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Evaluation of residual stresses in thin films by critical buckling observation of circular microstructures and finite element method
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Thin Solid Films 516 (2008) 4070 – 4075 www.elsevier.com/locate/tsf
Evaluation of residual stresses in thin films by critical buckling observation of circular microstructures and finite element method Yi-Ting Yu ⁎, Wei-Zheng Yuan, Da-Yong Qiao, Qing Liang Micro and Nano Electromechanical Systems Laboratory, Northwestern Polytechnical University, PO Box 638, 710072, Xi'an, China Received 1 March 2007; received in revised form 16 November 2007; accepted 27 December 2007 Available online 5 January 2008
Abstract An approach for evaluating residual stresses in thin films by critical buckling observation of circular microstructures is proposed, by which the states of residual stresses can be distinguished directly from the observed critical buckling patterns and their magnitudes can be estimated with finite element method after the critical etching length is measured. For practical operation, three samples were prepared by surface micromachining technique and a specially designed video system was set up for in-situ monitoring the whole process during the sacrificial layer etching. Then, measurements of residual stresses were performed and the results were compared with those obtained from micro rotating structures. As a result, the approach is proved to be relatively simple, both compressive and tensile residual stresses with wide range of amplitude can be evaluated by just using a single appropriately designed circular microstructure. © 2008 Elsevier B.V. All rights reserved. Keywords: Residual stresses; Thin films; Critical buckling observation; Circular microstructures; Finite element method; Sacrificial layer etching
1. Introduction Thin film materials are attractive for the fabrication of microsensors and microactuators in microelectromechanical systems (MEMS) fields. However, as structure sizes continue to shrink, material properties which were previously acceptable can cause problems [1]. One such concern is the residual stress, generally induced during thin film deposition. High residual stress, no matter compressive or tensile, can adversely affect structure performances, yield and service lifetime. As a result, various methods for evaluating residual stresses in MEMS thin films have been developed in the last two decades [2–3], among which critical buckling observation of clamped-clamped microbeams array for compressive residual stress and microrings array for tensile, both proposed by Guckel et al. [4–5], is most widely used. However, for surface micromachining applications, evaluation of residual stresses using these microstructures is usually executed after the sacrificial layer is etched completely and drying process has been finished. ⁎ Corresponding author. Tel.: +86 29 88460353 8110; fax: +86 29 88495102. E-mail address: [email protected] (Y.-T. Yu). 0040-6090/$ - see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2007.12.153
In fact, as the etching progresses, buckling of microstructures can also be observed even still in the etching solution. X. Zhang et al. [6–7] reported a few interesting findings on this subject of polysilicon microbeams during the sacrificial layer etching. In this paper, in-situ buckling observation of circular microstructures, often used for studying the release-etch mechanism in surface micromachining [8–9], was carried out during the sacrificial layer etching with a specially designed video system similar to X. Zhang's. Then, an approach for evaluating residual stresses was proposed and practical measurements were performed on three samples prepared by different surface micromachining processes. The results were compared with those obtained from commonly used micro rotating structures [2,10–11]. 2. Experimental preparations Schematic diagram of circular microstructures is shown in Fig. 1, and Fig. 1b is the cross section view in A–A direction. The principal process flows for fabricating these microstructures are illustrated in Fig. 2. Firstly, as shown in Fig. 2a, silicon substrate is coated with a sacrificial layer material and the
Y.-T. Yu et al. / Thin Solid Films 516 (2008) 4070–4075
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Table 1 Three samples prepared by different surface micromachining process No.
State of stress
Sacrificial layer/thickness [μm]
Structural layer/thickness [nm]
1
Compressive
LPCVD TEOS oxide/~3.00 LPCVD TEOS oxide/~0.75 LPCVD TEOS oxide/~0.75
LPCVD polysilicon/312
2 3
Fig. 1. Schematic diagram of circular microstructures.
anchor areas are formed. Then, the structural layer is deposited and patterned (Fig. 2b). Finally, selective etching of the sacrificial layer creates the free-standing micromechanical structures such as the cantilever beam shown in Fig. 2c. In the experiments, 4” n-type (100) silicon wafers were used as substrates. And three samples with different states of residual stress in structural layer were prepared, as shown in Table 1. All the sacrificial layer oxides were deposited by the decomposition of tetraethoxysilane (TEOS) in a low pressure chemical vapor deposition (LPCVD) furnace at 685 °C, 33.33 Pa and O2 flow rate of 200 sccm. Then, two types of structural layer were also LPCVD deposited, polysilicon for compressive residual stress and silicon nitride (Si3N4) for tensile. Polysilicon was deposited at 620 °C, 30 Pa, and using silane as a source gas of 250 sccm, while Si3N4 at 785 °C, 33.33 Pa, and using ammonia and dichlorosilane as source gases of 150 sccm and 10 sccm respectively. Thick-
Fig. 2. Principal process flows for fabricating circular microstructures.
