# Power Optimization of TiNiHf/Si Shape Memory Microactuators

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. TiNiHf Films

_{2}/Si film composites annealed at 635 °C showed favorable phase transformation properties including a phase transformation with a large thermal hysteresis above room temperature. This performance was shown to prevail upon downscaling the thickness of TiNiHf films down to 440 nm on Si substrates and 220 nm on SiO

_{2}/Si substrates [13].

_{40}.

_{4}Ni

_{48}Hf

_{11}.

_{6}. Further details on the sputtering process and material’s properties of the TiNiHf films can be found in [13]. Four-point electrical resistance measurements are carried out inside a cryostat to investigate the phase transformation of TiNiHf films constrained by a silicon-on-insulator (SOI) substrate. Quasi-stationary conditions are established by ramping the temperature step-wise and providing for sufficient waiting times in each step to guarantee that the influence of temperature change is negligible during measurement. Phase transformation temperatures are determined using the tangential method. Figure 1 shows the temperature-dependent electrical resistance of a TiNiHf film of 440 nm thickness upon cyclic heating and cooling.

## 3. Modelling and Design Approach

## 4. Fabrication of TiNiHf/Si Bimorph Microactuators

## 5. Evaluation of Critical Electrical Power

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

EBL | Electron beam lithography |

EDX | Energy-dispersive X-ray spectroscopy |

FEM | Finite element modeling |

MEMS | Micro-electro-mechanical systems |

RIE | Reactive ion etching |

SMA | Shape memory alloy |

SOI | Silicon-on-insulator |

## Appendix A

**Figure A1.**Experimental setup used for in situ SEM measurements of electrical resistance. (

**a**) Schematic of the chip layout consisting of many microactuators arranged in an array and electrical interconnections. Each microactuator has two contact pads (A and B) for electrical interconnection, whereby the contact pads A of each microcactuator are electrically connected with each other and with two large pads being interconnected via wire bonding. In addition, two nanomanipulators are used to establish electrical interconnections to the second contact pads B of each single microactuator in a time sequence one after another. (

**b**) SEM images taken during in situ electrical measurement showing a single microactuator and the nanomanipulator tips used for electrical interconnection.

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**Figure 1.**Temperature-dependent electrical resistance characteristic of a 440 nm thick TiNiHf film on a 2 µm thick Si device layer of a SOI substrate. The start and finish austenitic and martensitic transformation temperatures (As = 119.3 °C, Af = 163.7 °C, Ms = 100.2 °C, Mf = 65.6 °C) are determined using the tangential method.

**Figure 2.**(

**a**,

**b**): Coupled finite element simulation of the temperature profiles along x-direction of a TiNiHf/Si cantilever beam upon Joule heating for various values of electrical power. The beam length $l$, beam width $w$ and length of folded beams ${l}_{wing}$ are indicated. The reference design without additional folded beams shows much larger temperature gradients compared to the temperature-homogenized design with additional folded beams; (

**c**,

**d**): contour plots of martensite phase fraction for reference and temperature-homogenized design at an electrical power of 15 mW and 11.8 mW, respectively.

**Figure 3.**Schematic process flow for fabrication of TiNiHf /Si microactuators using an SOI wafer with 2 μm Si device layer, (

**a**) patterning of resist using EBL, (

**b**) chromium deposition, (

**c**) lift-off of chromium, (

**d**) RIE of Si using cryogenic etching, (

**e**) stripping of chromium and selective etching of SiOx sacrificial layer and (

**f**) sputtering and annealing of TiNiHf thin film.

**Figure 4.**Scanning electron micrographs of a freestanding TiNiHf /Si microactuator with folded beam structure for temperature homogenization. The thicknesses of the TiNiHf film and Si layer are 440 nm and 2 μm, respectively. Dimensions of cantilever beams: 75 μm length ($l$), 3 μm width ($w$ ) and 30 μm length of folded beam structure (${l}_{wing}$ ).

