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A characterization of the thermal parameters of thermally driven polysilicon microbridge actuators using electrical impedance analysis
Sensors and Actuators 75 Ž1999. 86–92
A characterization of the thermal parameters of thermally driven polysilicon microbridge actuators using electrical impedance analysis Jae-Youl Lee ) , Sang-Won Kang Department of Materials Science and Engineering, Korea AdÕanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon, 305-701, South Korea Received 8 June 1998; accepted 25 November 1998
Abstract We have fabricated microrelays with a thermally driven polysilicon microbridge actuator to characterize their thermal parameters. An electrically equivalent circuit for the thermal microactuator has been modeled in functions of experimental parameters. The thermal conductance and the thermal capacitance of the thermal microactuator have been derived at the same time from the model and the frequency response analysis results. For the thermal microactuator having a bridge length of 500 mm, a width of 40 mm and a thickness of 3 mm, the thermal conductance and the thermal capacitance were 3.3 = 10y4 Wr8C and 4.3 = 10y7 Jr8C at 16 mTorr, respectively. A radiation source, which is needed to oscillate the temperature of thermal sensors in other measurement method, is not necessary in this work because signal voltage supplied by a FRA ŽFrequency Response Analyzer. heats the thermal microactuator. The method also eliminates the error from the ambient temperature variation because it considers the change of dc resistance affected by the ambient temperature variation. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Thermal microactuator; Microrelay; Thermal conductance; Thermal capacitance; Thermal characterization method
1. Introduction Thermally driven microactuators have simpler device structures and fabrication process than other actuators using electrostatic force, electromagnetic force, piezoelectric force and etc., in addition, they are expected to have advantages such as relatively large force and displacement. Therefore, many efforts have been devoted to development of the microrelays w1x, microvalves w2x and micromotors w3x using thermal force. Modeling of thermal characteristics and extracting of thermal parameters are prerequisite for designing the operation speed and power consumption of thermal actuators and thermal sensors. In the early works for the IR sensors and thermal sensors w4,5x, the thermal conductance was obtained by dc method and the thermal capacitance was measured by ac method separately. A radiation source modulated by an optical chopper was used in ac method. The thermal time constant and the expected
operation speed of sensors were calculated from the output signal amplitude at the given chopper frequency. Therefore, these measurements require both dc method and ac method. Also, a radiation source is needed additionally for the ac method. In this work, we have introduced a new characterization method for extract the thermal parameters from thermal microactuators using a FRA ŽFrequency Response Analyzer.. Since this new method is based on an electrical impedance analysis, neither external radiation source nor additional dc method is not necessary. The parameters are derivable without the accuracy loss from the ambient temperature variation during the measurement. The effects of dc voltage, ac voltage and pressure were investigated to verify the characterization method.
2. Design and fabrication
)
Corresponding author. Tel.: q82-42-869-4261; Fax: q82-42-8693310; E-mail: [email protected]
The structure of a microrelay is shown in Fig. 1. The microrelay is comprised of silicon and glass substrate bonded together. Switching operation is provided by a
0924-4247r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 8 . 0 0 2 9 7 - 0
J.-Y. Lee, S.-W. Kangr Sensors and Actuators 75 (1999) 86–92
87
Fig. 1. Schematic drawing of a microrelay. Ža. Top view; Žb. cross-section view.
thermally driven polysilicon microbridge actuator fabricated on the silicon substrate. The signal metals for mechanical contact are patterned onto glass substrate. Application of current to the actuator power line causes Joule’s heating of the polysilicon microbridge actuator, which induces the displacement caused by the thermal expansion of polysilicon microbridge actuator towards the signal lines on the glass substrate. Then, the signal metal Ž1. and the signal metal Ž2. are electrically connected through the contact metal on the polysilicon microbridge actuator and the microrelay is ‘on’. As the driving current is removed, the microbridge returns to its free-standing position, the microrelay is ‘off’. Fig. 2 shows the microrelay fabrication process. In the first step, Si 3 N4rSiO 2 are deposited as electrical and
chemical insulating layers. Phosphorous doped polysilicon of 3 mm thickness and TEOS SiO 2 of 2 mm thickness are used as the structural and sacrificial materials respectively. Then another SiO 2 film, which is used to mask polysilicon bridge later, is deposited on the polysilicon layer and these layers are annealed in N2 to relieve any residual stress. After SiO 2 is patterned by BOE ŽBuffered Oxide Etchant. wet etch for masking of polysilicon microbridge patterns, polysilicon microbridges are formed by TMAH ŽTetra Methyl Ammonium Hydroxide. wet etch and the sacrificial SiO 2 is removed in BOE by time controlled etch stop. Polysilicon microbridges have lengths of 300, 500 and 700 mm and widths of 40 and 60 mm and thickness of 3 mm. As shown in Fig. 2b, PECVD SiO 2 film of 0.2 mm thickness is deposited for electrical isolation between Al
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J.-Y. Lee, S.-W. Kangr Sensors and Actuators 75 (1999) 86–92
etch of 0.5 mm to 1.5 mm in depth, Al film of 0.7 mm thickness is deposited and patterned to create the signal metals as shown in Fig. 2d. After fabricating the silicon and glass substrate, the two substrates are aligned together using a microscope system and then bonded using a general adhesive. For the last step, 25 mm thick Al wires are connected between contact pads of microrelay and copper lead frames.