Tensile
LPCVD polysilicon/312 LPCVD Si3N4/409
ness of the structural layer imposes great effects on the results. Consequently, accurate measurement of it for each sample is necessary. In our study, scanning electron microscopy (SEM) was adopted for the purpose. Before etching, an annealing at 950 °C for one hour in a standard diffusion furnace in the nitrogen atmosphere was performed. Wet etching of the sacrificial layer was conducted in a 5:1 buffered hydrofluoric acid solution at room temperature (22 °C). For in-situ monitoring the critical buckling patterns of circular microstructures during the etching, a specially designed video system was set up, as shown in Fig. 3. The etching can be stopped at will to freeze the temporal buckling patterns for SEM. 3. Buckling observation and analysis As the sample is put into the container with fresh etching solution, the sacrificial layer starts to be etched immediately. Fig. 4 presents a simplified model for the etching. R and t represent the radius and thickness of the structure, respectively. And δ denotes the etching length, which increases with the etching time. When etched, peripheral portion of the structure becomes free-standing and residual stress in it is released. Fig. 5 shows three characteristic evolutions of buckling patterns of a circular microstructure during the etching for polysilicon structural layer. At the beginning, the free-standing circular microstructure has enough stiffness to withstand the released stress loading when δ keeps a relatively small value. Therefore, it still remains flat observed in the microscope (Fig. 5a). As the etching time increases, more part of the structure is freed and its total stiffness gets smaller correspondingly. As a result, for a given residual stress, there exists a critical time when
Fig. 3. Experimental device for in-situ critical buckling observation.
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Y.-T. Yu et al. / Thin Solid Films 516 (2008) 4070–4075
Fig. 4. Model for a circular microstructure during the sacrificial layer etching.
the free-standing circular microstructure falls into an unsteady state and buckles immediately. This critical buckling pattern is shown in Fig. 5b and thereafter can be utilized for evaluating residual stress. (For this purpose, finite element program like ANSYS should be resorted to and buckling analysis should be performed when R, t and the critical etching length are achieved.) After that, as the etching continues, buckling pattern of the freestanding circular microstructure exists all the time. However, the number of Newton rings decreases gradually, as shown in Fig. 5c. As for the finite element analysis with ANSYS, the freestanding circular microstructure was modeled as a 2-dimensional annulus with clamped boundary conditions applied on the inner circle, corresponding to the etching front. And the state of plane stress was considered. Radius of the anchor area was taken to be 20 μm and polysilicon structural layer was assumed. Young's modulus, Poisson's ratio and thermal expansion coefficient of polysilicon are 163 GPa, 0.22 and 2.6 × 10− 6/°C respectively [12]. All these material properties were considered to be linear elastic with element type of SHELL63 and element size of 5 μm. Fig. 6 shows two typical critical buckling patterns of the annulus subjected to different states of residual stress, Fig. 6a with a wave shape for compressive residual stress and Fig. 6b with a bowl shape for tensile. Thus, it provides a convenient way to judge the states of residual stress by just observing the critical buckling patterns of circular microstructures during the sacrificial layer etching. Fig. 7 is the simulation results of critical buckling stress at various critical etching length when R = 150 μm and t = 0.5 μm, from which we can see that there exists a unique critical buckling stress, either compressive or tensile, for a specific critical etching length. Also, we can see that a wide range of
Fig. 6. Two typical critical buckling patterns of the annulus. (a) for compressive residual stress and (b) for tensile residual stress.
residual stresses from the order of MPa to GPa can be covered with a single appropriately designed circular microstructure. 4. Results and discussion Fig. 8 provides SEM results for the two critical buckling patterns of circular microstructures subjected to different states of residual stress, which consistent with the prediction in Fig. 6. For the two samples of polysilicon structural layer, critical buckling patterns of circular microstructures during the sacrificial layer etching were always in the wave shape, indicating the existence of compressive residual stress. Fig. 9a reveals the time when no buckling patterns happen for both
Fig. 5. Three characteristic evolutions of buckling patterns of a circular microstructure during the etching.
