**Abstract**

At the microscale, shape memory alloy (SMA) microelectromechanical system (MEMS) bimorph actuators offer great potential based on their inherently high work density. An optimization problem relating to the deflection and curvature based on shape memory MEMS bimorph was identified, formulated, and solved. Thicknesses of the SU-8 photoresist and nickel-titanium alloy (NiTi) was identified that yielded maximum deflections and curvature radius based on a relationship among individual layer thicknesses, elastic modulus, and cantilever length. This model should serve as a guideline for optimal NiTi and SU-8 thicknesses to drive large deflections and curvature radius that are most suitable for microrobotic actuation, micromirrors, micropumps, and microgrippers. This model would also be extensible to other phase-change-driven actuators where nonlinear and significant residual stress changes are used to drive actuation.

**Keywords:** shape memory alloy, thin film, microactuators, MEMS, optimization, radius of curvature, phase change

#### **1. Introduction**

In certain applications for MEMS microactuators, large deflections would be desired such as the case of micro-robotics [1–3], micromirrors [4–6], and microgrippers [3, 7]. Using a shape memory alloy (SMA), a material that undergoes large changes in stress during a temperature cycle due to a solid-solid phase change can be used to generate large, nonlinear deflections. We aim to find a relationship between deflections of a SMA MEMS actuator, and maximize the deflection of SMA MEMS bimorph. Shape memory alloy films based on sputtered NiTi have been exhaustively characterized in previous decades, leading to a wealth of information about the intricate interplay between Ni/Ti ratio, annealing temperatures and times, and thickness [8–31]. Bimorphic actuators can impart reversible deflection shape memory microactuators as previously demonstrated [32, 33].

To date, optimization of parameters for improving shape memory-induced actuation has not been explored. We chose for our candidate system an SU-8 patterned on top of NiTi SMA bimorph actuator. In this case, residual strains develop during the processing of MEMS actuators, and upon release from substrate, the device curls upward to relieve these strains. Thermal input converts the material into austenite, and shape memory effect drives the actuator into a more flat

position, a process that is reversible upon subsequent thermal cycles. Thermal effects can be delivered to the SMA MEMS using laser irradiation [34], and jouleheating [35], at frequencies up to at least 1 kHz. SU-8 is an ideal material due to its relative ease of use in MEMS, low modulus of elasticity enables more flexible devices with large deflection, and good chemical stability.

more interesting. The equation describing the recovery stress-induced deflection in

*Optimization of MEMS Actuator Driven by Shape Memory Alloy Thin Film Phase Change*

2 *NiTit* 2

where *σrec* ¼ recovery stress of the SMA MEMS actuator; *d* ¼ deflection of the SMA MEMS actuator; *l* ¼ total length of the SMA MEMS actuator; *ENiTi* ¼ elastic modulus of NiTi layer; *ESU*‐<sup>8</sup> <sup>¼</sup> elastic modulus of SU-8 layer; *TNiTi* <sup>¼</sup> thickness

**Figure 1** shows stress vs. temperature curves for NiTi on Si wafer. These curves are experimentally generated, and indicate the recovery stress (difference between highest and lowest stress values), and the thermal hysteresis. Here, as an illustrative example, the NiTi thickness is 900 nm, and the temperature cycle is performed

Assumptions: we assume operating temperatures go between RT and 100°C to ensure full phase change. In all calculations, for simplicity we use Young's modulus of NiTi as a fixed value. In reality, the Young's modulus changes curing the phase change. Martensite (lower temperature phase usually has a lower elastic modulus

**Figure 2** shows the process used to build the SMA MEMS bimorph actuator comprised of the NiTi shape memory (SMA) layer underneath the SU-8 elastic layer. In step (a) deposition of SMA onto Si wafer and pattern using photolithography. In step (b) ion milling is performed to transfer the pattern into the SMA layer. In step (c) we spin on SU-8 and pattern it with mask plate and photolithography. In

difluoride (XeF2) gas. In step (e) we thermally actuate the two-way shape memory

*Stress vs. temperature curves for NiTi on Si wafer. These curves are experimentally generated, and indicate the*

