Selective growth of platinum nanolines by helium ion beam induced deposition and atomic layer deposition.

Helium ion beam induced deposition (HIBID) is an attractive technique capable of precise fabrication of nanostructures. However, the damage caused by helium ion irradiation is the major drawback of conventional HIBID. In this study, area-selective atomic layer deposition (ALD) accompanied with the HIBID technique is explored to solve this problem. A platinum (Pt) seed layer was prepared by HIBID with a helium dose much lower than that of the conventional HIBID to reduce the damage due to the bombardment of energetic ions. Afterwards, Pt was selectively deposited on the seed layer to achieve area-selective ALD. Accordingly, the Pt nanolines with a feature size of ~15 nm are accomplished by the area-selective ALD and the HIBID technique under the condition of the damage-free does.

On the approximate zero of Newton method.

A judgment criterion to guarantee a point to be a Chen's approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen's approximate zero may not be a Smale's approximate zero. The error estimate obtained indicated the convergent order when we use /f(x)/ < epsilon to stop computation in software. The result can also be applied for solving partial derivative and integration equations.