**3. Optical-thermal coupling in laser-irradiated MEMS**

338 Microelectromechanical Systems and Devices

As discussed in the previous section, the optical response of laser-irradiated materials depends strongly on various parameters. For optically thick materials, the refractive index of the irradiated medium determines the reflectivity of the surface and thus the fraction of the energy that is deposited in the material. When the optical penetration depth is comparable to film thickness, the geometry and composition of the structure becomes as important as refractive index in dictating the optical response. This becomes evident when analyzing the response of sacrificial micromachined MEMS fabricated from polysilicon. In polysilicon-based MEMS the typical layer thickness is approximately 2 μm, with intermediate gaps of the same order (Carter et al., 2005; MEMS Technologies Department 2008). Such thicknesses are comparable to the penetration depth for both silicon and polysilicon for wavelengths above 550 nm (Jellison Jr & Modine, 1982a, 1982b; Lubberts et al., 1981; Xu & Grigoropoulos, 1993) and therefore the likelihood for thin film interference, as explained above, increases. Indeed, calculations carried out for air-spaced polysilicon structure fabricated from Sandia National Laboratories' SUMMiT-V™ process (MEMS Technologies Department, 2008), as shown in Fig. 6, show that the absorptance of the top-most layer can vary significantly as a function of the layer thickness. The multiple reflections from the various layers in the structure lead to conditions of local maxima and minima for different layer thicknesses. These extrema correspond to thicknesses where the interference between the multiply reflected waves is fully constructive or destructive as will

Fig. 6. (a) Schematic of a SUMMiT V™ polysilicon MEMS structure and (b) its optical response at different wavelengths as a function of the thickness of the top-most layer.

predict the thermal behavior of laser-irradiated MEMS accurately.

The variation in the amplitude and width of the absorptance peaks in this structure is related to the relative reflectivity of the two polysilicon surfaces at the particular wavelength much like a Fabry-Perot cavity (Born & Wolf, 1999) and will ultimately depend on the overall composition of the multilayered structure. For a coupled optical-thermal analysis, the existence of these periodic variations in the absorptance must be taken into account to

**2.2.2 MEMS** 

be shown later.

The previous section detailed the response of MEMS optical systems in strictly athermal terms. However, in laser-irradiated MEMS or MEMS exposed to extreme thermal environments the consequences of a changing thermal environment could be significant, especially in regards to the optical response. For simplicity, we shall consider cases where the incident laser energy is responsible for any temperature fluctuation in the irradiated structure, although the same principles are valid for structures subject to bulk external heating and laser irradiation (Burns & Bright, 1998).

Laser irradiation of an absorbing structure, such as micromachined polysilicon MEMS, will lead to a corresponding temperature increase. The magnitude of the induced temperature rise will depend on several factors, including the geometry, and thermal and optical properties of the irradiated materials. Because all of the parameters that play a role in determining the energy deposition exhibit some temperature dependence, the laser-induced heating of the structure will be dynamic in nature as the properties change during the heating event.

#### **3.1 Temperature-induced geometry changes**

We have already seen the potential effects of different layer thicknesses on the absorptance of an irradiated structure. However, while those fluctuations might arise out of manufacturing variability, the same effect can be observed during the heating of an as-built device. Geometrical and dimensional considerations during the heating result from any temperature-induced displacement and deformation of the MEMS when exposed to elevated temperatures (Knoernschild et al., 2010; Phinney et al., 2006). If the irradiating wavelength is in the optically thick regime for the irradiated material, the dimensional changes do not have a significant effect in the optical response of the structure since the incident energy is fully absorbed within the material. Nevertheless, depending on the structure, small deflections and deformations could have a significant effect on the heat transfer mechanisms on the heated device (Gallis et al., 2007; Wong & Graham, 2003).

