A Fracture Mechanics Model For The Repair of ... - Semantic Scholar
Proceedings of IMECE2005 2005 ASME International Mechanical Engineering Congress and Exposition November 5-11, 2005, Orlando, Florida USA
IMECE2005-81000 A FRACTURE MECHANICS MODEL FOR THE REPAIR OF MICROCANTILEVERS BY LASER INDUCED STRESS WAVES Zayd C. Leseman
1
1
Sai Koppaka
Thomas J. Mackin
2
1
Mechanical and Industrial Engineering The University of Illinois at Urbana-Champaign Urbana, IL 61801 2 Mechanical Engineering Department California Polytechnic San Luis Obispo, CA 93405 ABSTRACT A fracture mechanics model was developed, and experimentally verified, to model stress wave repair of stiction-failed microcantilevers. This model allows us to predict accurately the number of laser pulses, at a specific fluence and wavelength, required to fully repair stiction-failed microcantilevers. The proposed fracture mechanics model includes the strain energy stored in a stiction-failed microcantilever and the strain energy supplied by laser induced stress-waves propagating in the material. The ‘unstuck’ portion of the microcantilever is modeled as a crack so that crack growth reduces the stiction-failed length of the microcantilever.
In the stress-wave repair method, laser irradiation of the substrate initiates a compressive stress wave that propagates through the material. These compressive stress waves pass through the substrate, across the stiction-failed interface and reflect from the top free surface of the cantilever. Upon reflection, the compressive stress waves become tensile and propagate back through the structure passing across the stiction-failed interface and, potentially, rupturing the secondary bonds at that interface.
A full range of experiments have been performed to validate the model. Experiments using laser fluences ranging from 0.5 kJ/m2 – 45 kJ/m2 at two different wavelengths have been performed. The experiments are in good agreement with the model predictions. Additionally we have identified practical ranges for irradiation, including a lower bound fluence below which repair is impractical, and an upper bound above which damage to the substrate and microcantilevers occurs.
In this article we discuss a fracture mechanics model that we have developed [7] along with new experimental results. We show that our experimental results agree well with the previously developed theory and also present engineering guidelines for laser repair of stiction failed MEMS microcantilevers. These guidelines include the wavelength, fluence, number of pulses, etc. needed to repair stiction failed microcantilevers.
INTRODUCTION Construction of MEMS devices are typically limited by fabrication issues [1], primarily because microscale structures are extremely compliant and susceptible to failure by secondary forces. Failure by adhesion to neighboring structures or the substrate is commonly referred to as stiction. If stiction failures can be prevented or repaired, device yields would increase dramatically. As a result, a great deal of effort is focused on research into stiction prevention/repair.
THEORY Stiction failed beams are categorized as having either an sshaped failure or arc-shaped failure, Figure 1. The ‘un-stuck’ portion of the beam is modeled as a crack of length s, with the crack tip located at the point where the un-stuck portion of the beam meets the substrate (see Figure 1).
repair [2]; ultrasonic actuation[3]; pulsed Lorentz forces[4]; direct application of force[5]; and, most recently, stress wave debonding[6].
Stiction-failed microstructures have been repaired using many different methods, including: laser induced thermomechanical
1
Copyright © 2005 by ASME
of a sacrificial oxide is then grown in the LPCVD chamber from tetraethylorthosilicate (TEOS) and then patterned to accommodate the anchor supports of the microcantilevers. Subsequently, two polysilicon layers are deposited to a total thickness of 2.6 µm. This layer is patterned and then etched to give microcantilevers. At this point the wafer is diced into 1.5 cm squares and shipped with the sacrificial oxide still in tact. Figure 2 schematically illustrates this process. The final step in sample preparation is release by etching of the sacrificial oxide layer. Release begins with submerging each die in 49% HF for 15 minutes. The die is then rinsed twice in DI water for 5 minutes. Finally, the chip is rinsed for an additional 5 minutes in IPA and then baked out on a hot plate for 10 minutes at 110 oC. Due to the highly compliant nature of the microcantilevers, capillary forces pull the beams into contact with the substrate resulting in stiction failure.
