Sharp Tips from Crumples and Capillary Bridges
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Sharp Tips from Crumples and Capillary Bridges Sanjiv Sambandan1,2 Xerox Palo Alto Research Center, 3333 Coyote Hill Road, California, USA 94304 2 Division of Mathematical and Physical Sciences, Indian Institute of Science, India 1
ABSTRACT We describe two techniques to create sharp tips. The first involves the buckling of thin metal films deposited on soft, stretchable substrates. The second involves the formation of narrow necked capillary bridges. INTRODUCTION Sharp tips for field emission are currently manufactured by either photo lithography or molding techniques with low work function materials, or using vertically structured nanopillars made from carbon nanotubes or other metallic or semiconducting nanowires [1], [2]. In this paper we consider two approaches to achieve the low temperature self organization of sharp tips. The first method takes advantage of the sharp features formed of crumples of metal films. The ridges and tips seen in a crumple have an elemental geometric entity - the developable cone (d-cone). We self assemble d-cones using two-dimensional buckling of thin metal films deposited on flexible substrates. The second approach is to use low melting point metals (such as Tin/Lead or Gallium) and create a capillary bridge between the molten metal ‘droplet’ and a foreign micro-tip. The metal is frozen as the bridge is drawn. If the bridge is thin enough, we are left with the formation of a sharp tip. MICRO CRUMPLES FOR SHARP TIPS Theory Crumpling is ubiquitous in nature and occurs due to a combination of bending and stretching, with more bending than stretching [3]. When a foil is crumpled, the energy is focused at vertices and ridges with the focus points providing the reaction to the applied force. These focus points in a crumple lead to the formation of sharp features.
Figure 1: The geometry of a d-cone.
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The developable cone (d-cone) has been identified as a possible building block for the geometry of a crumple [4],[5]. A d-cone can be constructed by taking a circular foil forcing its face into a cylinder of smaller radius via a point force applied at its center. The surface area of the foil is conserved in the confinement by taking the shape of a d-cone as shown in Figure 1. Strong crumpling forces cause folding and creasing creating the main ridge, and left and right flap creases with the top being a sharp crescent. The upper part of the main ridge appears like an inverted elliptic cone with the crescent as its base since it is energetically cheaper to bend the main ridge far away from crescent. The creased left and right flaps appear like upright elliptic cones. The flap cones, unlike the main ridge cone, are wider at the bottom since any folding force results in the flaps moving towards each other without much creasing and at the expense of creasing the main ridge. The minimization of the bending and stretching energies of the main ridge define the radius of the crescent to be proportional to t1/ 3 , where t is the thickness of the foil [6]. Thus crumples on thinner foils have sharper
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