Verification of FEM analysis of load-deflection methods for measuring mechanical properties of thin films

Pan, Jeffrey Y.; Lin, Pinyen; Maseeh, Fariborz; Senturia, S.D.

doi:10.1109/solsen.1990.109823

Cited by 90 publications

(43 citation statements)

References 5 publications

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“…The width of the membrane was set to be much larger than its length between clamps, so that the load was insensitive to variations in the shape and distance between free edges. Within the regime of small indentation, the elastic response of the membrane without electric field was determined by its Young's modulus Y 2D , Poisson's ratio ν and pre-stress σ 2D in cubic polynomial form with two geometry-dependent prefactors 27 . Taking ν = 0.25 from ref.…”

mentioning

confidence: 99%

Observation of piezoelectricity in free-standing monolayer MoS2

Zhu¹,

Wang²,

Xiao³

et al. 2014

Nature Nanotech

762

577

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Piezoelectricity allows precise and robust conversion between electricity and mechanical force, and arises from the broken inversion symmetry in the atomic structure [1][2][3] . Reducing the dimensionality of bulk materials has been suggested to enhance piezoelectricity 4 . However, when the thickness of a material approaches a single molecular layer, the large surface energy can cause piezoelectric structures to be thermodynamically unstable 5 . Transition-metal dichalcogenides can retain their atomic structures down to the single-layer limit without lattice reconstruction, even under ambient conditions 6 . Recent calculations have predicted the existence of piezoelectricity in these two-dimensional crystals due to their broken inversion symmetry 7 . Here, we report experimental evidence of piezoelectricity in a free-standing single layer of molybdenum disulphide (MoS 2 ) and a measured piezoelectric coefficient of e 11 = 2.9 × 10 -10 C m −1 . The measurement of the intrinsic piezoelectricity in such free-standing crystals is free from substrate effects such as doping and parasitic charges. We observed a finite and zero piezoelectric response in MoS 2 in odd and even number of layers, respectively, in sharp contrast to bulk piezoelectric materials. This oscillation is due to the breaking and recovery of the inversion symmetry of the two-dimensional crystal. Through the angular dependence of electromechanical coupling, we determined the two-dimensional crystal orientation. The piezoelectricity discovered in this single molecular membrane promises new applications in low-power logic switches for computing and ultrasensitive biological sensors scaled down to a single atomic unit cell 8,9 .Since its discovery in 1880, piezoelectricity has found a wide range of applications in actuation, sensing and energy harvesting. The rapidly growing demand for high-performance and miniaturized devices in micro-electro-mechanical systems (MEMS) and electronics 10-12 calls for nanoscale piezoelectric materials, motivating theoretical investigations into novel low-dimensional systems such as nanotubes and single molecules 13,14 . Transition-metal dichalcogenides (TMDCs) are ideal candidates as low-dimensional piezoelectric materials because of their structural non-centrosymmetry 7 . Although there has been extensive research interest in the unique properties originating from such symmetry breaking, including circular dichroism and second harmonic generation (SHG) [15][16][17][18][19] , experimental quantitative determination of the intrinsic piezoelectric properties of these two-dimensional crystals has yet to be demonstrated. Here, we report the observation of piezoelectricity in freestanding monolayer MoS 2 membranes. Interestingly, we found that this molecular piezoelectricity only exists when there are an odd number of layers in the two-dimensional crystal where inversion symmetry breaking occurs. We observed an angular dependence of the piezoelectric response in agreement with the three-fold symmetry of the crystal, and based...

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mentioning

confidence: 99%

Observation of piezoelectricity in free-standing monolayer MoS2

Zhu¹,

Wang²,

Xiao³

et al. 2014

Nature Nanotech

762

577

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“…It will be talked first. In all cases, the deflection of membrane under pressure is described by in equation (1) (Vlassak, 1992;Pan, 1990): () 3 10 2 24 (1 )…”

Section: Silicon Nitride Membrane Deflectionmentioning

confidence: 99%

“…These parameters are listed in Table. For square membranes, the magnitude of the deflection, z, as a function of position on the membrane, x and y, can be described by (Pan, 1990).…”

Section: Btmentioning

confidence: 99%

Microfabricated Implantable Pressure Sensor for Flow Measurement

Liu¹,

Farrow²,

Thomas³

2012

Flow Measurement

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“…Tabata 20 was able to calculate biaxial modulus and Poisson's ratio from deflection characteristics of rectangular membranes. Pan et al 21 compared the analytical solution with finite element method analysis and found that the functional form of the analytical solution is correct, but the constants needed minor correction. Several additional models were also developed to improve accuracy of material characterization from the load-displacement data.…”

Section: A Analytical Modelmentioning

confidence: 99%

High speed wafer scale bulge testing for the determination of thin film mechanical properties

Orthner

Rieth

Solzbacher

2010

Review of Scientific Instruments

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A wafer scale bulge testing system has been constructed to study the mechanical properties of thin films and microstructures. The custom built test stage was coupled with a pressure regulation system and optical profilometer which gives high accuracy three-dimensional topographic images collected on the time scale of seconds. Membrane deflection measurements can be made on the wafer scale ͑50-150 mm͒ with up to nanometer-scale vertical resolution. Gauge pressures up to 689 kPa ͑100 psi͒ are controlled using an electronic regulator with and accuracy of approximately 0.344 kPa ͑0.05 psi͒. Initial testing was performed on square diaphragms 350, 550, and 1200 m in width comprised of 720Ϯ 10 nm thick low pressure chemical vapor deposited silicon nitride with ϳ20 nm of e-beam evaporated aluminum. These initial experiments were focused on measuring the system limitations and used to determine what range of deflections and pressures can be accurately measured and controlled. Gauge pressures from 0 to ϳ8.3 kPa ͑1.2 psi͒ were initially applied to the bottom side of the diaphragms and their deflection was subsequently measured. The overall pressure resolution of the system is good ͑ϳ350 Pa͒ but small fluctuations existed at pressures below 5 kPa leading to a larger standard deviation between deflection measurements. Analytical calculations and computed finite element analysis deflections closely matched those empirically measured. Using an analytical solution that relates pressure deflection data for the square diaphragms the Young's modulus was estimated for the films assuming a Poisson's ratio of v = 0.25. Calculations to determine Young's modulus for the smaller diaphragms proved difficult because the pressure deflection relationship remained in the linear regime over the tested pressure range. Hence, the calculations result in large error when used to estimate the Young's modulus for the smaller membranes. The deflection measurements of three 1200ϫ 1200 m 2 Si 3 N 4−x membranes were taken at increased pressures ͑Ͼ25 kPa͒ to increase nonlinearity and better determine Young's modulus. This pressure-deflection data were fit to an analytical solution and Young's modulus estimated to be 257Ϯ 3 GPa, close to those previously reported in literature.

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Verification of FEM analysis of load-deflection methods for measuring mechanical properties of thin films

Cited by 90 publications

References 5 publications

Observation of piezoelectricity in free-standing monolayer MoS2

Observation of piezoelectricity in free-standing monolayer MoS2

Microfabricated Implantable Pressure Sensor for Flow Measurement

High speed wafer scale bulge testing for the determination of thin film mechanical properties

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