*recovery stress (difference between highest and lowest stress values), and the thermal hysteresis.*

step (d) we release the MEMS bimorph by etching Si substrate with xenon

<sup>þ</sup> *<sup>E</sup>*<sup>2</sup>

2

3 *SU*‐<sup>8</sup> *SU*‐8*<sup>t</sup>* 4 *SU*‐<sup>8</sup> (1)

*SU*‐<sup>8</sup> <sup>þ</sup> <sup>4</sup>*tNiTit*

shape memory alloy (SMA) MEMS actuator is:

*NiTi* <sup>þ</sup> *ESU*‐<sup>8</sup>*ENiTi* <sup>4</sup>*<sup>t</sup>*

*DOI: http://dx.doi.org/10.5772/intechopen.92393*

using a heating and cooling rate of 1°C/min.

MEMS device between curled and flat states.

compared to the higher temperature austenite phase).

*E*2 *NiTit* 4

**Figure 1.**

**27**

*<sup>d</sup>* <sup>¼</sup> <sup>3</sup>*ENiTiσrectNiTitSU*‐8ð Þ *tNiTi* <sup>þ</sup> *tSU*‐<sup>8</sup> *<sup>l</sup>*

3

modulus of NiTi layer; *TSU*‐<sup>8</sup> <sup>¼</sup> thickness modulus of SU-8 layer.

*NiTitSU*‐<sup>8</sup> <sup>þ</sup> <sup>6</sup>*<sup>t</sup>*

Much literature exists for thin film development and characterization of nickeltitanium shape memory alloy [1–4]. Although many demonstrations of SMA MEMS actuators have been shown [9, 34–43], none of these citations perform design optimization studies to maximize deflection or curvature radius due to residual stress changes due to phase change. When the nitinol is thermally cycled between martensite and austenite phases, there is a corresponding change in residual stress, which is used to drive the nonlinear deflections. This nonlinear and large change in stress is defined as the recovery stress, and is a principal factor influencing the deflection and curvature radius. Our novel contributions take a realistic SMA MEMS bimorph design based on SU-8 on NiTi, and determine optimal thickness combinations to yield maximized deflections, which would be desirable in certain applications were large strokes are desired. We feed into the model the Young's modulus values for NiTi thin films that have been determined previously using nanoindentation techniques [44, 45].

#### **2. Building and characterizing the SMA MEMS actuators**

The nickel-titanium alloy (NiTi) would be co-sputtered onto a 4″ silicon wafer based on the methods reported in previous works [8, 34–36]. The substrate is rotated and heated during deposition to ensure crystallization of the film. The wafer stress vs. temperature measurements are performed, using Stoney's equation to determine recovery stress, hysteresis, and residual stress in the NiTi film. After verification of good shape memory alloy properties in the film at wafer level, a photomask is used to pattern bimorph actuator. Ion milling is used to remove portions of the NiTi film on the wafer. The SU-8 2000.5 is spin coated (where the RPM is used to control SU-8 thickness) and another mask plate is used to pattern SU-8 on top of the NiTi cantilever. Finally, the device is released by etching the Si substrate away in xenon difluoride (XeF2) gas. In practice, SU-8 thickness would be controlled by varying spin speed, and NiTi thickness based on sputtering time.

#### **2.1 Problem identification**

The design problem is to maximize the deflection of a MEMS bimorph cantilever beam based on the nonlinear shape memory alloy (SMA) as the actuating mechanism. The deflection is dependent in large part on the parameter called recovery stress. The larger the recovery stress, the larger the deflection. We may also wish to decrease the overall mass or volume of the actuator, of minimize the curvature radius. The objectives are competing in that reduction in the shape memory alloy thickness, generally leads to reduction of the recovery stress. The bimorph actuator could consist of SU-8 on top of NiTi thin film, but this optimization model would be easily extensible to other cases of interest.

We should consider that the equation describing the recovery stress-induced deflection in shape memory alloy MEMS actuator is (Eq. 1).