When the conditions are such that thin film interference becomes important in the optical response, particularly for multilayered systems, the deformation will have a more dramatic effect. Depending on the design and geometry of the irradiated structure, the heating can alter both the thickness of the individual layers (via thermal expansion) and the spacing between them (via thermal expansion, buckling, etc.). Such deformations will produce changes in the absorptance of the laser irradiation, as shown in Fig. 7 for a Poly4 SUMMiT V™ structure similar to the one described by Phinney et al, (Phinney et al., 2006) and shown in Fig. 6a. The cantilevered structure in that reference suffered deflections of over 10 μm during laser irradiation. In Fig. 7, just a variation in the air gap height of ±500 nm suffices to demonstrate the type of deflection-induced changes in absorptance encountered in these tests. Assuming the deflection is caused by the temperature excursion of the structure, then a small change in gap height can lead to as much as a six-fold change in absorptance.

Additionally, due to the phase changes upon reflection, the trends in absorptance repeat for different values of thicknesses and gaps, as seen in Figs 6 and 7. The recurrence period can be estimated from Eq. 9 by finding the thickness increase *d* for which the path length difference is equivalent to an integer multiple of :

Optical-Thermal Phenomena in Polycrystalline Silicon MEMS During Laser Irradiation 341

For silicon-based materials, the complex index of refraction has been extensively studied as a function of temperature (Jellison Jr & Modine, 1982a, 1983; Sun et al., 1997; Xu & Grigoropoulos, 1993; Yavas et al., 1993). These works all show that the real part of the

> *o o dn nn TT dT*

on the order of 10-4 K-1 (Jellison Jr & Modine, 1982a, 1983; Sun et al., 1997; Xu & Grigoropoulos, 1993). The complex portion of the index, on the other hand, follows an

*<sup>o</sup> k ke*

where *<sup>o</sup> k* is complex index at *To* and the temperature *TR* is an empirically determined reference temperature, which ranges in value from 498 K for bulk silicon (Jellison Jr & Modine, 1982a, 1983) to 680 K for different types of polysilicon (Sun et al., 1997; Xu &

In optically thick systems, the change in complex refractive index will manifest itself as a change in surface reflectivity as a function of temperature. For silicon and polysilicon, this change is on the order of 10–5 K–1 (Jellison Jr & Modine, 1983) such that its impact on the thermal and mechanical response of irradiated devices is small. The same cannot be said for multilayered structures that are optically thin. In this case, the linear increase in the real part of the refractive index increases the effective path length difference between multiply reflected waves, changing the conditions for constructive and destructive interference from those present at the initial temperature. The exponential increase in the complex portion of the index, however, leads to a decrease in the optical penetration depth, reducing the effect of interference from deeper layers in the material. More importantly, the interplay between the two trends, when applied to the thin film interference equations discussed in the previous section, leads to temperature-dependent variations in the absorptance, as shown in Fig. 8 for the structure in Fig. 6a irradiated with 800 nm light. The most noticeable characteristic of the curves is the presence of temperature-periodic peaks. These result from the increase in the path length difference as the real portion of the index increases with temperature as given by Eq. 27. When the condition for fully destructive interference of the surface reflected waves is met, the absorptance of the layer increases. This condition is

*o R T T T*

, (*m* = 1, 2, 3, …). (29)

*1*

. (30)

Solving the above relation for *nˆ* , and relating that to the temperature change through Eq.

*2 2*

*2z n sin ˆ ˆ dT* 

*m n dn <sup>ˆ</sup> T Re*

*i*

(27)

(28)

*dT* typically has values

refractive index depends linearly with temperature:

exponential trend of the form:

Grigoropoulos, 1993).

satisfied for

27, we get:

where *no* is the index at a reference temperature *To* and the slope *dn*

 *2 2 <sup>2</sup> <sup>2</sup> 2 2 i i d Re n n sin d Re n sin m ˆ ˆ ˆ*

$$\Delta d = \frac{m\lambda}{2\operatorname{Re}\left(\sqrt{\hat{n}^2 - \sin^2\Theta\_i}\right)}, m = 1, 2, 3... \tag{26}$$

which, for the 800 nm example discussed, yields a recurrence period of 400 nm.

Fig. 7. Absorptance map for the geometry shown in Fig. 6a for λ = 808 nm as a function of layer and gap dimensions. The circle indicates the nominal dimensions for the geometry.