3. Theoretical model Fig. 3 shows a simple lumped model of a thermally equivalent circuit for the thermal microactuator to calculate the average temperature increase of microactuator when a driving voltage is applied. The Gt is the heat conductance between the thermal microactuator and environments through the microbridge and surrounding gas, the thermal capacitance Ct represents the heat storage of the thermal microactuator, the P represents the heat generation term that is the product of the current and the voltage, T is the average temperature of the thermal microactuator and T0 is the ambient temperature. The thermal impedance Zt of the model can be expressed as Zt s
Gt 2 Gt q v 2 Ct2
y
v Ct 2 Gt q v 2 Ct2
j
Ž 1.
where v is the angular frequency of applied ac voltage. If FRA apply the superimposed dc and ac voltage to microactuator, the current has the dc and ac current components as Ž3.. V s Vdc q Vac sin v t
Ž 2.
I s Idc q Iac sin Ž v t y u .
Ž 3.
where u is the phase shift between the ac voltage and the ac current.
Fig. 2. Fabrication process of a microrelay.
metal and polysilicon bridges. Then PECVD SiO 2 film is etched to create contact areas for electrical paths to microbridge. Next, Al film of 0.7 mm thickness is deposited and patterned. This layer forms both metal pads of 2 = 3 mm2 area Žactuator power line. for microbridge and contact metal. Glass etch is performed to create the cavity, which provides the space needed to allow the signal metals away from the contact metal patterned onto the microbridge while driving current is not applied. Following the glass
Fig. 3. A thermally equivalent circuit of the thermal microactuator.
J.-Y. Lee, S.-W. Kangr Sensors and Actuators 75 (1999) 86–92
From these two equations, Joule’s heat generation becomes P s Vdc Idc q
Iac Vac cos u 2
q Idc Vac sin v t
An effective method for the analysis of impedance results is to plot real part and imaginary part in the complex plane, now known as a Nyquist diagram. Putting Ž1. into Ž9. to separate real and imaginary parts, one obtains
p Iac Vac sin q Vdc Iac sin Ž v t y u . y
ž
2
q2vtyu
/
Xs
2 3 Gt2 R dc qCt2 R dc v 2 yGt Idc R 0 R dc a qGt Idc R 0 Vdc a y Idc R 20 Vdc a 2 2 4 Gt2 q v 2 Ct2 y2Gt Idc R 0 a q Idc R 20 a 2
2
Ž 10 .
Ž 4. When Iac < Idc and Vac < Vdc in Ž4., the last term on the right side can be neglected. The temperature difference DT between the average temperature T of the thermal microactuator and the ambient temperature T0 can be written as Ž5.. The DT also divided into the dc and ac components since the heat generation term consists of the dc and ac parts. DT s DTdc q DTac s PdcrGt q Zt Pac Pdc s Vdc Idc q
Iac Vac cos u 2
89
Ysy
Pac s Idc Vac sin v t q Vdc Iac sin Ž v t y u .
Center
Ž 5. Ž 5.1 . Ž 5.2 .
Ž
.
Ž 11 .
R 02 a 2
Ž10. and Ž11. yield a full semicircle with its center on the real axis of the complex plane and the center and radius of the semicircle can be derived to give a result
s f Vdc Idc
Ct Idc R 0 va Idc R dc q Vdc 2 4 Gt q v 2 Ct2 y 2Gt Idc2 R 0 a q Idc
ž
2Gt R dc y Idc2 R 0 R dc a q Idc R 0 Vdc a 2 Ž Gt y Idc2 R 0 a .
Vdc Idc R 0 a
/
,0 r
Ž 12 .
Gt y Idc2 R 0 a .
