Kinetic Monte Carlo Simulations of Dislocation Etch-Pits
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KINETIC MONTE CARLO SIMULATIONS OF DISLOCATION ETCH-PITS Daniel N. Bentz and Kenneth A. Jackson Department of Materials Science and Engineering, University of Arizona 4715 E Fort Lowell Road Tucson, AZ 85712 Abstract Chemical mechanical polishing and stress corrosion cracking result from chemical attack at stressed regions. To better understand the combined effects of chemical attack and stress, a kinetic Monte Carlo (kMC) study of the formation of dislocation etch pits is being pursued. In the simulations, atoms from a diamond cubic lattice are irreversibly removed with a probability which depends on an atom’s number of nearest neighbors as well the local stress developed from its physical location with respect to a dislocation in the lattice. In accordance with experimental observations, both faceted and non-faceted dislocation etch-pits have been observed. Simulations have been performed for various values of the strength to the etchant attack and the magnitude of the stress produced by the dislocation. Introduction Chemical mechanical polishing (CMP) is now widely used in the semiconductor industry. CMP, stress corrosion cracking and dislocation etches share the common feature that the rate of chemical attack depends on the local stress level. In both CMP and stress corrosion cracking the combined effect of chemical attack and mechanical stress is an order of magnitude greater than either acting alone. In this project, we model the formation of dislocation etch pits by using kinetic Monte Carlo (kMC) simulations in order to study the interaction of stress on etching process. Dislocation etches have been used extensively to evaluate the perfection of crystals. [1, 2, 3] There have also been a few simulations of etch pit formation which have focused on the geometry of the crystal around the dislocation. [4, 5, 6] These simulations were performed without including stress effects. But experimental dislocation etch pits are often non-crystallographic, and most are deep, unlike the shallow pits which would be expected from spiral dissolution. This study focuses on the effects of stress rather than lattice geometry around a dislocation. Simulation Description We are implementing a kinetic Monte Carlo (kMC) algorithm to simulate dislocation etching on a silicon surface. The dislocation is assumed to be straight and perpendicular to the surface. Atoms are irreversibly removed from the lattice at random with a weighted probability depending on the number of nearest neighbors as well as their physical location in the lattice. This probability is expressed as in the rate expression: ν− = νo e−n(φ−E(n,r))
(1)
P2.5.1
Here ν− is the frequency that atoms are removed from the solid and νo is a pre-exponential factor. E is the geometric energy representing a weakening of the bonds. The strength of the unstressed bond in the etching solution is represented by φ. n is the number of nearest neighbor solid atoms and r is the distance from the center of the dislocation. At the interface the concentration of the etchant is uniform and
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