Nanomechanical Imaging

Macromechanical characterization is an extremely mature field. The basic theory of mechanics was founded on empirical observations that solid bodies exhibit a deformation of some sort (i.e., shape or volume) under the action of applied forces [4]. Standard continuum mechanical theory describes the change in distance between any two points in a solid under the application of an external stress. Assuming linear response, this treatment results in the conventional definitions of elastic constants (bulk modulus, shear modulus, Poisson's ratio, etc.) and the generalized form of Hooke's law. Mechanical characterization beyond elastic behavior is primarily concerned with the onset of inelastic (plastic) deformations and the investigation of material hardness, fracture toughness, and yield (tensile/compressive) strength. Consequently, the study of mechanics is, in large part, the study of deformation. The study of nanomechan-ics is no different from the previous discussion of nano-materials illustrated. Recall that the elastic response of an ideal ordered material is directly determined by the local electrostatic atomic, ionic, or molecular potential energy well, the minimum of which is approximately parabolic. If the local atomic, ionic, or molecular mechanical response is preserved in nanoscale structures, it is reasonable to assume that some analogy to "classical" mechanics will exist, and that analogs to classical mechanical measurements will exist. This assumption is the foundation for the fields of nanoindentation, nanotribology, and nanomechanical imaging. These techniques, generally, utilize some type of point contact probe with a nanometer characteristic length scale. Classical mechanics has, for the most part, been used to interpret the results of such experiments, providing empirical confirmation of the propriety of such models. Acoustic, optical, and ultrasonic microscopy techniques have long been the choice for the micrometer-scale characterization of certain surface and subsurface mechanical properties of solids; however, the inherent resolution limitations in far-field lenses and/or coupling media have limited their application at the nanoscale [7]. Nanotribology is an exciting vibrant field and, although intimately related to nanomechanics, is beyond the scope of this review [8]. Nanoindentation is the culmination of decades of empirical research, and is now on the verge of a truly nanoscale characterization technique, although it is typically implemented as a destructive methodology better suited to planar surfaces than nanoscale structures [9]. Since the rising fields of nanoscience and nanotechnology focus on emergent functionality, it is appropriate to restrict detailed discussions to those methodologies that provide not only nanoscale resolution, but that are appropriate for the characterization of nanoscale structures and devices. Consequently, this section will focus on nanomechanical imaging, defined as the cadre of techniques capable of spatially resolving the variation of mechanical properties of nanomaterials, structures, and devices on the nanometer-length scale. Since the mechanics of these techniques use models developed, in part, for nanoindentation, it will be referenced throughout this discussion. The remainder of this section is organized as follows. First, a brief overview is presented of the simple mechanics of a point-probe contact with a surface. This is followed by a brief description of the experimental apparatus used to control such contacts with nanoscale precision, and to exploit them for the extraction of nanomechanical image data. Third, the development and application of a variety of these techniques will be reviewed with respect to the current literature. Lastly, a review of recent results will be presented to demonstrate the potential of nanomechanical imaging and its coming role in the development of nanotechnology.

If an object is of insufficient size or disposition to measure its deformation upon application of an external stress to determine elastic moduli, it is often necessary to apply a point probe to characterize mechanical properties. Hertz was the first to treat such a situation to determine the deformation of two objects in direct contact under an external load [10-11]. (The original problem treated two hemispherical surfaces. A sphere/plane system was recovered by letting one radius diverge to infinity.) The situation and the necessary parameters are outlined in Figure 1. Assuming only elastic deformation (short-range forces) and no interfacial adhesion between the tip probe and sample surfaces, the relation between the contact radius a of the tip/sample contact and the load F is

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