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Fig. 7. Critical buckling stress versus critical etching length when R = 150 μm and t = 0.5 μm.
circular microstructures. As the etching continues, the structure with radius of 300 μm buckles firstly (Fig. 9b) and then follows the radius of 150 μm (Fig. 9c). The measured values of critical etching length for both structures are listed in Table 2. Therefore, using ANSYS, residual stresses in these microstructures can be determined, the results also listed in Table 2. For comparison, micro rotating structures undergoing entirely the same manufacturing processes were used. Fig. 10 is the SEM result for one micro rotating structure. Finite element
Fig. 9. Critical buckling observation of circular microstructures under compressive residual stress.
method can still be employed for evaluating residual stresses in these microstructures [11]. And the values are − 34.23 MPa for sample 1, − 51.75 MPa for sample 2, both agree well with those obtained by the critical buckling observation of circular microstructures.
Table 2 Critical etching length for circular microstructures under compressive residual stress No. Radius [μm] Critical etching Residual stress [MPa] Average [MPa] length [μm] 1 Fig. 8. SEM results for the two critical buckling patterns. (a) for compressive residual stress and (b) for tensile residual stress.
2
150 300 150 300
27.5 24.0 23.0 22.0
−36.79 −43.93 −51.01 −52.04
− 40.36 − 51.53
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Y.-T. Yu et al. / Thin Solid Films 516 (2008) 4070–4075 Table 3 Critical etching length for circular microstructures under tensile residual stress No.
Radius [μm]
Critical etching length [μm]
Residual stress [MPa]
Average [MPa]
3
150 300
17.5 21.5
646.95 689.87
668.41
modified structural design are necessary for large tensile residual stress applications [11]. 5. Conclusion
Fig. 10. SEM result for one micro rotating structure.
For the Si3N4 structural layer, critical buckling patterns of circular microstructures were always in the bowl shape, indicating the existence of tensile residual stress. Fig. 11a reveals the situation when the structure with radius of 150 μm buckles firstly and then follows the radius of 300 μm (Fig. 11b). The measured values of critical etching length for both structures and evaluated residual stresses are all listed in Table 3, from which we can see that residual stress remains a considerable quantity even after the annealing, resulting in cracks in the connection parts of micro rotating structures (Fig. 12), disabling the measurement of residual stresses. That is a limitation for this paper. In our further research, micro rotating structures with
By detailed analysis and experiments, it is proved that in-situ critical buckling observation of circular microstructures provides a convenient way for evaluating residual stresses in thin films. Both compressive and tensile residual stresses with wide range of amplitude can be measured, just using a single appropriately designed circular microstructure. However, the same as other buckling observation methods, error exists during the observation and measurement of critical buckling patterns. As a result, more accurate results should be assured using more advanced apparatuses. Some simplifications were introduced in this work. For example, contact between the free-standing part of a circular microstructure subjected to compressive residual stress and the substrate was not taken into account when the finite element analysis was performed. But, it will probably happen in practice, especially when the buckling deformation is considerably large. Fortunately, it imposes no effect on the final results of measured residual stresses. Another example, structural layer material or thickness used in this paper seemed transparent under microscope to observe the etching front during the etching, enabling the measurement of critical etching length. But in reality, opaque structural layer will probably be used. In that case, the circular microstructures array with gradually varied radius can be adopted similar to Guckel's methods [4–5]. Acknowledgements This work was supported by the Cultivation Fund of the Key Scientific and Technical Innovation, Ministry of Education (Grant No. 706055), Program for New Century Excellent Talents in Universities, Ministry of Education (Grant No. 05-0869), Xi'an Applied Materials Innovation Fund (Grant No. 200610) and the
Fig. 11. Critical buckling observation of circular microstructures under tensile residual stress.
Fig. 12. Crack caused by excessive tensile residual stress.