Figure 1: The two types of stiction failures: a) Arc-shaped and b) S-shaped The strain energy release rate, G, associated with crack growth, is used to capture the energetics of stress-wave repair. In this approach, the stored elastic energy in the system consists of an elastic beam deflection term and a stress-wave energy term. Laser irradiation initiates a stress-wave that carries elastic energy to the interface and extends the stictionfree beam length, s, resulting in an expression for the crack length, s as a function of the number of laser pulses, N, given by:
3s 04 h 2 t 3 E s= 3h 2 t 3 E − s 04 ∆l c NPrad
1 4
(1)
where s0 is the initial crack length, h is the width of the beam, t is thickness of the beam, E is the elastic modulus of poly-Si, Prad is the radiation pressure of the laser pulse, and ∆lc is a change in characteristic gage length of the stress wave. The details of the derivation appear elsewhere [7]. This prediction of the crack length, s, can be compared with experimentally measured crack lengths to validate the theory. SAMPLE FABRICATION Arrays of microcantilevers were fabricated by Sandia National Laboratories using the 4-layer SUMMiT IVTM process to produce cantilevers 30 µm wide, 1500 µm long, and 2.6 µm thick, suspended 1.9 µm above the substrate.
Figure 2: Samples are fabricated in the following manner: a) 0.6 µm of thermally grown oxide, b) Deposit LPCVD Nitride to a thickness of 0.8 µm, c) LPCVD deposition of 0.3 µm polysilicon, d) Deposition of 1.9 µm of a sacrificial LPCVD silicon dioxide and its subsequent patterning, e) Deposition and patterning of two polysilicon layers, f) Release of the microcantilevers by etching of the sacrificial SiO2 After release, each array was inspected using an optical microscope with a Michelson interferometer to measure beam displacement profiles. The 1500 µm long beams studied here always exhibited s-shaped failures. Figure 3 shows a typical interferometric image looking down on a die, accompanied by a schematic sideview that illustrates the beam profile.
The SUMMiT IVTM process is a surface micromachining process that uses polysilicon structural layers and sacrificial oxide layers. The process begins with a 150 mm (100) single side polished (SSP) n-type Si wafer, onto which a 0.6 µm thick oxide layer is thermally grown. Next, a 0.8 µm thick low stress SiNx layer is deposited by LPCVD. A 0.3 µm thick layer of polysilicon is deposited and then doped (P0). 1.9 µm
2
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Figure 3: Typical interferometric image of s-shaped beam failures (top) and a schematic representation of the beam profile associated with the interferometric image (bottom). EXPERIMENTAL TECHNIQUE FOR STRESS WAVE REPAIR Laser fluences ranging from 0.5 kJ/m2 to 45 kJ/m2 were used to irradiate the uncoated back-side of the sample to repair the stiction failed beams, Figure 4. Experiments were also carried out at two different wavelengths, 532 nm and 1064 nm. Following release, baseline interferometric images were captured and the sample was attached to an xyz stage and irradiated.
Figure 5: Stress wave repair by a multiple pulse technique. Two different experimental set-ups were used to perform the experiments. The first is schematically illustrated in Figure 4. This setup was used for experiments at fluences of 5, 10, 15, and 20 kJ/m2. The second setup is shown in Figure 6, and includes a CCD camera for continuous monitoring of crack length. This setup was used for irradiation at the 0.5 kJ/m2 fluence level. This revised setup was necessary due to the large number of pulses needed for release of the microcantilevers at this fluence. It was impractical to remove the die and inspect it after each pulse in experiments at low fluences. Another addition to the setup was a 90:10 beam splitter. The laser used in these experiments is not stable at a fluence of 0.5 kJ/m2, hence the beamsplitter was used to dump 90% of the original pulse and deliver a more stable 10% of the pulse at the desired fluence of 0.5 kJ/m2.
Figure 4: Experimental procedure for stress wave repair. The repair process was carried out in steps, with each step consisting of irradiation with a single pulse from the Nd:YAG laser, followed by interferometric imaging to measure the change in stiction length. This process was repeated, at the same fluence, until the cantilevers were completely repaired, Figure 5.