Two intersections between the semicircle and the real axis are expressed as Ž13., and the dc resistance R dc can be measured from the smaller value of intersections. Gt R dc q Idc R 0 Vdc a X s R dc , Ž 13 . Gt y Idc2 R 0 a
In particular, for heavily doped polycrystalline silicon, the temperature characteristic of resistivity obeys the linear relationship w6x. For much larger pads than the bridge width, we can assume that the pad contact resistance is much smaller than the resistance of microbridge. Therefore, the resistance of polysilicon microbridge actuator can assume an equation as
From the relation that the maximum value of Y is equal to the radius, the thermal conductance Gt and the thermal capacitance Ct can be obtained as
R Ž T . s R 0 1 q a Ž T y T0 . 4 s R 0 1 q a DT 4
Gt s
Ž 6.
where R 0 is the resistance of actuator at temperature T0 and a is the temperature coefficient of resistance. Since the electrical characteristic of the thermal microactuator consists of only resistance that is a function of the temperature change, the relation between the voltage and the current can be written as Ž7.. If Iac < Idc and a DTac - 1 q a DTdc , then the last term on the right side can be neglected. V s IRs Idc q Iac sin Ž v t y u . 4 R 0 1 q a Ž DTdc q DTac . 4
Vdc2 a
Ž 14 .
r Gt
Ct s
ž
v0 1q
r R dc
f
/
Gt
v0
Ž 15 .
where r is the radius of the semicircle in the impedance plane, v 0 is the angular frequency at the top point of the semicircle. If r < R dc , Ž15. can be simplified as Gtrv 0 . Ž14. and Ž15. can yield an electrically equivalent circuit model of the thermal microactuator as shown in Fig. 4.
s R 0 Idc Ž 1 q a DTdc . q Iac Ž 1 q a DTdc . sin Ž v t y u . qIdc a DTac q Iac a DTac sin Ž v t y u . 4 f Idc R 0 Ž 1 q a DTdc . 4 q Iac R 0 Ž 1 q a DTdc . =sin Ž v t y u . q Idc R 0 a DTac 4
Ž 7.
The voltage in Ž7. can be divided into the dc and ac parts. Then by comparing these two parts with Ž2. and Ž3., the dc resistance R dc and ac electrical impedance Ze are respectively obtained as R dc s R 0 1 q a DTdc 4 Ze s
R dc q Idc R 0 a ZtVdc 1 y Idc2 R 0 a Zt
Ž 8. s X q Yj.
Ž 9. Fig. 4. An electrically equivalent circuit of the thermal microactuator.
J.-Y. Lee, S.-W. Kangr Sensors and Actuators 75 (1999) 86–92
90
The thermal conductance and thermal capacitance, when r and v 0 are measured at Vdc and we know a , can be derived at the same time from Ž14. and Ž15..
4. Experimental As mentioned above, we have to know the temperature coefficient of resistance of the thermal microactuator in order to measure the Gt and Ct . So the temperature characteristics of resistance have been measured by oil-bath method. The microrelay is immersed in electrically insulating silicon oil. The oil acts as a heat reservoir, holding the thermal microactuator temperature at a series of values of Toil that are adjusted by a hot chuck used as an external heat source. This oil-bath method ensures uniform temperature for entire parts of the thermal microactuator. The resistances of the thermal microactuator are measured by a multimeter. Fig. 5 shows the electrical impedance measurement system for the thermal microactuators in a controlled vacuum environment. The measurements are performed under various conditions by changing dc voltage, ac voltage, pressure and frequency using a Solartron 1255 FRA and potentiostat M273, which are interfaced by a PC through a GPIB card.
5. Results and discussion Fig. 6 is a photograph of a completed thermal microactuator as viewed with light through the glass substrate. This particular thermal microactuator has a bridge length of 500 mm, a width of 40 mm and a thickness of 3 mm. The polysilicon microbridge is shown as a dark area under the fingers of the signal metals on the glass substrate. The bright area on the microbridge is the contact metal for electrical contact with the metal fingers. In order to obtain a , we have measured the temperature dependence on the resistance of the thermal microactuator as shown in Fig. 7. Measured resistances are the sum of the microbridge resistance and the pad contact resistance. These data could be fitted linearly as Ž6. in the temperature
Fig. 5. A schematic diagram of impedance measurement system.
Fig. 6. Thermal microactuator as viewed through the glass substrate.
range from 208C up to 2008C and a was measured as 1.38 = 10y3 r8C. Fig. 8 shows the electrical impedance diagram of the thermal microactuator as a function of pressure. Although the arc center has to be on the real axis according to Ž12., the centers of experimental arcs are slightly displaced below the real axis because the temperature of the thermal microactuator does not have one value but a profile along the length of microbridge. Therefore, the relaxation time is not single valued but is distributed continuously around a mean Ž1rv 0 .. The angle by which such a semicircular arc is depressed below the real axis could be related to the width of the relaxation time distribution. Fig. 9 shows the dependence of impedance on the applied dc voltage at 16 mTorr. The radiuses of semicircular arcs are proportional to Vdc2 . Above result matches with Ž14. because the Gt is a constant under the constant pressure condition. The smaller value of intersections, R dc , increases as Vdc increases because an increase in Joule’s heat generation from the DVdc induces a rise of DTdc in
Fig. 7. Temperature coefficient of resistance of the thermal microactuator.
