Scanning Tunneling Microscopy Study of the Dynamic Scaling Properties of Rough Vapor-Deposited Silver Films
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ABSTRACT We investigated the scaling behaviour of vapor-deposited silver films at room temperature by means of scanning tunneling microscopy. The film-thickness range was ; 10 - 1000 nm. The roughness exponent H is observed to be H = 0.82 - 0.05. The growth and dynamic scaling exponents are respectively observed to be/1 = 0.29 ± 0.06, and z = 2.53 + 0.50.
I. INTRODUCTION The surface morphology of thin solid films grown under non-equilibrium conditions has been the subject of much atomic-scale computer simulation and scaling theory.[1] In general, self-affine surfaces are expected to develop. [2,3] The surface morphology of a thin film has a profound effect on many of its physical properties (electrical, mechanical, optical, etc.), the origins of which can be understood only if characterized at a nanometer level. A random rough surface is defined by a vertical height z(x, y) (measured from its mean position) where A = (x, y) is a positional vector in the xy plane, and z(x, y) is "asingle valued random function. The height-height fluctuations are characterized by "amean-square surface fluctuation or height-difference correlation function which for an isotropic surface is given by g(R) =< [z(x, y) - z(0, 0)] 2 >. The symbol < ... > denotes an average over all possible choices of the origin for all points which are a distance R apart. Films grown under non-equilibrium conditions are expected to develop selfaffine surfaces, whose height-difference correlation scales as g(R) oc R 2 H,0 < H < 1.[3,4] The parameter H is referred to as the "static" scaling or roughness exponent, which characterizes the degree of surface irregularity.[2-5] A real self-affine surface is also characterized by an in-plane correlation length ý, since g(R) must saturate at large length scale to the value 2a2 where a =< z(z, y) 2 >1/1 is the saturated rms surface width. For films grown on an initially fiat surface, the correlation length is expected to increase with time as oc tl/z, where z is the "dynamic" scaling exponent. The saturated rms width a is expected to scale with time as a cct0. The exponents 8, H, and z should be related by [6] H
111 Mat. Res. Soc. Syrup. Proc. Vol. 317. @1994 Materials Research Society
This is a fundamental relation of the scaling theory approach. It establishes a parallel between non-equilibrium growth of rough surfaces, and dynamic scaling in critical phenomena.[4] The central result of this paper is to report measurements of H, a, and ý for thermally evaporated silver films which lead to independent measurements for all three of the scaling exponents H, f3, and z, so as to test the validity of Eq.(1).
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R (nm) FIGURE 1 Comparison of surface width and height-difference correlation data.
IH. EXPERIMENTAL METHODS The films studied here were produced by collimated thermal evaporation of 99.999 percent pure silver (Ag) at normal incidence, 10- -_10' torr, and deposition rate 0.03 nm/s (0.12 layers/s) onto optically polished quartz substrates. Data were recorded for individua
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