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Displacement sensing of a micro-electro-thermal actuator using a monolithically integrated thermal sensor
Sensors and Actuators A 150 (2009) 137–143
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Displacement sensing of a micro-electro-thermal actuator using a monolithically integrated thermal sensor Jacky Chow, Yongjun Lai ∗ Department of Mechanical and Materials Engineering, Queen’s University, Kingston, ON, Canada, K7L 3N6
a r t i c l e
i n f o
Article history: Received 27 June 2008 Received in revised form 21 October 2008 Accepted 7 November 2008 Available online 27 November 2008 Keywords: Micro-electro-thermal actuator Micro thermal sensor In-situ displacement sensing MetalMUMPS
a b s t r a c t The present paper describes a novel concept that employs a thermal-based approach for in-situ displacement sensing of electro-thermal actuators. A device encompassing an in-plane electro-thermal actuator and a thermal sensor was monolithically fabricated using the MetalMUMPS process. Analytical models were developed for both the actuator and the thermal sensor. Simulation and experimental results demonstrated good agreement. The experimental results indicated that the sensor achieved high linearity and sensitivity (∼4.5 nm/). © 2008 Elsevier B.V. All rights reserved.
1. Introduction Microelectromechanical systems (MEMS) based electrothermal actuators comprise an important class of MEMS actuators that have tremendous potential in a wide range of prospective micro-actuation applications. Electro-thermal actuators are mechanically compliant structures that rely on the thermal expansion of its heated components to achieve thermal actuation. A variety of electro-thermal actuators have been explored that each exhibits different functional characteristics [1,2]. Closed loop feedback control of micro-actuators is often desirable for micro-actuation applications that demand high degrees of displacement precision, such as micro-manipulation [3] and nanopositioning [4]. For these purposes, in-situ displacement sensors are often necessary to provide a means for on-chip displacement sensing of the micro-actuators. Devices that require in-situ displacement sensing of micro-actuators typically employ capacitive, piezoresistive or piezoelectric based micro-sensors [2]. The concept of exploiting thermal conduction as a mechanism for displacement sensing of dynamic articles had received relatively little attention. At the macroscopic scale, size-effects typically render thermal conduction, especially across fluid mediums, an inefficient and unfeasible mechanism for signal transport and transduction in displacement sensing applications. Conversely as size scales tend towards the micro-scale, continuum heat transfer principles dictate that the increasingly smaller heat transfer
∗ Corresponding author. E-mail address: [email protected] (Y. Lai). 0924-4247/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2008.11.014
distances tend to make energy transfer via thermal conduction more effective than at larger size scales. Furthermore, effects of fluid convection are often less significant at the micro-scale due to size-effects [5], making thermal-conduction as a signal transmission mechanism more feasible than at the macroscopic scale. The increased research initiatives at the micro-scale over recent decades naturally lead the way for some of the first conceptual demonstrations of thermal conduction based displacement sensing. In 1986, Williams and Wickramasinghe [6] first demonstrated position feedback control of a thermal-based surface profiler tip using a thermal-based proximity transduction concept. In 1991, Hiratsuka et al. [7] introduced the first thermal-based MEMS accelerometer. Kim et al. [8] followed a similar approach of [6] and characterized the out-of-plane displacement of atomic force microscope tips. Lantz et al. [9] developed a thermal-based displacement sensor for 2D translational nano-positioning stages. The abovementioned conceptual demonstrations of thermalbased displacement sensing, all commonly involve utilizing the nature of thermal conduction based heat flow between two dynamically interacting surfaces as the principle mean to determine the displacement of the articles of interest. Herein this paper we describe the novel approach of using a similar thermalbased displacement transduction principle, but applied to sense the displacement of MEMS electro-thermal actuators in-situ of device operation. In this concept, the heat responsible for actuating electro-thermal actuators and the thermal conduction phenomenon are individually exploited as sensory signals and the signal transmission mechanism, respectively. This facilitates displacement transduction by means of relating heat flow between the actuator and the sensor, to the displacement of the electro-thermal
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heat flux towards the sensor. Stray heat flux is ignored in this diagrammatic depiction. Fig. 1a and b depicts motion sensing of the actuator that occurs in the plane parallel to the sensor surface; Fig. 1c illustrates the motion sensing of the actuator that occurs perpendicular to the sensor surface. By relating varying heat flux (Fig. 1a and c) or interface area (Fig. 1b) to the displacement indirectly, displacement sensing of actuators can be realized. Similar sensing methods shown in Fig. 1b and c for non-actuator dynamic articles have been reported in [9] and [6–8], respectively. This paper reports on the sensing method demonstrated in Fig. 1a and applied in a novel manner specifically for MEMS electrothermal actuators. Unlike prior works of [7–9] where thermal signal generation served only the purpose for displacement sensing, the heat generated in the electro-thermal actuator herein serves two functional purposes, namely thermal compliant actuation and as thermal signals. 3. Design and fabrication
Fig. 1. Concepts for thermal-based displacement sensing of electro-thermal actuators.