J.-Y. Lee, S.-W. Kangr Sensors and Actuators 75 (1999) 86–92
91
Fig. 8. Complex impedance plot of the thermal microactuator as a function of pressure.
Fig. 10. Complex impedance plot of the thermal microactuator as a function of ac voltage at 16 mTorr.
Ž8.. This change of R dc as a function of dc voltage does not exactly correspond with Ž5., Ž5.1. and Ž8.. It is because R 0 , a variable of R dc , is sensitive to the variation of the ambient temperature T0 and the pad temperature, and so these temperature variations can cause the deviation of R dc from the expected values. But this method enables the elimination of error from the ambient temperature variation since the Gt is independent of R 0 and R dc , the Ct is a function of not R 0 but R dc according to Ž15. and R dc is measured from the smaller value of the intersections at the same time. Fig. 10 shows that the ac voltage effect on the electrical impedance is not noticeable in the given ac voltage range. At Vac < Vdc , Joule’s heat generation by the ac voltage is
much smaller than that by the dc voltage. But Joule’s heat generation by the ac voltage cannot be neglected in Ž4., Ž5. and Ž7. when Vac f Vdc . Therefore, the requirement for improving the accuracy of thermal characteristics is that the experiments must be performed in the range of Vac < Vdc . The Gt and Ct values, which have been derived at the same time from Fig. 8 using Ž14. and Ž15., are plotted as a function of pressure in Fig. 11. It is clearly seen that the Gt reaches a constant value when the pressure is lowered to less than approximately 1 Torr. It indicates that the heat is directly conducted through only the microbridge itself to the contact pads at low pressure. Fig. 11 also shows that the Ct , obtained by the fitting, which is basically insensitive to pressure, and can be considered as a constant. This
Fig. 9. Complex impedance plot of the thermal microactuator as a function of dc voltage at 16 mTorr.
Fig. 11. Thermal conductance and thermal capacitance of the thermal microactuator as a function of pressure.
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J.-Y. Lee, S.-W. Kangr Sensors and Actuators 75 (1999) 86–92
result is in accordance with the fact that only materials composing the thermal microactuator, not ambient pressure, can influence the heat storage capacity.
6. Conclusions Obtaining thermal characteristics is important in design and test of a thermal microactuator. This work includes the fabrication of a thermal microactuator for microrelay and the thermal characterization method to measure the thermal capacitance Ct and the thermal conductance Gt between the thermal microactuator and its surroundings. These parameters have been derived at the same time from the electrically equivalent circuit model when the radius of impedance semicircular arc and the angular frequency at the top point of the arc are measured at the given dc voltage. This thermal characteristics measurement method does not have to use a dc method nor an external radiation source to oscillate the temperature of the thermal microactuator. The error from the variation of surrounding temperature is eliminated. For the thermal microactuator having a bridge length of 500 mm, a width of 40 mm and a thickness of 3 mm, the measured Gt and Ct are 3.3 = 10y4 Wr8C and 4.3 = 10y7 Jr8C at 16 mTorr, respectively.
Acknowledgements This project has been supported by the Ministry of Information and Communication of Korea through the Projects of Fundamental Research in University.
References w1x T. Seki, M. Sakata, T. Nakajima, M. Matsumoto, Thermal buckling actuator for micro relays, Transducers 97 Ž1997. 1153–1156. w2x H.J. Quenzer, A. Maciossek, B. Wagner, H. Pott, Surface micromachined metallic microactuator with buckling characteristics, Transducer 95 Eurosensors IX, Ž1995. 128–131. w3x J.H. Comtois, V.M. Bright, Applications for surface-micromachined polysilicon thermal actuators and arrays, Sensors and Actuators A 58 Ž1997. 19–25. w4x P. Eriksson, J.Y. Anderson, G. Stemme, Thermal characterization of surface-micromachined silicon nitride membranes for thermal infrared detectors, J. Microelectromech. Syst. 6 Ž1997. 55–61. w5x Y.-M. Chen, J.-S. Shie, T. Hwang, Parameter extraction of resistive thermal sensors, Sensors and Actuators A 55 Ž1996. 43–47. w6x J.-H. Chae, J.-Y. Lee, S.-W. Kang, Measurement of thermal expansion coefficient of poly-Si using microgauge sensors, SPIE Smart Electronics and MEMS, Ž1997. 202–211.