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Figure 7: Experimental data for a fluence of 0.5 kJ/m2 at a wavelength of 1064 nm. Figure 6: Experimental setup for in-situ observation of experiments. EXPERIMENTAL RESULTS The experiments in Ref. 7 were performed at fluences of 5, 10, 15, and 20 kJ/m2 at a wavelength of 532 nm. These experiments showed good agreement with theory. An additional experiment, at 10 kJ/m2, but at a wavelength of 1064 nm, was carried out to determine if the theoretically predicted linear relationship between Gstress wave and Prad was consistent across wavelengths:
G stresswave =
1 Prad ∆l c 2
When this fluence condition was added to previous experiments relating laser pressure to strain energy release rate (Eqn. 2), we see that confirmation of the linear relationship at different wavelengths and low fluences, Figure 8.
(2)
where Gstress wave is the stress wave contribution to the strain energy release rate , Prad is the radiation pressure generated by the laser pulse, and ∆lc is a characteristic length of the system. Indeed, this experiment did confirm the linear relationship. In the present article we explored fluences 10 times lower than previously attempted, and compared these experiments to previous results to affirm the linear dependence shown in Eqn. 2. To explore extremely low fluences, we chose a fluence of 0.5 kJ/m2, and also chose to coat the backside of the die with a 500 nm thick layer of evaporated aluminum. The Al layer was deposited to increase reflectivity and assure that sample heating by laser absorption was not playing a role in stiction repair. Figure 7 shows a plot of crack length, s, against the number of nano-second laser pulses at a fluence of 0.5 kJ/m2 and a wavelength of 1064 nm. The sample was irradiated with 700 pulses at a frequency of 1 Hz, after which time there was no observable damage to either side of the die. An analysis of images taken after 700 pulses showed an increase in crack length of only 93 microns. This shows that the proposed repair method can work at very low fluences.
Figure 8: A plot of the strain energy release rate contribution of the stress wave versus the radiation pressure that continues to exhibit a linear trend after addition of the data from a fluence of 0.5 kJ/m2. The radiation pressure and sample heating are calculated using the sample transmissivity, T, absorptivity, A, and reflectivity, R. By coating the die with 600 nm of Al the sample absorptivity was A=0.04 and the reflectivity, R, was increased to R=0.96, whereas in experiments without the Al coating the absorptivity was as high as A=0.33 [1]. We used the absorptivity to perform a thermal analysis of the die using a finite difference method. Because a thermal analysis of a die with so many different layers proved very difficult, the analysis was restricted to the effect of irradiation of the Si substrate. This is a safe assumption because the aluminum layer thickness is small compared to the thickness of the wafer and the Al absorbs all the energy in its thickness, see Figure 9. The thermal analysis showed an average temperature increase of 0.18 K for the cantilever array side of the Al film. Such small changes in temperature would not be sufficient to repair the beams by thermomechanical means [8]. Furthermore, in all cases we observed that the cantilevers in the arrays surrounding the array targeted for repair remained firmly stuck
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to the substrate. This indicates that the repair was by stress waves since any thermal stress repair would have created a wafer curvature that would have driven repair in neighboring cantilevers.
Figure 9: A plot of the R, T, and A values versus thickness of the Al thin film layer. Note that at 50 nm there is an insignificant amount of transmission, thus all energy is consumed in the Al thin film. In addition to low fluence experiments, experiments were performed at fluences up to 45 kJ/m2. It was found that, at a fluence of 45 kJ/m2, not only were the beams released, but the anchor supports were uprooted from the substrate. Similar results were observed by Gupta et al. [6]. These experiments designate an upper threshold for useful fluence. Clearly, at or above this fluence permanent damage occurs to the microcantilevers. Furthermore these experiments reveal a fluence level that can fracture the bonds formed during deposition between the P1 and P0 polysilicon layers. Finally we explored the effect of pulse frequency on stress wave repair. We found that, for the experiments at fluences of 5, 10, 15, and 20 kJ/m2, waiting 5 minutes between pulses allowed for heat dissipation, and left both the front and back side undamaged. Similarly, in the experiments at 0.5 kJ/m2, we found no damage to either side when the laser was pulsed at a 1 Hz frequency. When pulsed at 20 Hz at a fluence level of 20 kJ/m2 at a wavelength of 532 nm we found blistering of the substrate. Figure 10 shows optical micrographs and line scans from a Sloan Dektak3 ST profilimeter. Figure 10a shows an irradiated backside surface of a die following exposure to 10 laser pulses at 20 kJ/m2 where the sample rested 5 minutes between pulses. Its corresponding line scan shows a roughness typical of an unpolished wafer surface and shows no damage from laser irradiation. Figure 10b shows a sample that was irradiated by 400 pulses at a frequency of 20 Hz at a fluence of 20 kJ/m2, showing significant damage to the irradiated surface. Though the laser spot size was 3.2 mm the diameter of the damage zone is far greater. More interesting is the fact that the damage zone appears as a raised blister, indicating sub-surface debonding and subsequent
buckling of one or several layers of the substrate. We know that this is a buckled, because the amount of force applied by the profilimeter had a significant effect on the blister amplitude.
