Effect of characteristics of plasma plume on the diamond-like film deposition

Pulsed KrF lasers of two different durations (30 ns, 500 fs) are used to deposit DLC films. By optical emission spectroscopy and ion probe, the composite species of laser generated plasma plume are identified, the average kinetic energy of ions, the plume flux and their variation with laser energy density, and the distance from the target are investigated. The relation of the properties of deposited films with the plasma characteristics is studied.     

Minimal energy configurations of strained multi-layers

We derive an effective plate theory for internally stressed thin elastic layers as are used, e.g., in the fabrication of nano- and microscrolls. The shape of the energy minimizers of the effective energy functional is investigated without a priori assumptions on the geometry. For configurations in two dimensions (corresponding to Euler-Bernoulli theory) we also take into account a non-interpenetration condition for films of small but non-vanishing thickness.      

Thermodynamic Energy of Semi-Infinite Solids with a Two-Dimensional Hot Electron Gas near the Surface

Expressions for the thermodynamic energy of semi-infinite solids with a hot electron layer near the stress-free surface are derived for films and for large samples. Conditions are determined under which this energy is associated with the hot electron excitation energy, with the nonequilibrium Rayleigh waves energy, and with the equilibrium bulk phonon energy. The calculations use the Keldysh diagram technique.     

Amorphisation and Growth Mechanisms of Carbon Films under Ion Beam Irradiation

Amorphisation mechanisms during Physical Vapour Deposition of diamond-like carbon films are presented and illustrate the role of ion bombardment on the microstructure and disorder of the deposited films. It is shown that, at low energy, densification of the carbon film is produced by an ion pinning effect, leading to cross-bonding between graphitic planes present in the layers. Increase of the sp³ concentration is observed as ion energy is increased until an optimum value at which irradiation induced defect migration leads to graphitisation of the layers. The effect of amorphisation–recystallisation depends strongly on the ion mass, ion energy and ion flux per deposited atom. A simple model of the ion beam assisted deposition mechanism is proposed and is in good qualitative agreement with experimental results.     

Variational methods for a singular SPDE yielding the universality of the magnetization ripple

The magnetization ripple is a microstructure formed in thin ferromagnetic films. It can be described by minimizers of a nonconvex energy functional leading to a nonlocal and nonlinear elliptic SPDE in two dimensions driven by white noise, which is singular. We address the universal character of the magnetization ripple using variational methods based on Γ-convergence. Due to the infinite energy of the system, the (random) energy functional has to be renormalized. Using the topology of Γ-convergence, we give a sense to the law of the renormalized functional that is independent of the way white noise is approximated. More precisely, this universality holds in the class of (not necessarily Gaussian) approximations to white noise satisfying the spectral gap inequality, which allows us to obtain sharp stochastic estimates. As a corollary, we obtain the existence of minimizers with optimal regularity.     

A justification of the theory of martensitic thin films in the absence of an interfacial energy

In the framework of Nonlinear Elasticity, the asymptotic behavior of the free energy of a martensitic material is studied as the height of the sample tends to zero. The effective thin film energy is identified in terms of parametrized probability measures, which allows for a justification of the kinematic compatibility conditions proposed in Bhattacharya and James' theory of thin films of martensitic materials, in the absence of higher order interfacial energy contributions to the three-dimensional bulk energy.     

Atomic scale epitaxial growth of BaTiO3 thin films by laser molecular beam epitaxy

By using laser molecular beam epitaxy (L-MBE), atomic scale epitaxid growth of BaTiO₃(BTO) thin films on SrTiO₃ (STO) substrates is achieved. Measurements of reflection high energy electron diffraction (RHEED), X-ray diffraction (XRD), scanning electron microscopy, and transmission electron microscopy reveal that the BTO films arec-axis oriented single crystals with smooth surface. The multi-layer ferroelectric/superconducting heterostructures are also prepared and the ferroelectric properties of BTO films are studied. The results show that by using L-MBE technique, high quality BTO films and improved device performance can be obtained. Project supported by the National Natural Science Foundation of China, the National Department of Finance, and the National Center for R and D on Superconductivity of China.     

A two-gradient approach for phase transitions in thin films

Motivated by solid-solid phase transitions in elastic thin films, we perform a Γ-convergence analysis for a singularly perturbed energy related to second order phase transitions in a domain of vanishing thickness. Under a two-wells assumption, we derive a sharp interface model with an interfacial energy depending on the asymptotic ratio between the characteristic length scale of the phase transition and the thickness of the film. In each case, the interfacial energy is determined by an explicit optimal profile problem. This asymptotic problem entails a nontrivial dependance on the thickness direction when the phase transition is created at the same rate as the thin film, while it shows a separation of scales if the thin film is created at a faster rate than the phase transition. The last regime, when the phase transition is created at a faster rate than the thin film, is more involved. Depending on growth conditions of the potential and the compatibility of the two phases, we either obtain a sharp interface model with scale separation, or a trivial situation driven by rigidity effects.     