Y.-T. Yu et al. / Thin Solid Films 516 (2008) 4070–4075
Doctorate Foundation of Northwestern Polytechnical University (Grant No. CX200611), all in China. References [1] S.P. Murarka, T.F. Retajczyk, J. Appl. Phys. 54 (1983) 2069. [2] B.P. van Drieënhuizen, J.F.L. Goosen, P.J. French, R.F. Wolffenbuttel, Sens. Actuators, A, Phys. 37/38 (1993) 756. [3] N.D. Masters, M.P. de Boer, B.D. Jensen, M.S. Baker, D. Koester, ASTM Spec. Tech. Publ. 1413 (2001) 1. [4] H. Guckel, T. Randazzo, D.W. Burns, J. Appl. Phys. 57 (1985) 1671. [5] H. Guckel, D.W. Burns, C.C.G. Visser, H.A.C. Tilmans, D. Deroo, IEEE Trans. Electron Devices 35 (1988) 800.
4075
[6] T.-Y. Zhang, X. Zhang, Y. Zohar, J. Micromechanics Microengineering 8 (1998) 243. [7] X. Zhang, T.-Y. Zhang, Y. Zohar, Mater. Res. Soc. Symp. Proc. 518 (1998) 155. [8] W.P. Eaton, J.H. Smith, R.L. Jarecki, in: S.W. Pang, S.-C. Chang (Eds.), Micromachining and Microfabrication Process Technology II, Austin, U.S. A., October 14-15, 1996, Proceedings of the SPIE, vol. 2879, 1996, p. 80. [9] W.P. Eaton, R.L. Jarecki, J.H. Smith, Proceedings of the International Conference on Solid State Sensors and Actuators, Transducers'97. Chicago, U.S.A., June 16-19, vol. 1, 1997, p. 249. [10] P.J. French, B.P. van Drieënhuizen, D.P. Poenar, J.F.L. Goosen, R. Mallée, P.M. Sarro, R.F. Wolffenbuttel, J. Microelectromech. Syst. 5 (1996) 187. [11] X. Zhang, T.-Y. Zhang, Y. Zohar, Thin Solid Films 335 (1998) 97. [12] K. Gall, M.L. Dunn, Y. Zhang, B.A. Corff, Mech. Mater. 36 (2004) 45.
Thin Solid Films 516 (2008) 4070 – 4075 www.elsevier.com/locate/tsf
Evaluation of residual stresses in thin films by critical buckling observation of circular microstructures and finite element method Yi-Ting Yu ⁎, Wei-Zheng Yuan, Da-Yong Qiao, Qing Liang Micro and Nano Electromechanical Systems Laboratory, Northwestern Polytechnical University, PO Box 638, 710072, Xi'an, China Received 1 March 2007; received in revised form 16 November 2007; accepted 27 December 2007 Available online 5 January 2008
Abstract An approach for evaluating residual stresses in thin films by critical buckling observation of circular microstructures is proposed, by which the states of residual stresses can be distinguished directly from the observed critical buckling patterns and their magnitudes can be estimated with finite element method after the critical etching length is measured. For practical operation, three samples were prepared by surface micromachining technique and a specially designed video system was set up for in-situ monitoring the whole process during the sacrificial layer etching. Then, measurements of residual stresses were performed and the results were compared with those obtained from micro rotating structures. As a result, the approach is proved to be relatively simple, both compressive and tensile residual stresses with wide range of amplitude can be evaluated by just using a single appropriately designed circular microstructure. © 2008 Elsevier B.V. All rights reserved. Keywords: Residual stresses; Thin films; Critical buckling observation; Circular microstructures; Finite element method; Sacrificial layer etching
1. Introduction Thin film materials are attractive for the fabrication of microsensors and microactuators in microelectromechanical systems (MEMS) fields. However, as structure sizes continue to shrink, material properties which were previously acceptable can cause problems [1]. One such concern is the residual stress, generally induced during thin film deposition. High residual stress, no matter compressive or tensile, can adversely affect structure performances, yield and service lifetime. As a result, various methods for evaluating residual stresses in MEMS thin films have been developed in the last two decades [2–3], among which critical buckling observation of clamped-clamped microbeams array for compressive residual stress and microrings array for tensile, both proposed by Guckel et al. [4–5], is most widely used. However, for surface micromachining applications, evaluation of residual stresses using these microstructures is usually executed after the sacrificial layer is etched completely and drying process has been finished. ⁎ Corresponding author. Tel.: +86 29 88460353 8110; fax: +86 29 88495102. E-mail address: [email protected] (Y.-T. Yu). 0040-6090/$ - see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2007.12.153
In fact, as the etching progresses, buckling of microstructures can also be observed even still in the etching solution. X. Zhang et al. [6–7] reported a few interesting findings on this subject of polysilicon microbeams during the sacrificial layer etching. In this paper, in-situ buckling observation of circular microstructures, often used for studying the release-etch mechanism in surface micromachining [8–9], was carried out during the sacrificial layer etching with a specially designed video system similar to X. Zhang's. Then, an approach for evaluating residual stresses was proposed and practical measurements were performed on three samples prepared by different surface micromachining processes. The results were compared with those obtained from commonly used micro rotating structures [2,10–11]. 2. Experimental preparations Schematic diagram of circular microstructures is shown in Fig. 1, and Fig. 1b is the cross section view in A–A direction. The principal process flows for fabricating these microstructures are illustrated in Fig. 2. Firstly, as shown in Fig. 2a, silicon substrate is coated with a sacrificial layer material and the
Y.-T. Yu et al. / Thin Solid Films 516 (2008) 4070–4075
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Table 1 Three samples prepared by different surface micromachining process No.