Figure 10: (a) No damage observed after repair on 10 pulses at a laser fluence of 20 kJ/m2 (b) Damage to the substrate on multiple pulse irradiation involving 400 pulses at a laser fluence of 20 kJ/m2 In summary we have identified a range of fluences and numbers of pulses required for stress wave repair of stiction failed microcantilevers. The plot in Figure 11 summarizes these findings. This plot is specific to the SUMMiT IVTM process and is applicable for microcantilevers of length 1500 µm and shorter. Longer beams are more compliant and may require more pulses, and MEMS fabricated by other processes will require a new set of optical parameters (R, T, and A) in order to determine Prad. Operation outside of the shaded area of Figure 11 will result in undesirable results. Using too high a fluence will damage the micromachined structure on the frontside of the die. Using too low a fluence will result in an exorbitant amount of pulses for full repair. We have also found it advisable to irradiate the die at frequencies below 1 Hz in order to avoid damage due to accumulated heat in the thin film layers.
Figure 11: A plot showing the recommended range for practical stress wave repair.
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Copyright © 2005 by ASME
CONCLUSIONS The stress wave repair technique proved highly effective for repairing stiction-failed microcantilevers. The repair process is well described using a fracture mechanics model that treats the free portion of stiction-failed microcantilevers as a crack. The model incorporates the elastic stored energy of stress waves to account for the stiction repair. This approach enables a convenient prediction of the number of pulses required to repair a microcantilever, and is robust enough to account for differences in fluence and irradiation wavelength. These REFERENCES [1] R. T. Howe, “Surface Micromachining for Microsensors and Microactuators,” Journal of Vacuum Science and Technology B, 6 (6), 1988, pp. 1809-1813. [2] J. Rogers, T. Mackin, and L. Phinney, “A thermomechanical model for adhesion reduction of MEMS cantilevers," Journal of Microelectromechanical Systems, vol. 11, 2002, pp. 512-520. [3] V. Kaajakari, S. –H. Kan, L. –J. Lin, A. Lal, and S. Rodgers, "Ultrasonic Actuation for MEMS Dormancy-Related Stiction Reduction," Proceedings of SPIE, MEMS Reliability for Critical Applications, 4180, R. A. Lawton, ed., 2000, pp. 60-65. [4] B. P. Gogoi and C. H. Mastrangelo, “Adhesion Release and Yield Enhancement of Microstructures Using Pulsed Lorentz Forces,” Journal of Microelectromechanical Systems, 4, 1995, pp. 185-192.
experiments validate and extend the previous results by Gupta et al. [6], and show that stress waves are very effective in repairing stiction-failed cantilevers without damaging the repaired cantilevers. We have also shown that repairs are only a stress wave effect and not a thermal effect. Additionally we have identified practical ranges for irradiation, including a lower bound fluence below which repair is impractical, and an upper bound above which damage to the substrate and microcantilevers occurs.
modeling and experiments,” Journal of the Mechanics and Physics of Solids, 51(8), 2003, pp. 1601-1622. [6] V. Gupta, R. Snow, M. C. Wu, A. Jain, and J. Tsai, “Recovery of stiction-failed MEMS structures using laserinduced stress waves," Journal of Microelectromechanical Systems, v. 13, n. 4, August, 2004, p 696-700. [7] Z. C. Leseman, S. Koppaka, and T. J. Mackin, “A fracture mechanics model for stress-wave repair of stiction failed microcantilevers,” Journal of Microelectromechanical Systems, July 2005, submitted. [8]J. W. Rogers, L. M. Phinney, “Transient, interferometric imaging of polycrystalline silicon MEMS devices during laser heating,” Microscale Thermophysical Engineering, Mar. 2004, Vol. 8 Issue 1, pp. 43-59.