actuator based on coupled heat transfer and mechanical models for the actuator-sensor system. 2. General principle Electro-thermal actuators typically operate in conditions where the main mode of heat transfer for practical considerations is through thermal conduction. Thermal conduction, qcond , is typically modeled by Fourier’s law of thermal conduction, which is given by: qcond = −k A
T x
(1)
where k is thermal conductivity, A is the cross sectional area, and T /x is the temperature gradient. The effects of fluid convection are typically less significant at the microscopic scale [5]. Fig. 1 demonstrates three general configurations for thermalbased displacement sensing. Arrows towards the sensor in Fig. 1 indicate heat flux, where higher density of arrows indicates greater
An in-plane V-shaped electro-thermal actuator was chosen for the purposes of demonstrating this sensing strategy. The sensor is thermally coupled directly underneath the electro-thermal actuator. The sensor was designed to cover the entire substrate area for which the electro-thermal actuator is designed to operate. This is to ensure that the thermal sensor has maximum capture of thermal energy from the electro-thermal actuator during device operation. A schematic of the test device is shown in Fig. 2. The electro-thermal actuator and thermal sensor device developed in this paper (see Fig. 3) was monolithically fabricated using the MetalMUMPS process [10]. This commercial fabrication process is comprised of several thin film deposition and photolithography steps conducted on the (1 0 0) surface of a lightly phosphorousdoped single crystal silicon (SCS) substrate. The thermal sensor is fabricated from a 0.7 m thick highly phosphorous-doped polycrystalline silicon (polysilicon) layer. The polysilicon sensor is selectively enclosed by two 0.35 m thick silicon nitride (nitride) layers for electrical insulation and structural support. A 27.5 m air gap spacing is anisotropically wet-etched under the enclosed polysilicon sensor to provide improved thermal insulation of the thermal sensor in an effort to increase the sensitivity of the thermal sensor. The sensor takes the geometry of a meandering polysilicon wire that covers the entire substrate
Fig. 2. Schematic of V-shaped electro-thermal actuator fabricated on top of the thermal sensor. (a) Ni V-shaped thermal actuator and probe pads for the sensor, (b) top nitride membrane, (c) polysilicon serpentine thermal sensor, (d) bottom nitride membrane, (e) substrate with a trench, (f) assembly of the sensor and actuator, (g) cross-sectional view of the assembly.
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139
Fig. 3. Scanning electron micrograph of the electro-thermal actuator and thermal sensor: (a) top view, (b) perspective view.
real-estate area for which the electro-thermal actuator is designed to operate. The polysilicon wire is 10 m in width and 2205 m in length. The electro-thermal actuator is fabricated from a 20 m thick electroplated polycrystalline nickel (Ni) layer that is suspended 1.1 m above the surface nitride layer. The V-shaped electrothermal actuator is fabricated directly above the polysilicon sensor relative to the substrate plane and sensor location. The actuator is attached to a Ni probe pad. The probe pad is anchored to the substrate and electrically insulated by a 0.35 m thick nitride layer. Each Ni V-shaped micro-actuator beam has a width of 8 m and a length of 400 m. 4. Modeling A thermal model of the experimental setup was developed. Thermal conduction is considered to be the principle mode of heat transfer in this model. A single V-shaped thermal actuator beam is used in the following models to reduce modeling complexity (see Fig. 4). Geometric and material properties are tabulated in Table 1. The heating of the electro-thermal actuator is accomplished by Joule heating of the actuator structures. Thermal conductivity of the
Ni layer is assumed to be constant. A shape factor [11], S, was incorporated into the thermal model to account for the heat dissipated to substrate from side and top surfaces of the actuation beam. The steady state heat transfer is governed by the following 2nd order partial differential equation: kNi
∂2 T S (Ta − T ) + + J 2 Ni 1 + Ni (T − Ta ) = 0 tNi UT ∂x2
(2)
where kNi and tNi are the thermal conductivity and thickness of nickel actuator, respectively. The thermal conductivity of Ni is assumed to be constant in this model. The symbol Ni is the electrical resistivity of Ni at the reference temperature of 298 K. The temperature dependence of electrical resistivity for Ni is assumed to be linear, where Ni is the linear temperature coefficient of electrical resistivity of Ni. The ambient temperature, Ta , is 298 K. The symbol J denotes the current density of the actuation beam along the x-axis. Here, T is the temperature at position x along the electro-thermal
Table 1 Geometric and material properties. Parameter
Value
Reference
Lact tNi ta1 tsn tps ta2 wact Lsen wsen kNi ka ksn kps ˛ Ni Ni ps ps residual E
400 m 20 m 1.1 m 0.35 m 0.7 m 27.5 m 8 m 0.05 rad 2200 m 10 m 90.9 W/m K 0.027 W/m K 2.25 W/m K 41 W/m K 1.33E−05 0.08 m 0.0045 1/K 17.853 m 0.002 1/K 100 MPa 195 GPa
N/A [10] [10] [10] [10] [10] N/A N/A N/A N/A [12] [12] [14] [14] [12] [10] [12] N/A [11] [10] [15]
Fig. 4. Schematic of device (filled dot indicates internal heat generation via Joule heating. Curved arrows emanating from Joule heating spot indicate heat flow due to thermal conduction).
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Fig. 5. Photograph of experimental setup.