The outcome of such a variation in energy deposition can be detrimental—an increase in absorptance will cause additional heating and possibly lead to damage—or beneficial—a decrease in absorptance will permit the structure to withstand higher incident powers and avoid damage (Serrano & Phinney, 2009). Which situation is encountered with a particular device will depend on the irradiating conditions (wavelength and incidence angle), the optical properties, as well as the initial condition and the geometry of the device and the thermomechanical response of the structure. Because MEMS are primarily mechanical devices, these thermomechanical effects can typically be accounted and corrected for to reduce their contribution, much like it is done for electrically heated devices (Sassen et al., 2008).

#### **3.2 Temperature-induced optical changes**

In addition to purely mechanical effects caused by the heating, the temperature excursion will induce changes in the optical and thermal properties of the irradiated materials. While the variations in the thermal properties with temperature play a very important role in the thermal behavior of any laser-irradiated structure, their effects are generally noticeable for large temperature excursions. As we will show, the role of the temperature dependence of the material optical properties is, in some cases, more dominant and leads to marked changes in the thermal and optical performance of the irradiated structure over small temperature excursions.

*i*

, *m* = 1, 2, 3… (26)

*2 2*

Fig. 7. Absorptance map for the geometry shown in Fig. 6a for λ = 808 nm as a function of layer and gap dimensions. The circle indicates the nominal dimensions for the geometry.

2008).

**3.2 Temperature-induced optical changes** 

temperature excursions.

The outcome of such a variation in energy deposition can be detrimental—an increase in absorptance will cause additional heating and possibly lead to damage—or beneficial—a decrease in absorptance will permit the structure to withstand higher incident powers and avoid damage (Serrano & Phinney, 2009). Which situation is encountered with a particular device will depend on the irradiating conditions (wavelength and incidence angle), the optical properties, as well as the initial condition and the geometry of the device and the thermomechanical response of the structure. Because MEMS are primarily mechanical devices, these thermomechanical effects can typically be accounted and corrected for to reduce their contribution, much like it is done for electrically heated devices (Sassen et al.,

In addition to purely mechanical effects caused by the heating, the temperature excursion will induce changes in the optical and thermal properties of the irradiated materials. While the variations in the thermal properties with temperature play a very important role in the thermal behavior of any laser-irradiated structure, their effects are generally noticeable for large temperature excursions. As we will show, the role of the temperature dependence of the material optical properties is, in some cases, more dominant and leads to marked changes in the thermal and optical performance of the irradiated structure over small

*2Re n sin ˆ*

which, for the 800 nm example discussed, yields a recurrence period of 400 nm.

*<sup>m</sup> <sup>d</sup>*

For silicon-based materials, the complex index of refraction has been extensively studied as a function of temperature (Jellison Jr & Modine, 1982a, 1983; Sun et al., 1997; Xu & Grigoropoulos, 1993; Yavas et al., 1993). These works all show that the real part of the refractive index depends linearly with temperature:

$$m = n\_o + \frac{dn}{dT}(T - T\_o) \tag{27}$$

where *no* is the index at a reference temperature *To* and the slope *dn dT* typically has values on the order of 10-4 K-1 (Jellison Jr & Modine, 1982a, 1983; Sun et al., 1997; Xu & Grigoropoulos, 1993). The complex portion of the index, on the other hand, follows an exponential trend of the form:

$$\mathbf{k} = \mathbf{k}\_o \mathbf{c}^{\left(\frac{T - T\_o}{T\_R}\right)} \tag{28}$$

where *<sup>o</sup> k* is complex index at *To* and the temperature *TR* is an empirically determined reference temperature, which ranges in value from 498 K for bulk silicon (Jellison Jr & Modine, 1982a, 1983) to 680 K for different types of polysilicon (Sun et al., 1997; Xu & Grigoropoulos, 1993).