[5] E. E. Jones, M. R. Begley, and K. D. Murphy, “Adhesion of micro-cantilevers subjected to mechanical point-loading:
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IMECE2005-81000 A FRACTURE MECHANICS MODEL FOR THE REPAIR OF MICROCANTILEVERS BY LASER INDUCED STRESS WAVES Zayd C. Leseman
1
1
Sai Koppaka
Thomas J. Mackin
2
1
Mechanical and Industrial Engineering The University of Illinois at Urbana-Champaign Urbana, IL 61801 2 Mechanical Engineering Department California Polytechnic San Luis Obispo, CA 93405 ABSTRACT A fracture mechanics model was developed, and experimentally verified, to model stress wave repair of stiction-failed microcantilevers. This model allows us to predict accurately the number of laser pulses, at a specific fluence and wavelength, required to fully repair stiction-failed microcantilevers. The proposed fracture mechanics model includes the strain energy stored in a stiction-failed microcantilever and the strain energy supplied by laser induced stress-waves propagating in the material. The ‘unstuck’ portion of the microcantilever is modeled as a crack so that crack growth reduces the stiction-failed length of the microcantilever.
In the stress-wave repair method, laser irradiation of the substrate initiates a compressive stress wave that propagates through the material. These compressive stress waves pass through the substrate, across the stiction-failed interface and reflect from the top free surface of the cantilever. Upon reflection, the compressive stress waves become tensile and propagate back through the structure passing across the stiction-failed interface and, potentially, rupturing the secondary bonds at that interface.
A full range of experiments have been performed to validate the model. Experiments using laser fluences ranging from 0.5 kJ/m2 – 45 kJ/m2 at two different wavelengths have been performed. The experiments are in good agreement with the model predictions. Additionally we have identified practical ranges for irradiation, including a lower bound fluence below which repair is impractical, and an upper bound above which damage to the substrate and microcantilevers occurs.
In this article we discuss a fracture mechanics model that we have developed [7] along with new experimental results. We show that our experimental results agree well with the previously developed theory and also present engineering guidelines for laser repair of stiction failed MEMS microcantilevers. These guidelines include the wavelength, fluence, number of pulses, etc. needed to repair stiction failed microcantilevers.
INTRODUCTION Construction of MEMS devices are typically limited by fabrication issues [1], primarily because microscale structures are extremely compliant and susceptible to failure by secondary forces. Failure by adhesion to neighboring structures or the substrate is commonly referred to as stiction. If stiction failures can be prevented or repaired, device yields would increase dramatically. As a result, a great deal of effort is focused on research into stiction prevention/repair.
THEORY Stiction failed beams are categorized as having either an sshaped failure or arc-shaped failure, Figure 1. The ‘un-stuck’ portion of the beam is modeled as a crack of length s, with the crack tip located at the point where the un-stuck portion of the beam meets the substrate (see Figure 1).
repair [2]; ultrasonic actuation[3]; pulsed Lorentz forces[4]; direct application of force[5]; and, most recently, stress wave debonding[6].
Stiction-failed microstructures have been repaired using many different methods, including: laser induced thermomechanical
1
Copyright © 2005 by ASME
of a sacrificial oxide is then grown in the LPCVD chamber from tetraethylorthosilicate (TEOS) and then patterned to accommodate the anchor supports of the microcantilevers. Subsequently, two polysilicon layers are deposited to a total thickness of 2.6 µm. This layer is patterned and then etched to give microcantilevers. At this point the wafer is diced into 1.5 cm squares and shipped with the sacrificial oxide still in tact. Figure 2 schematically illustrates this process. The final step in sample preparation is release by etching of the sacrificial oxide layer. Release begins with submerging each die in 49% HF for 15 minutes. The die is then rinsed twice in DI water for 5 minutes. Finally, the chip is rinsed for an additional 5 minutes in IPA and then baked out on a hot plate for 10 minutes at 110 oC. Due to the highly compliant nature of the microcantilevers, capillary forces pull the beams into contact with the substrate resulting in stiction failure.