Initially, the contour plots of SU-8 and NiTi thickness showed that the optimization problem was not interesting for the simplest case of constant recovery stress over the range of NiTi thickness. To our advantage, the NiTi recovery stress is a parameter that depends on NiTi thickness, which makes the optimization problem

more interesting. The equation describing the recovery stress-induced deflection in shape memory alloy (SMA) MEMS actuator is:

$$d = \frac{3E\_{\text{NTiT}} \sigma\_{\text{re}} t\_{\text{NTiT}} t\_{\text{SU-8}} (t\_{\text{NTiT}} + t\_{\text{SU-8}}) l^2}{E\_{\text{NTiT}}^2 t\_{\text{NTiT}}^4 + E\_{\text{SU-8}} E\_{\text{NTiT}} \left( 4t\_{\text{NTiT}}^3 t\_{\text{SU-8}} + 6t\_{\text{NTiT}}^2 t\_{\text{SU-8}}^2 + 4t\_{\text{NTiT}} t\_{\text{SU-8}}^3 \right) + E\_{\text{SU-8}}^2 t\_{\text{SU-8}}^4} \tag{1}$$

where *σrec* ¼ recovery stress of the SMA MEMS actuator; *d* ¼ deflection of the SMA MEMS actuator; *l* ¼ total length of the SMA MEMS actuator; *ENiTi* ¼ elastic modulus of NiTi layer; *ESU*‐<sup>8</sup> <sup>¼</sup> elastic modulus of SU-8 layer; *TNiTi* <sup>¼</sup> thickness modulus of NiTi layer; *TSU*‐<sup>8</sup> <sup>¼</sup> thickness modulus of SU-8 layer.

**Figure 1** shows stress vs. temperature curves for NiTi on Si wafer. These curves are experimentally generated, and indicate the recovery stress (difference between highest and lowest stress values), and the thermal hysteresis. Here, as an illustrative example, the NiTi thickness is 900 nm, and the temperature cycle is performed using a heating and cooling rate of 1°C/min.

Assumptions: we assume operating temperatures go between RT and 100°C to ensure full phase change. In all calculations, for simplicity we use Young's modulus of NiTi as a fixed value. In reality, the Young's modulus changes curing the phase change. Martensite (lower temperature phase usually has a lower elastic modulus compared to the higher temperature austenite phase).

**Figure 2** shows the process used to build the SMA MEMS bimorph actuator comprised of the NiTi shape memory (SMA) layer underneath the SU-8 elastic layer. In step (a) deposition of SMA onto Si wafer and pattern using photolithography. In step (b) ion milling is performed to transfer the pattern into the SMA layer. In step (c) we spin on SU-8 and pattern it with mask plate and photolithography. In step (d) we release the MEMS bimorph by etching Si substrate with xenon difluoride (XeF2) gas. In step (e) we thermally actuate the two-way shape memory MEMS device between curled and flat states.

#### **Figure 1.**

*Stress vs. temperature curves for NiTi on Si wafer. These curves are experimentally generated, and indicate the recovery stress (difference between highest and lowest stress values), and the thermal hysteresis.*

position, a process that is reversible upon subsequent thermal cycles. Thermal effects can be delivered to the SMA MEMS using laser irradiation [34], and jouleheating [35], at frequencies up to at least 1 kHz. SU-8 is an ideal material due to its relative ease of use in MEMS, low modulus of elasticity enables more flexible

Much literature exists for thin film development and characterization of nickeltitanium shape memory alloy [1–4]. Although many demonstrations of SMA MEMS actuators have been shown [9, 34–43], none of these citations perform design optimization studies to maximize deflection or curvature radius due to residual stress changes due to phase change. When the nitinol is thermally cycled between martensite and austenite phases, there is a corresponding change in residual stress, which is used to drive the nonlinear deflections. This nonlinear and large change in stress is defined as the recovery stress, and is a principal factor influencing the deflection and curvature radius. Our novel contributions take a realistic SMA MEMS bimorph design based on SU-8 on NiTi, and determine optimal thickness combinations to yield maximized deflections, which would be desirable in certain applications were large strokes are desired. We feed into the model the Young's modulus values for NiTi thin films that have been determined previously using