In optically thick systems, the change in complex refractive index will manifest itself as a change in surface reflectivity as a function of temperature. For silicon and polysilicon, this change is on the order of 10–5 K–1 (Jellison Jr & Modine, 1983) such that its impact on the thermal and mechanical response of irradiated devices is small. The same cannot be said for multilayered structures that are optically thin. In this case, the linear increase in the real part of the refractive index increases the effective path length difference between multiply reflected waves, changing the conditions for constructive and destructive interference from those present at the initial temperature. The exponential increase in the complex portion of the index, however, leads to a decrease in the optical penetration depth, reducing the effect of interference from deeper layers in the material. More importantly, the interplay between the two trends, when applied to the thin film interference equations discussed in the previous section, leads to temperature-dependent variations in the absorptance, as shown in Fig. 8 for the structure in Fig. 6a irradiated with 800 nm light. The most noticeable characteristic of the curves is the presence of temperature-periodic peaks. These result from the increase in the path length difference as the real portion of the index increases with temperature as given by Eq. 27. When the condition for fully destructive interference of the surface reflected waves is met, the absorptance of the layer increases. This condition is satisfied for

$$\frac{2\pi}{\lambda}d\operatorname{Re}\left(\sqrt{\left(\hat{n}+\Delta\hat{n}\right)^{2}-\sin^{2}\Theta\_{i}}\right) = \frac{2\pi}{\lambda}d\operatorname{Re}\left(\sqrt{\hat{n}^{2}-\sin^{2}\Theta\_{i}}\right) + m\pi\,\,\mathrm{tr}\,\,\left(m=1\,2\,3\,\ldots\right). \tag{29}$$

Solving the above relation for *nˆ* , and relating that to the temperature change through Eq. 27, we get:

$$
\Delta T = \text{Re}\left(\frac{m\lambda\hat{\mathbf{n}}}{2z\sqrt{\hat{n}^2 - \sin^2\hat{\Theta}\_i}}\right) \left(\frac{dn}{dT}\right)^{-1}.\tag{30}
$$

Optical-Thermal Phenomena in Polycrystalline Silicon MEMS During Laser Irradiation 343

Serrano et al., 2009). In this section, we will briefly look over some of the experimental results for laser-induced damage in the context of the optical and thermal analysis discussed

For optically-powered MEMS thermal actuators (Baglio et al, 2002; Phinney & Serrano, 2007; Serrano & Phinney, 2009) most of the studies have mainly focused on empirically establishing the threshold power for damage. Typically, damage is defined as visible damage at the surface—in the form of a crater-like feature as shown Fig. 9—after initial irradiation of the surface. However, these studies also showed that damage could be initiated after prolonged exposure (on the order of minutes) to the laser irradiation, indicating the presence of a slow heating process. This behavior agrees qualitatively with the concepts discussed in the previous section. Thermal equilibrium for the irradiated structure cannot be achieved for the temperature where the absorptance exhibits a peak. Therefore, the system reaches a metastable equilibrium in the valleys of the absorptance curve as shown in Figs. 6 and 8. These valleys, however, do not represent a flat absorptance, but rather a slowly varying one. Thus, as the devices slowly heats up, the material's absorptance increases until the next absorptance peak is encountered and the deposited energy density is enough to cause damage of the device. The time-delayed damage observed is then evidence of the slow heating and approach of the temperature to the

Fig. 9. Typical laser-induced damage on polysilicon MEMS structures. The scale bar on both

The effect of the absorptance peaks can also explain the damage thresholds in laserirradiated microsystems (Serrano & Phinney, 2009) that do not correlate with the number of layers present in the structure. The results show that a single-layer structure exhibited greater power handling capability than various multilayered ones. In said structures, the thin film interference phenomena leads to a minimum in absorptance, like the one shown Fig. 8 for normal incidence near room temperature. This minimum, coupled to improved

is equivalent to 50 μm. (Phinney & Serrano, 2007; Serrano & Phinney, 2009)

in the previous sections.

absorptance peak.

Fig. 8. Absorptance as a function of temperature and incidence angle for the geometry shown in Fig. 6a for λ = 800 nm.

The consequences of the peaks and valleys are significant for the behavior of laser-irradiated polysilicon MEMS. An incident laser on the surface will induce heating, leading to a change in absorptance, and corresponding changes in the sample temperature. The non-linear absorptance response thus creates stable and unstable conditions depending on the temperature of the sample. For temperatures in the range where the slope of the absorptance curves is negative, the system can achieve equilibrium since a temperature rise leads to decreased absorptance, reducing the energy deposition. For temperatures lying in the opposite side of the absorptance peak, the increase in temperature induces an increase in absorptance, leading to a significant increase in energy deposition and consequently an even greater temperature rise.

