Journal of the Mechanics and Physics of Solids 51 (2003) 1371 – 1394 www.elsevier.com/locate/jmps Analysis of dislocation nucleation from a crystal surface based on the Peierls–Nabarro dislocation model Guanshui Xu * , Chuanli Zhang Department of Mechanical Engineering, University of California, Riverside, CA 92521, USA Received 18 October 2002; accepted 3 April 2003 Abstract Dislocation nucleation from a stressed crystal surface is analyzed based on the Peierls– Nabarro dislocation model. The variational boundary integral approach is used to obtain the proles of the embryonic dislocations in various three-dimensional nucleation congurations. The stress-dependent activation energies required to activate dislocations from their stable to unstable saddle point congurations are determined. Compared to previous analyses of this type of problem based on continuum elastic dislocation theory, the present analysis eliminates the uncertain core cuto parameter by allowing for the existence of an extended dislocation core as the embryonic dislocation evolves. Moreover, atomic information can be incorporated to reveal the dependence of the nucleation process on the prole of the atomic interlayer potential as compared to continuum elastic dislocation theory in which only elastic constants and Burgers vector are relevant. Finally, the presented methodology can also be readily used to study dislo- cation nucleation from the surface heterogeneities such as cracks, steps, and quantum structures of electronic devices. ? 2003 Elsevier Science Ltd. All rights reserved. Keywords: Dislocation nucleation; Surface; Activation energy; Peierls–Nabarro dislocation model; Atomic interlayer potential 1. Introduction The fundamental mechanisms of dislocation nucleation from a crystal surface have been of considerable interest in a wide variety of scientic and engineering problems. One example is the growth of high-quality strained heteroepitaxial layer structures ∗ Corresponding author. Tel.: 909-787-2497; fax: 909-787-2899. E-mail address: gxu@engr.ucr.edu (G. Xu). 0022-5096/03/$ - see front matter ? 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0022-5096(03)00067-X