Nanopore fabrication in amorphous Si: Viscous flow model and comparison to experiment

Abstract

Nanopores fabricated in free-standing amorphous silicon thin films were observed to close under 3 keV argon ion irradiation. The closing rate, measured in situ, exhibited a memory effect: at the same instantaneous radius, pores that started larger close more slowly. An ion-stimulated viscous flow model is developed and solved in both a simple analytical approximation for the small-deformation limit and in a finite element solution for large deformations. The finite-element solution exhibits surprising changes in cross-section morphology, which may be extremely valuable for single biomolecule detection, and are untested experimentally. The finite-element solution reproduces the shape of the measured nanopore radius versus fluence behavior and the sign and magnitude of the measured memory effect. We discuss aspects of the experimental data not reproduced by the model, and successes and failures of the competing adatom diffusion model.

Thermal activation and saturation of ion beam sculpting

“…The strong temperature-enhancement of the closing rate, which is readily explained by the adatom diffusion model, cannot arise from a viscous flow model through a temperature-enhanced fluidity: Hutchinson et al 6 have shown that the evolving shape of the pore is affected negligibly by the elasticity and the viscosity in the viscous flow model. A temperature dependence could enter this model through the temperature-dependence of the magnitude of anisotropic deformation induced per unit of fluence.…”

“…5 Moreover, the closing rate of a nanopore displays a "memory effect" wherein it depends not only on the pore's instantaneous size, but also on its initial size. 6 These observations are better explained by another hypothesized mechanism: 1,6 the creation by the ion beam of a very thin, stressed viscous surface layer, where compressive stress caused by the ion beam is relieved; viscous flow of the thin surface layer with a viscosity reduced by ion irradiation acts to close the pore. The viscous flow model explains the restriction to amorphous materials and accounts quantitatively for the memory effect.…”

“…The viscous flow model explains the restriction to amorphous materials and accounts quantitatively for the memory effect. 6 In this article, we report a study of nanopore opening and closure in SiN x , amorphous Si (a-Si), and crystalline Si (c-Si). We observe a critical temperature T c above which pores close, and three temperature regimes.…”

Ion-sculpting of nanopores in amorphous metals, semiconductors, and insulators

“…13 In this model, compressive in-plane stress generated during ion irradiation by anisotropic deformation is relieved within a concurrentlyformed thin viscous surface layer exhibiting radiationenhanced fluidity; the resulting flow of the amorphous viscous layer into the pore causes pore closure. A competing model of adatom diffusion has also been shown to account for various features of the closure of silicon nitride pores under ion irradiation, including a flux pulsing effect and a temperature regime where pore closing rates are strongly Tdependent.…”

“…Our results showing that the sculpting effect is limited to amorphous materials are predicted by an irradiation-induced anisotropic deformation mechanism that occurs only in amorphous materials. 12,13 Samples were prepared as follows, unless stated otherwise: (1) fabrication of 50 mm μ 50 mm free-standing membranes by a series of photolithography and wet etching steps, (2) milling of pores in the free-standing membranes using a 50 keV Ga 2+ focused ion beam (FIB) machine, and (3) low energy argon irradiation.…”