Measurement of the Length and Strength of Adhesive Interactions in a Nanoscale Silicon–Diamond Interface

Abstract

the interaction (characterized by the range of adhesion z 0 ).The intrinsic work of adhesion W adh is the energy per unit area required to separate two planar surfaces from equilibrium contact to infi nite separation. In terms of surface energy (γ i of surface i ) and interfacial energy (γ ij between surfaces i and j ), the work of adhesion is calculated as follows:In accordance with prior literature on adhesion and roughness, [ 9 ] the intrinsic work of adhesion W adh,int is defi ned as the work of adhesion between two perfectly fl at, planar surfaces. While W adh,int is a continuum concept, it can be robustly mapped onto an atomistic description of two atomically fl at, single-crystal surfaces in contact. The effective work of adhesion, W adh,eff , is defi ned as the work of adhesion for the same material pair and the same global geometry (planar), but with the addition of local surface roughness on one or both surfaces. The distinction between W adh,int and W adh,eff is shown schematically in Figure 1 . The W adh,int is determined by the identity of the materials in contact, and the environment, whereas W adh,eff is a function of W adh,int and the local surface topography. For hard, non-conforming materials, W adh,eff is typically much smaller than W adh,int . The primary reason for this is that the roughness increases the effective separation between the two materials, and therefore signifi cantly increases γ ij between the materials as they can no longer make intimate contact. Roughness can also increase the surface energies γ i and γ j , but this effect is typically overwhelmed by the change in γ ij . This distinction is drawn because many experimental techniques exist to measure W adh,eff (for example, using microfabricated beam tests [ 10 ] ), but generally applicable techniques to deduce from this the W adh,int are not well established.Physically, z 0 describes the equilibrium separation distance between perfectly fl at surfaces, i.e., the separation distance at which their interaction force is zero. However, in many mathematical descriptions of adhesion (for instance, refs. [ 5,7,8,11 ] ) z 0 also scales the distance over which adhesion acts for a particular material. Therefore, the parameter z 0 is referred to in this paper as the "range of adhesion," (in accordance with Greenwood, [ 5 ] who calls it the "range of action of the surface forces").The adhesive interactions between nanoscale silicon atomic force microscope (AFM) probes and a diamond substrate are characterized using in situ adhesion tests inside of a transmission electron microscope (TEM). In particular, measurements are presented both for the strength of the adhesion acting between the two materials (characterized by the intrinsic work of adhesion W adh,int ) and for the length scale of the interaction (described by the range of adhesion z 0 ). These values are calculated using a novel analysis technique that requires measurement of the AFM probe geometry, the adhesive force, and the position where the snap-in instability occurs. Values ...

A Technique for the Experimental Determination of the Length and Strength of Adhesive Interactions Between Effectively Rigid Materials

“…The uncertainty in the technique has been estimated at no more than 12 % for a wide range of reasonable geometric and physical parameters, and is typically less than 10 %. Overall, the method is widely applicable for characterizing the adhesion parameters between a variety of material pairs, as shown, for example, for a silicon/diamond interface [24].…”

“…The final section presents concluding remarks. Application of the present technique to in situ experimental data is presented elsewhere [24].…”

“…Note that this is simulated data used for purposes of illustration only; to see the method applied to experimental data, refer to Ref. [24]. Using the tip profile from Fig.…”

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