Jae-Youl Lee received a BS degree in Metallurgical Engineering from Hanyang University in 1992 and an MS degree in Electronic Science and Engineering from KAIST ŽKorea Advanced Institute of Science and Technology. in 1994. He is currently working toward a PhD degree in the field of microelectromechanical system at KAIST.
Sang-won Kang is an Associate Professor at the Department of Materials Science and Engineering in KAIST. He received a BS degree in Materials Engineering from Seoul National University in 1976, an MS degree in Materials Science and Engineering from KAIST in 1978 and a PhD degree in Materials Science and Engineering from KAIST in 1990. He was previously employed at Electronics and Telecommunication Research Institute from 1978 until 1993. He had been a visiting research engineer at AT&T Bell Laboratory Center from 1984 until 1986. His interests are atomic layer deposition for interconnection, high dielectric thin film and chemical mechanical polishing equipment and process.
A characterization of the thermal parameters of thermally driven polysilicon microbridge actuators using electrical impedance analysis Jae-Youl Lee ) , Sang-Won Kang Department of Materials Science and Engineering, Korea AdÕanced Institute of Science and Technology, 373-1 Kusong-dong, Yusong-gu, Taejon, 305-701, South Korea Received 8 June 1998; accepted 25 November 1998
Abstract We have fabricated microrelays with a thermally driven polysilicon microbridge actuator to characterize their thermal parameters. An electrically equivalent circuit for the thermal microactuator has been modeled in functions of experimental parameters. The thermal conductance and the thermal capacitance of the thermal microactuator have been derived at the same time from the model and the frequency response analysis results. For the thermal microactuator having a bridge length of 500 mm, a width of 40 mm and a thickness of 3 mm, the thermal conductance and the thermal capacitance were 3.3 = 10y4 Wr8C and 4.3 = 10y7 Jr8C at 16 mTorr, respectively. A radiation source, which is needed to oscillate the temperature of thermal sensors in other measurement method, is not necessary in this work because signal voltage supplied by a FRA ŽFrequency Response Analyzer. heats the thermal microactuator. The method also eliminates the error from the ambient temperature variation because it considers the change of dc resistance affected by the ambient temperature variation. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Thermal microactuator; Microrelay; Thermal conductance; Thermal capacitance; Thermal characterization method
1. Introduction Thermally driven microactuators have simpler device structures and fabrication process than other actuators using electrostatic force, electromagnetic force, piezoelectric force and etc., in addition, they are expected to have advantages such as relatively large force and displacement. Therefore, many efforts have been devoted to development of the microrelays w1x, microvalves w2x and micromotors w3x using thermal force. Modeling of thermal characteristics and extracting of thermal parameters are prerequisite for designing the operation speed and power consumption of thermal actuators and thermal sensors. In the early works for the IR sensors and thermal sensors w4,5x, the thermal conductance was obtained by dc method and the thermal capacitance was measured by ac method separately. A radiation source modulated by an optical chopper was used in ac method. The thermal time constant and the expected
operation speed of sensors were calculated from the output signal amplitude at the given chopper frequency. Therefore, these measurements require both dc method and ac method. Also, a radiation source is needed additionally for the ac method. In this work, we have introduced a new characterization method for extract the thermal parameters from thermal microactuators using a FRA ŽFrequency Response Analyzer.. Since this new method is based on an electrical impedance analysis, neither external radiation source nor additional dc method is not necessary. The parameters are derivable without the accuracy loss from the ambient temperature variation during the measurement. The effects of dc voltage, ac voltage and pressure were investigated to verify the characterization method.
2. Design and fabrication
)
Corresponding author. Tel.: q82-42-869-4261; Fax: q82-42-8693310; E-mail: [email protected]
The structure of a microrelay is shown in Fig. 1. The microrelay is comprised of silicon and glass substrate bonded together. Switching operation is provided by a
0924-4247r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 8 . 0 0 2 9 7 - 0
J.-Y. Lee, S.-W. Kangr Sensors and Actuators 75 (1999) 86–92
87
Fig. 1. Schematic drawing of a microrelay. Ža. Top view; Žb. cross-section view.
