**4.3 Force**

Figure 9 shows the force for the P123F thermal actuator versus displacement when actuated at a constant current and voltage, 15 mA and 6.1V (Baker et al., 2004). For this test, the thermal actuator was held at a constant applied current and allowed to displace to its maximum unloaded position, which corresponds to the point on the graph where the curve intersects with the X-axis. Then using a probe tip, the force gauge was pulled away from the actuator, stretching the folded-beam spring in series between the probe tip and the actuator and applying a force to the thermal actuator center shuttle. The spring elongation was used to calculate the applied force and was recorded along with the actuator displacement. As the actuator is pulled back, the force increased to a maximum of 205 N at ~6.75 m. When pulled beyond this, the force begins to decrease due to buckling of the actuator legs. It is important to understand that this force curve represents the available output force of this single actuator design at this single applied power level. To fully characterize the force

Thermal Microactuators 423

Due to the challenges associated with obtaining spatially resolved temperature measurements on MEMS, thermal microactuator models have often been validated primarily from displacement and electrical measurements. Thermal microactuator performance depends on the temperatures of the microactuator legs. Experimentally measured temperatures are invaluable for understanding and improving thermal microactuator performance, model validation, and design optimization. Raman thermometry techniques were used to measure temperatures on electrically powered bent-beam thermal microactuators and laser powered

Raman thermometry has been used to measure temperature profiles along the actuator legs of bent-beam and flexure thermal microactuators (Kearney et al., 2006a and 2006b; Serrano et al., 2006). Raman thermometry was performed using a Renishaw inVia Raman microscope. The microscope uses a 180° backscattering geometry and a 488 nm Ar+ laser as the probe that produces a diffraction-limited spot of 560 nm in diameter when focused by a 50×, 0.50-numerical-aperture objective. The actual measurement diameter within the sample is larger, 1.20 m, because of spreading of the probe laser within the sample. The Raman signal from the sample surface is collected through the objective, dispersed by a grating spectrograph, and detected with a back-side illuminated, thermoelectrically cooled CCD camera (Princeton Instruments Pixis). Dispersion of the Raman signal at the CCD is

Laser power at the sample is attenuated to minimize localized heating of the sample that would otherwise introduce a bias into the temperature measurement. Minimal heating of the sample is confirmed by obtaining Raman spectra at decreasing laser powers from a room-temperature sample until no change in the Raman peak position was observed. The 1.2 m in-plane resolution of the Raman probe is capable of resolving widths of 2 m to 4 m for thermal microactuator legs. A detailed uncertainty analysis reveals that the reported Raman-measured temperatures are reliable to within ±10 to 11 K (Kearney et al., 2006a). These experimental results show that high-quality, reliable temperature measurements can be obtained. Most Raman thermometry measurements are performed when the devices are operating in a steady state in order to allow sufficient time for data collection with sufficient signal strength. Typical data collection times are on the order of tens of seconds to a few minutes. Transient measurements using periodic excitation are

**4.4.2 Steady state electrically powered bent-beam thermal microactuator results**  The temperature profiles reported in this section were taken using the Raman thermometry techniques reported by Kearney et al. (2006a, 2006b) and summarized in Section 4.4.1 on the surface micromachined actuators described in Section 3.1. Temperature measurements are made along one leg of the thermal microactuators starting from an anchor and ending at the center shuttle since the design and performance are symmetric. The chips with the P123 and P123F thermal microactuators were die attached and wire bonded in 24-pin Dual-in-Line Packages (DIP) that were inserted into a zero insertion force (ZIF) socket for the testing in laboratory air. The devices were powered with a Keithley 2400 Source Meter with a single

**4.4 Temperature measurements** 

flexure thermal microactuators.

0.57 cm–1/pixel.

mentioned in Section 4.4.4.

lead on each anchor of the thermal microactuator.

**4.4.1 Raman thermometry methods** 

output of an actuator design, a force curve would need to be measured at several different power levels. This family of curves would then map out the full force versus displacement behavior. The error bars shown for each force level were determined based on an uncertainty analysis performed on the spring design, taking into account the uncertainty in beam width, length, thickness, and Young's Modulus, as well as the measurement uncertainty in the spring elongation.

Fig. 8. Resistance versus current for the P123 thermal actuator

Fig. 9. Force versus position of the actuator at 15 mA for the P123F thermal actuator

output of an actuator design, a force curve would need to be measured at several different power levels. This family of curves would then map out the full force versus displacement behavior. The error bars shown for each force level were determined based on an uncertainty analysis performed on the spring design, taking into account the uncertainty in beam width, length, thickness, and Young's Modulus, as well as the measurement

**Resistance Comparison**

0 5 10 15 20 25 **Applied Current (mA)**

**Force Comparison**

0 2 4 6 810 **Displacement (m)**

Fig. 9. Force versus position of the actuator at 15 mA for the P123F thermal actuator

uncertainty in the spring elongation.