Figure 1: The two types of stiction failures: a) Arc-shaped and b) S-shaped The strain energy release rate, G, associated with crack growth, is used to capture the energetics of stress-wave repair. In this approach, the stored elastic energy in the system consists of an elastic beam deflection term and a stress-wave energy term. Laser irradiation initiates a stress-wave that carries elastic energy to the interface and extends the stictionfree beam length, s, resulting in an expression for the crack length, s as a function of the number of laser pulses, N, given by:
3s 04 h 2 t 3 E s= 3h 2 t 3 E − s 04 ∆l c NPrad
1 4
(1)
where s0 is the initial crack length, h is the width of the beam, t is thickness of the beam, E is the elastic modulus of poly-Si, Prad is the radiation pressure of the laser pulse, and ∆lc is a change in characteristic gage length of the stress wave. The details of the derivation appear elsewhere [7]. This prediction of the crack length, s, can be compared with experimentally measured crack lengths to validate the theory. SAMPLE FABRICATION Arrays of microcantilevers were fabricated by Sandia National Laboratories using the 4-layer SUMMiT IVTM process to produce cantilevers 30 µm wide, 1500 µm long, and 2.6 µm thick, suspended 1.9 µm above the substrate.
Figure 2: Samples are fabricated in the following manner: a) 0.6 µm of thermally grown oxide, b) Deposit LPCVD Nitride to a thickness of 0.8 µm, c) LPCVD deposition of 0.3 µm polysilicon, d) Deposition of 1.9 µm of a sacrificial LPCVD silicon dioxide and its subsequent patterning, e) Deposition and patterning of two polysilicon layers, f) Release of the microcantilevers by etching of the sacrificial SiO2 After release, each array was inspected using an optical microscope with a Michelson interferometer to measure beam displacement profiles. The 1500 µm long beams studied here always exhibited s-shaped failures. Figure 3 shows a typical interferometric image looking down on a die, accompanied by a schematic sideview that illustrates the beam profile.
The SUMMiT IVTM process is a surface micromachining process that uses polysilicon structural layers and sacrificial oxide layers. The process begins with a 150 mm (100) single side polished (SSP) n-type Si wafer, onto which a 0.6 µm thick oxide layer is thermally grown. Next, a 0.8 µm thick low stress SiNx layer is deposited by LPCVD. A 0.3 µm thick layer of polysilicon is deposited and then doped (P0). 1.9 µm
2
Copyright © 2005 by ASME
Figure 3: Typical interferometric image of s-shaped beam failures (top) and a schematic representation of the beam profile associated with the interferometric image (bottom). EXPERIMENTAL TECHNIQUE FOR STRESS WAVE REPAIR Laser fluences ranging from 0.5 kJ/m2 to 45 kJ/m2 were used to irradiate the uncoated back-side of the sample to repair the stiction failed beams, Figure 4. Experiments were also carried out at two different wavelengths, 532 nm and 1064 nm. Following release, baseline interferometric images were captured and the sample was attached to an xyz stage and irradiated.
Figure 5: Stress wave repair by a multiple pulse technique. Two different experimental set-ups were used to perform the experiments. The first is schematically illustrated in Figure 4. This setup was used for experiments at fluences of 5, 10, 15, and 20 kJ/m2. The second setup is shown in Figure 6, and includes a CCD camera for continuous monitoring of crack length. This setup was used for irradiation at the 0.5 kJ/m2 fluence level. This revised setup was necessary due to the large number of pulses needed for release of the microcantilevers at this fluence. It was impractical to remove the die and inspect it after each pulse in experiments at low fluences. Another addition to the setup was a 90:10 beam splitter. The laser used in these experiments is not stable at a fluence of 0.5 kJ/m2, hence the beamsplitter was used to dump 90% of the original pulse and deliver a more stable 10% of the pulse at the desired fluence of 0.5 kJ/m2.
Figure 4: Experimental procedure for stress wave repair. The repair process was carried out in steps, with each step consisting of irradiation with a single pulse from the Nd:YAG laser, followed by interferometric imaging to measure the change in stiction length. This process was repeated, at the same fluence, until the cantilevers were completely repaired, Figure 5.
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Figure 7: Experimental data for a fluence of 0.5 kJ/m2 at a wavelength of 1064 nm. Figure 6: Experimental setup for in-situ observation of experiments. EXPERIMENTAL RESULTS The experiments in Ref. 7 were performed at fluences of 5, 10, 15, and 20 kJ/m2 at a wavelength of 532 nm. These experiments showed good agreement with theory. An additional experiment, at 10 kJ/m2, but at a wavelength of 1064 nm, was carried out to determine if the theoretically predicted linear relationship between Gstress wave and Prad was consistent across wavelengths:
G stresswave =
1 Prad ∆l c 2
When this fluence condition was added to previous experiments relating laser pressure to strain energy release rate (Eqn. 2), we see that confirmation of the linear relationship at different wavelengths and low fluences, Figure 8.