actuator. The total thermal resistance (see Fig. 4), UT , between the electro-thermal actuator and the substrate plane is given by: UT =
tps ta1 2tn ta2 + + + ka kn kps ka
(3) Vact =
where ta1 , ta2 , tn , and tps represent the thicknesses of the air gap, the air trench, the nitride and the polysilicon layers, respectively (Fig. 4). The thermal conductivities of the air gap, the air trench, the nitride and the polysilicon layers are represented by ka , kn , and kps , respectively. The shape factor S [11] is given by: S=
tNi wact
2(ta1 + ta2 + 2tn + tps ) +1 tNi
+1
(4)
where wact is the width of the electro-thermal actuator. The probe pads at the end of the electro-thermal actuator are set at the ambient room temperature Ta as boundary conditions. The heat transfer towards the sensor and substrate is modeled using a thermal resistance model (see Fig. 4). The following expression was derived that relates the temperature of the polysilicon sensor, Tsen , as a function of the actuator temperature, Tact , given by:
Tsen = Tact 1 −
U 1
UT
+ Ta
U 1
UT
(5)
The thermal resistance between the actuator and the sensor, U1 is given by: U1 =
ta1 tn + ka kn
(6)
The thermal sensor relies on the temperature dependent electrical resistivity of polysilicon to sense temperature changes. The electrical resistance of the thermal sensor, Rsen , is represented by an empirical based relationship given by: Rsen
the actuator. The actuator voltage (Vact ) to current (Iact ) relationship is given by:
Lsen ps (1 + ps (Tsen − Ta )) = wsen tps
Ni (1 + Ni (T − Ta ))Lact Iact 4wNi tNi
An analytical thermal–mechanical model that relates the average temperature and displacement of V-shaped electro-thermal actuators was originally derived by Enikov et al. [12]. It has been shown that residual stress may influence the performance of MEMS thermal–mechanical structures, specifically thermalcompliant actuation [13]. The residual stress, residual, of the electroplated Ni layer in the MetalMUMPS process is reported to be 100 MPa tensile at room temperature [10,15]. Similarly, changes in geometric parameters of the fabrication structure were observed compared to the design parameters. For these reasons, the phenomenon of thermal relaxation of residual stresses in electro-thermal actuators is considered in this modeling approach. By considering the influence of the residual stress, and having no external loads in this case, the expression relating the actuator temperature increment to displacement in [12] was modified accordingly, given by: ε Lact ˛T act Lact b2 ILact − relax − 2 2 2A +
1 tan2 2
Lact + tan2 4
3L
act
4
bL
act
+
(7) + tan2
2 b
tan
sin(bLact ) 4b
1 + 2k
4
− cos(bLact ) − 3) −
where Lsen and wsen are the length and width of the polysilicon sensor wire, respectively. The electrical resistivity of polysilicon at the reference temperature of 298 K and the linear temperature coefficient of electrical resistivity of polysilicon is given by ps and ps , respectively. To simulate the voltage–current relationship for the actuator, the individual arms of the V-shaped electro-thermal actuator was modeled as resistive wires that are connected in equivalent electrical circuit configurations to yield an overall electrical resistance for
(8)
4 tan
1 − tan2
bL
act
4
bL
act
4
cos
bL
act
2
2 sin bLact /2 b
bL
act
4
−
Lact 2
=0
(9)
where Tact = Tact − Ta . The length and initial offset angle of the Ni electro-thermal actuator are represented by Lact and , respectively. The symbol I denotes the second moment of inertia of the electrothermal actuator and ˛ denotes the thermal expansion coefficient of Ni. The symbol b is an eigenvalue to be solved from the equation. The plane strain contribution, εrelax , due to the relaxation of the
J. Chow, Y. Lai / Sensors and Actuators A 150 (2009) 137–143
141
Fig. 6. Actuator displacement versus input current.
residual stresses of the film layer is modeled by:
εrelax =
⎧ ⎨ residual
E T0,relax − Ta
Fig. 7. Experimental and simulation voltage and current curves of Ni micro-electrothermal actuator.
(Tact − Ta ) , Ta < Tact < T0,relax (10)
⎩ residual ,
Tact > T0,relax
E
where E is the Young’s modulus of the electroplated Ni layer. T0,relax is the equivalent temperature in which the residual stresses are completely relaxed. In the case of MetalMUMPS, T0,relax is assumed to be the electroplating temperature of Ni taken as 348 K [15]. Using the Tact , εrelax and eigenvalue b found from Eqs. (9) and (10), respectively, the displacement of the actuator can be determined from the following [12]: ı = tan()
2
bcos
tan
bL
act
4
−
bLact 2
(11)
5. Results and discussion Thermal actuation is accomplished by applying a constant DC current across the Ni actuator to initiate Joule heating of the electro-thermal actuator structure. Electrical measurements were conducted using a four-point Kelvin sensing methodology to avoid wire resistance contributions due to the low resistivity of Ni. Digital image capture and analysis techniques were used to determine the displacement of the electro-thermal actuator. A photograph of the setup is shown in Fig. 5. No external mechanical load was applied to the electro-thermal actuator. The displacement of the V-shaped electro-thermal actuator as a function of input current with and without residual stress relaxation contributions is shown in Fig. 6. Finite element analysis (FEA) simulations with COMSOL MultiphysicsTM were also performed using the same abovementioned assumptions and material and geometric properties (Table 1). FEA simulation is compared with the theoretical model and experimental results. Fig. 6 shows that the modeling results which included the contribution of residual stress relaxation correspond well with experimental data. For the purposes of comparison, modeling results that did not account for the relaxation of the residual stress (i.e. εrelax = 0) and by assuming the electro-thermal actuator is thermally insulated (i.e. S = 0), is also shown in Fig. 6. Fig. 6 indicates that the maximum temperature change due to Joule heating is attained in the model without considering the relaxation of residual stress. Such maximum temperature change induces the maximum actuation displacement. However, this maximum displacement is still insufficient to match experimental results. The experimental and simulated I–V curves were compared in Fig. 7 to further exclude other possible fac-
tors, such as, differences of the input power used in modeling and testing. The agreement between experimental and simulated I–V curves verified that the correct amount of power was being dissipated into the actuator at any particular input current level. Figs. 6 and 7 appear to indicate the importance of including the contributions of residual stress relaxation in the thermal–mechanical displacement models of electro-thermal actuators, especially perhaps when the magnitude of residual stress in the material is high such as for the electroplated Ni layer in the MetalMUMPS process [10]. In this model, it is assumed that the temperature distribution of the thermal sensor along the x-axis is a function of the temperature of the actuator along the x-axis, as determined using the thermal resistance model (Eq. (5)). Fig. 8 demonstrates that the actuator and sensor have similar temperature profiles along x-axis. In addition, it is shown that as the location is closer to the centre of the actuator along the x-axis, the sensor experience larger local temperature differences when driving current changes in the actuator. This indicates that the placement of thermal sensors near region where the actuator experiences the highest temperature changes
Fig. 8. Temperature distribution of the micro-electro-thermal actuator and thermal sensor for selected currents with air trench.
