Quantifying stress distribution in ultra-large graphene drums through mode shape imaging

Suspended drums made of 2D materials hold potential for sensing applications. However, the industrialization of these applications is hindered by significant device-to-device variations presumably caused by non-uniform stress distributions induced by the fabrication process. Here we introduce a new...

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Published inarXiv.org
Main Authors Sarafraz, Ali, Liu, Hanqing, Cvetanović, Katarina, Spasenović, Marko, Vollebregt, Sten, Garcia, Tomas Manzaneque, Steeneken, Peter G, Alijani, Farbod, Verbiest, Gerard J
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LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.11.2023
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Abstract Suspended drums made of 2D materials hold potential for sensing applications. However, the industrialization of these applications is hindered by significant device-to-device variations presumably caused by non-uniform stress distributions induced by the fabrication process. Here we introduce a new methodology to determine the stress distribution from their mechanical resonance frequencies and corresponding mode shapes as measured by a laser Doppler vibrometer (LDV). To avoid limitations posed by the optical resolution of the LDV, we leverage a unique manufacturing process to create ultra-large graphene drums with diameters of up to 1000 um. We solve the inverse problem of a F\"oppl--von Kármán plate model by an iterative procedure to obtain the stress distribution within the drums from the experimental data. Our results show that the generally used uniform pre-tension assumption overestimates the pre-stress value, exceeding the averaged stress obtained by more than 47%. Moreover, it is is found that the reconstructed stress distributions are bi-axial, which likely originates from the transfer process. The introduced metholodogy allows one to estimate the tension distribution in drum resonators from their mechanical response and thereby paves the way for linking the used fabrication processes to the resulting device performance.
AbstractList Suspended drums made of 2D materials hold potential for sensing applications. However, the industrialization of these applications is hindered by significant device-to-device variations presumably caused by non-uniform stress distributions induced by the fabrication process. Here we introduce a new methodology to determine the stress distribution from their mechanical resonance frequencies and corresponding mode shapes as measured by a laser Doppler vibrometer (LDV). To avoid limitations posed by the optical resolution of the LDV, we leverage a unique manufacturing process to create ultra-large graphene drums with diameters of up to 1000 um. We solve the inverse problem of a F\"oppl--von Kármán plate model by an iterative procedure to obtain the stress distribution within the drums from the experimental data. Our results show that the generally used uniform pre-tension assumption overestimates the pre-stress value, exceeding the averaged stress obtained by more than 47%. Moreover, it is is found that the reconstructed stress distributions are bi-axial, which likely originates from the transfer process. The introduced metholodogy allows one to estimate the tension distribution in drum resonators from their mechanical response and thereby paves the way for linking the used fabrication processes to the resulting device performance.
Author Spasenović, Marko
Alijani, Farbod
Cvetanović, Katarina
Steeneken, Peter G
Verbiest, Gerard J
Liu, Hanqing
Vollebregt, Sten
Garcia, Tomas Manzaneque
Sarafraz, Ali
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Snippet Suspended drums made of 2D materials hold potential for sensing applications. However, the industrialization of these applications is hindered by significant...
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SubjectTerms Axial stress
Diameters
Graphene
Inverse problems
Iterative methods
Laser doppler vibrometers
Mechanical analysis
Stress distribution
Two dimensional materials
Title Quantifying stress distribution in ultra-large graphene drums through mode shape imaging
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