thermally driven polysilicon microbridge actuator fabricated on the silicon substrate. The signal metals for mechanical contact are patterned onto glass substrate. Application of current to the actuator power line causes Joule’s heating of the polysilicon microbridge actuator, which induces the displacement caused by the thermal expansion of polysilicon microbridge actuator towards the signal lines on the glass substrate. Then, the signal metal Ž1. and the signal metal Ž2. are electrically connected through the contact metal on the polysilicon microbridge actuator and the microrelay is ‘on’. As the driving current is removed, the microbridge returns to its free-standing position, the microrelay is ‘off’. Fig. 2 shows the microrelay fabrication process. In the first step, Si 3 N4rSiO 2 are deposited as electrical and
chemical insulating layers. Phosphorous doped polysilicon of 3 mm thickness and TEOS SiO 2 of 2 mm thickness are used as the structural and sacrificial materials respectively. Then another SiO 2 film, which is used to mask polysilicon bridge later, is deposited on the polysilicon layer and these layers are annealed in N2 to relieve any residual stress. After SiO 2 is patterned by BOE ŽBuffered Oxide Etchant. wet etch for masking of polysilicon microbridge patterns, polysilicon microbridges are formed by TMAH ŽTetra Methyl Ammonium Hydroxide. wet etch and the sacrificial SiO 2 is removed in BOE by time controlled etch stop. Polysilicon microbridges have lengths of 300, 500 and 700 mm and widths of 40 and 60 mm and thickness of 3 mm. As shown in Fig. 2b, PECVD SiO 2 film of 0.2 mm thickness is deposited for electrical isolation between Al
88
J.-Y. Lee, S.-W. Kangr Sensors and Actuators 75 (1999) 86–92
etch of 0.5 mm to 1.5 mm in depth, Al film of 0.7 mm thickness is deposited and patterned to create the signal metals as shown in Fig. 2d. After fabricating the silicon and glass substrate, the two substrates are aligned together using a microscope system and then bonded using a general adhesive. For the last step, 25 mm thick Al wires are connected between contact pads of microrelay and copper lead frames.
3. Theoretical model Fig. 3 shows a simple lumped model of a thermally equivalent circuit for the thermal microactuator to calculate the average temperature increase of microactuator when a driving voltage is applied. The Gt is the heat conductance between the thermal microactuator and environments through the microbridge and surrounding gas, the thermal capacitance Ct represents the heat storage of the thermal microactuator, the P represents the heat generation term that is the product of the current and the voltage, T is the average temperature of the thermal microactuator and T0 is the ambient temperature. The thermal impedance Zt of the model can be expressed as Zt s
Gt 2 Gt q v 2 Ct2
y
v Ct 2 Gt q v 2 Ct2
j
Ž 1.
where v is the angular frequency of applied ac voltage. If FRA apply the superimposed dc and ac voltage to microactuator, the current has the dc and ac current components as Ž3.. V s Vdc q Vac sin v t
Ž 2.
I s Idc q Iac sin Ž v t y u .
Ž 3.
where u is the phase shift between the ac voltage and the ac current.
Fig. 2. Fabrication process of a microrelay.
metal and polysilicon bridges. Then PECVD SiO 2 film is etched to create contact areas for electrical paths to microbridge. Next, Al film of 0.7 mm thickness is deposited and patterned. This layer forms both metal pads of 2 = 3 mm2 area Žactuator power line. for microbridge and contact metal. Glass etch is performed to create the cavity, which provides the space needed to allow the signal metals away from the contact metal patterned onto the microbridge while driving current is not applied. Following the glass
Fig. 3. A thermally equivalent circuit of the thermal microactuator.
J.-Y. Lee, S.-W. Kangr Sensors and Actuators 75 (1999) 86–92
From these two equations, Joule’s heat generation becomes P s Vdc Idc q
Iac Vac cos u 2
q Idc Vac sin v t
An effective method for the analysis of impedance results is to plot real part and imaginary part in the complex plane, now known as a Nyquist diagram. Putting Ž1. into Ž9. to separate real and imaginary parts, one obtains
p Iac Vac sin q Vdc Iac sin Ž v t y u . y
ž
2
q2vtyu
/
Xs
2 3 Gt2 R dc qCt2 R dc v 2 yGt Idc R 0 R dc a qGt Idc R 0 Vdc a y Idc R 20 Vdc a 2 2 4 Gt2 q v 2 Ct2 y2Gt Idc R 0 a q Idc R 20 a 2
2
Ž 10 .
Ž 4. When Iac < Idc and Vac < Vdc in Ž4., the last term on the right side can be neglected. The temperature difference DT between the average temperature T of the thermal microactuator and the ambient temperature T0 can be written as Ž5.. The DT also divided into the dc and ac components since the heat generation term consists of the dc and ac parts. DT s DTdc q DTac s PdcrGt q Zt Pac Pdc s Vdc Idc q
Iac Vac cos u 2
89
Ysy
Pac s Idc Vac sin v t q Vdc Iac sin Ž v t y u .
Center
Ž 5. Ž 5.1 . Ž 5.2 .
Ž
.
Ž 11 .
R 02 a 2
Ž10. and Ž11. yield a full semicircle with its center on the real axis of the complex plane and the center and radius of the semicircle can be derived to give a result
s f Vdc Idc
Ct Idc R 0 va Idc R dc q Vdc 2 4 Gt q v 2 Ct2 y 2Gt Idc2 R 0 a q Idc
ž
2Gt R dc y Idc2 R 0 R dc a q Idc R 0 Vdc a 2 Ž Gt y Idc2 R 0 a .
