Physica A 207 (1994) 379-383

Diffuse x-ray scattering from interfaces of Co/Pt multilayers

Xiao Yanl Department of Physics, The Hong Kong University of Science and Technology, Clearwater Bay,

Kowloon, Hong Kong

Abstract

We show that the x-ray scattering experiment which includes the diffuse intensity of a multilayered film can be used to probe detailed interfacial information of the multilayers. By assuming that the interfaces are rough, and are correlated in the entire multilayers, we show that, in the (001) oriented Co/Pt multilayers, the roughness of the interfaces, characterized by the height-height correlation function g(r) = ([h(r) - h(O)]*), was found to be scaled with the lateral spacing r to a power of 4/3, or r4’3. The result will be discussed with respect to the nature of the interfaces and the film growth process.

1. Introduction

Many physical properties of multilayers are affected by the detailed growth process even for the same average structure. Such examples can be easily found in magnetic and superconducting multilayers (for a recent review, see [l]). This demands a detailed structural characterization of the interfaces of the multilayers. Among other techniques, x-ray scattering is sensitive to the buried interfaces as well as non-destructive. Moreover, its intensity can be understood in the kinematic approximation without considering multiple scattering. Thus it is an excellent tool to provide detailed interface structure through an ensemble average. Recently, we have shown that the x-ray scattering which includes the diffuse, or non-specular, intensity at low angle from a periodic multilayered film, can be used to determine separately the atomic interdiffusion [2] and the roughness [3] of the interfaces of the Co/Pt multilayers. In this paper, we summarize the theoretical and experimental investigation on interfacial rough- ness, and discuss the nature of the interfaces and the growth process.

1 E-mail: phxyan@usthk.bitnet.

0378-4371/94/$07.00 @ 1994 Elsevier Science B.V. All rights reserved SSDI 0378-4371(93)E0568-Y

380 X. Yan I Physica A 207 (1994) 379-383

2. Diffuse scattering from correlated rough interfaces

In the kinematic approximation, the scattered x-ray intensity in a material can be denoted by

Z(Q) = 2 j$ exp(iQ *R”) , 1.1

(1)

where R” stands for the spatial separation between the ith and jth atom, A, the atomic form factor for the ith atom, and Ci,j for summation over i and j. Eq. (1) may be simplified by using the continuous variables in the polar axis, or Q = (q, II. Q,), R’.‘+R = (r, z) + (u, h), where r and z are the distance between the two reference points projected along the parallel and perpendicular directions with respect to the multilayered film plane respectively, while u and h are the corresponding deviations along these two directions.

One may further assume that (i) q 4 n . Q,, so that the effect of u can be ignored, (ii) the multilayers has infinite numbers of bilayers (or superlattice) of period D, and (iii) the roughness of the interfaces are correlated, or conformal. Eq. (1) can now be simplified to [3]

L(q) = S, 1 J,(v) exp[-n2Q~gW/21 r dr, (2)

where Q, = 27rlD, J,(x) is the 0th order Bessel function,

g(r) = We) -WI*) (3)

is the height-height correlation function, and

S n = (‘A --fB)2 sin2(nQ,d/2) , n*

(4)

in which d is the thickness of the type B layer, and fA and fs are the atomic scattering factor for atom A and B respectively. Eq. (2) indicates that, for an integral n, Z,(q) is a two-dimensional Fourier transfer of the function exp(-n2Qtg(r)/2). That is, the correlated interfaces characterized by g(r) can be measured directly from Z,(q).

There are two important cases worth mentioning. First, when g(r) = (+’ = constant, since the fourier transfer of a constant is a delta function, there are no diffuse intensities and Z,(q) has only a specular component with its strength

I, = S, exp(-n2Qicr2/2). c-9

The constant v is frequently used to characterize the degree of atomic mixing, or interdiffusion, at the interfaces of a multilayers. It can be measured by the intensity pattern for integral n’s according to Eqs. (4) and (5).

Second, when g(r) - a’(r/[)“, where CY is a positive exponent, and CT and 5 are constant, the intensities are dominated by diffused ones. It can be shown [3] that

X. Yan I Physica A 207 (1994) 379-383 381

the functional dependence of Z,(q) on q for different n’s is identical, or Z,(q) - Z,(qlr,), where Z,lZ, = nziol. When there are significant diffuse components, the conventional way of counting only the specular x-ray intensity (at q = 0) underestimates the total intensity. Consequently, one should include the diffuse intensities for finite q's in counting the total intensity, in order to evaluate the local nature of the atomic interdiffusion from the intensity pattern [3].

