# MEMS Device for Quantitative In Situ Mechanical Testing in Electron Microscope

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## Abstract

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## 1. Introduction

## 2. Mechanical Testing System

#### 2.1. Description of the System

_{a}and x

_{b}are the center deflections of beams A and B, respectively, and l

_{0}is the initial length of the specimen.

_{b}is the driving force acting on beam B and S is the cross-sectional area of the specimen. Using a push-to-pull structure, the external compressive stress on the specimen was transferred to a tensile stress, as shown in Figure 1b.

#### 2.2. Sensor Design

_{1}and R

_{2}, located at the roots of the beams A and B, measure the beam deflection. The resistances of the other two resistors, R

_{3}and R

_{4}, attached to the substrate, remain constant during the beam deflection. The four resistors are electrically connected with aluminum (Al) interconnects. To improve the consistency of the process and to partially compensate the influence of temperature, the resistors on the beam and those on the substrate were placed as close as possible to each other [52]. The beams and the piezoresistors are aligned along the <110> direction on the (100) plane of a silicon wafer substrate for obtaining a better sensor sensitivity [53].

_{l}and σ

_{t}are the longitudinal and transverse stresses, and π

_{l}and π

_{t}are the piezoresistance coefficients along the longitudinal and transverse directions. Since σ

_{t}is much smaller than σ

_{l}, the term ${\mathsf{\pi}}_{\mathrm{t}}{\mathsf{\sigma}}_{\mathrm{t}}$ can be neglected [51]. Figure 3 shows the positions of the piezoresistors on the beam and the parameters used in Equations (4) and (5). In the case of small deformation, the variance of the resistance can be written as:

_{p}is the piezoresistor length, ω is the beam center deflection, and d′ is the distance between the resistor centerline and neutral plane of the beam. The value d′ can be expressed as:

_{p}is the width of the piezoresistor, and d″ is the distance between the outer edge of the piezoresistor and the beam. Figure 3 shows all the parameters in Equation (5).

_{3}and R

_{4}have an equal resistance variance ΔR, the bridge output voltage is given as:

_{B}is the bridge bias voltage.

_{B}is the Boltzmann constant, T is the absolute temperature, N

_{p}is the dopant concentration, q is the amount of the carrier charge, μ

_{p}is the hole mobility, d

_{p}is the piezoresistor thickness, α is a non-dimensional fitting parameter depending on the annealing conditions, and f

_{max}and f

_{min}are the upper and lower measurement frequency limits. The displacement resolution of the sensors is defined as the ratio of the noise to the displacement sensitivity (only considering Johnson and 1/f noise), and can be written as:

_{p}). For a nearly constant d″, depending on the MEMS technology, the d′ will become shorter when w

_{p}is increased, leading to a decrease in the displacement sensitivity. To obtain an optimal width (w

_{p-optimal}), the resolution R

_{D}can be partially differentiated against the piezoresistor width. The optimal width thus obtained is:

_{p}, of the piezoresistor has an opposite influence on the power density of the Hooge and Johnson noises, i.e., a decrease in the Hooge noise but an increase in the Johnson noise. It is further noted from Equation (7) that increase in l

_{p}can also lead to a loss in the displacement sensitivity. Because of the complicated effect of l

_{p}on the displacement resolution and sensitivity, the resolution was partially differentiated against l

_{p}to obtain an optimal length contributing to a high resolution. For each clamped beam length, L, an optimal l

_{p-optimal}is obtained. Figure 4 shows the evolution of l

_{p-optimal}/L as a function of the clamped beam length. The results show that the l

_{p-optimal}/L decreases with increasing L.

## 3. Experiment

#### 3.1. Fabrication Process

_{2}insulation layer was grown on each side of the wafer by thermal oxidation (Figure 5a). The thermal oxidation SiO

_{2}layer on the device side was patterned and etched as a mask for subsequent ion implantation. The piezoresistors, with resistivity of $1.17\times {10}^{-2}$ Ω·cm, were prepared by boron doping by means of ion implantation at 100 keV with a dose of ${10}^{15}$ ${\mathrm{cm}}^{-2}$ (p-doped, Figure 5b). Using the same process, electrical contacts were created with an implantation energy of 100 keV and a dose of $3\times {10}^{15}$ ${\mathrm{cm}}^{-2}$ (p+ doped, Figure 5c). A 1-μm-thick aluminum film was then sputtered on the surface and then etched using potassium hydroxide (KOH) solution to form interconnects and pads (Figure 5d). The device layer was then etched by inductively coupled plasma (ICP) etching (Figure 5e). Finally, ICP was used to etch out the handle and buried oxide layers from the backside to create a movable structure (Figure 5f). Figure 6a shows a SEM image of a MEMS fabricated device. Figure 6b shows a magnified view of sensor B. The corresponding lithography maps are shown in Figure 6c,d. Comparison between the fabricated device and the lithography maps shows that the lateral undercutting of both ICP etching and aluminum film wet etching was less than 1 μm, indicating a well-controlled etching processes.