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J. Chow, Y. Lai / Sensors and Actuators A 150 (2009) 137–143
The transient response of electro-thermal actuators due to an applied step input current typically ranges from tens of microseconds [16] to tens of milliseconds [17]. For the purposes of this study, experiments were conducted at the steady state. Fig. 10 shows the average actuator displacement as a function of average sensor resistance from multiple experiments. Experimental deviations from the average of ±1% for displacement measurements and ±5% for electrical resistance measurements were observed. The modeling results of Fig. 10 included the effects of residual stresses. The resistivity of polysilicon, ps , was experimentally determined to be 17.853 m. Experimental results indicate a linear correlation between the actuation displacement and sensor resistance, given the actuator input power range studied in this paper. The model taking into account residual stresses demonstrated agreement with the experimental results. The sensitivity of the thermal sensor was approximately 4.5 nm/ with ±6% experimental deviations. 6. Summary
Fig. 9. Temperature distribution of the micro-electro-thermal actuator and thermal sensor for selected currents without air trench underneath thermal sensor.
may be advantageous in maximizing sensor sensitivity and reducing redundant sensor structures. The temperature profile of the electro-thermal actuator and thermal sensor without the 27.5 m air trench was found by modifying the total thermal resistance, UT (Eq. (3)), without the air trench parameters (see Fig. 9). The thermal sensor without the air trench exhibits insignificant changes in temperatures. This indicates that in such a case, the sensor is ineffective in thermal detection due to the quick heat loss to the SCS substrate which acts as a heat sink. For instance, the sensor with air trench has an approximate local temperature difference of 40 K at the center region of the actuator (along the x-axis) when driving current for the actuator changes from 0.5 to 1 A. However, the sensor without the air trench, but at the same location, would experience almost no change in temperature. This indicates that having an air trench underneath the thermal sensor, or other forms of thermal insulation of the sensor from the substrate, appears to be critically important.
The present paper studied a device encompassing a Vshaped electro-thermal actuator with a monolithically integrated thermal-sensor for in-situ displacement sensing. The device was fabricated using the MetalMUMPs process and tested. Analytical models for the device, i.e. both thermal actuation and thermal sensing, have been developed. The thermal–mechanical model of the actuator incorporated the influence of the residual stress relaxation. Simulated results agreed relatively well with experimental results. The model and experimental actuator displacement versus input current results seem to indicate that residual stress should be taken into account for the actuator that exhibit high residual stresses, such as, MetalMUMPs. A strategy for designing a thermal-based displacement sensor for electro-thermal actuators with higher sensitivity has been discussed in the paper. In this study, experimental results demonstrated that the thermal sensor has a sensitivity of 4.88 nm/. The experimental relationship between the actuator displacement and the resistance of the thermal sensor was shown to exhibit a high linearity. Acknowledgements The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for the support. The authors also would like to thank Prof. M. Daymond (Dept. of Mechanical and Materials Engineering, Queen’s University) for his valuable discussion on how to consider the residual stress in the model. References
Fig. 10. Actuator displacement versus sensor resistance.
[1] Y.J. Lai, J. McDonald, M. Kujath, T. Hubbard, Force, deflection and power measurements of toggled microthermal actuators, J. Micromech. Microeng. 14 (2004) 49–56. [2] D.J. Bell, T.J. Lu, N.A. Fleck, S.M. Spearing, MEMS actuators and sensors: observations on their performance and selection for purpose, J. Micromech. Microeng. 15 (2005) 153–164. [3] H. Chang, J.M. Tsai, H. Tsai, W. Fang, Design, fabrication, and testing of a 3DOF HARM micromanipulator on (1 1 1) silicon substrate, Sens. Actuators A 125 (2006) 438–445. [4] S. Bergna, J.J. Gorman, N.G. Dagalakis, Design and modeling of thermally actuated MEMS nanopositioners, in: Proc. ASME IMECE, Orlando, Florida USA, 2005, pp. 1–8. [5] Z.Y. Guo, Z.X. Li, Size effect on single-phase channel flow and heat transfer at microscale, Int. J. Heat Fluid Flow 24 (2003) 284–298. [6] C.C. Williams, H.K. Wickramasinghe, Scanning thermal profiler, Appl. Phys. Lett. 49 (1986) 1587–1589. [7] R. Hiratsuka, D.C. van Duyn, T. Otaredian, P. de Vries, A novel accelerometer based on a silicon thermopile, in: Technical Digest 6th International Conference
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[8]
[9]
[10] [11] [12]
on Solid-State Sensors and Actuators (Transducers’91), San Francisco, CA, USA, June 24–27, 1991, pp. 420–423. K.J. Kim, K. Park, J. Lee, Z.M. Zhang, W.P. King, Nanotopographical imaging using a heated atomic force microscope cantilever probe, Sens. Actuators A 136 (2007) 95–103. M.A. Lantz, G.K. Binnig, M. Despont, U. Drechsler, A micromechanical thermal displacement sensor with nanometre resolution, Nanotechnology 16 (2005) 1089–1094. MetalMUMPS Design Handbook MEMSCAP Inc. L. Lin, M. Chiao, Electrothermal responses of lineshape microstructures, Sens. Actuators A A55 (1996) 35–41. E.T. Enikov, S.S. Kedar, K.V. Lazarov, Analytical model for analysis and design of Vshaped thermal microactuators, J. Microelectromech. Syst. 14 (2005) 788–798.