Vdc Idc R 0 a
/
,0 r
Ž 12 .
Gt y Idc2 R 0 a .
Two intersections between the semicircle and the real axis are expressed as Ž13., and the dc resistance R dc can be measured from the smaller value of intersections. Gt R dc q Idc R 0 Vdc a X s R dc , Ž 13 . Gt y Idc2 R 0 a
In particular, for heavily doped polycrystalline silicon, the temperature characteristic of resistivity obeys the linear relationship w6x. For much larger pads than the bridge width, we can assume that the pad contact resistance is much smaller than the resistance of microbridge. Therefore, the resistance of polysilicon microbridge actuator can assume an equation as
From the relation that the maximum value of Y is equal to the radius, the thermal conductance Gt and the thermal capacitance Ct can be obtained as
R Ž T . s R 0 1 q a Ž T y T0 . 4 s R 0 1 q a DT 4
Gt s
Ž 6.
where R 0 is the resistance of actuator at temperature T0 and a is the temperature coefficient of resistance. Since the electrical characteristic of the thermal microactuator consists of only resistance that is a function of the temperature change, the relation between the voltage and the current can be written as Ž7.. If Iac < Idc and a DTac - 1 q a DTdc , then the last term on the right side can be neglected. V s IRs Idc q Iac sin Ž v t y u . 4 R 0 1 q a Ž DTdc q DTac . 4
Vdc2 a
Ž 14 .
r Gt
Ct s
ž
v0 1q
r R dc
f
/
Gt
v0
Ž 15 .
where r is the radius of the semicircle in the impedance plane, v 0 is the angular frequency at the top point of the semicircle. If r < R dc , Ž15. can be simplified as Gtrv 0 . Ž14. and Ž15. can yield an electrically equivalent circuit model of the thermal microactuator as shown in Fig. 4.
s R 0 Idc Ž 1 q a DTdc . q Iac Ž 1 q a DTdc . sin Ž v t y u . qIdc a DTac q Iac a DTac sin Ž v t y u . 4 f Idc R 0 Ž 1 q a DTdc . 4 q Iac R 0 Ž 1 q a DTdc . =sin Ž v t y u . q Idc R 0 a DTac 4
Ž 7.
The voltage in Ž7. can be divided into the dc and ac parts. Then by comparing these two parts with Ž2. and Ž3., the dc resistance R dc and ac electrical impedance Ze are respectively obtained as R dc s R 0 1 q a DTdc 4 Ze s
R dc q Idc R 0 a ZtVdc 1 y Idc2 R 0 a Zt
Ž 8. s X q Yj.
Ž 9. Fig. 4. An electrically equivalent circuit of the thermal microactuator.
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The thermal conductance and thermal capacitance, when r and v 0 are measured at Vdc and we know a , can be derived at the same time from Ž14. and Ž15..
4. Experimental As mentioned above, we have to know the temperature coefficient of resistance of the thermal microactuator in order to measure the Gt and Ct . So the temperature characteristics of resistance have been measured by oil-bath method. The microrelay is immersed in electrically insulating silicon oil. The oil acts as a heat reservoir, holding the thermal microactuator temperature at a series of values of Toil that are adjusted by a hot chuck used as an external heat source. This oil-bath method ensures uniform temperature for entire parts of the thermal microactuator. The resistances of the thermal microactuator are measured by a multimeter. Fig. 5 shows the electrical impedance measurement system for the thermal microactuators in a controlled vacuum environment. The measurements are performed under various conditions by changing dc voltage, ac voltage, pressure and frequency using a Solartron 1255 FRA and potentiostat M273, which are interfaced by a PC through a GPIB card.
5. Results and discussion Fig. 6 is a photograph of a completed thermal microactuator as viewed with light through the glass substrate. This particular thermal microactuator has a bridge length of 500 mm, a width of 40 mm and a thickness of 3 mm. The polysilicon microbridge is shown as a dark area under the fingers of the signal metals on the glass substrate. The bright area on the microbridge is the contact metal for electrical contact with the metal fingers. In order to obtain a , we have measured the temperature dependence on the resistance of the thermal microactuator as shown in Fig. 7. Measured resistances are the sum of the microbridge resistance and the pad contact resistance. These data could be fitted linearly as Ž6. in the temperature
Fig. 5. A schematic diagram of impedance measurement system.
