Ten million atom multiresolution molecular-dynamics simulations are performed on parallel computers to determine atomic-level stress distributions in a 54 nm nanopixel on a 0.1 m silicon substrate. Effects of surfaces, edges, and lattice mismatch at the Si͑111͒/Si 3 N 4 ͑0001͒ interface on the stress distributions are investigated. Stresses are found to be highly inhomogeneous in the nanopixel. The top surface of silicon nitride has a compressive stress of ϩ3 GPa and the stress is tensile, Ϫ1 GPa, in silicon below the interface. © 1998 American Institute of Physics.
͓S0003-6951͑98͒00116-8͔Sub-100 nm pixel sizes pose special challenges in Si electronics. In this regime, the significance of spatial inhomogeneities in the dopant distribution to the device characteristics is being increasingly appreciated.1 Spatially nonuniform stresses induced by such nanoscale pixellation may have profound impact 2 -rapidly varying stresses at and near edges may lead to defect formation or even initiate a crack. Understanding the stress distribution is therefore essential in the design of nanoscale devices.On larger (Ͼ1 m) length scales, edge stresses in Si/SiO 2 and Si/Si 3 N 4 have been examined utilizing the framework of linear elasticity and finite-element ͑FE͒ simulations. 3,4 In nanoscale devices, however, the surface-tovolume ratio is so large that the influence of surfaces, edges, and corners on elastic properties become significant. In addition, chemical bonding at the Si/Si 3 N 4 interface introduces types of stresses not present in silicon or silicon nitride materials. These effects have to be included in constitutive relations to achieve realistic description of nanoscale devices in the FE approach. An alternative approach is to use molecular-dynamics ͑MD͒ simulations where surface and interface bonding effects are explicitly included at the atomistic level. With recent progress in parallel computer architectures, it has now become possible to carry out direct atomistic simulations for submicron structures with realistic descriptions of the materials involved. In particular, largescale MD simulations have proven to be useful in the study of dynamic fracture.5 MD simulations provide spatially resolved stress distributions on the length scales not accessible to experimental techniques, such as MicroRaman spectroscopy.6 Such numerical experiments can be used to establish the validity of constitutive relations used in FE simulations, in particular the treatment of surface/interface/ edge effects.In this letter, the results of a ten million atom moleculardynamics study of atomic stress distribution in a Si/Si/Si 3 N 4 nanopixel are reported. The simulations were performed on 128 processors of the 256-processor HP Exemplar at Caltech requiring a total of 180 h of computational time. We have considered a crystalline Si 3 N 4 film forming a coherent Si͑111͒/Si 3 N 4 ͑0001͒ interface 7 with the Si mesa. An interatomic potential model for the Si/Si 3 N 4 interface has been developed using the charge transfer values computed from...