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[13] M. Chiao, L. Lin, Self-buckling of micromachined beams under resistive heating, J. Microelectromech. Syst. 9 (2000) 146–151. [14] D. Yan, A. Khajepour, R. Mansour, Design and modeling of a MEMS bidirectional vertical thermal actuator, J. Micromech. Microeng. 14 (2004) 841–850. [15] J.K. Luo, M. Pritschow, A.J. Flewitt, S.M. Spearing, N.A. Fleck, W.I. Milne, Effects of process conditions on properties of electroplated Ni thin films for microsystem applications, J. Electrochem. Soc. 153 (2006) 155–161. [16] R. Hickey, D. Sameoto, T. Hubbard, M. Kujath, Time and frequency response of two arm micromachined thermal actuators, J. Micromech. Microeng. 13 (2003) 40–46. [17] C.D. Lott, T.W. McLain, J.N. Harb, L.L. Howell, Modeling the thermal behavior of a surface-micromachined linear-displacement thermomechanical microactuator, Sens. Actuators A 101 (2002) 239–250.
Contents lists available at ScienceDirect
Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Displacement sensing of a micro-electro-thermal actuator using a monolithically integrated thermal sensor Jacky Chow, Yongjun Lai ∗ Department of Mechanical and Materials Engineering, Queen’s University, Kingston, ON, Canada, K7L 3N6
a r t i c l e
i n f o
Article history: Received 27 June 2008 Received in revised form 21 October 2008 Accepted 7 November 2008 Available online 27 November 2008 Keywords: Micro-electro-thermal actuator Micro thermal sensor In-situ displacement sensing MetalMUMPS
a b s t r a c t The present paper describes a novel concept that employs a thermal-based approach for in-situ displacement sensing of electro-thermal actuators. A device encompassing an in-plane electro-thermal actuator and a thermal sensor was monolithically fabricated using the MetalMUMPS process. Analytical models were developed for both the actuator and the thermal sensor. Simulation and experimental results demonstrated good agreement. The experimental results indicated that the sensor achieved high linearity and sensitivity (∼4.5 nm/). © 2008 Elsevier B.V. All rights reserved.
1. Introduction Microelectromechanical systems (MEMS) based electrothermal actuators comprise an important class of MEMS actuators that have tremendous potential in a wide range of prospective micro-actuation applications. Electro-thermal actuators are mechanically compliant structures that rely on the thermal expansion of its heated components to achieve thermal actuation. A variety of electro-thermal actuators have been explored that each exhibits different functional characteristics [1,2]. Closed loop feedback control of micro-actuators is often desirable for micro-actuation applications that demand high degrees of displacement precision, such as micro-manipulation [3] and nanopositioning [4]. For these purposes, in-situ displacement sensors are often necessary to provide a means for on-chip displacement sensing of the micro-actuators. Devices that require in-situ displacement sensing of micro-actuators typically employ capacitive, piezoresistive or piezoelectric based micro-sensors [2]. The concept of exploiting thermal conduction as a mechanism for displacement sensing of dynamic articles had received relatively little attention. At the macroscopic scale, size-effects typically render thermal conduction, especially across fluid mediums, an inefficient and unfeasible mechanism for signal transport and transduction in displacement sensing applications. Conversely as size scales tend towards the micro-scale, continuum heat transfer principles dictate that the increasingly smaller heat transfer
∗ Corresponding author. E-mail address: [email protected] (Y. Lai). 0924-4247/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2008.11.014
distances tend to make energy transfer via thermal conduction more effective than at larger size scales. Furthermore, effects of fluid convection are often less significant at the micro-scale due to size-effects [5], making thermal-conduction as a signal transmission mechanism more feasible than at the macroscopic scale. The increased research initiatives at the micro-scale over recent decades naturally lead the way for some of the first conceptual demonstrations of thermal conduction based displacement sensing. In 1986, Williams and Wickramasinghe [6] first demonstrated position feedback control of a thermal-based surface profiler tip using a thermal-based proximity transduction concept. In 1991, Hiratsuka et al. [7] introduced the first thermal-based MEMS accelerometer. Kim et al. [8] followed a similar approach of [6] and characterized the out-of-plane displacement of atomic force microscope tips. Lantz et al. [9] developed a thermal-based displacement sensor for 2D translational nano-positioning stages. The abovementioned conceptual demonstrations of thermalbased displacement sensing, all commonly involve utilizing the nature of thermal conduction based heat flow between two dynamically interacting surfaces as the principle mean to determine the displacement of the articles of interest. Herein this paper we describe the novel approach of using a similar thermalbased displacement transduction principle, but applied to sense the displacement of MEMS electro-thermal actuators in-situ of device operation. In this concept, the heat responsible for actuating electro-thermal actuators and the thermal conduction phenomenon are individually exploited as sensory signals and the signal transmission mechanism, respectively. This facilitates displacement transduction by means of relating heat flow between the actuator and the sensor, to the displacement of the electro-thermal
138
J. Chow, Y. Lai / Sensors and Actuators A 150 (2009) 137–143
heat flux towards the sensor. Stray heat flux is ignored in this diagrammatic depiction. Fig. 1a and b depicts motion sensing of the actuator that occurs in the plane parallel to the sensor surface; Fig. 1c illustrates the motion sensing of the actuator that occurs perpendicular to the sensor surface. By relating varying heat flux (Fig. 1a and c) or interface area (Fig. 1b) to the displacement indirectly, displacement sensing of actuators can be realized. Similar sensing methods shown in Fig. 1b and c for non-actuator dynamic articles have been reported in [9] and [6–8], respectively. This paper reports on the sensing method demonstrated in Fig. 1a and applied in a novel manner specifically for MEMS electrothermal actuators. Unlike prior works of [7–9] where thermal signal generation served only the purpose for displacement sensing, the heat generated in the electro-thermal actuator herein serves two functional purposes, namely thermal compliant actuation and as thermal signals. 3. Design and fabrication
Fig. 1. Concepts for thermal-based displacement sensing of electro-thermal actuators.
