Au

Solid State Communications, printed in Great Britain.

Vol. 70, No. 11, pp. 991-995,

1989.

0038-1098/89$3.O(M.O0 Pergamon Press plc

FRACTAL PATTERNS IN THE ANNEALED SANDWICH Au/a-Ge/Au Fundamental Technology

Zheng Xin and Physics Center, of China, Hefei, (Received

1 April

Wu Zi-Qin University of Anhui 230026,

Science and P.R.China

1989 by W.Y. Kuan)

In this study, we observe the fractal crystallization in the sandwich Au/a-Ge/Au by use of TEH. The results indicate that variation of the annealing temperature gives rise to different morphology of fractals of polycrystalline Ge, whose may be controlled by the interplay of diffusion and growths It is also found that the long range field of nucleation. stress has an impact on the growth of the fractals.

growth

INTRODUCTION Since the idea was put forward by morphology Mandelbrot that the irregular be characterized with the concept of can many people dimensionC13, the fractal investigation have paid attention to the of the snowflake-like stochastic fractals which films, amorphous thin solid in often originate from crystallization, as amorphous a new direction in a result, being formedE2,3,4,51. The physics is is stimulated both by strut iny intense the realization of such physical phenomethe of nonequilibrium growths and by na application of amorphous materials on the ground that the morphology of microstructures often strongly influences the numewith made of devices properties rous the growth mechanism of However, them. it is the fractals isn’t yet made clear, believed that additional expegenerally needed to are still rimental supports growth develop a reasonable model of the In our previous workC6,71, fractals. of growths were closely rewe found their the presence of metal films. In lated to we study a new santhis communication, which has two Au films dwich Au/a-Ge/Au, that the effect of metal films on the so growth of fractals may become prominent. new results have been obsuch 1 ndeed, together with previous stutained,which dies are helpful to completely understand the growth. whose are such structures Fractals characterisincrease in mass H with the tic length L obeys the scaling law: H-L

systems gives rise to a number of f racdistinct morphology with different tal dimensions, and the annealing temperature,we think, can be regarded as such an important parameter since crystallization of amorphous materials is usually so that our condependent on annealing, cerning is natural to be confined to the format ion of fractals generated from annealing. EXPERIMENT AND RESULTS The sandwich Au/a-Ge/Au we studied was prepared by vacuum evaporation in a vacuum system with two evaporating sources of resistive $eat ing. The vacuum was kept below 1 X 10 t without being broken, the new cleaved surfaces of single and crystal NaCl were used as substrates, were maintained at room temperawhich ture. Each Au film was controlled to be about 20nm thick, and Ge film about 30nm. More details about the procedure can be seen in the similar onesC6.71. The elecpatterns over the astron diffraction deposited sandwich showed they were composed of amorphous Ge and polycrystalline After they were annealed in a vacuum Au. ambient respectively at 100°C for 3h, at 1OO’C for 5h. at 200°C for 0.5h and at they were divided into 3OO*C for 0.5h, correspondent kinds of samples: A, four B, C and D,these samples were respectively floated on distilled water by solving substrates and scooped on copper their Then H800-TEH equipped with Edax meshes. 9100 X-ray EDS was employed to examine them. SAD over At first, we performed it was found that the amorphous Ge them, of all annealed samples had crystallized. many From TEH bright field micrographs, snowflake-like clusters were observed in anaFig.lA,B), the sample A and Bfsee much of EDS showed they contained lyses also indimore Ge, and SAD over clusters the Ge was in the polycrystalline cated The clusters in the sample B were state.

D

the exponent D just is the fractal where divide we often In fact, dimensionC81. disks patterns into concentric fractal and counter the radii R, various with within fragtals N of pixels of number thus D is each disk,then N scales as R, It is now recognized that the abstracted. variation of controlled parameters in the 991

992

FRACTAL

PATTERNS

IN THE ANNEALED

SANDWICH AU/~-G~/AU

Vol. 70, No. 11

Vol.

70, No.

