Evolving material structures of small feature sizes Z. Suo* Mechanical and Aerospace Engineering Department, and Princeton Materials Institute, Princeton University, Princeton NJ 08544, USA Abstract Modern electronic and photonic devices are solid structures of small feature sizes. During fabrication and use, diusive processes can relocate matter, so that the structures evolve over time. A ®lm may break into droplets, and a conducting line may grow cavities. Stress and electric current have long been understood as forces that drive the changes. Evidence has accumulated that, while important, these forces are insucient to account for diverse experimental phenomena, suggesting forces of other physical origins also operate. In a structure, collective actions of atoms, electrons, and photons contribute to the free energy. When the structure changes its con®guration, the free energy also changes. The free energy change de®nes a thermodynamic force which, in its turn, drives the con®gurational change of the structure. This article illustrates the concepts with speci®c phenomena. Emphasis is placed on physical descriptions of forces of diverse origins, including elasticity, electrostatics, capillarity, electric current, composition gradient, photon dispersion, and electron con®nement. The eects of some of these forces are particularly signi®cant in structures of small feature sizes, say, between a few to hundreds of nanometers. Insights into these forces are increasingly valuable as devices miniaturize. This area of research holds great promises for solid mechanics innovation. # 1999 Elsevier Science Ltd. All rights reserved. 1. Introduction A solid structure, such as a ®lm on a substrate, is not a peaceful object. Inside it atoms jiggle all the time. Most atoms vibrate around their equilibrium positions with amplitudes smaller than the atomic spacing. Occasionally, an atom moves so violently that it jumps into a dierent equilibrium position. If such jumps are random, with equal probability for all atoms in all directions, their collective eects will average out: no change will be perceived at gross length and time scales. If the jumps are not completely random, perceptible changes will occur. For example, the ®lm on the substrate may break into many droplets. A particular jump is more likely than other jumps if it lowers the free energy of the structure. International Journal of Solids and Structures 37 (2000) 367±378 0020-7683/00/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S0020-7683(99)00100-6 www.elsevier.com/locate/ijsolstr * Tel: +1-609-258-0250; Fax: +1-609-258-6123. E-mail address: suo@princeton.edu (Z. Suo)