Resonant cavity light emitting diodes with two single quantum wells of different widths
Resonant cavity light emitting diodes containing two single quantum wells of different well width were fabricated. The quantum wells, consisting of GaAs with AlGaAs barriers, were placed in separate a...
Resonant cavity light emitting diodes containing two single quantum wells of different well width were fabricated. The quantum wells, consisting of GaAs with AlGaAs barriers, were placed in separate a...
Ion dynamics and oscillation frequencies in a linear combined trap
Ion traps have been pivotal in opening new frontiers for the precision spectroscopy of stable ions. We report on the demonstration of an additional ion trap: the linear combined trap. This device is p...
Ion traps have been pivotal in opening new frontiers for the precision spectroscopy of stable ions. We report on the demonstration of an additional ion trap: the linear combined trap. This device is p...
Surface stress induced deflections of cantilever plates with applications to the atomic force microscope: Rectangular plates
J. Appl. Phys. 89, 2911 (2001); doi:10.1063/1.1342018
Issue Date: 1 March 2001
You are not logged in to this journal. Log in
Surface stress is a material property that underpins many physical processes, such as the formation of self-assembled monolayers and the deposition of metal coatings. Due to its extreme sensitivity, atomic force microscopy (AFM) has recently emerged as an important tool in the measurement of surface stress. Fundamental to this application is theoretical knowledge of the effects of surface stress on the deflections of AFM cantilever plates. In this article, a detailed theoretical study of the effects of surface stress on the deflections of rectangular AFM cantilever plates is given. This incorporates the presentation of rigorous finite element results and approximate analytical formulas, together with a discussion of their limitations and accuracies. In so doing, we assess the validity of Stoney's equation, which is commonly used to predict the deflections of these cantilevers, and present new analytical formulas that greatly improve upon its accuracy. ©2001 American Institute of Physics.
| History: | Received 19 June 2000; accepted 20 November 2000 |
| Permalink: |
http://link.aip.org/link/?JAPIAU/89/2911/1 |
| BUY THIS ARTICLE | (US$28) |
|
|
|
|
Connotea
CiteULike
del.icio.us
BibSonomy
KEYWORDS and PACS
- 68.37.Ps
Surfaces and interfaces; thin films and low-dimensional systems (structure and nonelectronic properties) Microscopy of surfaces, interfaces, and thin films Atomic force microscopy (AFM) - 07.79.Lh
Instruments, apparatus, and components common to several branches of physics and astronomy Scanning probe microscopes and components Atomic force microscopes - 02.70.Dh
Mathematical methods in physics Computational techniques Finite-element and Galerkin methods - YEAR: 2001
RELATED DATABASES
PUBLICATION DATA
0021-8979 (print)
1089-7550 (online)
AIP
REFERENCES (30)
For access to fully linked references, you need to log in.
For access to fully linked references, you need to Log in.
- G. Hass and R. E. Thun, Physics of Thin Films (Academic, New York, 1966).
- L. I. Maissel and M. H. Francombe, An Introduction to Thin Films (Gordon and Breach, New York, 1973).
- A. W. Adamson, Physical Chemistry of Surfaces (Wiley, New York, 1990).
- H. Ibach,
Surf. Sci. Rep. 29, 193 (1997) . - G. G. Stoney,
Proc. R. Soc. London, Ser. A 82, 172 (1909) . - A. Brenner and S. Senderoff,
J. Res. Natl. Bur. Stand. 42, 105 (1949) . - R. Berger, E. Delamarche, H. P. Lang, C. Gerber, J. K. Gimzewski, E. Meyer, and H. J. Guntherodt,
Science 276, 2021 (1997) . - M. C. Payne, N. Roberts, R. J. Needs, M. Needels, and J. D. Joannopoulos,
Surf. Sci. 211, 1 (1989) . - V. Fiorentini, M. Methfessel, and M. Scheffler, Phys. Rev. Lett. 71, 1051 (1993).
- H. J. Wassermann and J. S. Vermaak,
Surf. Sci. 78, 459 (1978) . - R. Koch and R. Abermann,
Thin Solid Films 129, 63 (1985) . - P. A. Flinn, D. S. Gardner, and W. D. Nix,
IEEE Trans. Electron Devices ED-34, 689 (1987) . - R. E. Martinez, W. M. Augustyniak, and J. E. Golovchenko, Phys. Rev. Lett. 64, 1035 (1990).
- A. J. Schell-Sorokin and R. M. Tromp, Phys. Rev. Lett. 64, 1039 (1990).
- A. J. Schell-Sorokin and R. M. Tromp,
Surf. Sci. 319, 110 (1994) . - Stoney originally considered the case of uniaxial stress, which was later corrected to account for isotropic and homogeneous surface stresses.
- R. Raiteri and H. J. Butt,
J. Phys. Chem. 99, 15728 (1995) . - H. J. Butt,
J. Colloid Interface Sci. 180, 251 (1996) . - T. A. Brunt, T. Rayment, S. J. O'Shea, and M. E. Welland,
Langmuir 12, 5942 (1996) . - S. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw-Hill, New York, 1951).
- P. H. Townsend, D. M. Barnett, and T. A. Brunner, J. Appl. Phys. 62, 4438 (1987).
- E. Reissner and M. Stein, NACA Tech. Note No. 2369 (June 1951).
- J. E. Sader (in preparation).
- S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1959).
- J. N. Reddy, Theory and Analysis of Elastic Plates (Taylor and Francis, Philadelphia, 1999).
- Maximum deflections exhibited in practice are typically far smaller than the thickness of the plate.
- From Saint Venant's principle, a thin boundary layer is expected at the clamped end x = 0 for L/b
1. Such an expansion will enable the modeling of this boundary layer. - From Saint Venant's principle, thin boundary layers are expected at the free ends y = ±b/2 for L/b
1. Such a power series will enable the modeling of these boundary layers. - LUSAS is a trademark of, and is available from FEA Ltd. Forge House, 66 High St., Kingston Upon Thames, Surrey KT1 1HN, UK. Quadrilateral thin plate elements with linear interpolation were used throughout.
- End-tip displacements can be measured with a scanning tunneling microscope tip, whereas the slope can be measured using the optical deflection technique.