#### **4. Laser-induced damage of polycrystalline silicon MEMS**

The combination of multilayered design, coupled with temperature-induced changes in the optical properties ultimately leads to failure of laser-irradiated MEMS. From a design perspective, in addition to considering the primary mechanical function of the device—such as an actuator (Baglio et al., 2002; Oliver et al., 2003; Phinney et al., 2005; Phinney & Serrano, 2007; Serrano et al., 2005) or a shutter (Wong & Graham, 2003)—the design should also consider the optical and thermal behavior of the structure to reduce the likelihood of damage. To gain a better understanding of the design concerns associated with polysilicon optical MEMS, various experiments have been carried out that have provided insights into the importance of composition, optical energy deposition and thermal transport of heating (Baglio et al., 2002; Oliver et al., 2003; Phinney & Serrano, 2005; Serrano & Phinney, 2009;

Fig. 8. Absorptance as a function of temperature and incidence angle for the geometry

**4. Laser-induced damage of polycrystalline silicon MEMS** 

The consequences of the peaks and valleys are significant for the behavior of laser-irradiated polysilicon MEMS. An incident laser on the surface will induce heating, leading to a change in absorptance, and corresponding changes in the sample temperature. The non-linear absorptance response thus creates stable and unstable conditions depending on the temperature of the sample. For temperatures in the range where the slope of the absorptance curves is negative, the system can achieve equilibrium since a temperature rise leads to decreased absorptance, reducing the energy deposition. For temperatures lying in the opposite side of the absorptance peak, the increase in temperature induces an increase in absorptance, leading to a significant increase in energy deposition and consequently an even

The combination of multilayered design, coupled with temperature-induced changes in the optical properties ultimately leads to failure of laser-irradiated MEMS. From a design perspective, in addition to considering the primary mechanical function of the device—such as an actuator (Baglio et al., 2002; Oliver et al., 2003; Phinney et al., 2005; Phinney & Serrano, 2007; Serrano et al., 2005) or a shutter (Wong & Graham, 2003)—the design should also consider the optical and thermal behavior of the structure to reduce the likelihood of damage. To gain a better understanding of the design concerns associated with polysilicon optical MEMS, various experiments have been carried out that have provided insights into the importance of composition, optical energy deposition and thermal transport of heating (Baglio et al., 2002; Oliver et al., 2003; Phinney & Serrano, 2005; Serrano & Phinney, 2009;

shown in Fig. 6a for λ = 800 nm.

greater temperature rise.

Serrano et al., 2009). In this section, we will briefly look over some of the experimental results for laser-induced damage in the context of the optical and thermal analysis discussed in the previous sections.

For optically-powered MEMS thermal actuators (Baglio et al, 2002; Phinney & Serrano, 2007; Serrano & Phinney, 2009) most of the studies have mainly focused on empirically establishing the threshold power for damage. Typically, damage is defined as visible damage at the surface—in the form of a crater-like feature as shown Fig. 9—after initial irradiation of the surface. However, these studies also showed that damage could be initiated after prolonged exposure (on the order of minutes) to the laser irradiation, indicating the presence of a slow heating process. This behavior agrees qualitatively with the concepts discussed in the previous section. Thermal equilibrium for the irradiated structure cannot be achieved for the temperature where the absorptance exhibits a peak. Therefore, the system reaches a metastable equilibrium in the valleys of the absorptance curve as shown in Figs. 6 and 8. These valleys, however, do not represent a flat absorptance, but rather a slowly varying one. Thus, as the devices slowly heats up, the material's absorptance increases until the next absorptance peak is encountered and the deposited energy density is enough to cause damage of the device. The time-delayed damage observed is then evidence of the slow heating and approach of the temperature to the absorptance peak.

