The structure of epitaxially grown thin films: a study of niobium on sapphire

Abstract

The x-ray scattering from epitaxially grown films of niobium on sapphire has been measured as the thickness of niobium was varied. For thicknesses d larger than 80 Å, the mean square displacements perpendicular to the growth planes increase as where , and the correlation length for these displacements increases as with . A model is put forward to account for these results in terms of the strains when the film thickness is larger than the distance between the misfit dislocations.

Epitaxial growth of thin films - a statistical mechanical model

“…Normally we would expect that a two-dimensional system such as the corresponding to the experiment in [3] would exhibit logarithmic roughening [1], rather than the power-law roughening indicated by our measurement of the temporal roughening exponent, β. Since the simplest theories state that two-dimensional surfaces are at the critical dimension for which the roughening shows logarithmic behaviour when the diffusive term is present, the power law result is unexpected.…”

“…For small q x (and corresponding to a lengthscale larger than the film thickness d), they were largely independent of q x , but for larger q x , they increased approximately linearly with q x . This was earlier [3] given the interpretation that in the latter case, the displacements with these wavevectors did not propagate through the film, while in the former case, the scattering profile was characteristic of the whole thickness of the film. Another way of seeing this, however, is to say that the distribution of the atomic displacements < u 2 z > depends on the length scale over which it is examined.…”

“…(8) is slowed down, as a result of which the higher-order nonlinear term (whose coefficient is B, in this case) appears to win out. We hope that the relative success of our minimal model in explaining quantitative observations on the sapphire-Nb film analysed in [3] will lead to some of these issues being resolved, and to new theoretical developments in the study of thin films and multilayers , for which the thickness is in the important range between 100 and 10000Å. …”

Diode laser spectroscopy of gaseous HCl

“…It is possibly a consequence of the unusually thick 10 000 Å seed layer. It is known [4] that the width of the transverse scans in thick layers tends to decrease with increasing thickness.…”

“…Using this theory with a modification by Downes [2] for intermediate strains gives the critical thickness of niobium on sapphire as about 70 Å. The structure of niobium layers on sapphire has been well studied [3][4][5][6]. For layers with a thickness of less than 1000 Å, the scattering has a characteristic two-component lineshape for the transverse scans.…”