Fig. 6. Thermal microactuator as viewed through the glass substrate.
range from 208C up to 2008C and a was measured as 1.38 = 10y3 r8C. Fig. 8 shows the electrical impedance diagram of the thermal microactuator as a function of pressure. Although the arc center has to be on the real axis according to Ž12., the centers of experimental arcs are slightly displaced below the real axis because the temperature of the thermal microactuator does not have one value but a profile along the length of microbridge. Therefore, the relaxation time is not single valued but is distributed continuously around a mean Ž1rv 0 .. The angle by which such a semicircular arc is depressed below the real axis could be related to the width of the relaxation time distribution. Fig. 9 shows the dependence of impedance on the applied dc voltage at 16 mTorr. The radiuses of semicircular arcs are proportional to Vdc2 . Above result matches with Ž14. because the Gt is a constant under the constant pressure condition. The smaller value of intersections, R dc , increases as Vdc increases because an increase in Joule’s heat generation from the DVdc induces a rise of DTdc in
Fig. 7. Temperature coefficient of resistance of the thermal microactuator.
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Fig. 8. Complex impedance plot of the thermal microactuator as a function of pressure.
Fig. 10. Complex impedance plot of the thermal microactuator as a function of ac voltage at 16 mTorr.
Ž8.. This change of R dc as a function of dc voltage does not exactly correspond with Ž5., Ž5.1. and Ž8.. It is because R 0 , a variable of R dc , is sensitive to the variation of the ambient temperature T0 and the pad temperature, and so these temperature variations can cause the deviation of R dc from the expected values. But this method enables the elimination of error from the ambient temperature variation since the Gt is independent of R 0 and R dc , the Ct is a function of not R 0 but R dc according to Ž15. and R dc is measured from the smaller value of the intersections at the same time. Fig. 10 shows that the ac voltage effect on the electrical impedance is not noticeable in the given ac voltage range. At Vac < Vdc , Joule’s heat generation by the ac voltage is
much smaller than that by the dc voltage. But Joule’s heat generation by the ac voltage cannot be neglected in Ž4., Ž5. and Ž7. when Vac f Vdc . Therefore, the requirement for improving the accuracy of thermal characteristics is that the experiments must be performed in the range of Vac < Vdc . The Gt and Ct values, which have been derived at the same time from Fig. 8 using Ž14. and Ž15., are plotted as a function of pressure in Fig. 11. It is clearly seen that the Gt reaches a constant value when the pressure is lowered to less than approximately 1 Torr. It indicates that the heat is directly conducted through only the microbridge itself to the contact pads at low pressure. Fig. 11 also shows that the Ct , obtained by the fitting, which is basically insensitive to pressure, and can be considered as a constant. This
Fig. 9. Complex impedance plot of the thermal microactuator as a function of dc voltage at 16 mTorr.
Fig. 11. Thermal conductance and thermal capacitance of the thermal microactuator as a function of pressure.
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result is in accordance with the fact that only materials composing the thermal microactuator, not ambient pressure, can influence the heat storage capacity.
6. Conclusions Obtaining thermal characteristics is important in design and test of a thermal microactuator. This work includes the fabrication of a thermal microactuator for microrelay and the thermal characterization method to measure the thermal capacitance Ct and the thermal conductance Gt between the thermal microactuator and its surroundings. These parameters have been derived at the same time from the electrically equivalent circuit model when the radius of impedance semicircular arc and the angular frequency at the top point of the arc are measured at the given dc voltage. This thermal characteristics measurement method does not have to use a dc method nor an external radiation source to oscillate the temperature of the thermal microactuator. The error from the variation of surrounding temperature is eliminated. For the thermal microactuator having a bridge length of 500 mm, a width of 40 mm and a thickness of 3 mm, the measured Gt and Ct are 3.3 = 10y4 Wr8C and 4.3 = 10y7 Jr8C at 16 mTorr, respectively.
Acknowledgements This project has been supported by the Ministry of Information and Communication of Korea through the Projects of Fundamental Research in University.
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Jae-Youl Lee received a BS degree in Metallurgical Engineering from Hanyang University in 1992 and an MS degree in Electronic Science and Engineering from KAIST ŽKorea Advanced Institute of Science and Technology. in 1994. He is currently working toward a PhD degree in the field of microelectromechanical system at KAIST.
Sang-won Kang is an Associate Professor at the Department of Materials Science and Engineering in KAIST. He received a BS degree in Materials Engineering from Seoul National University in 1976, an MS degree in Materials Science and Engineering from KAIST in 1978 and a PhD degree in Materials Science and Engineering from KAIST in 1990. He was previously employed at Electronics and Telecommunication Research Institute from 1978 until 1993. He had been a visiting research engineer at AT&T Bell Laboratory Center from 1984 until 1986. His interests are atomic layer deposition for interconnection, high dielectric thin film and chemical mechanical polishing equipment and process.