Theory of thin-fUm orientation by ion bombardment ...

4 downloads 0 Views 436KB Size Report
R. Mark Bradley, James M. E. Harper, and David A. Smith. IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598. (Received 24 ...
Theory of thin-fUm orientation by ion bombardment during deposition R. Mark Bradley, James M. E. Harper, and David A. Smith IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598

(Received 24 June 1986; accepted for publication 5 September 1986) We study the development of orientationaI order in thin films grown with off-normal incidence ion bombardment during deposition. The overall orientational order in our model results from the dependence of the sputtering yield on grain orientation. We demonstrate that the degree of orientational order at the surface of a thick film grows slowly with increasing ion flux until, at a critical value of the flux, it begins to rise more steeply and then saturates at its maximum value. The time needed to approach the thick-film limit displays a peak as the ion flux is varied. We compare our work with the experimental results ofYu et al. [App!. Phys. Lett. 47, 932 (1985) 1and use our results to show how the deposition technique can be optimized.

I. INTRODUCTION

Thin-film deposition by evaporation or sputtering methods often produces a polycrystalline film with a nonrandom distribution of grain orientations. I Pronounced fiber textures are commonly found, even on amorphous substrates, in which all film grains share a crystallographic axis oriented perpendicular to the plane of the substrate. For example, bcc films often have a (110) preferred orientation, and fcc films have a (Ill) preferred orientation. I These films typically have a random distribution of orientations in the azimuthal direction. Recent experiments by Yu et aU-4 and Cuomo et al. 5 have demonstrated that the azimuthal distribution can be restricted greatly by off-normal incidence ion bombardment applied during film growth. Niobium films deposited by ion-beam sputtering showed the usual (110) fiber texture when deposited in the absence of ion bombardment and had no azimuthal order. However, films deposited with simultaneous 200-eV Ar+ -ion bombardment at 20· from the glancing angle showed increasing azimuthal order as the ion/atom flux ratio was increased. The crystal orientations selected by the ion beam were found to be channeling directions between (110) planes. In this paper we present a theory of thin-film orientation by ion bombardment during deposition which accounts for the essential features of this ion-beam alignment effect. The theory gives the asymptotic degree of orientational order as a function of the ion/atom flux ratio r, and also the time needed to approach this state. We show that the asymptotic degree of order increases slowly as r is increased until, near a critical value of r, it rises more rapidly and then saturates at its maximum value. Under some conditions, the critical value of r cannot be reached because at this point more material is resputtered than is deposited, so ion bombardment will not be a practical means of alignment. We also show that the convergence time is not a monotonicailly decreasing function of the ion/atom flux ratio, but instead has a peak at the critical value of r. Our theoretical framework suggests several. strategies to follow in optimizing the effects of ion bombardment on thin-film orientation. II. FORMULATION OF THE THEORY

Yu et al. 2-4 have argued cogently that the selection mechanism for grain orientation is the difference in sputter4160

J. Appl. Phys. 60 (12), 15 December 1986

ing 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 materials6 leads to a larger growth rate for aligned grains than for misaligned grains, and hence to overall orientational order. Although other possibilities have been considered for the ordering mechanism,2-4 we shaH assume that the resputtering mechanism is dominant. As will be seen, this assumption leads to results consistent with experiment. Our microscopic theory depends on four material-dependent parameters which must be taken from experiment or from a detailed microscopic calculation. Roughly speaking, one of the parameters measures the extent to which the resputtering yields from aligned and misaligned grains differ. Another characterizes the degree of epitaxy in the absence of ion bombardment, and the third is the total acceptance angle of the channeling directions. The fourth and final parameter is the value of r at which the rates of deposition and resputtering are equal. Later in the paper we shall show how these parameters can be measured. The deposition and resputtering processes took place concurrently in the experiments ofYu et al. 2-4 In formulating a theory, however, it is simpler if we instead. build up the film in a layer-by-layer process in which deposition and resputtering alternate. Thus, we first deposit a layer of thickness d with the ion beam turned off. The layer thickness de is to b~ much larger than the interatomic spacing, but small compared to the length characterizing the variation of orientationalorder. We then tum on the ion beam long enough for r ions to impinge on the layer for every atom deposited. Another layer is then deposited and this is in tum bombarded, and so on. It is intuitively dear that this discrete process of alternating deposition and resputtering will coincide with the real continuous process with ion/atom arrival rate ratio r in the limit de - 0, provided that the parameters are given the correct de dependence. This will be verified in detail in the foHowing section. We shall limit ourselves to studying deposition problems in which one of the crystal axes of the deposited material is locked parallel to the normal to the substrate surface. (Niobium is an example. 2-4) The crystallites then have one remaining degree offreedom, namely, the angle t/J between the projections of a reference crystal axis and the direction of the incident beam onto the substrate. Suppose that the last

0021-8979/86/244160-05$02.40

@ 1986 American Institute of Physics

4160

Downloaded 08 Oct 2010 to 129.82.140.57. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions

layer to be deposited has a fraction x (ifJ) of its volume in the orientation ifJ after resputtering. We shall assume that the layer deposited Over this has the fraction x (ifJ) in the orientation ifJ before resputtering, where x(ifJ) = (l-A)X(ifJ)

+ (A/217).