FRACTAL PATTERNS IN THE ANNEALEDSANDWICHAu/a-Ge/Au

993

Fig.1 The bright field micrographs of TEM of the sandwich Au/a-Ge/Au after ling (A)at 1OO’C for 3h;fB)at TOO’?“~,“, 5h; (C)at 2OO’C for 0.5h;fD)at 3OO’C for 0.5h. a few larger than in the sample A, but they looked similar to each other. In the sample C, there were also such clusters, they were scattered densely and isobut from each other by a dark lated networktsee Fig. ICI. As for the sample D whose annealing temperature was raised to 3OO’C the clusters became indistinct, and the bright irregular spots occurred, which consisted of larger crystal grains of Getsee Fig.lD). Therefore, it can be seen that anneal i ng temperatures different these result in different morphology of that those of A and B clusters, except were similar to each other because of the same annealing temperature. According tp the above remarks about we first examined the fractal dimension, their scale property after image procesthe measurement indicated the clussing, B and C satisfied ters in the sample A, thus their fractal dimethe scaling law, nsions were determined to be respectively The calculaabout 1.84, 1.81 and 1.73. tion about the sample B is shown in Fig.2. we also observed In the sample A, the fractals in the region near a 1 arger the stress distribution crack or hole, by these defects has an compact induced fractals, and on the morphology of the those their sizes became 3um larger than Oi fractals distant from the defectscsee The measurement presented the Fig.3A). dimension of the former, about fractal 1.71, which was also less than the latteWe also perforr,about 1.84fsee Pig.4). the Ge (111) med SAD over these regions, appear in diffraction pattern over ring but it hardly became visibthe fractals, le in the one outside themfsee Fig.IB,C). aggreThis also demonstrate that the Ge to form the fractals when crystalgates 1 izing.

5

LNIRI

The calculation of fractal Fig.2 fractals in the sample B: dimension of (A) the digitized image; (B) the seconda(Cl determination of ry digitized image; dimension by the least squarefractal fitting over the linear range.

DISCUSSION The growth often involves in mass If the growth of fractals is transport. controlled by the diffusion, completely with fractal dimensions increase their the annealing temperature because the the temperature make it 1 onger higher

994

Vol.

FRACTAL PATTERNS IN THE ANNEALED SANDWICB AU/~-Ge/Au

70, No. 11

Fig.3 (A) The fractal in the stress field originated from a crack; (B) the diffracdiftion pattern over a fractal;(Cf the fraction pattern over the region outside fractals. but our experiments diffusion iengthC91, with not completely in agreement are According to our results, the fracthis. tal dimension of fractals in sample A is greater than in sample C while the annealower temperature of the former is ling but when it is raised to than the latter, the irregular 300 C in the sample D, spots are formedtsee Fig.LD), whose fracdimension is approximately equal to tal about 2.1 dimension
4:16

I

I

I

I

I

24

32

40

48

56

LN 16’)

Xld’

Fig.4 The calculation of fractal dimension of fractals round the defects in the sample A: (Althe digitized image;(B) the secondary digitized image; (C) determination of least fractal dimension by the square-fitting over the linear range.

Vol. 70, No. 11

FRACTAL PATTERNS IN THE ANNEALED SANDWICH Au/a-Ge/Au

one of the intrinsic conditions of the formation of fractalsC101. the fractal’s denIn the sample A, greater than sity is about 5 X 10b/mmr ones in the a-Ge/Au/a-Ge by one order of magnitude, this may be because the grain boundar i es in the interior of Au films also contribute to the formation of nuclei of fractals besides those at the number is the same as interfaces whose boundathe a-Ge/Au/a-Ge, so more grain in the Au/a-Ge/Au bring about more ries by which the difference between nuclei, the growths in the Au/a-Ge/Au and in the caused. What a-Ge/Au/a-Ge is primarily

995

is more, it is found that the density of fractals is related to nuclei of the field induced by defects as shown stress it become small in Fig.3A. Accordingly, these so fractals in round the defects, On the other region grow 1 arger. hand, field is of the long range the stress as other fieldsCll1, so it correlation can result in the well-developed fractals lower fractal dimension; on the with the nucleation, which belongs contrary. the short range interaction, enhances to Thus the fractals the fractal dimension. near the defects are different from ones distant away.

REFERENCE (to be 1. B. B. Handelbrot, The Fractal Geometry 6. Zheng Xin and Wu Zi-Bin published in Z.Phys.B-Condensed Hatter) of Nature (Freeman, San Francisco, 1982) Wu Zi-Bin (to be 2. C.C.Tsai,R.J.Nemanich and H.J.Thompson 7. Zheng Xin and published in Solid State Communications) J.Vac.Sci.Technol., 21(2), 632 (1982) Cond.Hat.Phys. Comments 8. R.Jullien 3. E.Ben-Jacob, G.Deutscher, P.Garik, 177 (1987) and Y.Lareah Nigel D. Goldenfeld i3’Zheng Xin and Wu Zi-Qin Z.Phys. B73, Phys.Rev.Lett. 57. 1903 (1986) 129 (1988) 4.. B.X.Liu, L.J.Huang, K.Tao, C.H.Shang lO.T.Vicsek Phys.Rev.Lett.53,2281 (1984) and H.D.Li Phvs.Rev.Lett. 59.745 (1987) ll.P.Meakin Phys.Rev. A36,325(1987) Gy.Radnoczi, T.Vicsek, L.I;(.Sander and 5. D.Grier Phys.Rev. A35, 4012 (1987)