(2)
where Gstress wave is the stress wave contribution to the strain energy release rate , Prad is the radiation pressure generated by the laser pulse, and ∆lc is a characteristic length of the system. Indeed, this experiment did confirm the linear relationship. In the present article we explored fluences 10 times lower than previously attempted, and compared these experiments to previous results to affirm the linear dependence shown in Eqn. 2. To explore extremely low fluences, we chose a fluence of 0.5 kJ/m2, and also chose to coat the backside of the die with a 500 nm thick layer of evaporated aluminum. The Al layer was deposited to increase reflectivity and assure that sample heating by laser absorption was not playing a role in stiction repair. Figure 7 shows a plot of crack length, s, against the number of nano-second laser pulses at a fluence of 0.5 kJ/m2 and a wavelength of 1064 nm. The sample was irradiated with 700 pulses at a frequency of 1 Hz, after which time there was no observable damage to either side of the die. An analysis of images taken after 700 pulses showed an increase in crack length of only 93 microns. This shows that the proposed repair method can work at very low fluences.
Figure 8: A plot of the strain energy release rate contribution of the stress wave versus the radiation pressure that continues to exhibit a linear trend after addition of the data from a fluence of 0.5 kJ/m2. The radiation pressure and sample heating are calculated using the sample transmissivity, T, absorptivity, A, and reflectivity, R. By coating the die with 600 nm of Al the sample absorptivity was A=0.04 and the reflectivity, R, was increased to R=0.96, whereas in experiments without the Al coating the absorptivity was as high as A=0.33 [1]. We used the absorptivity to perform a thermal analysis of the die using a finite difference method. Because a thermal analysis of a die with so many different layers proved very difficult, the analysis was restricted to the effect of irradiation of the Si substrate. This is a safe assumption because the aluminum layer thickness is small compared to the thickness of the wafer and the Al absorbs all the energy in its thickness, see Figure 9. The thermal analysis showed an average temperature increase of 0.18 K for the cantilever array side of the Al film. Such small changes in temperature would not be sufficient to repair the beams by thermomechanical means [8]. Furthermore, in all cases we observed that the cantilevers in the arrays surrounding the array targeted for repair remained firmly stuck
4
Copyright © 2005 by ASME
to the substrate. This indicates that the repair was by stress waves since any thermal stress repair would have created a wafer curvature that would have driven repair in neighboring cantilevers.
Figure 9: A plot of the R, T, and A values versus thickness of the Al thin film layer. Note that at 50 nm there is an insignificant amount of transmission, thus all energy is consumed in the Al thin film. In addition to low fluence experiments, experiments were performed at fluences up to 45 kJ/m2. It was found that, at a fluence of 45 kJ/m2, not only were the beams released, but the anchor supports were uprooted from the substrate. Similar results were observed by Gupta et al. [6]. These experiments designate an upper threshold for useful fluence. Clearly, at or above this fluence permanent damage occurs to the microcantilevers. Furthermore these experiments reveal a fluence level that can fracture the bonds formed during deposition between the P1 and P0 polysilicon layers. Finally we explored the effect of pulse frequency on stress wave repair. We found that, for the experiments at fluences of 5, 10, 15, and 20 kJ/m2, waiting 5 minutes between pulses allowed for heat dissipation, and left both the front and back side undamaged. Similarly, in the experiments at 0.5 kJ/m2, we found no damage to either side when the laser was pulsed at a 1 Hz frequency. When pulsed at 20 Hz at a fluence level of 20 kJ/m2 at a wavelength of 532 nm we found blistering of the substrate. Figure 10 shows optical micrographs and line scans from a Sloan Dektak3 ST profilimeter. Figure 10a shows an irradiated backside surface of a die following exposure to 10 laser pulses at 20 kJ/m2 where the sample rested 5 minutes between pulses. Its corresponding line scan shows a roughness typical of an unpolished wafer surface and shows no damage from laser irradiation. Figure 10b shows a sample that was irradiated by 400 pulses at a frequency of 20 Hz at a fluence of 20 kJ/m2, showing significant damage to the irradiated surface. Though the laser spot size was 3.2 mm the diameter of the damage zone is far greater. More interesting is the fact that the damage zone appears as a raised blister, indicating sub-surface debonding and subsequent
buckling of one or several layers of the substrate. We know that this is a buckled, because the amount of force applied by the profilimeter had a significant effect on the blister amplitude.