(1)

Here A is a parameter which characterizes the tendency for newly deposited crystallites to be aligned with the grains beneath them. Perfect epitaxy corresponds to the limit A = 0, whereas random orientation of new grains occurs for A = 1. Note that x is normalized to one, as it should be. We shall also assume that the ion/atom arrival rate ratio r and the ion-beam energy are low enough that (i) the new layer is not completely removed, and (ii) the ion bombardment has a negligible effect on the underlying layers. This means that the state of a layer is completely determined by that of its immediate predecessor, and that its structure is fixed once a new layer is deposited on top of it. Resputtering induced by ion bombardment will leave behind a certain fraction f( ifJ) of the material in the newly deposited layer which is in the orientation ifJ. The fraction of the new layer in the orientation

yt /2d.)

$

+ [1 -

= [(y - 1)2

+ 4Ay]- 1/2de ly

(27)

1.0,------------------,

+ 1-

y

+ 2yx(0)

(n)

+ 2yx(0) ]tanh($yt /2d.) 1)2 + 4Ay}1/2. We shaH first study Y

where (P== [(y the t -+ 00 limit of this solution, and then the rate of convergence to the asymptotic steady state. 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 type of substrate. s This is indeed the case: Eq. (23) shows that xU) converges to the t-+ 00 limit (23) for aU x(O) in the interval. [0,1]. Two limits are of interest here. For smally, 4162

(26)

J. Appl. Phys., Vol. 60. No. 12, 15 December 1986

8

"

o

2

3

y-

FIG. 1. Plot of the asymptotic degree of orientational order

x~

vs

y = (d,ldb)r for several values of fl. Bradley, Harper, and Smith

4162

Downloaded 08 Oct 2010 to 129.82.140.57. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions

is a measure of how long the film must be grown before the asymptotic ordering is approached. Like x"" , 7 is independent of x(O). The coefficient A does depend on x(O), however. As shown in Fig. 2, the relaxation time 7 is a decreasing function of b. for fixed r. This is to be expected since as b. is increased, the ion beam becomes more effective in inducing orientational order. For y< I, (28) rr/de = 1 + (1 - 2b.)y + O(y), and in particular, 7 = d.ly for r = O. Thus, defy is simply the relaxation time when the ion beam is turned off. In the large y limit, on the other hand, yT/de =y-] + (1- 2b.)y-2 + O(y-3). (29)

Therefore, Y7 (1 - 2b.)db/de. V. DISCUSSION

Weare now in a position to discuss the significance of the parameters b., r*, de' and db and to suggest means to measure them. This task is simple for the first two of these parameters. By definition, b. is the fraction of orientations ifJ which channel the ion beam. It can be determined simply by extrapolating Xoo to the limit r-+O. The parameter r* is the ion/atom arrival rate ratio where deposition and resputtering balance to give no net deposition or removal; it can be

found using the fact that the fraction of material resputtered is r/r* in the steady state. The length de is the thickness of film which must be deposited for the steady state to be approached in the absence of ion bombardment, since y7 = de when r = O. Thus, by studying the approach of the film surface to its final state with the ion beam turned off, de can be determined. Since convergence can only be observed if the initial and final states differ, care must be taken to prepare an initial state which is not too close to the randomly oriented final state. One way this could be achieved is by first depositing a layer with the ion beam turned on, and then depositing on top of this layer with the ion beam turned off. The length db was defined by the relation

p = 1 - f2/f]

= (dJd b )r.

Therefore, it measures the extent to which the resputtering yields from aligned and misaligned material differ. Since y7 = db/rwhen de = 00, the time needed for the steady state to be approached in the limit of perfect epitaxy is db/y when r = 1. This does not provide a practicable means of measuring db' because de and db cannot be varied independently. However, db can be determined by performing a two-parameter fit to data for x as a function of r. This fit would yield values for b. and dJd b. Combining this with the value of de found by convergence measurements would then yield db' The observations of Yu et at. 2-4 are in qualitative agreement with our theory. In particular, their data for x"" rise slowly as r is increased from zero until, as a critical value of r is approached, x begins to grow more rapidly. (See Fig. 3.) Although there is considerable scatter in the data, we can see that b.....,

a.J

0.21-

0

I

0.0 0.0

• 0.1

• -:• ... •• 0.2

0.3

0.4

0.5

CURRENT DENSITY AT SUBSTRATE (mAlcm 2 )

a

2

3

FIG. 2. Plot of the relaxation time 1'vsy = (d,ld b )rforseveral values of fl.. 4163