actuator based on coupled heat transfer and mechanical models for the actuator-sensor system. 2. General principle Electro-thermal actuators typically operate in conditions where the main mode of heat transfer for practical considerations is through thermal conduction. Thermal conduction, qcond , is typically modeled by Fourier’s law of thermal conduction, which is given by: qcond = −k A
T x
(1)
where k is thermal conductivity, A is the cross sectional area, and T /x is the temperature gradient. The effects of fluid convection are typically less significant at the microscopic scale [5]. Fig. 1 demonstrates three general configurations for thermalbased displacement sensing. Arrows towards the sensor in Fig. 1 indicate heat flux, where higher density of arrows indicates greater
An in-plane V-shaped electro-thermal actuator was chosen for the purposes of demonstrating this sensing strategy. The sensor is thermally coupled directly underneath the electro-thermal actuator. The sensor was designed to cover the entire substrate area for which the electro-thermal actuator is designed to operate. This is to ensure that the thermal sensor has maximum capture of thermal energy from the electro-thermal actuator during device operation. A schematic of the test device is shown in Fig. 2. The electro-thermal actuator and thermal sensor device developed in this paper (see Fig. 3) was monolithically fabricated using the MetalMUMPS process [10]. This commercial fabrication process is comprised of several thin film deposition and photolithography steps conducted on the (1 0 0) surface of a lightly phosphorousdoped single crystal silicon (SCS) substrate. The thermal sensor is fabricated from a 0.7 m thick highly phosphorous-doped polycrystalline silicon (polysilicon) layer. The polysilicon sensor is selectively enclosed by two 0.35 m thick silicon nitride (nitride) layers for electrical insulation and structural support. A 27.5 m air gap spacing is anisotropically wet-etched under the enclosed polysilicon sensor to provide improved thermal insulation of the thermal sensor in an effort to increase the sensitivity of the thermal sensor. The sensor takes the geometry of a meandering polysilicon wire that covers the entire substrate
Fig. 2. Schematic of V-shaped electro-thermal actuator fabricated on top of the thermal sensor. (a) Ni V-shaped thermal actuator and probe pads for the sensor, (b) top nitride membrane, (c) polysilicon serpentine thermal sensor, (d) bottom nitride membrane, (e) substrate with a trench, (f) assembly of the sensor and actuator, (g) cross-sectional view of the assembly.
J. Chow, Y. Lai / Sensors and Actuators A 150 (2009) 137–143
139
Fig. 3. Scanning electron micrograph of the electro-thermal actuator and thermal sensor: (a) top view, (b) perspective view.
real-estate area for which the electro-thermal actuator is designed to operate. The polysilicon wire is 10 m in width and 2205 m in length. The electro-thermal actuator is fabricated from a 20 m thick electroplated polycrystalline nickel (Ni) layer that is suspended 1.1 m above the surface nitride layer. The V-shaped electrothermal actuator is fabricated directly above the polysilicon sensor relative to the substrate plane and sensor location. The actuator is attached to a Ni probe pad. The probe pad is anchored to the substrate and electrically insulated by a 0.35 m thick nitride layer. Each Ni V-shaped micro-actuator beam has a width of 8 m and a length of 400 m. 4. Modeling A thermal model of the experimental setup was developed. Thermal conduction is considered to be the principle mode of heat transfer in this model. A single V-shaped thermal actuator beam is used in the following models to reduce modeling complexity (see Fig. 4). Geometric and material properties are tabulated in Table 1. The heating of the electro-thermal actuator is accomplished by Joule heating of the actuator structures. Thermal conductivity of the
Ni layer is assumed to be constant. A shape factor [11], S, was incorporated into the thermal model to account for the heat dissipated to substrate from side and top surfaces of the actuation beam. The steady state heat transfer is governed by the following 2nd order partial differential equation: kNi
∂2 T S (Ta − T ) + + J 2 Ni 1 + Ni (T − Ta ) = 0 tNi UT ∂x2
(2)
where kNi and tNi are the thermal conductivity and thickness of nickel actuator, respectively. The thermal conductivity of Ni is assumed to be constant in this model. The symbol Ni is the electrical resistivity of Ni at the reference temperature of 298 K. The temperature dependence of electrical resistivity for Ni is assumed to be linear, where Ni is the linear temperature coefficient of electrical resistivity of Ni. The ambient temperature, Ta , is 298 K. The symbol J denotes the current density of the actuation beam along the x-axis. Here, T is the temperature at position x along the electro-thermal
Table 1 Geometric and material properties. Parameter
Value
Reference
Lact tNi ta1 tsn tps ta2 wact Lsen wsen kNi ka ksn kps ˛ Ni Ni ps ps residual E
400 m 20 m 1.1 m 0.35 m 0.7 m 27.5 m 8 m 0.05 rad 2200 m 10 m 90.9 W/m K 0.027 W/m K 2.25 W/m K 41 W/m K 1.33E−05 0.08 m 0.0045 1/K 17.853 m 0.002 1/K 100 MPa 195 GPa
N/A [10] [10] [10] [10] [10] N/A N/A N/A N/A [12] [12] [14] [14] [12] [10] [12] N/A [11] [10] [15]
Fig. 4. Schematic of device (filled dot indicates internal heat generation via Joule heating. Curved arrows emanating from Joule heating spot indicate heat flow due to thermal conduction).