State of stress
Sacrificial layer/thickness [μm]
Structural layer/thickness [nm]
1
Compressive
LPCVD TEOS oxide/~3.00 LPCVD TEOS oxide/~0.75 LPCVD TEOS oxide/~0.75
LPCVD polysilicon/312
2 3
Fig. 1. Schematic diagram of circular microstructures.
anchor areas are formed. Then, the structural layer is deposited and patterned (Fig. 2b). Finally, selective etching of the sacrificial layer creates the free-standing micromechanical structures such as the cantilever beam shown in Fig. 2c. In the experiments, 4” n-type (100) silicon wafers were used as substrates. And three samples with different states of residual stress in structural layer were prepared, as shown in Table 1. All the sacrificial layer oxides were deposited by the decomposition of tetraethoxysilane (TEOS) in a low pressure chemical vapor deposition (LPCVD) furnace at 685 °C, 33.33 Pa and O2 flow rate of 200 sccm. Then, two types of structural layer were also LPCVD deposited, polysilicon for compressive residual stress and silicon nitride (Si3N4) for tensile. Polysilicon was deposited at 620 °C, 30 Pa, and using silane as a source gas of 250 sccm, while Si3N4 at 785 °C, 33.33 Pa, and using ammonia and dichlorosilane as source gases of 150 sccm and 10 sccm respectively. Thick-
Fig. 2. Principal process flows for fabricating circular microstructures.
Tensile
LPCVD polysilicon/312 LPCVD Si3N4/409
ness of the structural layer imposes great effects on the results. Consequently, accurate measurement of it for each sample is necessary. In our study, scanning electron microscopy (SEM) was adopted for the purpose. Before etching, an annealing at 950 °C for one hour in a standard diffusion furnace in the nitrogen atmosphere was performed. Wet etching of the sacrificial layer was conducted in a 5:1 buffered hydrofluoric acid solution at room temperature (22 °C). For in-situ monitoring the critical buckling patterns of circular microstructures during the etching, a specially designed video system was set up, as shown in Fig. 3. The etching can be stopped at will to freeze the temporal buckling patterns for SEM. 3. Buckling observation and analysis As the sample is put into the container with fresh etching solution, the sacrificial layer starts to be etched immediately. Fig. 4 presents a simplified model for the etching. R and t represent the radius and thickness of the structure, respectively. And δ denotes the etching length, which increases with the etching time. When etched, peripheral portion of the structure becomes free-standing and residual stress in it is released. Fig. 5 shows three characteristic evolutions of buckling patterns of a circular microstructure during the etching for polysilicon structural layer. At the beginning, the free-standing circular microstructure has enough stiffness to withstand the released stress loading when δ keeps a relatively small value. Therefore, it still remains flat observed in the microscope (Fig. 5a). As the etching time increases, more part of the structure is freed and its total stiffness gets smaller correspondingly. As a result, for a given residual stress, there exists a critical time when
Fig. 3. Experimental device for in-situ critical buckling observation.