#### 3.2. Device Calibration and Quantitative Tensile Testing

_{a}and x

_{b}) based on the calibration. The deformation strain is then calculated according to Equation (1) by knowing the original length (l

_{0}) of the specimen prior to testing. The force applied on the specimen (F

_{b}) is calculated based on the displacement of beam B, as per Equation (16). The stress can then be calculated using Equation (2) by measuring the cross-sectional area (S) of the specimen prior to tensile testing.

#### 3.3. Specimen Preparation

## 4. Results and Discussion

#### 4.1. Sensors Performance

#### 4.2. Stress–Strain Curve

## 5. Conclusions

- (1)
- Sensors A and B have displacement sensitivities of 37.4 μV/nm and 4.8 μV/nm.
- (2)
- Sensor A has a theoretical displacement resolution of 0.19 nm and sensor B has a force resolution of 2.1 μN.
- (3)
- The MEMS device has a displacement range limit of 5.47 μm and a theoretical load range limit of 55.0 mN.
- (4)
- Measurement of the Young’s modulus of the Al film by the device verifies the reliability of the sensors.
- (5)
- The device has a dimension small enough to be integrated on the TEM holder to study the property–structure correlation at the atomic scale.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the testing system in scanning electron microscopes (SEM): (

**a**) the actuation control flow chart; and (

**b**) design of the testing apparatus.

**Figure 3.**Schematic of the piezoresistor beam positions and the parameters used in Equations (4) and (5).

**Figure 5.**Schematic of the main steps to fabricate the MEMS device: (

**a**) thermal oxidation; (

**b**) p− doped; (

**c**) p+ doped and contact hole; (

**d**) interconnects and pads; (

**e**) front side inductively coupled plasma (ICP); and (

**f**) structure release.

**Figure 6.**MEMS device with piezoresistive sensors: (

**a**) SEM image of the device; (

**b**) enlarged SEM image of the sensor B region; (

**c**) lithography map of the device; and (

**d**) lithography map of the sensor B region.

**Figure 7.**Setup for in situ tensile testing in SEM: (

**a**) the optical image of the testing system equipped in SEM; and (

**b**) schematic of the testing system.

**Figure 11.**Displacement calibrations of sensors in SEM: (

**a**–

**f**) the displacements of the two reference points for sensor A; and (

**g**–

**l**) their displacements for sensor B.

Parameters | Value | Unit | |
---|---|---|---|

Sensor A | Sensor B | ||

Α | 10^{−5} | - | |

T | 300 | K | |

μ_{p} | 0.934 × 10^{−2} | cm^{2}·V^{−1}·s^{−1} | |

Bias voltage | 3.0 | V | |

f_{max} | 1000 | Hz | |

f_{min} | 10 | Hz | |

Clamped beam length | 150 | 600 | Μm |

Clamped beam width | 60 | 60 | Μm |

Clamped beam thickness | 30 | 15 | Μm |

Piezoresistor length | 46 | 107 | Μm |

Piezoresistor width | 8 | 3 | Μm |

Piezoresistor thickness | 1.1 | 1.1 | Μm |

Theoretical displacement sensitivity | 77.1 | 7.1 | μV/nm |

Theoretical displacement resolution | 0.19 | 4.6 | nm |

Theoretical displacement range limit | 5.47 | 175.14 | μm |

Theoretical load range limit | 888 | 55.0 | mN |

Length (nm) | Width (nm) | Depth (nm) |
---|---|---|

4880 | 620 | 510 |

Sensors | Magnification | ||
---|---|---|---|

2000× | 8000× | 16,000× | |

Sensor A | 37.5 μV/nm | 37.2 μV/nm | 37.4 μV/nm |

Sensor B | 4.6 μV/nm | 4.9 μV/nm | 4.8 μV/nm |

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## Share and Cite

**MDPI and ACS Style**

Wang, X.; Mao, S.; Zhang, J.; Li, Z.; Deng, Q.; Ning, J.; Yang, X.; Wang, L.; Ji, Y.; Li, X.; Liu, Y.; Zhang, Z.; Han, X. MEMS Device for Quantitative In Situ Mechanical Testing in Electron Microscope. *Micromachines* **2017**, *8*, 31.
https://doi.org/10.3390/mi8020031

**AMA Style**

Wang X, Mao S, Zhang J, Li Z, Deng Q, Ning J, Yang X, Wang L, Ji Y, Li X, Liu Y, Zhang Z, Han X. MEMS Device for Quantitative In Situ Mechanical Testing in Electron Microscope. *Micromachines*. 2017; 8(2):31.
https://doi.org/10.3390/mi8020031

**Chicago/Turabian Style**

Wang, Xiaodong, Shengcheng Mao, Jianfei Zhang, Zhipeng Li, Qingsong Deng, Jin Ning, Xudong Yang, Li Wang, Yuan Ji, Xiaochen Li, Yinong Liu, Ze Zhang, and Xiaodong Han. 2017. "MEMS Device for Quantitative In Situ Mechanical Testing in Electron Microscope" *Micromachines* 8, no. 2: 31.
https://doi.org/10.3390/mi8020031