**Figure 5.**In situ SEM measurement of electrical resistance as a function of electrical heating power for different TiNiHf/Si microactuators. The beam length $l$, beam width $w$ and length of folded beams ${l}_{wing}$ are indicated. The required electrical power to complete the phase transformation is highlighted. (

**a**) Comparison of reference (top) and temperature-homogenized design (bottom), (

**b**) temperature-homogenized design for different lengths of the folded beams (${l}_{wing}$ ) of 30 and 40 µm.

**Figure 6.**Simulated characteristics of maximum temperature at the cantilever beam tip as a function of electrical heating power. Measured values of electrical power (dots) are compared to simulation results to estimate the maximum temperature at the cantilever beam tip.

**Table 1.**Material properties for coupled electro-thermo-mechanical simulation of temperature profiles for TiNiHf/Si bimorph microactuators. The Poisson ratio of Si is included in the COMSOL material library. A polynomial function approximates the thermal expansion coefficient of Si [18]: ${\alpha}_{Si}\left(T\right)=\left(-3.0451+0.035705\xb7T-{7.98110}^{-5}\xb7{T}^{2}+{9.578310}^{-8}\xb7{T}^{3}-{5.891910}^{-11}\xb7{T}^{4}+{1.461410}^{-14}\xb7{T}^{5}\right){10}^{-6}1/\mathrm{K}$.

Si [19,20] | TiNiHf [13,21] | |
---|---|---|

Electrical conductivity ${\beta}_{SMA}$ (S/m) | 10 | ${\sigma}_{NiTiHf}\left(T\right)$ |

Thermal expansion coefficient α (1/K) | ${\alpha}_{Si}\left(T\right)$ | ${\alpha}_{A}=30\times {10}^{-6}\phantom{\rule{0ex}{0ex}}{\alpha}_{M}=15\times {10}^{-6}$ |

Young’s modulus E (GPa) | 169 | ${\mathrm{E}}_{\mathrm{m}}=35\phantom{\rule{0ex}{0ex}}{E}_{\mathrm{a}}=83$ |

Poisson’s ratio ν | 0.22 | 0.39 |

**Table 2.**Summary of experimental results of critical electrical power upon Joule heating required for a complete hysteresis loop and corresponding power saving for different geometries of TiNiHf/Si microactuators.

Geometry/Parameter | Ref100 | #1 | #2 | Ref75 | #3 | #4 |
---|---|---|---|---|---|---|

$\mathrm{Beam}\mathrm{length}\left(l\right)$, µm | 100 | 100 | 100 | 75 | 75 | 75 |

$\mathrm{Beam}\mathrm{width}\left(w\right)$, µm | 5 | 5 | 3 | 3 | 3 | 3 |

Folded beam length ^{a} $\left({l}_{\mathrm{wing}}\right)$, µm | 0 | 30 | 30 | 0 | 30 | 40 |

Critical electrical power $\left({\mathit{E}}_{\mathbf{c}}\right)$, mW | 15 | 11.8 | 7.8 | 10 | 7.9 | 5.5 |

Power saving,% (as compared to reference) | 21.8 | 48 | 21 | 45 |

^{a}The wing width always coincides with the beam width of the cantilever.

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**MDPI and ACS Style**

Arivanandhan, G.; Li, Z.; Curtis, S.M.; Hanke, L.; Quandt, E.; Kohl, M.
Power Optimization of TiNiHf/Si Shape Memory Microactuators. *Actuators* **2023**, *12*, 82.
https://doi.org/10.3390/act12020082

**AMA Style**

Arivanandhan G, Li Z, Curtis SM, Hanke L, Quandt E, Kohl M.
Power Optimization of TiNiHf/Si Shape Memory Microactuators. *Actuators*. 2023; 12(2):82.
https://doi.org/10.3390/act12020082

**Chicago/Turabian Style**

Arivanandhan, Gowtham, Zixiong Li, Sabrina M. Curtis, Lisa Hanke, Eckhard Quandt, and Manfred Kohl.
2023. "Power Optimization of TiNiHf/Si Shape Memory Microactuators" *Actuators* 12, no. 2: 82.
https://doi.org/10.3390/act12020082