%0 Book Section %1 statphys23_0663 %A Nicoli, M. %A Castro, M. %A Cuerno, R. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K films growth instabilities interface kinetic morphological nonconserved phase-field roughening statphys23 thin topic-4 %T Phase-field model for diffusion-limited surface growth %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=663 %X We present a phase-field formulation of a recently proposed free boundary model (FBM) 1 that describes the growth of a solid aggregate from a diluted phase (a vapor, a solution, etc.), thus providing an unified framework for the growth of thin films by various techniques. Examples are, for instance, electrochemical deposition (ECD) and chemical vapor deposition (CVD). These two types of processes are of high technological relevance, in microelectronics (in case of ECD), or in microfluidics (in case of CVD). In these contexts, the quality and the efficiency of the devices that are manufactured correlate with a low roughness of the surface of the deposits; therefore, it is important e.g. to assess the experimental conditions under which a low roughness is obtained. \par From the equations of the FBM, the small-slope approximation leads to an effective equation for the height of the interface, that generically features a morphological instability combined with a Kardar-Parisi-Zhang nonlinearity. The linear dispersion relation depends on parameters that measure the efficiency of aggregation kinetics at the interface. Thus, in the case of slow kinetics, the height follows the well-known Kuramoto-Sivashinsky equation, whereas in the fast kinetics limit the instability is of the Mullins-Sekerka type. We perform a detailed numerical study of the latter case. \par In order to study the FBM beyond the small slope approximation, we have introduced a new one-sided phase-field model (PFM) with an anti-trapping term 2, that converges to the FBM in the thin-interface limit. The numerical integration of the PFM shows the formation of complex structures characterized by multivalued surfaces that could not be obtained within the previous effective equations for the local height. Nevertheless, during the small slope dynamical regime the PFM gives the same linear dispersion relation as obtained with the FBM. We provide morphological diagrams for the PFM both at short and at long times, where a large variety of behaviors occur, similarly to experimental observations, namely, from compact to columnar and ramified morphologies, some of whose fluctuations display (effective) kinetic roughening properties. Through the relation between the parameters of both models, we can compare the results from our simulations in 1+1 and 2+1 dimensions with those obtained from experiments. 1) R.\ Cuerno, M.\ Castro, Phys.\ Rev.\ Lett.\ 87, 236103 (2001).\\ 2) B.\ Echebarria, R.\ Folch, A.\ Karma, M.\ Plapp, Phys.\ Rev.\ E 70, 061604 (2004).

@incollection{statphys23_0663, abstract = {We present a phase-field formulation of a recently proposed free boundary model (FBM) [1] that describes the growth of a solid aggregate from a diluted phase (a vapor, a solution, etc.), thus providing an unified framework for the growth of thin films by various techniques. Examples are, for instance, electrochemical deposition (ECD) and chemical vapor deposition (CVD). These two types of processes are of high technological relevance, in microelectronics (in case of ECD), or in microfluidics (in case of CVD). In these contexts, the quality and the efficiency of the devices that are manufactured correlate with a low roughness of the surface of the deposits; therefore, it is important e.g. to assess the experimental conditions under which a low roughness is obtained. \par From the equations of the FBM, the small-slope approximation leads to an effective equation for the height of the interface, that generically features a morphological instability combined with a Kardar-Parisi-Zhang nonlinearity. The linear dispersion relation depends on parameters that measure the efficiency of aggregation kinetics at the interface. Thus, in the case of slow kinetics, the height follows the well-known Kuramoto-Sivashinsky equation, whereas in the fast kinetics limit the instability is of the Mullins-Sekerka type. We perform a detailed numerical study of the latter case. \par In order to study the FBM beyond the small slope approximation, we have introduced a new one-sided phase-field model (PFM) with an anti-trapping term [2], that converges to the FBM in the thin-interface limit. The numerical integration of the PFM shows the formation of complex structures characterized by multivalued surfaces that could not be obtained within the previous effective equations for the local height. Nevertheless, during the small slope dynamical regime the PFM gives the same linear dispersion relation as obtained with the FBM. We provide morphological diagrams for the PFM both at short and at long times, where a large variety of behaviors occur, similarly to experimental observations, namely, from compact to columnar and ramified morphologies, some of whose fluctuations display (effective) kinetic roughening properties. Through the relation between the parameters of both models, we can compare the results from our simulations in 1+1 and 2+1 dimensions with those obtained from experiments. 1) R.\ Cuerno, M.\ Castro, Phys.\ Rev.\ Lett.\ {\bf 87}, 236103 (2001).\\ 2) B.\ Echebarria, R.\ Folch, A.\ Karma, M.\ Plapp, Phys.\ Rev.\ E {\bf 70}, 061604 (2004).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Nicoli, M. and Castro, M. and Cuerno, R.}, biburl = {https://www.bibsonomy.org/bibtex/225c3ddc159100a3c153bc9cc0040d27f/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {256ea5e41b9363824e172f0406389959}, intrahash = {25c3ddc159100a3c153bc9cc0040d27f}, keywords = {films growth instabilities interface kinetic morphological nonconserved phase-field roughening statphys23 thin topic-4}, month = {9-13 July}, timestamp = {2007-06-20T10:16:26.000+0200}, title = {Phase-field model for diffusion-limited surface growth}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=663}, year = 2007 }