Coarsening In Thin Films Research Articles

Coarsening of Thin Films with Weak Condensation

Coarsening of Thin Films with Weak Condensation

Magnetically induced/enhanced coarsening in thin films

External magnetic fields influence the microstructure of polycrystalline materials. We explore the influence of strong external magnetic fields on the long time scaling of grain size during coarsening in thin films with an extended phase-field-crystal model. Additionally, the change of various geometrical and topological properties is studied. In a situation which leads to stagnation, an applied external magnetic field can induce further grain growth. The induced driving force due to the magnetic anisotropy defines the magnetic influence of the external magnetic field. Different scaling regimes are identified dependent on the magnetization. At the beginning, the scaling exponent increases with the strength of the magnetization. Later, when the texture becomes dominated by grains preferably aligned with the external magnetic field, the scaling exponent becomes independent of the strength of the magnetization or stagnation occurs. We discuss how the magnetic influence change the effect of retarding or pinning forces, which are known to influence the scaling exponent. We further study the influence of the magnetic field on the grain size distribution (GSD), next neighbor distribution (NND) as well as grain shape and orientation. If possible, we compare our predictions with experimental findings.

Stability of Polymer:PCBM Thin Films under Competitive Illumination and Thermal Stress

AbstractThe combined effects of illumination and thermal annealing on the morphological stability and photodimerization in polymer/fullerene thin films are examined. While illumination is known to cause fullerene dimerization and thermal stress their dedimerization, the operation of solar cells involves exposure to both. The competitive outcome of these factors with blends of phenyl‐C61‐butyric acid methyl ester (PCBM) and polystyrene (PS), supported on PEDOT:PSS is quantified. UV–vis spectroscopy is employed to quantify dimerization, time‐resolved neutron reflectivity to resolve the vertical composition stratification, and atomic force microscopy for demixing and coarsening in thin films. At the conventional thermal stress test temperature of 85 °C (and even up to the PS glass transition), photodimerization dominates, resulting in relative morphological stability. Prior illumination is found to result in improved stability upon high temperature annealing, compatible with the need for dedimerization to occur prior to structural relaxation. Modeling of the PCBM surface segregation data suggests that only PCBM monomers are able to diffuse and that illumination provides an effective means to control dimer population, and thus immobile fullerene fraction, in the timescales probed. The results provide a framework for understanding of the stability of organic solar cells under operating conditions.

Local and global existence of solutions to a fourth-order parabolic equation modeling kinetic roughening and coarsening in thin films

In this paper we study both the Cauchy problem and the initial boundary value problem for the equation $\partial_tu+\mbox{div}\left(\nabla\Delta u-{\bf g}(\nabla u)\right)=0$. This equation has been proposed as a continuum model for kinetic roughening and coarsening in thin films. In the Cauchy problem, we obtain that local existence of a weak solution is guaranteed as long as the vector-valued function ${\bf g}$ is continuous and the initial datum $u_0$ lies in $C^1(\mathbb{R}^N)$ with $\nabla u_0(x)$ being uniformly continuous and bounded on $\mathbb{R}^N$ and that the global existence assertion also holds true if we assume that ${\bf g}$ is locally Lipschitz and satisfies the growth condition $|{\bf g}(\xi) |\leq c|\xi|^\alpha$ for some $c>0, \alpha\in (2, 3)$, $\sup_{\mathbb{R}^N}|\nabla u_0|<\infty$, and the norm of $u_0$ in the space $L^{\frac{(\alpha-1)N}{3-\alpha}}(\mathbb{R}^N) $ is sufficiently small. This is done by exploring various properties of the biharmonic heat kernel. In the initial boundary value problem, we assume that ${\bf g}$ is continuous and satisfies the growth condition $|{\bf g}(\xi) |\leq c|\xi|^\alpha+c$ for some $c, \alpha\in (0,\infty)$. Our investigations reveal that if $\alpha\leq 1$ we have global existence of a weak solution, while if $1<\alpha<\frac{N^2+2N+4}{N^2}$ only a local existence theorem can be established. Our method here is based upon a new interpolation inequality, which may be of interest in its own right.

Phase Coarsening in Thin Films

Phase coarsening (Ostwald ripening) phenomena are ubiquitous in materials growth processes such as thin film formation. The classical theory explaining late-stage phase coarsening phenomena was developed by Lifshitz and Slyozov, and by Wagner in the 1960s. Their theory is valid only for a vanishing volume fraction of the second phase in three dimensions. However, phase coarsening in two-dimensional systems is qualitatively different from that in three dimensions. In this paper, the many-body concept of screening length is reviewed, from which we derive the growth law for a ‘screened’ phase island, and develop diffusion screening theory for phase coarsening in thin films. The coarsening rate constant, maximum size of phase islands in films, and their size distribution function will be derived from diffusion screening theory. A critical comparison will be provided of prior coarsening concepts and improvements derived from screening approaches.

