Faster simulations of step bunching during anisotropic etching: formation of zigzag structures on Si(1 1 0)

We propose that the formation of zigzag structures on Si(1 1 0) during anisotropic etching is mainly a result of the formation of inhomogeneous regions in the etchant due to diffusion phenomena. In the same way as the presence of these etchant inhomogeneities results in step bunches on miscut (1 1 1) surfaces, it results in zigzags on the (1 1 0) surface. To support this proposal, we present an incremental activity monitoring (IAM) method for the simulation of step bunching using a kinetic Monte Carlo scheme. For stepped (1 1 1) surfaces, comparison with a previous step density monitoring (SDM) method shows that IAM is typically faster by one order of magnitude and is well suited for the simulation of step bunching. By applying IAM to (1 1 0), the formation of zigzag structures can be simulated, strongly suggesting that the morphology of this surface is dominated by the formation of inhomogeneous regions close to the surface in the etchant phase. (Some figures in this article are in colour only in the electronic version)

[1]  A. B. Bortz,et al.  A new algorithm for Monte Carlo simulation of Ising spin systems , 1975 .

[2]  Risto M. Nieminen,et al.  Anisotropic wet chemical etching of crystalline silicon : atomistic Monte-Carlo simulations and experiments , 2001 .

[3]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[4]  M. Kotrla,et al.  Theory and simulation of crystal growth , 1997 .

[5]  Irena Zubel,et al.  Etch rates and morphology of silicon (h k l) surfaces etched in KOH and KOH saturated with isopropanol solutions , 2004 .

[6]  M. Shikida,et al.  Surface roughness of single-crystal silicon etched by TMAH solution , 2001 .

[7]  P. Maksym.  Fast Monte Carlo simulation of MBE growth , 1988 .

[8]  A. J. Nijdam,et al.  Micro-morphology of single crystalline silicon surfaces during anisotropic wet chemical etching in KOH: velocity source forests , 2001 .

[9]  P. Allongue,et al.  Digital computation and in situ STM approach of silicon anisotropic etching , 1997 .

[10]  Mitsuhiro Shikida,et al.  Micromorphology of single crystalline silicon surfaces during anisotropic wet chemical etching in KOH and TMAH , 2001 .

[11]  Mitsuhiro Shikida,et al.  Improvement in smoothness of anisotropically etched silicon surfaces: Effects of surfactant and TMAH concentrations , 2006 .

[12]  M. Elwenspoek,et al.  Silicon Micromachining , 1998 .

[13]  M. Hines,et al.  Etchant anisotropy controls the step bunching instability in KOH etching of silicon. , 2004, Physical review letters.

[14]  J. L. Blue,et al.  Faster Monte Carlo simulations. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.