A novel test structure to characterize the fracture strength of MEMS (Micro-electro-Mechanical Systems) thin films is presented. The test structure is comprised of a micro fabricated chevron-shaped thermal actuator and test specimen. The test structure is capable of producing large displacement and stress while keeping a relatively low temperature gradient across the test specimen. A voltage is applied across the beams of the chevron-shaped actuator, producing thermal expansion force to fracture the test specimen. Actuator deflection is computed based on elastic analysis of structures. To verify the test structure, simulations have been implemented using COMSOL Multiphysics. A 620 μm long, 410 μm wide, 10 μm thick test structure produced stress of 7.1 GPa while the applied voltage is 5 V. The results indicate that the test structure is suitable for in-situ measurement of the fracture strength of MEMS thin films.

  • Presented a novel test structure based on chevron-shaped actuator to measure the fracture strength of MEMS thin films.

  • Computed actuator deflection through analyzing the force and displacement provided by the test structure.

  • The test structure could produce large force and displacement at relatively low temperatures.

Micro-electro-Mechanical Systems (MEMS) have been implemented in many products that are used in our daily lives.1 Reliability and performance of MEMS devices greatly depend on the mechanical properties.2 Therefore, the mechanical reliability issues such as fracture strength of MEMS components have become progressively important so that the designers could be able to optimize the mechanical response and reliability of the devices.

During the past several years, some techniques have been developed to determine the mechanical properties of micro scale components, such as nanoindentation, bulge, torsion and the slack chain test.3 However, most of them are complex and require detailed analysis, which may include the consideration of geometrically necessary dislocations.

Actuators are designed to create small motions to drive other MEMS components, and thus can be used to characterize fracture strength of MEMS thin films. Electrostatic actuators operate at high frequency but require either high voltage to produce large forces. On the other hand, thermal actuators have effective application where low voltage, small footprints and high output forces are required. The most common thermal actuators are the chevron type, U-type and bimorph thermal actuators in MEMS applications.4 Chevron-shaped thermal actuators (TAs)5,6 can create a full stress-strain curve for each sample because they provide large force and displacement. It can provide a displacement of 3.5 μm while the applied voltage is only 3.3 V and the power consumption is approximately 3 mW.7 When a voltage is applied across V-shaped beams, current passes through the actuator, resulting in Joule heat and expansion of the beams which leads to a displacement in connected components. However, large thermal gradients may appear while testing, which will alter the mechanical properties of the test specimen. In order to avoid large temperature gradients across the thermal actuators used for material testing, some used heat sink beams which emanate from the shuttle and are connected to the substrate.8 This is an effective method and is used in the project.

In this study, a test structure is presented which is capable of generating large stress and displacement with relatively small driven voltage. The test structure is comprised of chevron-shaped actuators and test specimen. A theoretical model is developed and the test structure is analyzed and optimized using COMSOL Multiphysics software. This optimized design can be used for in-situ measurement of the fracture strength of MEMS thin films.

There are several different methods for quantifying the fracture strength of MEMS thin films:9 tensile test methods, compressive test, bending test and torsional test. Compressive test methods with an instrumented indenter or AFM are sometimes easier to conduct, in that they avoid many of the gripping, mounting, loading, and post-test characterization issues associated with tensile test methods. But many materials behave differently in compression than in tension. As a consequence, the results from compressive tests are sometimes difficult to interpret. Bending test methods also avoid many of the gripping, mounting, loading, and post-test characterization issues associated with tensile test methods, but Pantano et al. noted that bending test methods often require smaller loads and produce larger displacements.10 Torsional test methods are complicated and pure torsion is difficult to apply for loading schemes often result in superfluous axial and bending stresses, making results difficult to interpret.11 Therefore, tensile test methods are used in this paper.

A typical one-dimension geometric model of a V-beam thermal actuator is shown in Fig. 1. Gianchandani and Najafi put forward an analogous design12 to measure strain and later to amplify the displacement and actuate micro motors.13 In this system the motion of each side of the actuator is mechanically amplified by the central chevrons and transferred to the test specimen.

Fig. 1.

One-dimension geometric model of a V-beam thermal actuator.

Fig. 1.

One-dimension geometric model of a V-beam thermal actuator.

Close modal

A voltage is applied across the anchors and causes a temperature difference among anchor, beam, shuttle due to joule heating. The applied voltage is V. The length of the beam of the V-shaped actuator is L, the cross-sectional perimeter is P, the cross sectional area is A, the pre-bending angle is θ, and the resistance of the beam is R. The vertical gap between beam and substrate is ∆z. According to the boundary condition, the temperature increase ∆T of the V-shaped beams is given by Eq. (1).14 

d2Tdx2=kairP/2AkpolyΔzTV2RAkpolyL,
(1)

where T is the temperature difference relative to the substrate, kair is the thermal conductivity of the air and kpoly is the thermal conductivity of the polysilicon. In chevron actuator,

T(Lcosθ)=T(Lcosθ)=T0,
(2)

where T0 is the temperature of the anchors. Then the temperature distribution across the beam is found by solving Eqs. (1) and (2) as

T(x)=(T02ΔzkairPLV2R)cos(ωx)cos(ωLcosθ)+2ΔzkairPLV2R,
(3)

where ω=kairP/2AkpolyΔz. The average temperature increase in the V beam is given as

Tavg=1LcosθT(x)dx=(T02ΔzkairPLV2R)tan(ωx)ωLcosθ+2ΔzkairPLV2R,
(4)

The increase in length ∆L of the V beam due to thermal expansion is given by

ΔL=α(T(x)T0)dx=αLcosθ(TavgT0),
(5)

where α is the thermal expansion coefficient of polysilicon. The change in the pre bending angle of the V beam θ after expansion is given as

θ=arccos(LcosθL+ΔL),
(6)

Then the displacement of the node of the V beam ∆y can be derived as

Δy=(L+ΔL)sinθy,
(7)

The force generated by the chevron-shaped actuator with N pair of V beams is given by15 

F=NαTavgEAcosθsin2θψ+cos2θ,
(8)

where E is the Young's modulus of the material, the dimensionless parameter ψ = AL2/(12I) is defined as the axial over bending stiffness ratio, I is the moment of inertia of the cross section with respect to the out of plane axis z.

A chevron-shaped MEMS thermal actuator is designed in COMSOL Multiphysics. The actuator is fabricated using polysilicon and the test specimen is of PZFILM (Piezoelectric film, AlN). The diagram of this actuator is shown in Fig. 2.

Fig. 2.

The initial model of the test structure based on Chevron-shaped thermal actuator.

Fig. 2.

The initial model of the test structure based on Chevron-shaped thermal actuator.

Close modal

The test structure is comprised of a chevron-shaped thermal actuator and a test specimen. The thermal actuator consists of an array of heated beams, a freestanding, central movable shuttle. The beams are set with a pre-bent angle and linked to the anchored pads. A voltage is applied to the pad, inducing a current through the beams. The beams will expand due to joule heat and then produce linear motion which can fracture the test specimen. However, the current passing through the beams may lead to large heat flow and change the mechanical properties of the test specimen. Qin Q and Zhu Y have shown that heat sink beams are effective in controlling the temperature of thermal actuators.8 This method is used in the project.

A potential steadily increasing from 0 V to Vf until the test specimen is fractured. The cross-sectional area of the test specimen is B. Then from Eqs. (4) and (8) the fracture strength of the test specimen can be derived as

σ=FfB=NαEABcosθsin2θψ+cos2θ((T02ΔzkairPLVf2R)tan(ωx)ωLcosθ+2ΔzkairPLVf2R),
(9)

where Ff is the force generated by the test structure when the test specimen is just fractured.

To verify the analytical model, a multiphysics finite element analysis (FEA) was conducted using COMSOL Multiphysics. The FEA model was a coupled model of thermal, electrical and mechanical fields. The input parameter is the applied voltage and the outputs of interest are force and displacement. The mechanical boundary conditions were fixed restrictions at the anchors and the thermal boundary condition of constant temperature was set at the anchors. The electrical boundary condition of applied voltage was set at the anchors. Properties for polysilicon material are presented in Table 1.

Table 1.

Properties of polysilicon.

Material propertiesValueUnitReference
Young's modulus 160 GPa 16  
Poisson ratio 0.22 – 16  
Thermal expansion coefficient 2.8 × 10−6 K−1 17  
Electrical conductivity 7.69 × 106 S/m 18  
Thermal conductivity of polysilicon 3.2 × 107 pW/(μm·K) 19  
Thermal conductivity of air 0.026 × 106 pW/(μm·K) 19  
Material propertiesValueUnitReference
Young's modulus 160 GPa 16  
Poisson ratio 0.22 – 16  
Thermal expansion coefficient 2.8 × 10−6 K−1 17  
Electrical conductivity 7.69 × 106 S/m 18  
Thermal conductivity of polysilicon 3.2 × 107 pW/(μm·K) 19  
Thermal conductivity of air 0.026 × 106 pW/(μm·K) 19  

Six kinds of solid models with different dimensions are simulated and the results are analyzed to obtain the geometrical design optimization. The shape of the actuator remains the same while the length, width, number and the pre-bent angle of the beams, length and width of the shuttle, length and width of the heat sink are changed in each model. The output displacement and force increase with the increase in length of the shuttle and number of the beams. But considering fabrication costs, tradeoffs must be made to meet the desired load and displacement specifications. The geometric parameters selected for this work are shown in Table 2.

Table 2.

Geometric parameters selected for this work.

ParameterDesign valueParameterDesign value
Length of each beam 200 μm Width of the heat sink beam 25 μm 
Width of each beam 10 μm Thickness of the heat sink beam 10 μm 
Thickness of each beam 10 μm Length of PZFILM (Test Specimen AlN) 10 μm 
Angle of each beam 10° Width of PZFILM 10 μm 
Number of beams Thickness of PZFILM 0.7 μm 
Length of the shuttle 300 μm Length of each anchor 100 μm 
Width of the shuttle 20 μm Width of each anchor 100 μm 
Thickness of the shuttle 10 μm Thickness of each anchor 10 μm 
Length of the heat sink beam 300 μm   
ParameterDesign valueParameterDesign value
Length of each beam 200 μm Width of the heat sink beam 25 μm 
Width of each beam 10 μm Thickness of the heat sink beam 10 μm 
Thickness of each beam 10 μm Length of PZFILM (Test Specimen AlN) 10 μm 
Angle of each beam 10° Width of PZFILM 10 μm 
Number of beams Thickness of PZFILM 0.7 μm 
Length of the shuttle 300 μm Length of each anchor 100 μm 
Width of the shuttle 20 μm Width of each anchor 100 μm 
Thickness of the shuttle 10 μm Thickness of each anchor 10 μm 
Length of the heat sink beam 300 μm   

The above model can only provide a stress of approximately 1.1 GPa, which is not enough to fracture most of MEMS thin films. And the temperature of the test structure is about 400°C. Therefore, some methods should be taken to further optimize the test structure.

The heat flow near the test specimen is caused by the current through the shuttle. To reduce the heat flow, the way to apply the voltage is changed. A voltage of 5 V and a voltage of 0 V are separately applied to the two pads linked to the beams. This can decrease the current through the shuttle to about 0, which accordingly avoids large thermal gradient.

Figure 3 shows the potential distribution and the temperature variation of this model. The stress distribution is similar to the initial model. The temperature of the test specimen decreases to 330°C. This method of changing the way to apply the voltage can effectively limit the heat flow across the test specimen.

Fig. 3.

(a) Potential distribution of the changed model; (b) temperature variation of the changed model.

Fig. 3.

(a) Potential distribution of the changed model; (b) temperature variation of the changed model.

Close modal

Based on the analysis of above solid model, the structure which links the specimen and the actuator is changed to a dogbone shape to concentrate the stress on the test specimen. The dimensions and the way to apply the voltage remain unchanged.

Figure 4 shows the geometrical design and the stress distribution of the test structure with dogbone shaped connection. According to the results, the stress produced by the test structure increases to 7.1 GPa while the temperature is about 300°C. The dogbone shaped connection can concentrate the force on the test specimen, which can produce large forces and displacements while avoiding large temperature gradients across the test specimen. Fracture strength of Silicon is about 1 GPa, Silicon carbide 5.2 GPa and Diamond 5.3 GPa.20 Therefore, the stress and displacement required for testing the specimen are much lower than the full-range capabilities of this test structure.

Fig. 4.

(a) Model of the test structure with dogbone shaped connection; (b) stress distribution of the test structure with dogbone shaped connection.

Fig. 4.

(a) Model of the test structure with dogbone shaped connection; (b) stress distribution of the test structure with dogbone shaped connection.

Close modal

In this study, a test structure based on chevron-shaped thermal actuator to characterize the fracture strength of MEMS thin films is designed. The calculation formula is derived by analyzing the force and displacement produced by the actuator. The actuator design was modeled both analytically and by the use of FEA. The geometrical design parameters are optimized to produce large force and displacement. Moreover, the way to apply the voltage is changed to decrease the current through the shuttle to achieve low temperature gradient across the test specimen. To concentrates the force on the specimen, the structure which links the specimen and the actuator is changed to dogbone shaped connection. The overall dimensions of the test platform and the testing method make it suitable for use in in-situ measurement. The ability of the test structure to produce large stress and displacements with low thermal gradient makes its use possible for many material testing applications at the micro- and nano-scale.

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests

This research was supported by the National High Technology Program of P. R. China under Grant No. 2015AA042604.

1.
Hsu
TR
.
MEMS & Microsystems: Design, Manufacture, and Nanoscale Engineering
.
Hoboken, NJ, USA
:
Wiley
;
2008
.
2.
Allameh
SM
.
An introduction to mechanical-properties-related issues in MEMS structures
.
J. Mater. Sci.
2003
;
38
(
20
):
4115
4123
.
3.
Boyce
BL
.
A sequential tensile method for rapid characterization of extreme-value behavior in microfabricated materials
.
Exp. Mech.
2010
;
50
(
7
):
993
997
.
4.
Varona
J
,
Margarita
TT
,
Hamoui
AA
.
Design of MEMS vertical-horizontal chevron thermal actuators
.
Sens. Actuators, A
2009
;
153
(
1
):
127
130
.
5.
Rebecca
C
,
Howell
LL
.
Linear thermomechanical microactuators
.
Proc ASME IMECE
1999
:
181
188
.
6.
Que
L
,
Park
JS
,
Gianchandani
YB
.
Bent-beam electrothermal actuators-Part I: Single beam and cascaded devices
.
J. Microelectromech. Syst.
2001
;
10
(
2
):
247
254
.
7.
Ziko
MH
,
Koel
A
.
Theoretical and numerical investigations on a silicon-based MEMS chevron type thermal actuator
.
Ireland
:
18th IEEE International Conference on Nanotechnology; Cork
;
2018
.
8.
Qin
Q
,
Zhu
Y
.
Temperature control in thermal microactuators with applications to in-situ nanomechanical testing
.
Appl. Phys. Lett.
2013
;
102
(
1
):
013101
.
9.
Delrio
FW
,
Cook
RF
,
Boyce
RL
.
Fracture strength of micro- and nano-scale silicon components
.
Appl. Phys. Rev.
2015
;
2
(
2
):
021303
.
10.
Pantano
MF
,
Espinosa
HD
,
Pagnotta
L
.
Mechanical characterization of materials at small length scales
.
J. Mech. Sci. Technol.
2012
;
26
(
2
):
545
561
.
11.
Saif
MTA
,
Macdonald
NC
.
Micro mechanical single crystal silicon fracture studies torsion and bending
.
San Diego, CA, USA
:
Proceedings of the IEEE International Workshop on Micro Electro Mechanical Systems
;
1996
.
12.
Gianchandani
YB
,
Najafi
K
.
Bent-beam strain sensors
.
J. Microelectomech. Syst.
1996
;
5
(
1
):
52
58
.
13.
Park
JS
,
Chu
LL
,
Oliver
AD
, et al 
Bent-beam electrothermal actuators-Part II: Linear and rotary microengines
.
J. Microelectromech. Syst.
2001
;
10
(
2
):
255
262
.
14.
Lai
YJ
,
McDonald
J
,
Kujath
M
, et al 
Force, deflection and power measurements of toggled microthermal actuators
.
J. Micromech. Microeng.
2004
;
14
(
1
):
49
56
.
15.
Zhu
Y
,
Corigliano
A
,
Espinosa
HD
.
A thermal actuator for nanoscale in situ microscopy testing: Design and characterization
.
J. Micromech. Microeng.
2006
;
16
(
2
):
242
253
.
16.
Yan
D
,
Khajepour
A
,
Mansour
R
.
Modeling of two-hot-arm horizontal thermal actuator
.
J. Micromech. Microeng.
2003
;
13
:
312
322
.
17.
Madou
MJ
.
Fundamentals of Microfabrication: The Science of Miniaturization
. 2nd ed.
USA
:
CRC Press LLC
;
2002
.
18.
Pasumarthy
A
,
Dwivedi
M
,
Islam
A
.
Optimized design of Au-polysilicon electrothermal microgripper for handling micro-objects
.
Visakhapatnam, India
:
International Conference on Electrical, Electronics, Signals, Communication and Optimization (EESCO)
;
2015
. p.
1
5
.
19.
Shivhare
P
,
Uma
G
,
Umapathy
M
.
Design enhancement of a chevron electrothermally actuated microgripper for improved gripping performance
.
Microsyst. Technol.
2016
;
22
(
11
):
2623
2631
.
20.
Krauss
AR
,
Auciello
O
,
Gruen
DM
.
Ultrananocrystalline diamond thin films for MEMS and moving mechanical assembly devices
.
Diamond Relat. Mater.
2001
;
10
(
11
):
1952
1961
.