In-plane deformation of cantilever plates with applications to lateral force microscopy

Review of Scientific Instruments

Volumn 75, Issue 4, 2004, Pages 878-883

  Sader, John E ^a   Green, Christopher P ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

ASPECT RATIO; ATOMIC FORCE MICROSCOPY; CALCULATIONS; DEFORMATION; FORCE MEASUREMENT; IMAGING TECHNIQUES;

CANTILEVER PLATES; IN PLANE DEFORMATION; IN PLANE SPRING CONSTANTS; LATERAL FORCE MICROSCOPY;

MICROSCOPES;

EID: 2042543448     PISSN: 00346748     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1667252     Document Type: Article

References (19)

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9. Throughout, we delineate between cantilever deformation and imaging tip deformation.
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12. For rectangular cantilevers, we neglect the higher order correction that accounts for the inherent restraint against axial warping of the plate (Ref. 8). This was included in Ref. 8 to ensure formulas for all spring constants possessed similar accuracy. The neglect of this term here ensures consistency with the derived in-plane spring constant, which neglects all higher order corrections. For aspect ratios L/c > 2, the maximum effect of this correction is a 30% increase in the torsional spring constant. This effect decreases as the aspect ratio increases (Ref. 8).
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14. LUSAS is a trademark of, and is available from FEA Ltd. Forge House, 66 High Street, Kingston Upon Thames, Surrey, KT1 1HN, UK, Plane stress elements with quadratic interpolation were used throughout. The number of elements was refined to ensure accuracy better than 1%. Quadrilateral elements were used for the rectangular cantilevers. For the V-shaped cantilevers, quadrilateral elements were used along the skewed rectangular arms, and triangular elements were used in the triangular end section.
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18. y ∼ 1. The lateral stiffness of the equivalent rectangular cantilever is 0.6 times lower than the V-shaped cantilever.
19. We note that any imaging tip deformation (Ref. 17) will reduce the difference between the lateral spring constants of the V-shaped and rectangular cantilever/tip combinations, provided the same tip is attached to both cantilevers.