The nickel-titanium alloy (NiTi) would be co-sputtered onto a 4″ silicon wafer based on the methods reported in previous works [8, 34–36]. The substrate is rotated and heated during deposition to ensure crystallization of the film. The wafer stress vs. temperature measurements are performed, using Stoney's equation to determine recovery stress, hysteresis, and residual stress in the NiTi film. After verification of good shape memory alloy properties in the film at wafer level, a photomask is used to pattern bimorph actuator. Ion milling is used to remove portions of the NiTi film on the wafer. The SU-8 2000.5 is spin coated (where the RPM is used to control SU-8 thickness) and another mask plate is used to pattern SU-8 on top of the NiTi cantilever. Finally, the device is released by etching the Si substrate away in xenon difluoride (XeF2) gas. In practice, SU-8 thickness would be controlled by varying spin speed, and NiTi thickness based on sputtering time.

The design problem is to maximize the deflection of a MEMS bimorph cantilever beam based on the nonlinear shape memory alloy (SMA) as the actuating mechanism. The deflection is dependent in large part on the parameter called recovery stress. The larger the recovery stress, the larger the deflection. We may also wish to decrease the overall mass or volume of the actuator, of minimize the curvature radius. The objectives are competing in that reduction in the shape memory alloy thickness, generally leads to reduction of the recovery stress. The bimorph actuator could consist of SU-8 on top of NiTi thin film, but this optimization model would be

We should consider that the equation describing the recovery stress-induced

Initially, the contour plots of SU-8 and NiTi thickness showed that the optimization problem was not interesting for the simplest case of constant recovery stress over the range of NiTi thickness. To our advantage, the NiTi recovery stress is a parameter that depends on NiTi thickness, which makes the optimization problem

devices with large deflection, and good chemical stability.

**2. Building and characterizing the SMA MEMS actuators**

nanoindentation techniques [44, 45].

*Advanced Functional Materials*

**2.1 Problem identification**

**26**

easily extensible to other cases of interest.

deflection in shape memory alloy MEMS actuator is (Eq. 1).

shown to drop off completely, so we impose constraints for NiTi thickness to vary

*Optimization of MEMS Actuator Driven by Shape Memory Alloy Thin Film Phase Change*

Based on the curve fitting equation (*third-order polynomial*), the single-objective

2

100 *μm* ≤*l*≤ 300 *μm* (3) 150 *nm* ≤*tNiTi* ≤1000 *nm* (4) <sup>200</sup> *nm* <sup>≤</sup>*tSU*‐<sup>8</sup> <sup>≤</sup><sup>2000</sup> *nm* (5)

3 *SU*‐<sup>8</sup>

*σrec* ≥ 0 (6)

<sup>2</sup> <sup>þ</sup> <sup>2</sup>*:*45*E*15*tNiTi* � <sup>2</sup>*:*58*E*08 SI units ð Þ (7)

2

3 *SU*‐<sup>8</sup>

*SU*‐<sup>8</sup> <sup>þ</sup> <sup>4</sup>*tNiTit*

*<sup>g</sup>*<sup>1</sup> : <sup>100</sup> � <sup>10</sup>�<sup>6</sup> � *<sup>l</sup>* <sup>≤</sup>0; (9) *<sup>g</sup>*<sup>2</sup> : *<sup>l</sup>* � <sup>300</sup> � <sup>10</sup>�<sup>6</sup> <sup>≤</sup>0; (10) *<sup>g</sup>*<sup>3</sup> : <sup>150</sup> � <sup>10</sup>�<sup>9</sup> � *tNiTi* <sup>≤</sup>0; (11) *<sup>g</sup>*<sup>4</sup> : *tNiTi* � <sup>1300</sup> � <sup>10</sup>�<sup>9</sup> <sup>≤</sup>0; (12)

*<sup>g</sup>*<sup>5</sup> : <sup>200</sup> � <sup>10</sup>�<sup>9</sup> � *tSU*‐<sup>8</sup> <sup>≤</sup>0; (13) *<sup>g</sup>*<sup>6</sup> : *tSU*‐<sup>8</sup> � <sup>2000</sup> � <sup>10</sup>�<sup>9</sup> <sup>≤</sup>0; (14)

