(110) peak of the x-ray diffraction pattern of the granular niobium films of the studied samples. The sample parameters are listed in Table I.
HRTEM images. (a) Diffraction rings of sample 9 showing the bcc structure with lattice parameter of 3.33 . (b) Dark field image of sample 9 showing the typical grains in this sample. (c) Cross-sectional TEM image of sample 2 showing two different sets of planes corresponding to two different grains. The two corresponding regions have been marked by white lines to assist the reader. (d) Cross-sectional image of sample 2 near the substrate-film interface showing the presence of amorphous oxide at the interface. The inset in this micrograph is a lower resolution TEM image with oxide layer visible as a 2 nm thick bright band.
Variation of lattice parameter with thickness for grain sizes of (a) 7.2 and (b) 8.5 nm. Solid lines show the fitting to Eq. (1) with the fitting parameters listed in Table II.
Variation of lattice parameter in thick film limit. The solid squares show the lattice parameter in thick film limit as a function of grain size . The solid curve shows fitting.
Variation of and with .
Sample parameters for niobium thin films.
Fitting parameters for the thickness dependence of the lattice parameter.
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