Data Model (0.1 bias) Model (0.15 bias)

Fig. 8. Resistance versus current for the P123 thermal actuator

0

50

100

**Force ( N)**

150

200

250

Data Model

**Resistance (ohms)**

#### **4.4 Temperature measurements**

Due to the challenges associated with obtaining spatially resolved temperature measurements on MEMS, thermal microactuator models have often been validated primarily from displacement and electrical measurements. Thermal microactuator performance depends on the temperatures of the microactuator legs. Experimentally measured temperatures are invaluable for understanding and improving thermal microactuator performance, model validation, and design optimization. Raman thermometry techniques were used to measure temperatures on electrically powered bent-beam thermal microactuators and laser powered flexure thermal microactuators.

#### **4.4.1 Raman thermometry methods**

Raman thermometry has been used to measure temperature profiles along the actuator legs of bent-beam and flexure thermal microactuators (Kearney et al., 2006a and 2006b; Serrano et al., 2006). Raman thermometry was performed using a Renishaw inVia Raman microscope. The microscope uses a 180° backscattering geometry and a 488 nm Ar+ laser as the probe that produces a diffraction-limited spot of 560 nm in diameter when focused by a 50×, 0.50-numerical-aperture objective. The actual measurement diameter within the sample is larger, 1.20 m, because of spreading of the probe laser within the sample. The Raman signal from the sample surface is collected through the objective, dispersed by a grating spectrograph, and detected with a back-side illuminated, thermoelectrically cooled CCD camera (Princeton Instruments Pixis). Dispersion of the Raman signal at the CCD is 0.57 cm–1/pixel.

Laser power at the sample is attenuated to minimize localized heating of the sample that would otherwise introduce a bias into the temperature measurement. Minimal heating of the sample is confirmed by obtaining Raman spectra at decreasing laser powers from a room-temperature sample until no change in the Raman peak position was observed. The 1.2 m in-plane resolution of the Raman probe is capable of resolving widths of 2 m to 4 m for thermal microactuator legs. A detailed uncertainty analysis reveals that the reported Raman-measured temperatures are reliable to within ±10 to 11 K (Kearney et al., 2006a). These experimental results show that high-quality, reliable temperature measurements can be obtained. Most Raman thermometry measurements are performed when the devices are operating in a steady state in order to allow sufficient time for data collection with sufficient signal strength. Typical data collection times are on the order of tens of seconds to a few minutes. Transient measurements using periodic excitation are mentioned in Section 4.4.4.

#### **4.4.2 Steady state electrically powered bent-beam thermal microactuator results**

The temperature profiles reported in this section were taken using the Raman thermometry techniques reported by Kearney et al. (2006a, 2006b) and summarized in Section 4.4.1 on the surface micromachined actuators described in Section 3.1. Temperature measurements are made along one leg of the thermal microactuators starting from an anchor and ending at the center shuttle since the design and performance are symmetric. The chips with the P123 and P123F thermal microactuators were die attached and wire bonded in 24-pin Dual-in-Line Packages (DIP) that were inserted into a zero insertion force (ZIF) socket for the testing in laboratory air. The devices were powered with a Keithley 2400 Source Meter with a single lead on each anchor of the thermal microactuator.

Thermal Microactuators 425

accommodate a stage holding a 1:1 relay lens through which an 808 nm continuous wave fiber-coupled laser with a 100 m core fiber could be focused on a MEMS part. This enabled temperature measurements on a thermal microactuator surface during laser heating. The heating laser was at an angle of incidence of 60°, yielding a 200 m × 100 m elliptical spot on the surface. To avoid damage during measurement collection, a laser power of 314 mW was chosen. This power provides sufficient power to operate the device in a reliable fashion

The flexure thermal microactuator was fabricated from using the SUMMiT V process and is pictured in Fig. 11a. The thermal microactuator was 200 m long with a 2.5 m wide × 200 m long narrow leg. The opposite side consisted of the 100 m wide by 150 m long Poly4 target and a 2.5 m wide × 50 m long flexure element. The distance between the two legs was 5.0 m. The full temperature profile of a 100 m-wide Poly4 actuator was taken at 10 m steps starting at the base of the narrow leg and down the near edge (the edge closest to the narrow leg) of the target surface and up to the base of the flexure element. The profile, shown in Fig. 11b, reveals that the temperature along both narrow elements (the thin leg and the flexure) increases linearly from the substrate temperature at the bond pads to the target surface temperature. On the target surface, the temperature in the near edge remains somewhat uniform from the point nearest the narrow leg up to the mid-length of the surface. Beyond this point, the temperature decreases as the flexure element is approached. The temperature profile in Fig. 11b differs from that for an electrically heated flexure thermal microactuator which has the highest temperatures in the narrow leg (Serrano et al., 2006). Since the target of the laser powered thermal actuator achieves the highest temperatures, the wide leg expands more than the narrow leg and the actuator curls in the direction of the narrow leg when powered. For an electrically heated flexure thermal actuator, the narrow leg will expand more than the wide leg and the actuator will move in

> Flexure Target (Near Edge)

To Narrow Leg

Temperature (°C)

0 50 100 150 Position (μm)

Near edge Center Far Edge

> To Flexure

and avoid damaging the surface (Serrano and Phinney, 2008).

the direction of the wide leg.

and far edge of the thermal microactuator target.

Temperature (°C)

0 100 200 300 400 Position (μm)

Fig. 11. Temperature profiles along a laser heated flexure actuator a) picture of flexure thermal microactuator and measurement paths, b) temperature profile along the near edge of the flexure actuator (blue line), and c) temperature profiles along the near edge, center,

Comparing the profiles taken along the near, center and far edges of the target surface (Fig. 11c) reveals that the impact of the flexure element and the thin leg is most pronounced on the near edge. The presence of these elements results, on average, in average temperatures

a) b) c)

Narrow Leg

Raman thermometry was used to measure temperatures along the lower left leg of P123 (four cases) and P123F (one case) thermal microactuators (Figure 10, Table 2). P123 microactuators on two packages, P5 and P6, were tested at two currents, 12 mA and 15 mA. The agreement between the temperature profiles for the P5 and P6 microactuators is within the experimental uncertainty of ±10 to 11°C. Thus, the observed device-to-device variation is within the measurement uncertainty. As the current is increased from 12 mA to 15 mA, the maximum temperature increases significantly from 210°C to 377°C. The maximum temperatures along the microactuator legs occur at about two-thirds of the distance from the anchor to the shuttle. Since these tests were conducted at laboratory air pressures, heat transport from the shuttle to the cooler underlying substrate results in the shuttle acting as a heat sink. The temperature profile along a P123F microactuator leg (P5 F) at 12 mA decreases even more at the shuttle than for P123 microactuators tested at 12 mA due to the connection to the force gauge providing another pathway for energy transport away from the shuttle.

Fig. 10. Temperature profiles for the lower left leg of the P123 and P123F thermal actuators


Table 2. Average actuator displacements, electrical measurements, and maximum temperatures at laboratory air pressure

#### **4.4.3 Steady state laser powered flexure thermal microactuator results**

Temperature measurements have also been made on laser heated polysilicon MEMS surfaces using Raman thermometry (Serrrano and Phinney, 2008; Serrano et al., 2009; Serrano and Phinney, 2009). The Renishaw inVia microscope system was adapted to

Raman thermometry was used to measure temperatures along the lower left leg of P123 (four cases) and P123F (one case) thermal microactuators (Figure 10, Table 2). P123 microactuators on two packages, P5 and P6, were tested at two currents, 12 mA and 15 mA. The agreement between the temperature profiles for the P5 and P6 microactuators is within the experimental uncertainty of ±10 to 11°C. Thus, the observed device-to-device variation is within the measurement uncertainty. As the current is increased from 12 mA to 15 mA, the maximum temperature increases significantly from 210°C to 377°C. The maximum temperatures along the microactuator legs occur at about two-thirds of the distance from the anchor to the shuttle. Since these tests were conducted at laboratory air pressures, heat transport from the shuttle to the cooler underlying substrate results in the shuttle acting as a heat sink. The temperature profile along a P123F microactuator leg (P5 F) at 12 mA decreases even more at the shuttle than for P123 microactuators tested at 12 mA due to the connection to the force gauge providing another pathway for energy transport away from

**P123 Actuators Thermal Profiles**

P5 12 mA P6 12 mA P5 F 12 mA P5 15 mA P6 15 mA

> Maximum Temperature [°C]

0 100 200 300 **x (microns)**

> Voltage [V]

Table 2. Average actuator displacements, electrical measurements, and maximum

**4.4.3 Steady state laser powered flexure thermal microactuator results** 

Fig. 10. Temperature profiles for the lower left leg of the P123 and P123F thermal actuators

P123 12 3.89 6.67 210 P123 15 5.58 9.61 377

Temperature measurements have also been made on laser heated polysilicon MEMS surfaces using Raman thermometry (Serrrano and Phinney, 2008; Serrano et al., 2009; Serrano and Phinney, 2009). The Renishaw inVia microscope system was adapted to

Displacement [m]

the shuttle.

Actuator Current

temperatures at laboratory air pressure

[mA]

**Temperature (deg. C)**

accommodate a stage holding a 1:1 relay lens through which an 808 nm continuous wave fiber-coupled laser with a 100 m core fiber could be focused on a MEMS part. This enabled temperature measurements on a thermal microactuator surface during laser heating. The heating laser was at an angle of incidence of 60°, yielding a 200 m × 100 m elliptical spot on the surface. To avoid damage during measurement collection, a laser power of 314 mW was chosen. This power provides sufficient power to operate the device in a reliable fashion and avoid damaging the surface (Serrano and Phinney, 2008).

The flexure thermal microactuator was fabricated from using the SUMMiT V process and is pictured in Fig. 11a. The thermal microactuator was 200 m long with a 2.5 m wide × 200 m long narrow leg. The opposite side consisted of the 100 m wide by 150 m long Poly4 target and a 2.5 m wide × 50 m long flexure element. The distance between the two legs was 5.0 m. The full temperature profile of a 100 m-wide Poly4 actuator was taken at 10 m steps starting at the base of the narrow leg and down the near edge (the edge closest to the narrow leg) of the target surface and up to the base of the flexure element. The profile, shown in Fig. 11b, reveals that the temperature along both narrow elements (the thin leg and the flexure) increases linearly from the substrate temperature at the bond pads to the target surface temperature. On the target surface, the temperature in the near edge remains somewhat uniform from the point nearest the narrow leg up to the mid-length of the surface. Beyond this point, the temperature decreases as the flexure element is approached. The temperature profile in Fig. 11b differs from that for an electrically heated flexure thermal microactuator which has the highest temperatures in the narrow leg (Serrano et al., 2006). Since the target of the laser powered thermal actuator achieves the highest

temperatures, the wide leg expands more than the narrow leg and the actuator curls in the direction of the narrow leg when powered. For an electrically heated flexure thermal actuator, the narrow leg will expand more than the wide leg and the actuator will move in the direction of the wide leg.

Fig. 11. Temperature profiles along a laser heated flexure actuator a) picture of flexure thermal microactuator and measurement paths, b) temperature profile along the near edge of the flexure actuator (blue line), and c) temperature profiles along the near edge, center, and far edge of the thermal microactuator target.

Comparing the profiles taken along the near, center and far edges of the target surface (Fig. 11c) reveals that the impact of the flexure element and the thin leg is most pronounced on the near edge. The presence of these elements results, on average, in average temperatures

Thermal Microactuators 427

where the temperature is in degrees Celsius and the resistivity is in units of ohm-microns.

11 3 8 2 5 1 ( 2.2 10 ) (9.0 10 ) (1.0 10 ) 0.014 *<sup>p</sup> <sup>k</sup> TTT*

where the temperature is in degrees Celsius and the thermal conductivity is in W/m/°C. At room temperature the thermal conductivity of polysilicon is 72 W/m/°C, and it decreases with increasing temperature. A value of 164 GPa was used for the Young's Modulus of polysilicon. The model curves in Figures 7-9 were calculated using this model. As seen in these figures, the predicted and measured displacements, electrical resistance, and force are

The reliability of thermal microactuators depends on the packaging and environment as well as the initial design. Thermal microactuators have operated successfully for tens of millions of cycles; however, performance degradation mechanisms have been observed including plastic deformation of actuator legs, wear debris generation, void formation when operated in vacuum, changes in the grain structure, out of plane displacement, oxide growth, fracture of actuator legs, and die stress effects (Baker et al., 2004; Chu et al., 2006; Phinney et al., 2010b; Plass et al., 2004). Temperature measurements in reduced pressure environment and the effects of die stress are described in detail to illustrate the impact of

Microsystems devices are often packaged at pressures lower than atmospheric, which dramatically affects the thermal performance of the parts since energy transfer to the environment is substantially reduced as the pressure is reduced (Phinney et al., 2010a). Thus, temperature measurements of thermal microactuators in varying pressures are crucial

Raman measurements were performed at nitrogen pressures varying from 0.05 Torr to 630 Torr using the Raman thermometry methods described in Section 4.3.1 and Torczynski et al. (2008). For reduced pressure measurements inside a Linkam thermal stage for which the pressure was controllable, a SUMMiT die with a P123 microactuator was packaged on a printed circuit board (PCB) to which wire leads were soldered. Each bond pad on the beam structure is wire-bonded to two separate connections on the PCB to allow for four-point sensing of the voltage. Quick-disconnect connectors were used inside the Linkam thermal stage to allow for easy exchange of parts. The PCB was placed in the center of a quartz crucible inside the stage and held in place with vacuum-compatible carbon tape. The heating ability of the stage was used to heat the sample to a temperature of 300-310 K to ensure a consistent substrate temperature for the measurements. The devices were powered with a Keithley 2400 Source Meter in a four-point sensing configuration, where the current is sourced through the outside connections and the voltage is measured across the inner

Raman thermometry was used to measure the temperature profiles for a P123 microactuator leg at pressures ranging from 0.05 Torr to 630 Torr (Figure 12). In order to maintain similar

environment and packaging on thermal microactuator performance.

to optimizing device and package design as well as model validation.

**6.1 Reduced pressure environments** 

(2)

The thermal conductivity is defined using the equation

in good agreement.

**6. Reliability** 

ones.

~35°C and ~65°C higher along the center and the far edge, respectively, than at the near edge. Moreover, temperature measurements reveal that the top-right corner of the target surface attains the highest temperature, ~425°C. Subsequent measurements at varying laser powers revealed the effects of optical interference and temperature dependent optical properties on the peak temperatures (Serrano and Phinney, 2008; Serrano et al., 2009; Serrano and Phinney, 2009).

#### **4.4.4 Transient bent-beam measurements**

Raman thermometry usually requires data collection times on the order of tens of seconds to minutes to acquire sufficient signals from silicon and polysilicon thermal microactuators precluding transient measurements. Serrano and Kearney (2008) collected time resolved Raman thermometry measurements on polysilicon thermal microactuators using a phaselocked technique. They were able to achieve 100 s temporal resolution for a polysilicon two leg thermal microactuator design similar to a P123 microactuator but with w1 = 3.0 m and an offset of 12 m (Figure 3). Their measurements revealed that when the thermal microactuator is powered at 3.9 V it achieved a maximum temperature of ~150°C. The heating process took about 2 ms, and the thermal microactuator cooled in about 1.5 ms after turning off the power.

#### **5. Modeling**

Numerous research groups have developed numerical models of thermal microactuator performance (Baker et al., 2004; Bergna et al., 2005; Enikov et al., 2005; Howell et al., 2007; Lott et al., 2002; Mankame and Ananthasuresh, 2001; Serrano et al., 2006; and Wong and Phinney, 2007). These models include electrical, thermal, and mechanical effects and are implemented through finite difference as well as finite element approaches.

An example of a model for thermal microactuators is the coupled electro-thermo-mechanical model that was developed to predict actuator performance (displacement, temperature and output force) as a function of the geometry and applied current (Baker et al. (2004)). The model utilizes a finite-difference thermal model to predict the total thermal strain at a given input current, accounting for temperature dependent material properties including thermal conductivity, electrical resistivity, and coefficient of thermal expansion. Heat conduction through the air gap into the substrate is included through the use of a conduction shape factor that is determined from a two-dimensional thermal analysis using the commercial finite-element analysis software ANSYS. Shape factors were determined to be 1.9856 for a 2.0 m gap between a P123 actuator and the substrate and 2.2336 for a gap of 2.8 m. ANSYS is then used to model the structural response for the given thermal strain. This model is described in more detail by Baker et al. (2004).

The material properties used in the model include an electrical resistivity given by the following curve fit

$$\text{If } T \lhd 300 \text{ } \rho = (2.9713 \times 10^{-2})T + 20.858$$

$$\text{If } T \ge 300 \text{ and } T \le 700 \text{ } \rho = (6.1600 \times 10^{-5})T^2 - (7.2473 \times 10^{-3})T + 26.402 \tag{1}$$

$$\text{If T} \ge 700 \text{ } \rho = (8.624 \times 10^{-2})T - 8.8551$$

~35°C and ~65°C higher along the center and the far edge, respectively, than at the near edge. Moreover, temperature measurements reveal that the top-right corner of the target surface attains the highest temperature, ~425°C. Subsequent measurements at varying laser powers revealed the effects of optical interference and temperature dependent optical properties on the peak temperatures (Serrano and Phinney, 2008; Serrano et al., 2009;

Raman thermometry usually requires data collection times on the order of tens of seconds to minutes to acquire sufficient signals from silicon and polysilicon thermal microactuators precluding transient measurements. Serrano and Kearney (2008) collected time resolved Raman thermometry measurements on polysilicon thermal microactuators using a phaselocked technique. They were able to achieve 100 s temporal resolution for a polysilicon two leg thermal microactuator design similar to a P123 microactuator but with w1 = 3.0 m and an offset of 12 m (Figure 3). Their measurements revealed that when the thermal microactuator is powered at 3.9 V it achieved a maximum temperature of ~150°C. The heating process took about 2 ms, and the thermal microactuator cooled in about 1.5 ms after

Numerous research groups have developed numerical models of thermal microactuator performance (Baker et al., 2004; Bergna et al., 2005; Enikov et al., 2005; Howell et al., 2007; Lott et al., 2002; Mankame and Ananthasuresh, 2001; Serrano et al., 2006; and Wong and Phinney, 2007). These models include electrical, thermal, and mechanical effects and are

An example of a model for thermal microactuators is the coupled electro-thermo-mechanical model that was developed to predict actuator performance (displacement, temperature and output force) as a function of the geometry and applied current (Baker et al. (2004)). The model utilizes a finite-difference thermal model to predict the total thermal strain at a given input current, accounting for temperature dependent material properties including thermal conductivity, electrical resistivity, and coefficient of thermal expansion. Heat conduction through the air gap into the substrate is included through the use of a conduction shape factor that is determined from a two-dimensional thermal analysis using the commercial finite-element analysis software ANSYS. Shape factors were determined to be 1.9856 for a 2.0 m gap between a P123 actuator and the substrate and 2.2336 for a gap of 2.8 m. ANSYS is then used to model the structural response for the given thermal strain. This

The material properties used in the model include an electrical resistivity given by the

(2.9713 10 ) 20.858 *T*

(8.624 10 ) 8.8551 *T*

(6.1600 10 ) (7.2473 10 ) 26.402 *T T* (1)

implemented through finite difference as well as finite element approaches.

If T>700 <sup>2</sup> 

 If *T*>300 and *T*<700 5 2 <sup>3</sup> 

model is described in more detail by Baker et al. (2004).

If *T*<300 <sup>2</sup>

Serrano and Phinney, 2009).

turning off the power.

**5. Modeling** 

following curve fit

**4.4.4 Transient bent-beam measurements** 

where the temperature is in degrees Celsius and the resistivity is in units of ohm-microns. The thermal conductivity is defined using the equation

$$k\_p = \frac{1}{(-2.2 \times 10^{-11})T^3 + (9.0 \times 10^{-8})T^2 - (1.0 \times 10^{-5})T + 0.014} \tag{2}$$

where the temperature is in degrees Celsius and the thermal conductivity is in W/m/°C. At room temperature the thermal conductivity of polysilicon is 72 W/m/°C, and it decreases with increasing temperature. A value of 164 GPa was used for the Young's Modulus of polysilicon. The model curves in Figures 7-9 were calculated using this model. As seen in these figures, the predicted and measured displacements, electrical resistance, and force are in good agreement.

### **6. Reliability**

The reliability of thermal microactuators depends on the packaging and environment as well as the initial design. Thermal microactuators have operated successfully for tens of millions of cycles; however, performance degradation mechanisms have been observed including plastic deformation of actuator legs, wear debris generation, void formation when operated in vacuum, changes in the grain structure, out of plane displacement, oxide growth, fracture of actuator legs, and die stress effects (Baker et al., 2004; Chu et al., 2006; Phinney et al., 2010b; Plass et al., 2004). Temperature measurements in reduced pressure environment and the effects of die stress are described in detail to illustrate the impact of environment and packaging on thermal microactuator performance.

#### **6.1 Reduced pressure environments**

Microsystems devices are often packaged at pressures lower than atmospheric, which dramatically affects the thermal performance of the parts since energy transfer to the environment is substantially reduced as the pressure is reduced (Phinney et al., 2010a). Thus, temperature measurements of thermal microactuators in varying pressures are crucial to optimizing device and package design as well as model validation.

Raman measurements were performed at nitrogen pressures varying from 0.05 Torr to 630 Torr using the Raman thermometry methods described in Section 4.3.1 and Torczynski et al. (2008). For reduced pressure measurements inside a Linkam thermal stage for which the pressure was controllable, a SUMMiT die with a P123 microactuator was packaged on a printed circuit board (PCB) to which wire leads were soldered. Each bond pad on the beam structure is wire-bonded to two separate connections on the PCB to allow for four-point sensing of the voltage. Quick-disconnect connectors were used inside the Linkam thermal stage to allow for easy exchange of parts. The PCB was placed in the center of a quartz crucible inside the stage and held in place with vacuum-compatible carbon tape. The heating ability of the stage was used to heat the sample to a temperature of 300-310 K to ensure a consistent substrate temperature for the measurements. The devices were powered with a Keithley 2400 Source Meter in a four-point sensing configuration, where the current is sourced through the outside connections and the voltage is measured across the inner ones.

Raman thermometry was used to measure the temperature profiles for a P123 microactuator leg at pressures ranging from 0.05 Torr to 630 Torr (Figure 12). In order to maintain similar

Thermal Microactuators 429

0.050 4.910 1.67925 342.006 8.245 5.01 287 298.3 186 0.50 5.010 1.7133 341.976 8.584 5.01 284 297.9 185 1.1 5.150 1.76167 342.072 9.073 5.01 283 298.6 184 5.0 5.750 1.9653 341.791 11.300 5.01 269 297.6 182 50.0 8.090 2.7665 341.965 22.381 5.01 248 250.4 182 200 9.900 3.3844 341.859 33.506 5.01 238 230.4 182 630 12.000 4.1048 342.067 49.258 5.01 231 210.2 183 630 12.000 4.1023 341.858 49.228 5.01 230 210.2 184 Table 3. Actuator displacements, electrical measurements, location and magnitude of the temperature maxima, and average temperature under various nitrogen pressures

As seen in Figure 12, the location of the maximum temperature along the microactuator leg moves from around two-thirds of the distance from the anchor to the shuttle to the shuttle as the pressure is reduced. Heat transfer through the underlying gas from the microactuator to the cooler underlying substrate is significantly reduced as the pressure is decreased. At lower pressures, sufficient energy is not transferred from the shuttle to the substrate to allow the shuttle to maintain a lower temperature and act as a heat sink. The location of maximum temperature therefore moves from being on the microactuator legs at high pressures to being at the shuttle at the lower pressures. Table 3 summarizes the operating conditions used (pressure and current) as well as the voltage, resistance, power, displacement, magnitude and location of the temperature maximum, and the average temperature at the various pressures. It is important to note that, although the location and magnitude of the temperature

maximum varies with pressure the length-averaged temperature, <sup>1</sup>

fairly constant for all pressures, thus yielding the similar resistance and displacement values

The effects of die stress were investigated by measuring thermal microactuator displacement as a function of applied current on a four-point bending stage for stresses ranging from -250 MPa compressive to 200 MPa tenisile (Phinney et al., 2010b). Displacement as a function of both input current and applied external stress is shown in Figure 14 for three stress conditions corresponding to -18.7 MPa (the residual stress due to fabrication), 208 MPa tensile, and -261 MPa compressive. Increasing tensile stress decreases the initial displacement of the thermal microactuator, and the amount of displacement that occurs due to an applied current decreases when the device under test is subject to stress from the four-point bending stage. The numerical model predictions using the model described in Section 5 agree qualitatively with the average of the experimentally measured displacements. The initial displacement decreases and the displacement curves flatten with increasing applied stress. Additionally, the calculated displacements agree with the experimental data for currents up to 25 mA. In Fig. 14, the predicted displacements were calculated for distances between the bottom of the thermal microactuator and the substrate of 2.0 m and 2.8 m. At 35 mA, the predicted

Displacement [μm]

Maximum Temp. [°C]

Location of Maximum [μm]

*<sup>L</sup> T T x dx* , remains

Average Temp. [°C]

Power [mW]

Pressure [Torr]

observed.

**6.2 Effects of die stress** 

Current [mA]

Voltage [V]

Resistance []

maximum temperatures in the P123 microactuator as the pressure reduced, the power applied to the microactuator was reduced as the pressure was decreased. The P123 microactuator power versus pressure is plotted in Figure 13. At pressures below about 5 Torr, the rate of decrease in the power to maintain the maximum temperature is less than at higher pressures as seen in Figure 13.

Fig. 12. Temperature profiles for a P123 microactuator leg at 0.05 to 630 Torr

Fig. 13. Operating power for P123 thermal microactuator as a function of pressure for a constant actuator resistance

maximum temperatures in the P123 microactuator as the pressure reduced, the power applied to the microactuator was reduced as the pressure was decreased. The P123 microactuator power versus pressure is plotted in Figure 13. At pressures below about 5 Torr, the rate of decrease in the power to maintain the maximum temperature is less than

> 0 50 100 150 200 250 300 Position (μm)

> > 0.01 0.1 1 10 100 1000 Pressure (Torr)

Fig. 13. Operating power for P123 thermal microactuator as a function of pressure for a

Fig. 12. Temperature profiles for a P123 microactuator leg at 0.05 to 630 Torr

0

10

20

30

Power (mW)

40

50

60

**Anchor Shuttle**

8.245 mW, 0.050 Torr 8.584 mW, 0.50 Torr 9.073 mW, 1.1 Torr 11.300 mW, 5.0 Torr 22.381 mW, 50 Torr 49.258 mW, 630 Torr 49.228 mW, 630 Torr 33.506 mW, 200 Torr

at higher pressures as seen in Figure 13.

0

constant actuator resistance

50

100

150

Temperature (C)

200

250

300


Table 3. Actuator displacements, electrical measurements, location and magnitude of the temperature maxima, and average temperature under various nitrogen pressures

As seen in Figure 12, the location of the maximum temperature along the microactuator leg moves from around two-thirds of the distance from the anchor to the shuttle to the shuttle as the pressure is reduced. Heat transfer through the underlying gas from the microactuator to the cooler underlying substrate is significantly reduced as the pressure is decreased. At lower pressures, sufficient energy is not transferred from the shuttle to the substrate to allow the shuttle to maintain a lower temperature and act as a heat sink. The location of maximum temperature therefore moves from being on the microactuator legs at high pressures to being at the shuttle at the lower pressures. Table 3 summarizes the operating conditions used (pressure and current) as well as the voltage, resistance, power, displacement, magnitude and location of the temperature maximum, and the average temperature at the various pressures. It is important to note that, although the location and magnitude of the temperature maximum varies with pressure the length-averaged temperature, <sup>1</sup> *<sup>L</sup> T T x dx* , remains fairly constant for all pressures, thus yielding the similar resistance and displacement values observed.

### **6.2 Effects of die stress**

The effects of die stress were investigated by measuring thermal microactuator displacement as a function of applied current on a four-point bending stage for stresses ranging from -250 MPa compressive to 200 MPa tenisile (Phinney et al., 2010b). Displacement as a function of both input current and applied external stress is shown in Figure 14 for three stress conditions corresponding to -18.7 MPa (the residual stress due to fabrication), 208 MPa tensile, and -261 MPa compressive. Increasing tensile stress decreases the initial displacement of the thermal microactuator, and the amount of displacement that occurs due to an applied current decreases when the device under test is subject to stress from the four-point bending stage.

The numerical model predictions using the model described in Section 5 agree qualitatively with the average of the experimentally measured displacements. The initial displacement decreases and the displacement curves flatten with increasing applied stress. Additionally, the calculated displacements agree with the experimental data for currents up to 25 mA. In Fig. 14, the predicted displacements were calculated for distances between the bottom of the thermal microactuator and the substrate of 2.0 m and 2.8 m. At 35 mA, the predicted

Thermal Microactuators 431

resistance, force output, and temperature. Raman thermometry is a useful technique for acquiring spatially resolved temperature profiles along microactuator legs. The environment

Thermal, electrical, and mechanical measurements for bent-beam polycrystalline silicon thermal microactuators are reported, including displacement, overall actuator electrical resistance, force, and temperature profiles along microactuator legs in standard laboratory air pressures and reduced pressures down to 50 mTorr. Typical displacements are up to around 15 m with output forces of about 200 N. For such devices, electrical resistances are in the 100s of Ohms and temperatures will increase by 100s of degrees Celsius. When operated in laboratory air, heating and cooling times are around 1-2 ms. Decreasing the pressure in which the thermal microactuators are operated moves the location of maximum temperature from about two-thirds of the distance between the anchor and shuttle to being on the shuttle. At low pressures, the shuttle does not function as a heat sink since it is not able to transfer the energy to substrate. Laser heated flexure actuators flex in the opposite direction as electrically heated flexure actuators and have the highest temperature at the corner of the wide leg target that is furthest from the flexure and narrow leg. Increasing tensile stress on bent-beam thermal microactuator samples decreases the initial displacement, and applied stress reduces the displacement output for applied currents.

Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-

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Beechem, T.; Graham, S.; Kearney, S. P.; Phinney, L. M. & Serrano, J. R. (2007) Simultaneous

Bergna, S.; Gorman, J. J. & Dagalakis, N. G. (2005) Design and Modeling of Thermally

Chu, L. L.; Que, L.; Oliver, A. D. & Gianchandani, Y. B. (2006) Lifetime Studies of

Cochran, K. R.; Fan, L. & DeVoe, D. L. (2004) Moving Reflector Type Micro Optical Switch

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6635, Sandia National Laboratories, Albuquerque, NM

Polyimide Bimorph Actuators for a Ciliary Motion System. *Journal of* 

Thermomechanical MEMS Actuators LDRD #52553, Sandia Report SAND2004-

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and packaging impact thermal microactuator performance and lifetime.