*g*<sup>7</sup> : �*σrec* ≤0 (15)

<sup>2</sup> � <sup>2</sup>*:*<sup>45</sup> � 1015*tNiTi* <sup>þ</sup> <sup>2</sup>*:*<sup>58</sup> � <sup>10</sup><sup>8</sup> <sup>¼</sup> <sup>0</sup>

*SU*‐8*<sup>t</sup>* 4 *SU*‐<sup>8</sup>

*SU*‐<sup>8</sup>*<sup>t</sup>* 4 *SU*‐<sup>8</sup> (2)

(8)

(16)

*SU*‐<sup>8</sup> <sup>þ</sup> <sup>4</sup>*tNiTit*

*maximize* :

2 *NiTit* 2

<sup>þ</sup> *<sup>E</sup>*<sup>2</sup>

between 150 and 1300 nm.

*E*2 *NiTit* 4

*E*2 *NiTit* 4

*subjected to*::

*<sup>h</sup>*1: *<sup>σ</sup>rec* � <sup>5</sup>*:*<sup>36</sup> � <sup>10</sup><sup>26</sup>*tNiTi*

**3.2 MATLAB optimization toolbox (fmincon)**

*<sup>K</sup>* <sup>¼</sup> �*E*<sup>0</sup>

*tNiTi* <sup>¼</sup> <sup>359</sup> *nm*, *tSU*‐<sup>8</sup> <sup>¼</sup> <sup>824</sup> *nm*, *<sup>l</sup>* <sup>¼</sup> <sup>300</sup> *<sup>μ</sup>m*.

**3.3 Multi-objective optimization**

**29**

*subjected to*::

*σrec* ¼ 5*:*36*E*26*tNiTi*

optimization problem can be written as following:

*NiTi* <sup>þ</sup> *ESU*‐<sup>8</sup>*ENiTi* <sup>4</sup>*<sup>t</sup>*

*DOI: http://dx.doi.org/10.5772/intechopen.92393*

Covert to standard form in SI units:

*NiTi* <sup>þ</sup> *ESU*‐<sup>8</sup>*ENiTi* <sup>4</sup>*<sup>t</sup>*

*<sup>d</sup>* <sup>¼</sup> <sup>3</sup>*ENiTiσrectNiTitSU*‐8ð Þ *tNiTi* <sup>þ</sup> *tSU*‐<sup>8</sup> *<sup>l</sup>*

3

<sup>3</sup> � <sup>2</sup>*:*15*E*21*tNiTi*

*<sup>f</sup>* <sup>¼</sup> �3*ENiTiσrectNiTitSU*‐<sup>8</sup>ð Þ *tNiTi* <sup>þ</sup> *tSU*‐<sup>8</sup> *<sup>l</sup>*

3

*NiTitSU*‐<sup>8</sup> <sup>þ</sup> <sup>6</sup>*<sup>t</sup>*

*minimize* :

2 *NiTit* 2

<sup>þ</sup> *<sup>E</sup>*<sup>2</sup>

*NiTitSU*‐<sup>8</sup> <sup>þ</sup> <sup>6</sup>*<sup>t</sup>*

<sup>3</sup> <sup>þ</sup> <sup>2</sup>*:*<sup>15</sup> � <sup>10</sup><sup>21</sup>*tNiTi*

The curvature of a bilayer elastic material [46] is given as

*SU*‐<sup>8</sup>*tSU*‐<sup>8</sup>*E*<sup>0</sup>

*G E*<sup>0</sup>

According to the toolbox (and as shown in **Figure 4**), optimal solution is:

*SU*‐<sup>8</sup>*tSU*‐<sup>8</sup> <sup>þ</sup> *<sup>E</sup>*<sup>0</sup>

*NiTitNiTi*ð Þ *tNiTi* <sup>þ</sup> *tSU*‐<sup>8</sup>

*NiTitNiTi Δε* (17)

**Figure 2.** *SMA MEMS fabrication process for SU-8 on NiTi bimorph.*
