**4. Characterization**

During operation of an electrically powered thermal microactuator, a current is applied to heat the actuator and thereby create displacement or force output. Displacement and total actuator electrical resistance measurements as a function of input current are easily obtained and standard metrics of thermal microactuator performance that are used for design comparison and model validation. Output force as a function of position and spatially resolved temperature measurements are additional performance and reliability metrics that are more challenging to obtain.

The displacement, electrical resistance, and force measurements in sections 4.1, 4.2, and 4.3 were performed according to methods described Baker et al. (2004). Displacement and total electrical resistance results were measured on a probe station using a National Instruments Vision software package that performs sub-pixel image tracking. A displacement measurement error of ±0.25 m was achieved by using 200X magnification. Force measurements were made using the P123F actuator design, in which a linear bi-fold spring is attached to the movable shuttle of the actuator. Force is applied manually to the actuator with a probe tip through the pull-ring attached to the spring. The displacement for a given force is determined from the vernier scale with ±1/6 m resolution. The applied force is determined from the measured displacements and calculated spring stiffness. This method of force measurement was used due to the lack of other methods viable for force measurements at this scale. The displacement, electrical resistance, and force measurements are compared to the results from a model which will be described in Section 5.

Temperature measurements were obtained using Raman thermometry (Kearney et al., 2006a; Kearney et al., 2006b; Phinney et al., 2009; Phinney et al., 2010a; Serrano et al., 2006). In the Raman process, photons from the incident probe light source interact with the optical phonon modes of the irradiated material and are scattered to higher (anti-Stokes) or lower (Stokes) frequencies from the probe line frequency. In the case of silicon and polysilicon, the scattered Raman light arises from the triply degenerate optical phonon at the Brillouin zone center. The resulting spectrum for the Stokes (lower frequency) Raman response has a single narrow peak at approximately 520 cm–1 from the laser line frequency at room temperature. Increases in temperature affect the frequency, lifetime, and population of the phonon modes coupled to the Raman process, leading to changes in the Raman spectra, including shifting the peak positions, broadening of the Stokes Raman peak, and increasing the ratio of the anti-Stokes to Stokes signal. These changes in the Raman spectra are metrics for temperature mapping of MEMS. Peak width is sensitive only to surface temperature, and peak position is sensitive to both stress and temperature (Kearney et al., 2006a; Beechem et al., 2007). The ratio of the anti-Stokes to Stokes signal tends to require the longest data collection time for quality signals. Since the thermal microactuators are free to expand and relieve stress that would affect the Raman signal prior to the measurement, Raman peak position is used for the Raman thermometry measurements in this section.

#### **4.1 Displacement**

Figure 7 shows the displacement versus applied current for the P123 thermal microactuator. The positive displacement from the designed zero location at zero current is due to compressive residual stress resulting from fabrication processes. The model results shown on the figures are for the thermomechanical model presented by Baker et al. (2004) and summarized in Section 5. When a bias is specified after "Model" in the legend, the bias

During operation of an electrically powered thermal microactuator, a current is applied to heat the actuator and thereby create displacement or force output. Displacement and total actuator electrical resistance measurements as a function of input current are easily obtained and standard metrics of thermal microactuator performance that are used for design comparison and model validation. Output force as a function of position and spatially resolved temperature measurements are additional performance and reliability metrics that

The displacement, electrical resistance, and force measurements in sections 4.1, 4.2, and 4.3 were performed according to methods described Baker et al. (2004). Displacement and total electrical resistance results were measured on a probe station using a National Instruments Vision software package that performs sub-pixel image tracking. A displacement measurement error of ±0.25 m was achieved by using 200X magnification. Force measurements were made using the P123F actuator design, in which a linear bi-fold spring is attached to the movable shuttle of the actuator. Force is applied manually to the actuator with a probe tip through the pull-ring attached to the spring. The displacement for a given force is determined from the vernier scale with ±1/6 m resolution. The applied force is determined from the measured displacements and calculated spring stiffness. This method of force measurement was used due to the lack of other methods viable for force measurements at this scale. The displacement, electrical resistance, and force measurements

Temperature measurements were obtained using Raman thermometry (Kearney et al., 2006a; Kearney et al., 2006b; Phinney et al., 2009; Phinney et al., 2010a; Serrano et al., 2006). In the Raman process, photons from the incident probe light source interact with the optical phonon modes of the irradiated material and are scattered to higher (anti-Stokes) or lower (Stokes) frequencies from the probe line frequency. In the case of silicon and polysilicon, the scattered Raman light arises from the triply degenerate optical phonon at the Brillouin zone center. The resulting spectrum for the Stokes (lower frequency) Raman response has a single narrow peak at approximately 520 cm–1 from the laser line frequency at room temperature. Increases in temperature affect the frequency, lifetime, and population of the phonon modes coupled to the Raman process, leading to changes in the Raman spectra, including shifting the peak positions, broadening of the Stokes Raman peak, and increasing the ratio of the anti-Stokes to Stokes signal. These changes in the Raman spectra are metrics for temperature mapping of MEMS. Peak width is sensitive only to surface temperature, and peak position is sensitive to both stress and temperature (Kearney et al., 2006a; Beechem et al., 2007). The ratio of the anti-Stokes to Stokes signal tends to require the longest data collection time for quality signals. Since the thermal microactuators are free to expand and relieve stress that would affect the Raman signal prior to the measurement, Raman peak position is used for

Figure 7 shows the displacement versus applied current for the P123 thermal microactuator. The positive displacement from the designed zero location at zero current is due to compressive residual stress resulting from fabrication processes. The model results shown on the figures are for the thermomechanical model presented by Baker et al. (2004) and summarized in Section 5. When a bias is specified after "Model" in the legend, the bias

are compared to the results from a model which will be described in Section 5.

the Raman thermometry measurements in this section.

**4.1 Displacement** 

**4. Characterization** 

are more challenging to obtain.

represents an edge bias which is subtracted from each side of thermal actuator leg nominal width. If a bias is not specified, the nominal width, 4.0 m, is used in the model calculations. As the current is increased, the displacement versus current data exhibits an inflection point and roll-off in the curve. This is attributed to the maximum temperature in the thermal actuator legs becoming hot enough, above 550°C, that the polysilicon is softened or even melts (Baker et al., 2004). The thermal actuator legs have been observed to glow red under these conditions.

Fig. 7. Displacement versus current for the P123 thermal actuator

#### **4.2 Resistance**

Figure 8 shows the total electrical resistance for the actuators versus applied current for the P123 thermal microactuator. The resistance curve exhibits an inflection point, followed by a maximum, and then a decrease in resistance as the current is increased.