J. Appl. Phys., Vol. 60, No. 12, 15 December 1986

0.0 0.5 1.0 1.5 ION/ATOM ARRIVAL RATE RATIO

FIG. 3. The degree of orientational order in Nb films plotted vs the ionl atom arrival rate ratio (from Ref. 3). Bradley, Harper, and Smith

4163

Downloaded 08 Oct 2010 to 129.82.140.57. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions

Yu et af.2-4 also found that aligned Nb films several thousand angstroms thick could be grown without bombardment on thin layers of niobium which had been deposited with ion bombardment. This shows that de was at least several thousand A. This was true for db as well, because de and db were comparable in these experiments. Since de and db were large compared to the interatomic spacing, we are indeed justified in using our macroscopic theory to interpret these results. Several interesting avenues for experiment remain to be explored. By studying the approach of a growing film to its steady state, the prediction that x (t) converges exponentially to x'" could be checked. Moreover, it would be exciting to verify that the convergence time 1" has a peak as r is varied. Finally, a basic assumption of the theory is that the dominant ordering mechanism is the difference in resputtering yields from aligned and misaligned crystallites. The validity of this assumption could be tested by measuring the azimuthal dependence of the sputtering yield from the (lID) surface of a niobium crystal. To our knowledge, all work done to date on sputtering from crystals has probed the dependence of the sputtering yield on the polar angle alone. 6 Our theory has a number of implications for the efficacy of thin-film orientation by ion bombardment. As we commented above, if db/d. is greater than r* and a is small, ion bombardment cannot induce appreciable orientational order. To ensure that db/d. is much smaJjer than r*, we should look for circumstances in which the resputtering yields from channeling and nonchanneling orientations differ markedly, and in which epitaxy is good. If db/d. «r*, the increase in x '" obtained by an increase in r becomes smaller and smaller once r exceeds db/db' Moreover, this increase in order is bought only at the expense of slower and slower film growth. A value of r several times larger than db / de will yield a wellordered film and still give a reasonable deposition rate. Finally, values of r in the immediate vicinity of db/d. should be avoided since the convergence time 1" may be excessively long. Several variables can be adjusted in an experiment to optimize orientational order. The epitaxial coherence length de can be modified by changing the substrate temperature. The parameters a, db' and r* are functions of the angle e between the beam and the surface, the ion species, and the ion energy. As an example, consider the effect of changing the ion species. 9 An ion which is too large will not channel well, so a will be small. There also will be little difrerence between the resputtering yields from al.igned and misaligned materi.al, so db win be large. To maximize x'" ' therefore, the

4164

J. Appl. Phys., Vol. 60, NO.12,15 December 1986

smallest ions which do not react chemically with the substrate should be employed.

VI. CONCLUSIONS In this paper a macroscopic theory of thin-film orientation by ion bombardment has been developed. We found that if the total acceptance angle of the channeling directions is small, the asymptotic degree of orientational order x'" grows very slowly as a function of the ion/atom flux ratio r until r reaches the critical value db / d., The steady-state degree of order x", then rises more rapidly and tends asymptotically to its maximum value. In some systems this critical value of r will not be attainable, however, since the material may be resputtered more rapidly than it is deposited. when r = db/de' The orientational order at the surface was shown to converge exponentially toward the asymptotic steady state. Interestingly, the associated convergence time has a peak in the vicinity of the critical value of r. From a practical standpoint, our results indicate that values of r several times larger than db/d. must be employed if good orientational order is to be obtained. Ion/atom arrival rate ratios close to db/d. are to be avoided, moreover, because the time needed to reach the steady state may be excessively long. Finally, experiments to test the theory and determine the values of its parameters were suggested. ACKNOWLEDGMENT

We would like to thank P. N. Strenski for helpful discussions.

's. Mader, in Handbook of Thin Film Technology, edited by R. Giang and L. I. Maissel (McGraw-Hill, New York, 1970). 2L. S. Yu, J. M. E. Harper, J. J. Cuomo, and D. A. Smith, Appl. Phys. Lett. 47, 932 (1985). 3L. S. Yu, J. M. E. Harper, J. J. Cuomo, and D. A. Smith, 1. Vac. Sci. Technol. A 4, 443 (1986). 4L. S. Yu, M. S. thesis, Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA (1985). ~1.

1. Cuomo, C. R. Guarnieri, R. H. Hammond, 1. M. E. Harper, S. R. Herd, and D. S. Yee, IBM Tech. DiscI. Bull. 25, 3331 (1982). "For a review, see H. E. Roosendaal, in Sputtering by Particle Bombardment I, Vol. 47 of Topics in Applied Physics, edited by R. Behrisch (Springer, Berlin, 1981). 7Since the layer thickness after resputtering d, varies with I, it is simplest to use the time rather than the film thickness as the continuous independent variable. 80f course x ~ will be the same only for substrates which pin the same crystal axis normal to the substrate surface. 9The effect of varying (J on the growth of Nb films is discussed in Ref. 2 and

3.

Bradley. Harper, and Smith

4164

Downloaded 08 Oct 2010 to 129.82.140.57. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions