Surface Roughness Scaling of Plasma Polymer Films

Abstract

Atomic force microscopy data reveal self-affine scaling of plasma polymer films. The rms surface roughness o. increases with film thickness 7. as o( f ( ( )rp, and with measurement length L as o(f ) . L ' ) g ') -L, where g is the surface roughness correlation length. At the deposition rate R = 2 p, m/h, the scaling exponents n and P are 0.9 and 0.7, both increasing to 1 at R = I pm/h. A competition between surface relaxation and deposition rate determine o. and (', which increase rapidly with R or inverse temperature. PACS numbers: 68.55.8d, 05.70.Ln, 68.55.Jk Comparison between self-affine surface structure data, computer simulations, and theoretical models is often made using scaling exponents for the rms surface roughness o(L, t) . [1 -3]: t~cL". a(Lr) = (h, (r, i) 2-1/2 h(r, t)(1) where t is the time, r is the position in the plane perpendicular to the growing direction, h(r, t) is the height of the surface at time t and position r, (h(r, t))" is the spatial average of h(r, t), L is the length of the surface measured, and c is a constant. Thus, cr initially scales with time as tP but shows a saturated scaling as I for thick layers [4]. Knowing the functional form of a and P in terms of process conditions allows the prediction of the surface roughness for any sample size.For simple random deposition with no spatial or temporal correlations between the deposited particles (the extreme kinetic limit), P = 0.5, since o. grows as a "random walk, " and n = 0, since there is no saturated scaling with L, For a real surface, relaxation processes such as in the Langevin type models couple the 2 degrees of freedom in the surface roughness, L and t, so as to change the scaling exponents. For example, Edwards and Wilkinson (EW) [5] use a Langevin equation [Eq. (2) with A = 0] to model the evolution of a surface, and find in d = 1 + 1 1 1 dimensions n = 2 and P = 4. In d = 2 + 1 the power law behavior in Eq. (1) changes to a logarithmic dependence. Kardar, Parisi, and Zhang (KPZ) [6] allowed for a component of interface growth parallel to the plane. They used the equation dh(r, t) 2 dt 2 = vV h(r, t) + -[Vh(r, t)] + rl(r, t), (2)where v is related to surface relaxation, g is the random fluctuation in the incoming flux, which is assumed to be Gaussian with delta function correlation (71(r, t) g(r', t')) = 2DB(rr', tt'), and A is the growth velocity perpendicular to the surface. In d = 1 + 1 dimensions they 1 1 obtained the exponents u = 2 and P = 3. In d = 2 + 1, Amar and Family [7] find that when 10~A2D/2v 25, P -0.25 and n -0.4, while for A2D/2v~-1, the effective value of P decreases. This connects the scaling exponent P to the surface relaxation process (v), and the deposition rate (-D). For the growth of plasma polymer films presented here we find 1 & a & 0.9 and 1 & P~0 .6. Of the experimental studies of the deposition of thin films, only a few have been analyzed in terms of both scaling laws of Eq. (1) [8]. For these studies 1~ct~0.2 and 0.56~P~0.22 [9]. The values of a overlap our own" but our values of P are si...

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