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Review Article

Measuring and Understanding Contact Area at the Nanoscale: A Review

[+] Author and Article Information
Tevis D. B. Jacobs

Department of Mechanical Engineering
and Materials Science,
University of Pittsburgh,
3700 O'Hara Street,
Pittsburgh, PA 15261

Ashlie Martini

Department of Mechanical Engineering,
University of California Merced,
5200 N. Lake Road,
Merced, CA 95343

Manuscript received September 7, 2016; final manuscript received March 12, 2017; published online November 2, 2017. Editor: Harry Dankowicz.

Appl. Mech. Rev 69(6), 060802 (Nov 02, 2017) (18 pages) Paper No: AMR-16-1069; doi: 10.1115/1.4038130 History: Received September 07, 2016; Revised March 12, 2017

The size of the mechanical contact between nanoscale bodies that are pressed together under load has implications for adhesion, friction, and electrical and thermal transport at small scales. Yet, because the contact is buried between the two bodies, it is challenging to accurately measure the true contact area and to understand its dependence on load and material properties. Recent advancements in both experimental techniques and simulation methodologies have provided unprecedented insights into nanoscale contacts. This review provides a detailed look at the current understanding of nanocontacts. Experimental methods for determining contact area are discussed, including direct measurements using in situ electron microscopy, as well as indirect methods based on measurements of contact resistance, contact stiffness, lateral forces, and topography. Simulation techniques are also discussed, including the types of nanocontact modeling that have been performed and the various methods for extracting the magnitude of the contact area from a simulation. To describe and predict contact area, three different theories of nanoscale contact are reviewed: single-contact continuum mechanics, multiple-contact continuum mechanics, and atomistic accounting. Representative results from nanoscale experimental and simulation investigations are presented in the context of these theories. Finally, the critical challenges are described, as well as the opportunities, on the path to establishing a fundamental and actionable understanding of what it means to be “in contact” at the nanoscale.

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Figures

Grahic Jump Location
Fig. 1

Technological applications where contact area matters, including (a) characterization, (b) nanomanufacturing, and (c) nanodevices. (Image (a) reproduced with permission from Li et al. [18]. Copyright 2011 by American Physical Society. Image (b) reproduced with permission from Garcia et al. [10]. Copyright 2004 by American Chemical Society. Image (c) reproduced with permission from Loh and Espinosa [17]. Copyright 2012 by Nature Publishing Group)

Grahic Jump Location
Fig. 2

Conceptual illustration of contact at different length scales, ranging from the macroscale, where the true contact area can be viewed as the summation of the contacts from many asperities in the interface, to the nanoscale, where individual atoms may contribute and the concepts of true and apparent contact area are less well defined

Grahic Jump Location
Fig. 3

Various property measurements have been used as indirect measures of contact area. (a) The electrical conductance of an atomic-scale gold contact was measured at a temperature of 4.2 K. Reproduced with permission from Agrait et al. [37]. Copyright 2003 by Elsevier. (b) The thermal contact resistance was measured between a flattened silicon probe tip and a tetrahedral amorphous carbon surface. Reproduced with permission from Gotsmann and Lantz [38]. Copyright 2013 by Nature Publishing Group. (c) Normal contact stiffness was measured for three different silicon SPM tips against a fused quartz substrate. Reproduced from Kopycinska-Müller et al. [39]. Copyright 2006 by Elsevier. (d) Both the lateral contact stiffness of the sticking contact and the friction force of the sliding contact have been measured for a silicon nitride tip against a muscovite mica surface. Reproduced from Carpick et al. [40]. Copyright 1997 by American Institute of Physics. (e) The topography of a polymer surface has been measured and used to compute the power spectral density of the surface; the reduction in resolution at small wave vectors is attributed to the size of the contact. Reproduced with permission from Knoll [41]. Copyright 2013 by American Chemical Society.

Grahic Jump Location
Fig. 4

Electron microscopy has been used to image nanocontacts. Panels (a) and (b) show the spontaneous welding of a gold nanojunction. Images reproduced with permission from Merkle and Marks [78]. Copyright 2008 by Elsevier. Panel (c) shows a separate gold nanobridge, prior to failure in tension. Image reproduced with permission from Rodrigues et al. [79]. Copyright 2000 by American Physical Society. Panel (d) shows a dissimilar nanocontact (Pt/Ir on W) that does not spontaneously weld but instead the original interface remains distinct. Image reproduced with permission from Alsem et al. [80]. Copyright 2016 by Cambridge University Press.

Grahic Jump Location
Fig. 5

(a) A TEM image of the tip apex immediately before contact is made, with the crystallographic orientation and loading direction identified. (b) An MD model was made of the lowermost 10 nm of the tip shown in (a) that includes both the crystalline Si and amorphous Si (a-Si) material. (c) A cross-sectional image of the same MD model illustrates the matching of the crystallographic orientation and loading direction. Reproduced with permission from Vishnubhotla et al. [103]. Copyright 2017 by Springer.

Grahic Jump Location
Fig. 7

(a) For an amorphous contact, a significantly different number of atoms are identified as being in contact when measured over short time interval (red plusses) as compared to a long one (open blue circles). The large dashed circle shows the radius determined from the pressure distribution obtained from the long-time interval calculation. Image reproduced with permission from Cheng et al. [62]. Copyright 2010 by American Physical Society. (b) Some authors define an atomistic contact area using the contacting atoms, and an apparent contact area as the convex hull that contains all such atoms. Image reproduced with permission from Mo et al. [36]. Copyright 2009 by Nature Publishing Group. (A color version of this figure is available online.)

Grahic Jump Location
Fig. 6

Various methods are used to calculate contact area from atomistic simulations. The three key steps are: (a) define contact criterion, (b) identify contact atoms, and (c) calculate contact area.

Grahic Jump Location
Fig. 8

Competing theories predict different behavior: (a) single-contact continuum mechanics, (b) multiple-contact continuum mechanics, and (c) atomistic accounting. The graphs in (a), (b), and (c) were created using data from Refs. [95], [35], and [131], respectively.

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