Fig. 9. Typical laser-induced damage on polysilicon MEMS structures. The scale bar on both is equivalent to 50 μm. (Phinney & Serrano, 2007; Serrano & Phinney, 2009)

The effect of the absorptance peaks can also explain the damage thresholds in laserirradiated microsystems (Serrano & Phinney, 2009) that do not correlate with the number of layers present in the structure. The results show that a single-layer structure exhibited greater power handling capability than various multilayered ones. In said structures, the thin film interference phenomena leads to a minimum in absorptance, like the one shown Fig. 8 for normal incidence near room temperature. This minimum, coupled to improved

Optical-Thermal Phenomena in Polycrystalline Silicon MEMS During Laser Irradiation 345

Understanding the thermal and optical response of laser-irradiated microsystems requires careful consideration of not only the individual thermal, optical, and mechanical parameters, but also the coupling that exists between them. Of particular importance is the impact that the change in the optical properties with temperature can have in the performance and reliability of these structures. To gain insight into the role that temperature and geometry play in the optical performance of these devices, one must utilize the basic optical relations in a way that is compatible with thermal analyses of a laser-heated structure. The LTR method has proven to be a very useful technique in these types of analyses since it can easily incorporate temperature dependant optical properties and

Once the temperature and optical fields are coupled in the analysis, a more accurate picture emerges of the thermal and optical behavior of the irradiated device. These coupled optical-thermal effects give rise to non-linear absorptance that can, in some instances, lead to increased resistance to laser damage by dynamically reducing the absorptance as the incident laser power is increased, while in other cases, the nonlinear effects compound to enhance absorptance of the incident laser energy producing rapid temperature increases that eventually lead to device damage. A quantitative estimation of device robustness to determine in which regime of damage susceptibility a particular structure resides in therefore requires a complete description of the overall irradiating conditions as well as the device composition. For polysilicon-based devices, this type of analysis has shown reasonable agreement with the experimentally-observed thermal behavior, and can explain the observed damage trends of the laser-irradiated

The authors would like to acknowledge the help and assistance of Allen Gorby, James Rogers, Wayne Trott, and Jaime Castaneda. Sandia National Laboratories is a multiprogram laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National

Andrews, J. R., Martinez, T., Teare, S. W., Restaino, S. R., Wilcox, C. C., Santiago, F. & Payne,

Andrews, J. R., Teare, S. W., Restaino, S. R., Martinez, T., Wilcox, C. C., Wick, D. V., Cowan,

wavefront sensor. *Proceedings of SPIE,* Vol. 6888, pp. 68880C

D. M. (2011). A multi-conjugate adaptive optics testbed using two MEMS deformable mirrors. *Proceedings of MEMS Adaptive Optics V,* San Francisco, CA,

W. D., Spahn, O. B. & Bagwell, B. E. (2008). Performance of a MEMS reflective

readily provide the interlayer absorptances for the irradiated structures.

Nuclear Security Administration under contract DE-AC04-94AL85000.

**5. Conclusion** 

structures.

**6. Acknowledgment** 

**7. References** 

USA

heat dissipation to the underlying substrate, permits the single layer structure to exhibit increased robustness to the laser irradiation compared to the multilayered structures.

The optical-thermal effects can also explain the temperature discontinuities observed in the temperature measurements of laser irradiated cantilevers and actuators (Serrano & Phinney, 2007; Serrano et al., 2009), shown in Fig. 9. As predicted above, the discontinuity corresponds to the presence of the peak in the absorptance curve. The surface temperature increases rapidly by 200 K as the peak is encountered. The temperature-power relationship regains a linear relation after the temperature reaches the opposite side of the absorptance peak. Numerical simulations of this experiment, utilizing the non-linear absorptance and known material and geometrical parameters for the irradiated structure, are in good agreement with the measured values, reproducing temperature discontinuity. This type of sudden increase in the temperature makes predicting a threshold power for laser damage in polysilicon structures extremely challenging without accurate knowledge of optical and dimensional properties.

Fig. 10. Measured and modeled temperatures of a polysilicon MEMS structure measured irradiated with an λ = 808 nm laser. The discontinuity in the temperature results from a peak in the absorptance of the irradiated layer due to thin film interference effects (Serrano et al., 2009).