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Y.-T. Yu et al. / Thin Solid Films 516 (2008) 4070–4075
Fig. 4. Model for a circular microstructure during the sacrificial layer etching.
the free-standing circular microstructure falls into an unsteady state and buckles immediately. This critical buckling pattern is shown in Fig. 5b and thereafter can be utilized for evaluating residual stress. (For this purpose, finite element program like ANSYS should be resorted to and buckling analysis should be performed when R, t and the critical etching length are achieved.) After that, as the etching continues, buckling pattern of the freestanding circular microstructure exists all the time. However, the number of Newton rings decreases gradually, as shown in Fig. 5c. As for the finite element analysis with ANSYS, the freestanding circular microstructure was modeled as a 2-dimensional annulus with clamped boundary conditions applied on the inner circle, corresponding to the etching front. And the state of plane stress was considered. Radius of the anchor area was taken to be 20 μm and polysilicon structural layer was assumed. Young's modulus, Poisson's ratio and thermal expansion coefficient of polysilicon are 163 GPa, 0.22 and 2.6 × 10− 6/°C respectively [12]. All these material properties were considered to be linear elastic with element type of SHELL63 and element size of 5 μm. Fig. 6 shows two typical critical buckling patterns of the annulus subjected to different states of residual stress, Fig. 6a with a wave shape for compressive residual stress and Fig. 6b with a bowl shape for tensile. Thus, it provides a convenient way to judge the states of residual stress by just observing the critical buckling patterns of circular microstructures during the sacrificial layer etching. Fig. 7 is the simulation results of critical buckling stress at various critical etching length when R = 150 μm and t = 0.5 μm, from which we can see that there exists a unique critical buckling stress, either compressive or tensile, for a specific critical etching length. Also, we can see that a wide range of
Fig. 6. Two typical critical buckling patterns of the annulus. (a) for compressive residual stress and (b) for tensile residual stress.
residual stresses from the order of MPa to GPa can be covered with a single appropriately designed circular microstructure. 4. Results and discussion Fig. 8 provides SEM results for the two critical buckling patterns of circular microstructures subjected to different states of residual stress, which consistent with the prediction in Fig. 6. For the two samples of polysilicon structural layer, critical buckling patterns of circular microstructures during the sacrificial layer etching were always in the wave shape, indicating the existence of compressive residual stress. Fig. 9a reveals the time when no buckling patterns happen for both
Fig. 5. Three characteristic evolutions of buckling patterns of a circular microstructure during the etching.
Y.-T. Yu et al. / Thin Solid Films 516 (2008) 4070–4075
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Fig. 7. Critical buckling stress versus critical etching length when R = 150 μm and t = 0.5 μm.
circular microstructures. As the etching continues, the structure with radius of 300 μm buckles firstly (Fig. 9b) and then follows the radius of 150 μm (Fig. 9c). The measured values of critical etching length for both structures are listed in Table 2. Therefore, using ANSYS, residual stresses in these microstructures can be determined, the results also listed in Table 2. For comparison, micro rotating structures undergoing entirely the same manufacturing processes were used. Fig. 10 is the SEM result for one micro rotating structure. Finite element
Fig. 9. Critical buckling observation of circular microstructures under compressive residual stress.
method can still be employed for evaluating residual stresses in these microstructures [11]. And the values are − 34.23 MPa for sample 1, − 51.75 MPa for sample 2, both agree well with those obtained by the critical buckling observation of circular microstructures.
Table 2 Critical etching length for circular microstructures under compressive residual stress No. Radius [μm] Critical etching Residual stress [MPa] Average [MPa] length [μm] 1 Fig. 8. SEM results for the two critical buckling patterns. (a) for compressive residual stress and (b) for tensile residual stress.
2
150 300 150 300
27.5 24.0 23.0 22.0
−36.79 −43.93 −51.01 −52.04
− 40.36 − 51.53
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Y.-T. Yu et al. / Thin Solid Films 516 (2008) 4070–4075 Table 3 Critical etching length for circular microstructures under tensile residual stress No.
Radius [μm]
Critical etching length [μm]
Residual stress [MPa]
Average [MPa]
3
150 300
17.5 21.5
646.95 689.87
668.41
modified structural design are necessary for large tensile residual stress applications [11]. 5. Conclusion
Fig. 10. SEM result for one micro rotating structure.
