Monte Carlo Simulation of Dislocation-Nucleated Etching of Silicon {111} Surfaces
- PDF / 2,255,752 Bytes
- 6 Pages / 414.72 x 648 pts Page_size
- 21 Downloads / 176 Views
[7]. MC simulations have also been used to study growth on facets of perfect crystals [8], and facets with intersecting screw dislocations [9,10]. MC studies of crystal surface etching have not been carried out to the same extent as equilibrium and growth simulations. These studies have primarily considered the dissolution kinetics and morphology of perfect crystal faces [11], steps and edges [12]. Some studies of dissolution have also been done on surfaces intersecting screw dislocations [7], focusing on the geometrical effect of the resulting perpetual step and the resulting growth or etch spirals. Gilmer has performed MC simulations on a simple cubic crystal with a small columnar hole perpendicular to the surface that serves as a site for step nucleation during etching [13], but effects of elastic and core energies of dislocations on etching were not considered. Liu, Van der Eerden, and Bennema [14] have considered the effects of dislocation energies on the opening and closing of a hollow dislocation core (with the dislocation axis normal to the surface) using MC simulation of a (001) surface of a simple cubic crystal using the SOS approximation. Based on earlier work [15], an effective, cylindrical, strain-energy field was employed. In the presence of the dislocation strain-energy field, etch rates and the opening or closing the dislocation core were investigated under various chemical potential driving forces, temperatures, and strain-energy densities.
COMPUTATIONAL METHOD In order to focus on statistical mechanical and kinetic behavior, and in order to simulate relatively large surfaces efficiently, we have developed a solid-on-solid (SOS) model for {111 I surfaces of crystals with diamond cubic (DC) structure. While SOS models technically exclude voids and vacancies, such are included to a degree in our model. The DC structure is divided into columns of atoms, each with a specified height defining the surface. For a [111 ] DC surface, it is natural to divide the structure into three distinct types of columns, A, B, and C (Fig. 1). Each column can only terminate in certain "sheets", depending on the type of column and the type of sheet (a, b or c), where a sheet of atoms is separated from another by a layer of bonds parallel to (Fig. 2). For example, should sheet n in Fig. 2 be composed of A and C type atoms, sheet n- I would be composed of B and C types and sheet n+l would be composed of A and B types. Depending on which sheet a column of atoms of a particular type terminates during any point of the simulation, one can determine the nature and direction of nearest-neighbor bonding. Periodic border conditions are used throughout to minimize finite-size effects.
G B
Fig. 1. Schematic of the silicon structure projected on (111). Each circle represents a solid-on-solid column of atoms at heights dictated by the diamond cubic structure, grouped according A, B, and C types.
Metropolis MC is implemented as follows [16,171. A single MC step consists of selecting a surface site (in either a random or a staggered
Data Loading...
