3D Force and Displacement Sensor for SFA and AFM Measurements ² Kai Kristiansen, ‡,§ Patricia McGuiggan, | Greg Carver, ‡ Carl Meinhart, ⊥ and Jacob Israelachvili* ,‡,# Departments of Chemical Engineering and Mechanical Engineering, Materials Department, and Materials Research Laboratory, UniVersity of California, Santa Barbara, California 93106, Department of Physics, UniVersity of Oslo, N-0316 Oslo, Norway, and Department of Materials Science and Engineering, Johns Hopkins UniVersity, Baltimore, Maryland 21218 ReceiVed August 2, 2007. In Final Form: October 2, 2007 A new device has been designed, and a prototype built and tested, that can simultaneously measure the displacements and/or the components of a force in three orthogonal directions. The “3D sensor” consists of four or eight strain gauges attached to the four arms of a single cross-shaped force-measuring cantilever spring. Finite element modeling (FEM) was performed to optimize the design configuration to give desired sensitivity of force, displacement, stiffness, and resonant frequency in each direction (x, y, and z) which were tested on a “mesoscale” device and found to agree with the predicted values to within 4-10%. The device can be fitted into a surface forces apparatus (SFA), and a future smaller “microscale” microfabricated version can be fitted into an atomic force microscope (AFM) for simultaneous measurements of the normal and lateral (friction) forces between a tip (or colloidal bead probe) and a surface, and the topography of the surface. Results of the FEM analysis are presented, and approximate equations derived using linear elasticity theory are given for the sensitivity in each direction. Initial calibrations and measurements of thin film rheology (lubrication forces) using the “mesoscale” prototype show the device to function as expected. 1. Introduction to the 3D Sensor 1.1. Background. Measurements of intermolecular forces and interactions are the key to understanding many micro- and nanoscale phenomena and surface properties. 1 One commonly used high-resolution force-measuring and surface imaging technique is scanning probe microscopy (SPM). 2 Since its introduction in the mid-1980s, the scanning probe microscope has continually been modified and extended to far-reaching applications with excellent sensitivity. A large number of SPM- related techniques have been developed, based on the desire to measure various types of interactions between tips (probes) and samples, including mechanical, electrical, magnetic, optical, and chemical interactions. 3 Atomic force microscopy (AFM), friction or lateral force microscopy (FFM or LFM), magnetic force microscopy (MFM), and electrostatic force microscopy (EFM) are four such applications where specific types of interactions are measured. 3 One of the basic designs of a SPM device is a tip attached to a cantilever which acts as a spring. The displacement of the spring is measured by one of two methods: (1) The most common method, shown in Figure 1a, is the optical or beam bouncing method whereby a laser light beam is bounced from the free end of the cantilever spring onto a quadrant photodiode detector. The change in the position of the laser light gives the deflection of the cantilever in the vertical ((z) and horizontal ((x) directions, giving the normal and friction forces, respectively. (2) A less common method is the resistive method using resistance, semiconductor, or piezoresistive strain gauges in a quarter-bridge, half-bridge, or full-bridge configuration 4-7 to also give the normal and lateral forces (Figure 1b). Highly accurate measurements of the deflection of a tip (or a colloidal bead) normal to the surface (in the z-direction) can be obtained by these methods. The force is calculated by multiplying the spring constant of the cantilever by the deflection. The sensitivity of displacements is better than 0.1 nm, and forces as low as 1 pN can be measured in both vapors and liquids. Together with the similar high-precision in-plane positioning or scanning in the x-direction, an image of the surface down to the atomic scale can be obtained. Some SPM devices are more suited (sensitive) to force measurements, while others are more suited to imaging (displacements). Still others are designed to collect data rapidly, generally by having a high resonance frequency of their cantilever deflection modes. However, as elaborated below, there are deficiencies: most existing sensors work only in two directions (z and x), and due to cantilever-tip design they usually have different force sensitivities in these two directions. Tip displacements are generally nonlinear, and there is “cross-talk” where, for example, a pure displacement in the x-direction also produces an output signal as if coming from the z-direction (we refer to this as xfz cross-talk). SPM cantilevers are typically of two shapes, triangular or rectangular (Figure 1). In either case, one end of the cantilever is attached to a base, and the sensing end of the cantilever is free. ² Part of the Molecular and Surface Forces special issue. * To whom correspondence should be addressed. E-mail: Jacob@ engineering.ucsb.edu. ‡ Department of Chemical Engineering, University of California. § University of Oslo. | Johns Hopkins University. ⊥ Department of Mechanical Engineering, University of California. # Materials Department, and Materials Research Laboratory, University of California. (1) Israelachvili, J. N. Intermolecular and surface forces, 2nd ed.; Academic Press Limited: San Diego, CA, 2005. (2) Vilarinho, P. M., Rosenwaks, Y., Kingon, A., Eds.; Scanning Probe Microscopy: Characterization, Nanofabrication and DeVice Application of Functional Materials; Kluwer Academic: Algarve, Portugal, 2005. (3) Friedbacher, G.; Fuchs, H. Pure Appl. Chem. 1999, 71, 1337. (4) Jumpertz, R.; Schelten, J.; Ohlsson, O.; Saurenbach, F. Sens. Actuators, A 1998, 70, 88. (5) Jumpertz, R.; von der Hart, A.; Ohlsson, O.; Saurenbach, F.; Schelten, J. Microelectron. Eng. 1998, 42, 441. (6) Kirk, M. D.; Smith, I. R.; Tortonese, M.; Cahill, S. S.; Slater, T. G. U.S. Patent 5,444,244, 1995. (7) Tortonese, M.; Barrett, R. C.; Quate, C. F. Appl. Phys. Lett. 1993, 62, 834. 1541 Langmuir 2008, 24, 1541-1549 10.1021/la702380h CCC: $40.75 © 2008 American Chemical Society Published on Web 12/08/2007