 250 nm polysilicon was deposited at 580 ◦ C without annealing, and in the second group, the 250 nm polysilicon was deposited at 580 ◦ C followed by an annealing at 1050 ◦ C in tube furnace for 30 min. Scalloping-like bucklings were observed in releasing of both the two groups of samples and indicate the presence of compressive residual stress. Micro-photos in Fig. 6 demonstrate the phenomenon as indicated by the FEA results that the annular
Fig. 7. SEM photos of micro-rotating gauges. (a) Overview of the micro-rotating gauge without annealing, (b) enlarged view of the indicator without annealing, (c) overview of the micro-rotating gauge with annealing and (d) enlarged view of the indicator with annealing.
thin plate of larger ro leads to larger critical ri compared with that of smaller one when under compressive residual stress. When buckling occurs, the measured critical ri and the eigenvalue buckling analysis predicted residual strains and stresses of different annular thin plates with various ro are listed in Table 2.
D.-Y. Qiao et al. / Sensors and Actuators A 143 (2008) 409–414
413
Acknowledgements This work has been sponsored by Program for New Century Excellent Talents in University (05-0869), the Doctorate Foundation of Northwestern Polytechnical University and Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China (No. 706055). References
Fig. 8. The buckling of the annular thin plate with smaller ro occurs ahead of that with large ro under tensile stress.
The residual stresses were evaluated when 163 GPa was used as the Young’s modulus of the polysilicon. 4. Verification by the micro-rotating gauge method In order to verify measurement results of the annular thin plate buckling method, the micro-rotating gauges were fabricated within the same die. It can be easily observed that the indicators have moved to the left, which means a compressive strain occurred. The enlarged views of the indicators are shown in Fig. 7(b) and (d), which illustrate the tip movements of indicators. The residual strain/stress were then calculated according to the ANSYS simulation determined relationship between the stress and the tip movement and were listed in Table 3. It is found that measurement results of annular thin plates show reasonable agreement with results of micro-rotating gauges. To investigate the buckling under tensile stress, 300 nm LPCVD silicon nitride has been used as the structural layer instead of polysilicon, and the bowl-like buckling of the annular thin plate with smaller ro has been observed as shown in Fig. 8. Because the micro-rotating gauges got fractured due to the excessive tensile stress in silicon nitride layer and failed to measure the residual stress, the measurement comparison between these two methods has not been carried out. 5. Conclusions The buckling behavior of annular thin plates was investigated and employed to predict the residual stress of thin films. The buckling pattern was used to distinguish between tensile and compressive stress, and the critical inner radius determined during the structure releasing was used to predict the residual stress value via the eigenvalue buckling analysis of ANSYS software package. The measurements of compressive stress in thin polysilicon films have been carried out by this method and have shown reasonable agreement with results from micro-rotating gauge method.
[1] Y.H. Min, Y.K. Kim, In situ measurement of residual stress in micromachined thin films using a specimen with composite-layered cantilevers, J. Micromech. Microeng. 10 (2000) 314–321. [2] G.G. Stoney, The tension of metallic films deposited by electrolysis, Proc. R. Soc. 82 (1909) 172–175. [3] H. Guckel, et al., A simple technique for the determination of mechanical strain in thin films with applications to polysilicon, J. Appl. Phys. 57 (1985) 1671–1675. [4] H. Guckel, et al., Diagnostic microstructures for the measurement of intrinsic strain in thin films, J. Micromech. Microeng. 2 (1992) 86– 95. [5] L.M. Zhang, et al., Measurement of the mechanical properties of silicon microresonators, Sens. Actuators A 29 (1991) 79–84. [6] P.M. Osterberg, S.D. Senturia, M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures, J. Microelectromech. Syst. 6 (1997) 107–118. [7] H. Guckel, et al., Fine-grained polysilicon films with built-in tensile strain, IEEE Trans. Electron Devices 35 (1988) 800–801. [8] L.-W. Lin, et al., A micro strain gauge with mechanical amplifier, J. Microelectromech. Syst. 6 (1997) 313–321. [9] C.S. Pan, W. Hsu, A microstructure for in situ determination of residual strain, J. Microelectromech. Syst. 8 (1999) 200–207. [10] X. Zhang, Residual stresses in MEMS thin films, Ph.D thesis. Hong Kong University of Science and Technology, 1998. [11] W. Fang, J.A. Wicket, Determination mean and gradient residual stresses in thin films using micromachined cantilever, J. Micromech. Microeng. 6 (1996) 301–309. [12] K.R. Williams, R.S. Muller, Etch rates for micromachining processing, J. Microelectromech. Syst. 5 (1996) 256–269.
Biographies Da-Yong Qiao (1977) received the BS degree in mechanical engineering from TsingDao University, China in 2000, the MS degree in MicroElectroMechanical Systems from Northwestern Polytechnical University, China in 2003. He is currently working toward the PhD degree in Micro/Nano System Laboratory in Northwestern Polytechnical University, China. His research interests include micromachined actuators and microfabrication technologies. Wei-Zheng Yuan (1961) received his MS and PhD degrees from Northwestern Polytechnical University in 1986 and 1996, respectively. He is the director of Micro/Nano System Laboratory in Northwestern Polytechnical University. He was a visiting scholar with ENSMM in France, MEEM Department at City University of Hong Kong in HKSARS of China, and with NRC in Canada. His research fields are microfabrication technologies, modeling and simulation of MEMS, and intelligent sensors. He authored a book entitled Micromachine and Micromachining Fabrication Technology that was published by Northwestern Polytechnical University Press, 2000. Yu-Ting Yu (1980) received his BS and MS degrees in mechanical engineering from Northwestern Polytechnical University in 2003 and 2006, respectively. He is now pursuing his PhD degree in Micro/Nano System Laboratory in Northwestern Polytechnical University. His research interests are optical MEMS, microactuators and microfabrication technologies. Qing Liang (1982) received his BS degree in biomedical engineering from Northwestern Polytechnical University, China in 2001. He
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is currently working toward the MS degree in Micro/Nano System Laboratory in Northwestern Polytechnical University, China. His research interests include microsystem control and microfabrication technologies. Zhi-Bo Ma (1978) received the BS degree in mechanical engineering from TsingDao University, China in 2004, the MS degree in MicroElectroMechanical Systems from Northwestern Polytechnical University, China in 2007. His
research interests include micromachined sensors, actuators and microfabrication technologies. Xiao-ying li (1968) received her BS and MS degrees from Northwestern Polytechnical University in 1989 and 1992, respectively. She is working in Micro/Nano System Laboratory in Northwestern Polytechnical University. Her research fields are microfabrication technologies, micro-sensors and measurement technique.