Stress analysis, structure and magnetic properties of sputter deposited Ni–Mn–Ga ferromagnetic shape memory thin films

The residual stress instituted in Ni–Mn–Ga thin films during deposition is a key parameter influencing their shape memory applications by affecting its structural and magnetic properties. A series of Ni–Mn–Ga thin films were prepared by dc magnetron sputtering on Si(1 0 0) and glass substrates at four different sputtering powers of 25, 45, 75 and 100 W for systematic investigation of the residual stress and its effect on structure and magnetic properties. The residual stresses in thin films were characterized by a laser scanning technique. The as-deposited films were annealed at 600 °C for 1 h in vacuum for structural and magnetic ordering. The compressive stresses observed in as-deposited films transformed into tensile stresses upon annealing. The annealed films were found to be crystalline and possess mixed phases of both austenite and martensite, exhibiting good soft magnetic properties. It was found that the increase of sputtering power induced coarsening in thin films. Typical saturation magnetization and coercivity values were found to be 330 emu/cm 3 and 215 Oe, respectively. The films deposited at 75 and 100 W display both structural and magnetic transitions above room temperature.

A new phase-field model for strongly anisotropic systems

We present a new phase-field model for strongly anisotropic crystal and epitaxial growth using regularized, anisotropic Cahn–Hilliard-type equations. Such problems arise during the growth and coarsening of thin films. When the anisotropic surface energy is sufficiently strong, sharp corners form and unregularized anisotropic Cahn–Hilliard equations become ill-posed. Our models contain a high-order Willmore regularization, where the square of the mean curvature is added to the energy, to remove the ill-posedness. The regularized equations are sixth order in space. A key feature of our approach is the development of a new formulation in which the interface thickness is independent of crystallographic orientation. Using the method of matched asymptotic expansions, we show the convergence of our phase-field model to the general sharp-interface model. We present two- and three-dimensional numerical results using an adaptive, nonlinear multigrid finite-difference method. We find excellent agreement between the dynamics of the new phase-field model and the sharp-interface model. The computed equilibrium shapes using the new model also match a recently developed analytical sharp-interface theory that describes the rounding of the sharp corners by the Willmore regularization.

Simulations of Nonlinear Strongly Anisotropic, Misfitting Crystals and Thin Films

AbstractWe present a new approach for modeling strongly anisotropic crystal and epitaxial growth using regularized, anisotropic Cahn-Hilliard-type equations as a model for the growth and coarsening of thin films. When the surface anisotropy is sufficiently strong, sharp corners form and unregularized anisotropic Cahn-Hilliard equations become ill-posed. Our models contain a high order Willmore regularization to remove the ill posedness at the corners. A key feature of our approach is the development of a new formulation in which the interface thickness is independent of crystallographic orientation. In our previous work, we have provided matched asymptotic analysis to show the convergence of our diffuse interface model to the analytical sharp interface model. In previous models there was no such convergence to sharp interface model when the Willmore energy was considered. We present 2D numerical results using an adaptive, nonlinear multigrid finite-difference method. In particular, we find excellent agreement between the computed shapes using the Cahn-Hilliard approach, with a finite but small Willmore regularization, with dynamical numerical simulations of a sharp interface model. The equilibrium shapes from our diffuse model are compared with an analytical sharp-interface theory recently developed by Spencer [1] at the corners, and there is excellent match. Away from the corners there is an excellent agreement between the diffuse model and the classical Wulff shape. Finally, in order to model the misfit and displacement strains, we add the elastic energy and corresponding forces to our diffuse model. We analyze numerically the effect of elastic stress on the corner regularization in terms of two parameters: one parameter that describes the relative strength of the elastic energy to surface energy and the second that characteristics the strength of the surface energy anisotropy. Adding elastic energy modifies the equilibrium shape and in particular affects the shape of the corners. We can predict different Qdot shapes, such as pyramids and domes, based on the strength of the elastic interactions.

Thin films of van der Waals fluid: From interface interactions to wetting transitions

We present a theoretical study of wetting phenomena and interactions between liquid–vapor interfaces based on the local density functional theory. The focus is mostly on the impact of long-range van der Waals interactions both within the fluid and between the fluid and substrate. For the latter, we consider two models – hard wall and soft wall approximations – differing by the role of steric effects and leading to a qualitatively different character of phase transitions. We compute numerically the disjoining and conjoining potentials (which are important dynamically for spreading, spinodal dewetting, and coarsening in thin films, as well as resolution of interfacial singularities), and loci of intermediate and complete wetting transitions as functions of the Hamaker constant and temperature. We find that taking into account short-range interactions is essential for the description of wetting transitions in the soft wall limit. We derive an analytical form of the disjoining potential and analyze it in the context of the complete, frustrated and partial wetting.

