... M. E. Harper, and David A. Smith. Citation: J. Vac. Sci. Technol. A 5, 1792 (1987); doi: 10.1116/1.574498. View online: http://dx.doi.org/10.1116/1.574498.
Summary Abstract: Theory of thinfilm orientation by ion bombardment during deposition R. Mark Bradley, James M. E. Harper, and David A. Smith Citation: J. Vac. Sci. Technol. A 5, 1792 (1987); doi: 10.1116/1.574498 View online: http://dx.doi.org/10.1116/1.574498 View Table of Contents: http://avspublications.org/resource/1/JVTAD6/v5/i4 Published by the AVS: Science & Technology of Materials, Interfaces, and Processing
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Summary Abstract: Theory of thin-film orientation by ion bombardment during deposition R. Mark Bradley, James M. E. Harper, and David A. Smith IBM T. J. Watson Research Center, Yorktown Heights, New York 10598
(Received 18 September 1986; accepted 3 November 1986)
Thin-film deposition by evaporation or sputtering often produces a polycrystaUine film with a pronounced fiber texture, in which all grains share a crystallographic axis oriented perpendicular to the plane of the substrate.! The grains typically have a random distribution of orientations in the azimuthal direction. Recent experiments by Yu et al. 2 •3 on niobium films have demonstrated that significant azimuthal order can be induced by off-normal-incidence ion bombardment applied during growth. The crystal orientations selected by the ion beam were found to be channeling directions between (110) planes. We have developed a theory of thin-film orientation by off-normal ion bombardment applied during deposition. (For details, see Ref. 4.) The selection mechanism for grain orientation is taken to be the difference in sputtering yields between grains which are oriented so that they channel the ion beam and those which are not. This difference-which is as high as a factor of 5 in some materials 5-1eads to a larger growth rate for aligned grains than for misaligned grains, and hence to overall orientational order. As the film grows, it can be described by the fraction of material at the surface that channels the ion beam x (t) . We find that the time development of the orientational order at the surface is governed by the differential equation4 (1)
wherey= (de/db )r. Here ris the rate that the film thickness grows in the absence of ion bombardment, r is the ion/atom arrival rate ratio, and fl is the fraction of azimuthal orientations ifJ which channel the ion beam. The parameters de and db are material dependent and must be taken from experiment. Roughly speaking, de is the thickness of film which must be deposited for the steady state to be approached in the absence of ion bombardment, and db/ris the time needed for the steady state to be approached in the limit of perfect epitaxy with r = 1. On physical grounds one would expect the degree of orientational order far from the substrate in a thick film to be spatially unvarying and independent of the initial degree of order in the film. This is indeed the case: Eq. (1) shows that xU) converges to the t---> 00 limit xoo
=
[y -
1
00
7=
[(y-l)2+4Ay]-!/2d.ir
is a measure of how long the film must be grown before the asymptotic ordering is approached. Like Xoc , l' is independent of x (0). The coefficient A does depend on x (0), however. Perhaps the most surprising aspect of our expression for the relaxation time is that for A < ~j there is a peak in l' as a function of r. The peak occurs at y = 1 - 2A, where r achieves the valueHfl(1 - Ii)] - lf2d e lr. In real systems, Ii should be rather small, so the peak will be quite pronounced. It would be very interesting to observe this peak experimentally. Our theory has a number of implications for the efficacy of thin-film orientation by ion bombardment. For r greater than some critical value r*, sputtering will remove material more rapidly than it is being deposited. If db/de is greater than r* and A is small, ion bombardment cannot induce ap-
I.Or-------------------, 6=1.0
.
9
+ ICY::'" 1)2 +- 4.:iY ]12y
for all x(O) in the interval [0,1]. We expect Ii to be small in most systems. For Ii~ 1, Fig. 1 shows that as the ion/atom flux ratio r is increased from zero, the ion beam is unable to induce appreciable orientational order until r approaches the critical value db / de. As r is increased further, the asymptotic order x increases rapidly until it saturates at 1 for r~dhlde' Physically, this 00
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means that the ordering influence of the ion beam has little effect until it becomes strong enough to prevail over the disorder due to imperfect epitaxy. The observations of Yu et al.2,3 are in qualitative agreement with this prediction. In particular, their data for x rise slowly as ris increased from zero until, as a critical value of r is approached, x'" begins to grow more rapidly. Equation (1) is easily solved for x(t). For large enough times t, the degree of order at the film surfacex(t) converges exponentially towards Xoo , i.e., xU) -Xoo + Ae - Ilr. The relaxation time
J. Vac. Sci. Techno!. A 5 (4), Jul/Aug 1987
o
2
FIG. 1. Plot of the asymptotic degree oforientational order x~ vsy = (del db )r, for several values of A.
0734-2101/87/041792-02$01.00
@ 1987 American Vacuum Society
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