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Fig. 5. Photograph of experimental setup.
actuator. The total thermal resistance (see Fig. 4), UT , between the electro-thermal actuator and the substrate plane is given by: UT =
tps ta1 2tn ta2 + + + ka kn kps ka
(3) Vact =
where ta1 , ta2 , tn , and tps represent the thicknesses of the air gap, the air trench, the nitride and the polysilicon layers, respectively (Fig. 4). The thermal conductivities of the air gap, the air trench, the nitride and the polysilicon layers are represented by ka , kn , and kps , respectively. The shape factor S [11] is given by: S=
tNi wact
2(ta1 + ta2 + 2tn + tps ) +1 tNi
+1
(4)
where wact is the width of the electro-thermal actuator. The probe pads at the end of the electro-thermal actuator are set at the ambient room temperature Ta as boundary conditions. The heat transfer towards the sensor and substrate is modeled using a thermal resistance model (see Fig. 4). The following expression was derived that relates the temperature of the polysilicon sensor, Tsen , as a function of the actuator temperature, Tact , given by:
Tsen = Tact 1 −
U 1
UT
+ Ta
U 1
UT
(5)
The thermal resistance between the actuator and the sensor, U1 is given by: U1 =
ta1 tn + ka kn
(6)
The thermal sensor relies on the temperature dependent electrical resistivity of polysilicon to sense temperature changes. The electrical resistance of the thermal sensor, Rsen , is represented by an empirical based relationship given by: Rsen
the actuator. The actuator voltage (Vact ) to current (Iact ) relationship is given by:
Lsen ps (1 + ps (Tsen − Ta )) = wsen tps
Ni (1 + Ni (T − Ta ))Lact Iact 4wNi tNi
An analytical thermal–mechanical model that relates the average temperature and displacement of V-shaped electro-thermal actuators was originally derived by Enikov et al. [12]. It has been shown that residual stress may influence the performance of MEMS thermal–mechanical structures, specifically thermalcompliant actuation [13]. The residual stress, residual, of the electroplated Ni layer in the MetalMUMPS process is reported to be 100 MPa tensile at room temperature [10,15]. Similarly, changes in geometric parameters of the fabrication structure were observed compared to the design parameters. For these reasons, the phenomenon of thermal relaxation of residual stresses in electro-thermal actuators is considered in this modeling approach. By considering the influence of the residual stress, and having no external loads in this case, the expression relating the actuator temperature increment to displacement in [12] was modified accordingly, given by: ε Lact ˛T act Lact b2 ILact − relax − 2 2 2A +
1 tan2 2
Lact + tan2 4
3L
act
4
bL
act
+
(7) + tan2
2 b
tan
sin(bLact ) 4b
1 + 2k
4
− cos(bLact ) − 3) −
where Lsen and wsen are the length and width of the polysilicon sensor wire, respectively. The electrical resistivity of polysilicon at the reference temperature of 298 K and the linear temperature coefficient of electrical resistivity of polysilicon is given by ps and ps , respectively. To simulate the voltage–current relationship for the actuator, the individual arms of the V-shaped electro-thermal actuator was modeled as resistive wires that are connected in equivalent electrical circuit configurations to yield an overall electrical resistance for
(8)
4 tan
1 − tan2
bL
act
4
bL
act
4
cos
bL
act
2
2 sin bLact /2 b
bL
act
4
−
Lact 2
=0
(9)
where Tact = Tact − Ta . The length and initial offset angle of the Ni electro-thermal actuator are represented by Lact and , respectively. The symbol I denotes the second moment of inertia of the electrothermal actuator and ˛ denotes the thermal expansion coefficient of Ni. The symbol b is an eigenvalue to be solved from the equation. The plane strain contribution, εrelax , due to the relaxation of the
J. Chow, Y. Lai / Sensors and Actuators A 150 (2009) 137–143
141
Fig. 6. Actuator displacement versus input current.
residual stresses of the film layer is modeled by:
εrelax =
⎧ ⎨ residual
E T0,relax − Ta
Fig. 7. Experimental and simulation voltage and current curves of Ni micro-electrothermal actuator.
