Influence of the Angular Distribution Function of Incident Particles on the Microstructure and Anomalous Scaling Behavior of Thin Films

Abstract

The microstructure and the scaling properties of films grown by plasma enhanced chemical vapor deposition are reproduced with a discrete model that takes into account the angular distribution function of the particles and the lateral growth of the films. Both the experimental and simulated surfaces exhibit a granular microstructure and an anomalous scaling behavior characterized by values of the growth exponent that vary with the scale of measurement. Depending on the angular distribution function used in the model, values of ranging from 0.86 to 0.2 are obtained. DOI: 10.1103/PhysRevLett.96.236101 PACS numbers: 68.55.ÿa, 64.60.Ht, 68.47.ÿb, 81.15.Gh Rough surfaces and interfaces are ubiquitous in nature, and from the technological point of view the control of their roughness is becoming critical for applications in fields such as microelectronics, image formation, surface coating, or thin film growth [1]. In this context, during the last years there has been an increasing interest in the description of the self-affine kinetic roughening of surfaces [2 -6]. This regime is characterized by an increase of the roughness with time and/or the scale of observation in a self-affine fashion [7,8]. The conventional dynamic scaling theory, the theoretical background used for the description of these phenomena, is based on the so-called FamilyVicsec relation, which models the evolution of the surface roughness -defined as the rms value of the heights of the different points of the interface-with the deposition time and the scale of measurement by means of the following expression [8]:where is the so-called roughness exponent and the growth exponent. According to the dynamic scaling theory, there exist only a finite number of universality classes characterized by certain values of the ( ; ) exponents, so that all the experimental systems would fall into one of these classes. The dynamic scaling theory can then be understood as an extension of the theoretical framework used for the description of the scaling properties of equilibrium phase transitions to nonequilibrium systems [7].In the last years a number of experimental results have appeared that cannot be interpreted in terms of the conventional dynamic scaling theory. In some works, values of the and/or exponents which do not belong to any of the universality classes have been reported. An example of this behavior is the finding of very high values of the growth exponent (i.e., > 0:5) [2,9]. To account for these values, alternative explanations of that of the universality classes have been proposed. One of the most widely used models is the nondeterministic model of Das SarmaTamborenea [10], that relates the variations of the growth exponent with the control of film growth by surface diffusion. For 2D surfaces, this model accounts for values of this exponent ranging from 0.17 to 0.5, this latter value being only obtained if diffusion is neglected. In the same context, Elsholtz et al. [9] presented a model where they considered a diffusion energy with two contributio...

Relationship between scaling behavior and porosity of plasma-depositedTiO2thin films

“…Shadowing and development of a columnar microstructure is then a likely result. 24 This is in fact the situation found for this type of sample where similar-sized columns grow in height up to the surface of the films ͑cf. Fig.…”

“…38,39 It is important to stress that in plasma grown thin films lateral growth can be particularly important because plasma species may arrive to the surface according to off-normal directions. 24 …”

“…24,35 Typically, such a situation leads to the development of columnar microstructures. The analysis of the PSD curve of the sample prepared with a plasma of 100% O 2 fits within this scheme.…”

“…16 Such an approach has been successfully applied for thin films grown by evaporation, 18 sputtering, 19 thermal CVD, 35 or PECVD. 20,21,24 Here, besides applying this methodology, we will try to correlate the obtained information with the porosity and microstructure of the films.…”

“…As evidenced for SiO 2 and SiO x Cy films prepared by PECVD, a factor that contributes to the appearance of such an "anomalous" behavior in plasma films is the fact that species coming from the plasma may reach the surface under off-diagonal directions. 24 In the present work we try to get further insights about the influence of the plasma chemistry on the thin film microstructure and porosity. For this aim, a highly oxidative plasma of oxygen and other O 2 +Ar gas mixtures with a high concentration of Ar have been used for deposition of TiO 2 thin films.…”