Figure 10: (a) No damage observed after repair on 10 pulses at a laser fluence of 20 kJ/m2 (b) Damage to the substrate on multiple pulse irradiation involving 400 pulses at a laser fluence of 20 kJ/m2 In summary we have identified a range of fluences and numbers of pulses required for stress wave repair of stiction failed microcantilevers. The plot in Figure 11 summarizes these findings. This plot is specific to the SUMMiT IVTM process and is applicable for microcantilevers of length 1500 µm and shorter. Longer beams are more compliant and may require more pulses, and MEMS fabricated by other processes will require a new set of optical parameters (R, T, and A) in order to determine Prad. Operation outside of the shaded area of Figure 11 will result in undesirable results. Using too high a fluence will damage the micromachined structure on the frontside of the die. Using too low a fluence will result in an exorbitant amount of pulses for full repair. We have also found it advisable to irradiate the die at frequencies below 1 Hz in order to avoid damage due to accumulated heat in the thin film layers.
Figure 11: A plot showing the recommended range for practical stress wave repair.
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CONCLUSIONS The stress wave repair technique proved highly effective for repairing stiction-failed microcantilevers. The repair process is well described using a fracture mechanics model that treats the free portion of stiction-failed microcantilevers as a crack. The model incorporates the elastic stored energy of stress waves to account for the stiction repair. This approach enables a convenient prediction of the number of pulses required to repair a microcantilever, and is robust enough to account for differences in fluence and irradiation wavelength. These REFERENCES [1] R. T. Howe, “Surface Micromachining for Microsensors and Microactuators,” Journal of Vacuum Science and Technology B, 6 (6), 1988, pp. 1809-1813. [2] J. Rogers, T. Mackin, and L. Phinney, “A thermomechanical model for adhesion reduction of MEMS cantilevers," Journal of Microelectromechanical Systems, vol. 11, 2002, pp. 512-520. [3] V. Kaajakari, S. –H. Kan, L. –J. Lin, A. Lal, and S. Rodgers, "Ultrasonic Actuation for MEMS Dormancy-Related Stiction Reduction," Proceedings of SPIE, MEMS Reliability for Critical Applications, 4180, R. A. Lawton, ed., 2000, pp. 60-65. [4] B. P. Gogoi and C. H. Mastrangelo, “Adhesion Release and Yield Enhancement of Microstructures Using Pulsed Lorentz Forces,” Journal of Microelectromechanical Systems, 4, 1995, pp. 185-192.
experiments validate and extend the previous results by Gupta et al. [6], and show that stress waves are very effective in repairing stiction-failed cantilevers without damaging the repaired cantilevers. We have also shown that repairs are only a stress wave effect and not a thermal effect. Additionally we have identified practical ranges for irradiation, including a lower bound fluence below which repair is impractical, and an upper bound above which damage to the substrate and microcantilevers occurs.
modeling and experiments,” Journal of the Mechanics and Physics of Solids, 51(8), 2003, pp. 1601-1622. [6] V. Gupta, R. Snow, M. C. Wu, A. Jain, and J. Tsai, “Recovery of stiction-failed MEMS structures using laserinduced stress waves," Journal of Microelectromechanical Systems, v. 13, n. 4, August, 2004, p 696-700. [7] Z. C. Leseman, S. Koppaka, and T. J. Mackin, “A fracture mechanics model for stress-wave repair of stiction failed microcantilevers,” Journal of Microelectromechanical Systems, July 2005, submitted. [8]J. W. Rogers, L. M. Phinney, “Transient, interferometric imaging of polycrystalline silicon MEMS devices during laser heating,” Microscale Thermophysical Engineering, Mar. 2004, Vol. 8 Issue 1, pp. 43-59.
[5] E. E. Jones, M. R. Begley, and K. D. Murphy, “Adhesion of micro-cantilevers subjected to mechanical point-loading:
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