**8. Acknowledgment** 

AC04-94AL85000.

**9. References** 

displacements using the nominal distance between the bottom of the thermal microactuator and the substrate of 2.0 m are significantly lower than the measured displacements for all three stress conditions. For the -18.7 MPa case with a gap of 2.0 m, the predicted displacement is 14 m and the average of the measured values is 19 m. Interferometric measurements at stresses of -261 MPa, -122 MPa, -18.7 MPa, 115 MPa, and 212 MPa showed that at currents starting at 20 mA the thermal microactuator experiences upward out-ofplane displacement as well as forward displacement. The maximum measured out-of-plane displacement was 0.8 m at 35 mA and occurred for the actuator at -18.7 MPa. The upward deflection increases the underlying gap size under the center of the thermal microactuator. When the gap is increased to 2.8 m in the model, the predicted and measured thermal microactuator displacements are in good agreement. The remaining discrepancies are likely due to slight variations in the actuator geometry or material properties from nominal values.

Fig. 14. Predicted and measured thermal microactuator displacement as a function of applied current. The symbols are the average of the experimentally measured displacements. The dotted lines represent the predictions for a gap between the bottom of the thermal microactuator and the substrate of 2.0 m (long dashes) and 2.8 m (short dashes).

#### **7. Summary and conclusions**

Thermal microactuators function due to thermal expansion of heated members and are versatile components for MEMS designs. Thermal microactuators are part of MEMS devices such as optical microswitches, nanopositioners, and microsensors. Two common thermal microactuator designs are the bent-beam actuator with angled legs that expand when heated and the flexure actuator with asymmetric legs that flex to the side due to differential expansion when heated. Thermal microactuators can be powered, heated, electrically or optically. Both surface micromachining and silicon on insulator (SOI) processing are used to fabricate MEMS thermal microactuators. In order to optimize the design, performance, and reliability of thermal microactuators, both experimental characterization and predictive modeling are necessary. Experimental measurements include displacement, electrical

displacements using the nominal distance between the bottom of the thermal microactuator and the substrate of 2.0 m are significantly lower than the measured displacements for all three stress conditions. For the -18.7 MPa case with a gap of 2.0 m, the predicted displacement is 14 m and the average of the measured values is 19 m. Interferometric measurements at stresses of -261 MPa, -122 MPa, -18.7 MPa, 115 MPa, and 212 MPa showed that at currents starting at 20 mA the thermal microactuator experiences upward out-ofplane displacement as well as forward displacement. The maximum measured out-of-plane displacement was 0.8 m at 35 mA and occurred for the actuator at -18.7 MPa. The upward deflection increases the underlying gap size under the center of the thermal microactuator. When the gap is increased to 2.8 m in the model, the predicted and measured thermal microactuator displacements are in good agreement. The remaining discrepancies are likely due to slight variations in the actuator geometry or material properties from nominal values.

Fig. 14. Predicted and measured thermal microactuator displacement as a function of applied current. The symbols are the average of the experimentally measured

dashes).

**7. Summary and conclusions** 

displacements. The dotted lines represent the predictions for a gap between the bottom of the thermal microactuator and the substrate of 2.0 m (long dashes) and 2.8 m (short

Thermal microactuators function due to thermal expansion of heated members and are versatile components for MEMS designs. Thermal microactuators are part of MEMS devices such as optical microswitches, nanopositioners, and microsensors. Two common thermal microactuator designs are the bent-beam actuator with angled legs that expand when heated and the flexure actuator with asymmetric legs that flex to the side due to differential expansion when heated. Thermal microactuators can be powered, heated, electrically or optically. Both surface micromachining and silicon on insulator (SOI) processing are used to fabricate MEMS thermal microactuators. In order to optimize the design, performance, and reliability of thermal microactuators, both experimental characterization and predictive modeling are necessary. Experimental measurements include displacement, electrical resistance, force output, and temperature. Raman thermometry is a useful technique for acquiring spatially resolved temperature profiles along microactuator legs. The environment and packaging impact thermal microactuator performance and lifetime.

Thermal, electrical, and mechanical measurements for bent-beam polycrystalline silicon thermal microactuators are reported, including displacement, overall actuator electrical resistance, force, and temperature profiles along microactuator legs in standard laboratory air pressures and reduced pressures down to 50 mTorr. Typical displacements are up to around 15 m with output forces of about 200 N. For such devices, electrical resistances are in the 100s of Ohms and temperatures will increase by 100s of degrees Celsius. When operated in laboratory air, heating and cooling times are around 1-2 ms. Decreasing the pressure in which the thermal microactuators are operated moves the location of maximum temperature from about two-thirds of the distance between the anchor and shuttle to being on the shuttle. At low pressures, the shuttle does not function as a heat sink since it is not able to transfer the energy to substrate. Laser heated flexure actuators flex in the opposite direction as electrically heated flexure actuators and have the highest temperature at the corner of the wide leg target that is furthest from the flexure and narrow leg. Increasing tensile stress on bent-beam thermal microactuator samples decreases the initial displacement, and applied stress reduces the displacement output for applied currents.