The role of the transition function in a continuum model for kinetic roughening and coarsening in thin films

In the model for kinetic roughening and coarsening in high-temperature super-conducting thin films that Ortiz et al. suggest in (J. Mech. Phys. Solids 47(1999) 697.) a transition function is used which takes the energetics of the boundary layer at the film/substrate interface into account. Apart from having some basic properties, this function can be chosen quite arbitrarily. We show that certain decay and concavity properties of this function have a major impact on the film growth. In particular, a modified decay can circumvent the occurrence of negative film heights which is predicted in the original model, and a change in curvature alters stability properties of the film. These observations not only underscore the importance of the transition function in the model, but they also suggest to estimate the actual transition function from experimental data or from atomistic simulation.

Domain coarsening in thin films

We rigorously derive a mean-field model for Ostwald ripening in two-dimensional systems that arise in the growth of thin metallic films. This extends the classical LSW theory in two ways. First, it shows that an LSW-type model is also valid in two dimensions, even though the formal derivation seems less convincing than in three dimensions. Second, it clarifies the regime of validity and provides an inhomogeneous extension. © 2001 John Wiley & Sons, Inc.

A continuum model of kinetic roughening and coarsening in thin films

We present a phenomenological continuum model of film growth based on a series expansion of the deposition flux in powers of the profile gradient, consideration of the energetics of the film–substrate interface and the enforcement of Onsagers reciprocity relations. The interfacial term, which operates at very small thicknesses, is nonconservative and breaks the ± h symmetry of the remaining terms in the kinetic equation. By virtue of this term, very thin flat films are predicted to be stable within an appropriate range of parameters, and to loose stability and become rough at a well-defined critical thickness. This instability effectively provides an island nucleation mechanism. For thick films, the rate processes envisioned in the model favor a characteristic slope for the film profile, a feature which is in keeping with observation for a number of systems including YBCO films. The enforcement of reciprocity ensures the existance of a kinetic potential and enables the use of direct methods of the calculus of variations. Within this framework, we provide an explicit construction for the coarsening of the film profile based on a sharp interface approximation. The construction predicts characteristic exponents for the evolution of grain size and film roughness which are in close agreement with the observational evidence for YBCO. The predictions of the construction are also born out by numerical tests.

Numerical analysis of interface energy-driven coarsening in thin films and its connection to grain growth

Interface energy-driven coarsening in thin films is investigated using numerical analysis of a mean field growth model. The development of preferred orientation in an initially randomly oriented film is demonstrated. The coarsening process may also lead to the development of bimodal particle size distributions, but this is shown to depend sensitively on the shape of the interface energy vs orientation function. The rate of transformation to a state of preferred orientation is dependent on quantities such as the film thickness and the ratio of the interface energy anisotropy to the particle boundary energy. We discuss the applicability of the model, which was developed to describe coarsening of islands in a discontinuous thin film, to surface or interface energy-driven grain growth in a continuous thin film.

7163. Island growth and coarsening in thin films—conservative and nonconservative systems: HA Atwater and Chih M Yang, J Appl Phys, 67, 1990, 6202–6213

7163. Island growth and coarsening in thin films—conservative and nonconservative systems: HA Atwater and Chih M Yang, J Appl Phys, 67, 1990, 6202–6213

Island growth and coarsening in thin films—conservative and nonconservative systems

A model is developed for time-dependent growth and coarsening of islands in conservative and nonconservative thin-film systems with substrate coverages in the range 0&amp;lt;Φ&amp;lt;0.5. Solution of the continuity equation, for both matter-conservative and -nonconservative systems, coupled with mean-field or effective-medium rate laws for island coarsening, allows the evolution of arbitrary island size distributions to be modeled. For matter conservative systems with substrate coverage of Φ=0, all distributions investigated approach the dynamically scaling distribution and the steady-state power-law coarsening rate predicted by analytic theory following from the work of Lifschitz and Slyozov [J. Phys. Chem. Solids 19, 35 (1961)] and Wagner [Z. Electrochem. 65, 581 (1961)]. When it is assumed that Φ&amp;gt;0 but constant during coarsening, a dynamically scaling distribution and a steady state are also approached asymptotically. The form of the initial distribution has a significant effect on the coarsening kinetics in the transient regime before a dynamically scaling distribution is achieved. When the substrate coverage is allowed to vary for a conservative system, the coverage decreases monotonically with time. Simultaneous thin-film growth and coarsening in nonconservative systems (e.g., by vapor deposition, low-energy ion bombardment) is also examined. In particular, the relationship between growth and coarsening kinetics and mechanisms for ion-surface interactions is discussed.