3. Experimental results

Detailed descriptions of the multilayers and the x-ray experiments can be found in ref. [2] for instance. The nominal structure of the multilayered Co/Pt films is GaAs(001)/Co(10~)/Ag(200~)lPt(18~)l{Co(3~)lPt(18~)}‘5. The momen- tum resolutions of the x-ray diffraction were SQY = 0.05 nm-‘, SQ, = 0.19 cos 0 nm-‘, and SQ, = 0.0016Q. Fig. 1 shows the intensity at Q, = n * Q, (Q, = 2.83 nm-‘), or Z,(Q,), for n = 1 and 2. A good fit can be achieved assuming a Lorentzian-like shape,

ZAQ,) =L, [ Q2 : rz](1+e’2) > Y n

(6)

resulting r, = 0.047 nm-’ and Z2 = 0.113 nm-‘, with the same value of p = 1.4, as shown on the solid lines in Fig. 1. A similar fit can be obtained for n = 3 with Z, = 0.234 nm-‘. The same p suggests that Z,(Q,)/ZO vs. Q,lZ, may have the same form for all ~1, and Z,lZ, - rz*‘Ol. From the above three m’s, one may evaluate 2/a to be 1.5, or (Y = 4/3. That is, the perpendicular length scale of the

-0.05 0 0.05

Q,[A-‘I

Fig. 1. The intensity of nth superlattice peak vs. the parallel momentum transfer, I,(Q,), n = 1 and 2. Solid lines are the fits using Eq. (6).

382 X. Yan I Physica A 207 (1994) 379-383

0 20 40 60 Bo

0 20 49 to 80

r(nm) rtnm)

Fig. 2. I(r) (a) and g(r) (b), obtained via a 2DFT of I,(Q,) in Fig. 1 (see text).

roughed interfaces, is scaled with the lateral spacing r to a power of 2/3, or g(r) - r4’3.

Furthermore, via a two-dimensional Fourier transform (2DFT) of the Z,(Q,) according to Eq. (2), or numerically by

Z(r) = A c. Jo(v) qi 4 Z,(q,) > (7)

where qi stands for Q,, Aq is the interval in QY and A is the normalization factor so that Z(r = 0) = 1, one can obtain Z(r) as shown in Fig. 2a, where the size of the bar represents the total uncertainty due to the statistical counting error, the uncertainty in SQ,, and that due to a finite q,,,. The function g(r) was then deduced from -(2/Q:) ln[Z(r)], with its upper and lower bounds shown in Fig. 2b. The points in Fig. 2b are a fit to the data, by g(r) = 0.002645r4’3, which is well within the error bars. It is concluded, from both the peak fittings along QY and the direct determination of g(r) via 2DFT, that the perpendicular length scale of the interfaces, (g(r))“‘, scales with the lateral spacing r to a power of 213, at least for r less than n/c - 670 A.

4. Discussion

Let us now examine if one can understand the above scaling results from the film growth process. During the growth, the random steps may be created like a random walk, causing the perpendicular length scale of the roughed interfaces to be scaled with the square root of the lateral spacing r. If incoming particles are under a constant flux, the growth rate is independent of the height of the surface, (Y = 1 is expected. However, if the density of the incoming particle remains a constant rather than the flux, the growth rate is higher for a rougher surface due to an increased effective surface area. In the later case, the exponent (Y should be larger than 1, which is consistent with the experiment (413). The observed scaling thus suggests that, during the growth, the surface has steps with random heights and may be under a constant density of vapour.

The second plausible explanation is to assume that there are islands of minority Co atoms between the adjacent Pt blocks, and that the non-uniform distribution

X. Yan I Physica A 207 (1994) 379-383 383

of these islands gives rise to the diffused intensity. At present, we cannot rule out the possibility of distributed Co islands of a simple duplication of a rough substrate surface. On the other hand, it is interesting to note that there is a r 4’3-dependence for g(r), implying that a self-affined fractal with dimension of 2.23 (3 - 2/3) could be used to describe the interfaces for either their roughness or distributed minority islands.

5. Conclusions

It is demonstrated that a scattering experiment which includes diffuse intensities from a multilayers can be used to probe detailed interfacial structure. In the example of Co/Pt (001) oriented multilayers, it is found that the perpendicular length scale of the interfaces, is scaled with the lateral spacing r to a power of 2/3, from both peak fitting or a direct Fourier transform. This indicates that there is a kind of scaling relation about the interfaces. Should the growth process be the origin of the scaling in g(r), it is suggested that, during the growth, the surface has steps with random heights and may be under a constant density of vapour.

Acknowledgements

The author acknowledges T. Egami for his encouragement and collaboration, E.E. Marinero, R.F.C. Farrow and C.H. Lee for growing the Co/Pt and many stimulating discussions, and the financial support by HKUST via R192/93 .SCO7.

References

[l] L.M. Falicov, D.T. Pierce, S.D. Bader, R. Gronsky, K.B. Hathaway, H.J. Hopster, D.N.

Lambeth, S.S.P. Parkin, G. Prins, M. Salamon, I. Schuller and R.H. Victora, J. Mater. Res. 5

(1990) 1299.

[2] X. Yan, T. Egami, E.E. Marinero, R.F.C. Farrow and C.H. Lee, J. Mater. Res. 7 (1992) 1309.

[3] X. Yan and T. Egami, Phys. Rev. B 47 (1993) 2362.