New methods for measuring mechanical properties of thin films in micromachining: Beam pull-in voltage (VPI) method and long beam deflection (LBD) method

Zou, Quanbo; Z, Li; Liu, Litian

doi:10.1016/0924-4247(95)00987-6

Cited by 59 publications

(30 citation statements)

References 8 publications

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“…In MEMS, micromachined beams undergoing Euler buckling have been successfully used for this purpose. Prestrains of polysilicon [5], [8] and silicon oxide [10] have been measured. More complex buckled structures have been used to determine residual strains of diamond-like carbon [11], silicon oxide [12], and polysilicon thin films [9].…”

Section: Introductionmentioning

confidence: 99%

Strongly buckled square micromachined membranes

Ziebart

Oliver

Baltes

1999

J. Microelectromech. Syst.

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The buckling of compressively prestressed square membranes with built-in edges is investigated experimentally and analyzed theoretically. The buckling depends weakly on Poisson's ratio and essentially is a function of the reduced prestrain, " 0 = " 0 a 2 =h 2 , where " 0 is the physical prestrain, a is the width, and h is the thickness of the membrane. As " 0 becomes increasingly negative, the membrane undergoes two symmetry breaking buckling transitions. Beyond the first transition occurring at " cr1 , the buckling profile has all the reflection and rotation symmetries of a square. The reflection symmetries are lost through a second instability transition at "cr2: The bifurcation points, "cr1 and "cr2; and buckling profiles were calculated using analytical energy minimization and nonlinear finite-element simulation. Both methods agree. The buckling of micromachined plasma-enhanced chemical vapor deposition silicon nitride membranes on a silicon wafer is interpreted in terms of the theoretical results. Good matching between measured and calculated buckling profiles is found. The extracted strain values are consistent irrespective of the size and buckling mode of the membranes. From the average strain across the wafer " 0 = 03:50 2 10 04 and complementary wafer curvature measurements, a Young's modulus of 130 GPa is deduced. Methods for the straightforward extraction of " 0 from experimental center deflections of buckled square membranes are described. [443]

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Section: Introductionmentioning

confidence: 99%

Strongly buckled square micromachined membranes

Ziebart

Oliver

Baltes

1999

J. Microelectromech. Syst.

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“…It will be helpful to design and optimize related MEMS devices, as well as to implement process monitoring and material property extraction. In the case of single-layer cantilever and fixed-fixed beams, Zou et al (1995), and Gupta (1997) have studied the analytical model of pullin voltage. Nemirovsky (2001) presented a generalized model of pull-in voltage.…”

Section: Introductionmentioning

confidence: 99%

A comprehensive model to study nonlinear behavior of multilayered micro beam switches

Rezazadeh

2007

Microsyst Technol

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A novel model to study the pull-in behavior of nonlinear electromechanically coupled systems has been developed. The proposed model is based on the multilayered cantilever and fixed-fixed micro beam type MEMS switches. Due to the complexity of the nonlinear beam mechanics, exact analytical solutions are not generally available; therefore, the derived nonlinear equation has been numerically solved fully using the nonlinear finite difference method. Furthermore, the results obtained are summarized and compared with the other existing empirical and analytical models. These results can be useful in the optimization of MEMS switch designs or other actuators. In addition, the method developed in this paper has a good potential for analyzing other types of complex MEMS devices.

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“…Therefore, it is of significant interest to know the value of this parameter since knowledge of Young's modulus is required both for analysis and design. Significant amount of methods have been devoted to determining Young's modulus experimentally, which are categorized as static 2,3 and dynamic [4][5][6] .…”

Section: Introductionmentioning

confidence: 99%

Measuring Young's modulus using a self-mixing laser diode

Lin

et al. 2014

SPIE Proceedings

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This paper presents a novel approach for determining the Youngâ€™s modulus by using a self-mixing laser diode (SMLD). An SMLD system consists of a laser diode (LD), a microlens and an external target. With a small portion of light backscatterd or reflected by the target re-entering the LD inside cavity, both the amplitude and frequency of the LD power are modulated. This modulated LD power is referred as a selfmixing signal (SMS) which is detected by the photodiode (PD) packaged in the rear of the LD. The external target is the tested sample which is in damping vibration excited by a singular elastic strike with an impulse tool. The vibration information from the tested sample is carried in the SMS. Advanced data processing in frequency-domain is applied on the SMS, from which the resonant frequency of the vibration can be retrieved, and hence Youngâ€™s modulus is calculated. The proposed method has been verified by simulations. 2014 SPIE. ABSTRACTThis paper presents a novel approach for determining the Young's modulus by using a self-mixing laser diode (SMLD). An SMLD system consists of a laser diode (LD), a microlens and an external target. With a small portion of light backscatterd or reflected by the target re-entering the LD inside cavity, both the amplitude and frequency of the LD power are modulated. This modulated LD power is referred as a self-mixing signal (SMS) which is detected by the photodiode (PD) packaged in the rear of the LD. The external target is the tested sample which is in damping vibration excited by a singular elastic strike with an impulse tool. The vibration information from the tested sample is carried in the SMS. Advanced data processing in frequency-domain is applied on the SMS, from which the resonant frequency of the vibration can be retrieved, and hence Young's modulus is calculated. The proposed method has been verified by simulations.

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New methods for measuring mechanical properties of thin films in micromachining: Beam pull-in voltage (VPI) method and long beam deflection (LBD) method

Cited by 59 publications

References 8 publications

Strongly buckled square micromachined membranes

Strongly buckled square micromachined membranes

A comprehensive model to study nonlinear behavior of multilayered micro beam switches

Measuring Young's modulus using a self-mixing laser diode

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