For the Si3N4 structural layer, critical buckling patterns of circular microstructures were always in the bowl shape, indicating the existence of tensile residual stress. Fig. 11a reveals the situation when the structure with radius of 150 μm buckles firstly and then follows the radius of 300 μm (Fig. 11b). The measured values of critical etching length for both structures and evaluated residual stresses are all listed in Table 3, from which we can see that residual stress remains a considerable quantity even after the annealing, resulting in cracks in the connection parts of micro rotating structures (Fig. 12), disabling the measurement of residual stresses. That is a limitation for this paper. In our further research, micro rotating structures with
By detailed analysis and experiments, it is proved that in-situ critical buckling observation of circular microstructures provides a convenient way for evaluating residual stresses in thin films. Both compressive and tensile residual stresses with wide range of amplitude can be measured, just using a single appropriately designed circular microstructure. However, the same as other buckling observation methods, error exists during the observation and measurement of critical buckling patterns. As a result, more accurate results should be assured using more advanced apparatuses. Some simplifications were introduced in this work. For example, contact between the free-standing part of a circular microstructure subjected to compressive residual stress and the substrate was not taken into account when the finite element analysis was performed. But, it will probably happen in practice, especially when the buckling deformation is considerably large. Fortunately, it imposes no effect on the final results of measured residual stresses. Another example, structural layer material or thickness used in this paper seemed transparent under microscope to observe the etching front during the etching, enabling the measurement of critical etching length. But in reality, opaque structural layer will probably be used. In that case, the circular microstructures array with gradually varied radius can be adopted similar to Guckel's methods [4–5]. Acknowledgements This work was supported by the Cultivation Fund of the Key Scientific and Technical Innovation, Ministry of Education (Grant No. 706055), Program for New Century Excellent Talents in Universities, Ministry of Education (Grant No. 05-0869), Xi'an Applied Materials Innovation Fund (Grant No. 200610) and the
Fig. 11. Critical buckling observation of circular microstructures under tensile residual stress.
Fig. 12. Crack caused by excessive tensile residual stress.
Y.-T. Yu et al. / Thin Solid Films 516 (2008) 4070–4075
Doctorate Foundation of Northwestern Polytechnical University (Grant No. CX200611), all in China. References [1] S.P. Murarka, T.F. Retajczyk, J. Appl. Phys. 54 (1983) 2069. [2] B.P. van Drieënhuizen, J.F.L. Goosen, P.J. French, R.F. Wolffenbuttel, Sens. Actuators, A, Phys. 37/38 (1993) 756. [3] N.D. Masters, M.P. de Boer, B.D. Jensen, M.S. Baker, D. Koester, ASTM Spec. Tech. Publ. 1413 (2001) 1. [4] H. Guckel, T. Randazzo, D.W. Burns, J. Appl. Phys. 57 (1985) 1671. [5] H. Guckel, D.W. Burns, C.C.G. Visser, H.A.C. Tilmans, D. Deroo, IEEE Trans. Electron Devices 35 (1988) 800.
4075
[6] T.-Y. Zhang, X. Zhang, Y. Zohar, J. Micromechanics Microengineering 8 (1998) 243. [7] X. Zhang, T.-Y. Zhang, Y. Zohar, Mater. Res. Soc. Symp. Proc. 518 (1998) 155. [8] W.P. Eaton, J.H. Smith, R.L. Jarecki, in: S.W. Pang, S.-C. Chang (Eds.), Micromachining and Microfabrication Process Technology II, Austin, U.S. A., October 14-15, 1996, Proceedings of the SPIE, vol. 2879, 1996, p. 80. [9] W.P. Eaton, R.L. Jarecki, J.H. Smith, Proceedings of the International Conference on Solid State Sensors and Actuators, Transducers'97. Chicago, U.S.A., June 16-19, vol. 1, 1997, p. 249. [10] P.J. French, B.P. van Drieënhuizen, D.P. Poenar, J.F.L. Goosen, R. Mallée, P.M. Sarro, R.F. Wolffenbuttel, J. Microelectromech. Syst. 5 (1996) 187. [11] X. Zhang, T.-Y. Zhang, Y. Zohar, Thin Solid Films 335 (1998) 97. [12] K. Gall, M.L. Dunn, Y. Zhang, B.A. Corff, Mech. Mater. 36 (2004) 45.