MONTE CARLO SIMULATION OF DISLOCATION-NUCLEATED ETCHING OF SILICON {111} SURFACES

D. L. Woodraska, J. LaCosse, and J. A. Jaszczak

For more recent results see recent publications

For gif movies of the monte carlo simulations, CLICK HERE.

Silicon structure with [111] aligned vertically.

ABSTRACT

We investigate equilibrium properties and thermal etching of the {111} surfaces of silicon, both with and without perpendicular intersecting dislocations, using Monte Carlo computer simulation. A modified solid-on-solid (SOS) approach is employed which realizes the correct diamond-cubic (DC) crystal structure. Nearest-neighbor interactions (strength J) are incorporated to model the bonding, while the effects of a dislocation are incorporated by the addition of an energy field modeled as a core region and an elastic strained region.

Under equilibrium conditions a roughening transition at temperature kT/J=0.84 is observed through the Kosterlitz-Thouless behavior of the height difference correlation function. A pronounced preroughening transition is found at kT/J=0.362 through a divergences of the surface specific heat and the order-parameter susceptitility.

Dislocations are seen to nucleate the etching process and result in the formation of etch pits. Etch rates and etch-pit morphologies are investigated as a function of the chemical potential driving force for etching, the temperature, and the energy parameters used to model the dislocation.

Equilibrium Flat Surfaces:

Spline-fit surface and contour image of a diamond-cubic {111} surface containing 243 columns of atoms. Simulation was equilibrated for 400,000 Monte Carlo moves per surface site at a temperature kT=0.3J, where J is the bond energy.

Same as above except at a temperature kT=0.4J, where J is the bond energy. This surface is "prerough".

The specific heat of the surface, which is related to energy fluctiations, as a function of temperature is a useful indicator of the degree of surface fluctuations. The fact that the peak near T=0.35J/KB is due to preroughening and not true roughening is deduced from studies of the surface width and the step energy as functions of temperature.

Equilibrium Surfaces with Steps:

Spline-fit surface and contour image of a diamond-cubic {111} surface of 675 columns of atoms containing three "bilayer" steps whose average normal is parallel to [11-2]. Simulation was equilibrated for 10,000 Monte Carlo moves per surface site at a temperature kT=0.1J, where J is the bond energy. The steps were initially all stacked up togeather and spontaneously moved apart from one another.

Same as above except the steps now have an average normal parallel to [-1-12]. Steps of this orientation are unstable and spontaneously microfaceted to lower-energy orientations. Click here for an image of the same surface rotated by 180 degrees about the z axis (B&W).

Perfect Crystal Etching:

A dislocation-free diamond-cubic {111} surface of 11,907 surface sites after 4,600 Monte Carlo moves per site. A chemical potential driving force for etching, deltamu=-0.8J, and the temperature, kT=0.03J, where J is the bond energy, correspond to two-dimensional nucleation limited etching.

Similar etch pits occur on the {111} faces of natural diamond crystals.

This 3-mm diamond is in eclogite from the Udachnaya Mine, Republic of Sakha (Former Soviet Union).

Etch rates as a function of driving force for a dislocation-free {111} surface containing 11,907 sites, at various reduced temperatures. Rates, R, are given in units of bond-lengths (d=0.235nm) per Monte Carlo Sweep (MCS) through the surface.

Dislocation-Nucleated Etching:

A diamond-cubit surface of 11,907 surface sites and a perpendicular dislocation energetically modeled as a 60 degree perfect mixed dislocation in silicon. The core radius is 0.5 nm and the total core energy is 9.5ev/nm. For silicon, J=0.96eV. This surface was produced after 50,000 Monte Carlo moves per site at kT=0.05J and deltamu=-0.5J.

Etch rates as a function of driving force at various temperatures, for a {111} surface 11,907 sites, containing a normally-intersecting dislocation. Rates, R, are given in units of bond-lengths (d=0.235nm) per Monte Carlo Sweep (MCS) through the surface.

CONCLUSIONS AND OUTLOOK

A modified SOS model for Si {111} surfaces, correctly accounting for the DC structure, promises to be an efficient simulation method for investigating equilibrium and dynamical properties of such sufaces. Equilibrium results are in satisfactory agreement with non-SOS models yet allow for substantially larger and longer simulations to be conducted. Dislocations intersecting the surface are shown to nucleate etching and produce pyramidal etch pits. Continuing studies will quantify the surface roughness, roughening temperature, energy barriers for nucleation, etch rates both near and away from dislocations, dynamical roughening, and growth. Work is underway to include surface diffusion, incline the dislocation lines, include surface steps emanating from screw components, dynamically move the dislocation along the surface, and finally, to develop methods to simulate plasma etching of Si surfaces with dislocations.

For more information see: "Monte Carlo Simulation of Dislocation-nucleated Etching of Silicon {111} Surfaces," D. L. Woodraska, J. A. LaCosse, and J. A. Jaszczak, In Modeling and Simulation of Thin-Film Processing, edited by C.A. Volkert, R.J. Kee, D.J. Srolovitz, and M.J. Fluss. Materials Research Society Symposium Proceedings. Spring, 1995 meeting.

D.L. Woodraska and J.A. Jaszczak. manuscripts submitted to Surface Science and Physical Review Letters.

This work was supported in part by the Phillips Laboratory, Air Force Material Command, USAF, through the use of the MHPCC under copperative agreement number F29601-93-2-0001. We are also grateful to Steve Carr, Phil Sweany and the DEC External Research Program for making computer time available.