We study shape relaxation of a two-dimensional fractal aggregate, during annealing after the rapid crystallization on a substrate. The edge length of the aggregate decreases with time in a power law with the exponent ( d -1 -D)/(@ + l), where d = 2 is the spatial dimension, D is the fractal dimension and p depends on the relaxation mechanism as to be 3 , 2 and 1 for edge diffusion, surface diffusion and edge kinetics, respectively. With Monte Carlo simulation, we c o n f i the predicted exponents for the diffusion-limited aggregation with two different diffusion mechanisms. 0 Les Editions de Physique * * * This work is supported by the Grant from the Ministry of Education, Science and Culture (No. 04227108). YS and MU benefited by the interuniversity cooperative research program
A clean tungsten (W) tip apex with a robust atomic plane is required for producing a stable tunneling electron emission under strong electric fields. Because a tip apex fabricated from a wire by aqueous chemical etching is covered by impurity layers, heating treatment in ultra-high vacuum is experimentally known to be necessary. However, strong heating frequently melts the tip apex and causes unstable electron emissions. We investigated quantitatively the tip apex and found a useful method to prepare a tip with stable tunneling electron emissions by controlling electron-bombardment heating power. Careful characterizations of the tip structures were performed with combinations of using field emission I-V curves, scanning electron microscopy, X-ray diffraction (transmitted Debye-Scherrer and Laue) with micro-parabola capillary, field ion microscopy, and field emission microscopy. Tips were chemically etched from (1) polycrystalline W wires (grain size ∼1000 nm) and (2) long-time heated W wires (grain size larger than 1 mm). Heating by 10-40 W (10 s) was found to be good enough to remove oxide layers and produced stable electron emission; however, around 60 W (10 s) heating was threshold power to increase the tip radius, typically +10 ± 5 nm (onset of melting). Further, the grain size of ∼1000 nm was necessary to obtain a conical shape tip apex.
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