(Tact − Ta ) , Ta < Tact < T0,relax (10)
⎩ residual ,
Tact > T0,relax
E
where E is the Young’s modulus of the electroplated Ni layer. T0,relax is the equivalent temperature in which the residual stresses are completely relaxed. In the case of MetalMUMPS, T0,relax is assumed to be the electroplating temperature of Ni taken as 348 K [15]. Using the Tact , εrelax and eigenvalue b found from Eqs. (9) and (10), respectively, the displacement of the actuator can be determined from the following [12]: ı = tan()
2
bcos
tan
bL
act
4
−
bLact 2
(11)
5. Results and discussion Thermal actuation is accomplished by applying a constant DC current across the Ni actuator to initiate Joule heating of the electro-thermal actuator structure. Electrical measurements were conducted using a four-point Kelvin sensing methodology to avoid wire resistance contributions due to the low resistivity of Ni. Digital image capture and analysis techniques were used to determine the displacement of the electro-thermal actuator. A photograph of the setup is shown in Fig. 5. No external mechanical load was applied to the electro-thermal actuator. The displacement of the V-shaped electro-thermal actuator as a function of input current with and without residual stress relaxation contributions is shown in Fig. 6. Finite element analysis (FEA) simulations with COMSOL MultiphysicsTM were also performed using the same abovementioned assumptions and material and geometric properties (Table 1). FEA simulation is compared with the theoretical model and experimental results. Fig. 6 shows that the modeling results which included the contribution of residual stress relaxation correspond well with experimental data. For the purposes of comparison, modeling results that did not account for the relaxation of the residual stress (i.e. εrelax = 0) and by assuming the electro-thermal actuator is thermally insulated (i.e. S = 0), is also shown in Fig. 6. Fig. 6 indicates that the maximum temperature change due to Joule heating is attained in the model without considering the relaxation of residual stress. Such maximum temperature change induces the maximum actuation displacement. However, this maximum displacement is still insufficient to match experimental results. The experimental and simulated I–V curves were compared in Fig. 7 to further exclude other possible fac-
tors, such as, differences of the input power used in modeling and testing. The agreement between experimental and simulated I–V curves verified that the correct amount of power was being dissipated into the actuator at any particular input current level. Figs. 6 and 7 appear to indicate the importance of including the contributions of residual stress relaxation in the thermal–mechanical displacement models of electro-thermal actuators, especially perhaps when the magnitude of residual stress in the material is high such as for the electroplated Ni layer in the MetalMUMPS process [10]. In this model, it is assumed that the temperature distribution of the thermal sensor along the x-axis is a function of the temperature of the actuator along the x-axis, as determined using the thermal resistance model (Eq. (5)). Fig. 8 demonstrates that the actuator and sensor have similar temperature profiles along x-axis. In addition, it is shown that as the location is closer to the centre of the actuator along the x-axis, the sensor experience larger local temperature differences when driving current changes in the actuator. This indicates that the placement of thermal sensors near region where the actuator experiences the highest temperature changes
Fig. 8. Temperature distribution of the micro-electro-thermal actuator and thermal sensor for selected currents with air trench.
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The transient response of electro-thermal actuators due to an applied step input current typically ranges from tens of microseconds [16] to tens of milliseconds [17]. For the purposes of this study, experiments were conducted at the steady state. Fig. 10 shows the average actuator displacement as a function of average sensor resistance from multiple experiments. Experimental deviations from the average of ±1% for displacement measurements and ±5% for electrical resistance measurements were observed. The modeling results of Fig. 10 included the effects of residual stresses. The resistivity of polysilicon, ps , was experimentally determined to be 17.853 m. Experimental results indicate a linear correlation between the actuation displacement and sensor resistance, given the actuator input power range studied in this paper. The model taking into account residual stresses demonstrated agreement with the experimental results. The sensitivity of the thermal sensor was approximately 4.5 nm/ with ±6% experimental deviations. 6. Summary
Fig. 9. Temperature distribution of the micro-electro-thermal actuator and thermal sensor for selected currents without air trench underneath thermal sensor.
may be advantageous in maximizing sensor sensitivity and reducing redundant sensor structures. The temperature profile of the electro-thermal actuator and thermal sensor without the 27.5 m air trench was found by modifying the total thermal resistance, UT (Eq. (3)), without the air trench parameters (see Fig. 9). The thermal sensor without the air trench exhibits insignificant changes in temperatures. This indicates that in such a case, the sensor is ineffective in thermal detection due to the quick heat loss to the SCS substrate which acts as a heat sink. For instance, the sensor with air trench has an approximate local temperature difference of 40 K at the center region of the actuator (along the x-axis) when driving current for the actuator changes from 0.5 to 1 A. However, the sensor without the air trench, but at the same location, would experience almost no change in temperature. This indicates that having an air trench underneath the thermal sensor, or other forms of thermal insulation of the sensor from the substrate, appears to be critically important.
The present paper studied a device encompassing a Vshaped electro-thermal actuator with a monolithically integrated thermal-sensor for in-situ displacement sensing. The device was fabricated using the MetalMUMPs process and tested. Analytical models for the device, i.e. both thermal actuation and thermal sensing, have been developed. The thermal–mechanical model of the actuator incorporated the influence of the residual stress relaxation. Simulated results agreed relatively well with experimental results. The model and experimental actuator displacement versus input current results seem to indicate that residual stress should be taken into account for the actuator that exhibit high residual stresses, such as, MetalMUMPs. A strategy for designing a thermal-based displacement sensor for electro-thermal actuators with higher sensitivity has been discussed in the paper. In this study, experimental results demonstrated that the thermal sensor has a sensitivity of 4.88 nm/. The experimental relationship between the actuator displacement and the resistance of the thermal sensor was shown to exhibit a high linearity. Acknowledgements The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for the support. The authors also would like to thank Prof. M. Daymond (Dept. of Mechanical and Materials Engineering, Queen’s University) for his valuable discussion on how to consider the residual stress in the model. References
Fig. 10. Actuator displacement versus sensor resistance.
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