Plateau's Problem as a Singular Limit of Capillarity Problems

Soap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning condition. This point of view introduces a length scale in the classical Plateau's problem, which is in turn recovered in the vanishing volume limit. This approximation of area minimizing hypersurfaces leads to an energy based selection principle for Plateau's problem, points at physical features of soap films that are unaccessible by simply looking at minimal surfaces, and opens several challenging questions. © 2020 Wiley Periodicals LLC.     

Qualitative properties of a continuum theory for thin films

We discuss qualitative aspects of a continuum theory for thin films rigorously derived in [B. Schmidt, On the passage from atomic to continuum theory for thin films, preprint 82/2005, Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig]. The stored energy density is examined for convexity properties and limiting behavior under large and small strains. A study of the dependence of the theory on relaxation parameters leads to the result that the scale of convergence used in [B. Schmidt, On the passage from atomic to continuum theory for thin films, preprint 82/2005, Max-Planck Institut für Mathematik in den Naturwissenschaften, Leipzig] is the only scale for which a limiting theory that also accounts for atomic relaxation effects is non-trivial.     

Synthesis and characterization of C3N4 hard films

C3N4 films have been synthesized on both Si and Pt substrates by microwave plasma chemical vapor deposition (MPCVD) method. X-ray spectra were calculated for single phase α-C3N4 and β-C3N4 respectively. The experimental X-ray spectra of films deposited on both Si and Pt substrates showed all the strong peaks of α-C3N4 and β-C3N4, so the films are mixtures of α-C3N4 and β-C3N4. The N/C atomic ratio is in the range of 1.0-2.0. X-ray photoelectron spectroscopy (XPS) analysis indicated that the binding energy of C 1s and N 1s are 286.2 eV and 399.5 eV respectively, corresponding to polarized C-N bond. Fourier transform infrared absorption (FT-IR) and Raman spectra support the existence of C-N covalent bond in the films. Nano-indentation hardness tests showed that the bulk modulus of a film deposited on Pt is up to 349 GPa.     

Renormalized Energy with Vortices Pinning Effect

This paper is a continuation of the previous paper in the Journal of Partial Differential Equations [1]. We derive in this paper the renormalized energy to further determine the locations of vortices in some case for the variational problem related to the superconducting thin films having variable thickness.     

The gradient flow motion of boundary vortices

We consider the gradient flow of a family of energy functionals describing the formation of boundary vortices in thin magnetic films. We obtain motion laws for the singularities in all time scalings by using the method of Γ-convergence of gradient flows.     

Energy Spectrum Width and Nonequilibrium Energy of Rayleigh Waves Scattered on a Two-Dimensional Near-Surface Electron Layer

We obtain expressions for the energy spectrum widths of Rayleigh waves corresponding to their deformational coupling to Fermi and Boltzmann electrons in a two-dimensional layer near the surface of a semibounded solid. We evaluate the nonequilibrium energy of Rayleigh waves that depends on these widths and is caused by the same coupling to the corresponding hot electrons. We show that this energy is independent of the degeneracy degree of the electrons and is given by the mean energy of free Rayleigh waves heated up to temperature of the electrons. We find conditions under which the thermodynamics is determined by this nonequilibrium energy of Rayleigh waves in films of a certain thickness with Fermi electrons near the surface and by the equilibrium energy of bulk phonons in thicker samples. All the results are obtained using the Keldysh diagram technique applied to the case of semibounded media.     

A finite difference scheme for solving parabolic two‐step micro‐heat transport equations in a double‐layered micro‐sphere heated by ultrashort‐pulsed lasers

Ultrashort‐pulsed lasers with pulse durations of the order of sub‐picosecond to femtosecond domain possess exclusive capabilities in limiting the undesirable spread of the thermal process zone in the heated sample. Parabolic two‐step micro heat transport equations have been widely applied for thermal analysis of thin metal films exposed to picosecond thermal pulses. In this study, we develop a three‐level finite difference scheme for solving the micro heat transport equations in a double‐layered micro sphere. It is shown by the discrete energy method that the scheme is unconditionally stable. Numerical results for thermal analysis of a gold layer coated on a chromium padding layer are obtained. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Brittle Thin Films

A two-dimensional model for brittle thin films is obtained from a three-dimensional fracture model for elastic material. Γ -convergence techniques are used to identify the limiting effective energy as the thickness of the sample approaches zero. Accepted 27 March 2001. Online publication 9 August 2001.     

On Plateau’s problem for soap films with a bound on energy

We prove existence and almost everywhere regularity of an area minimizing soap film with a bound on energy spanning a given Jordan curve in Euclidean space R ³.The energy of a film is defined to be the sum of its surface area and the length of its singular branched set. The class of surfaces over which area is minimized includes images of disks, integral currents, nonorientable surfaces and soap films as observed by Plateau with a bound on energy. Our area minimizing solution is shown to be a smooth surface away from its branched set which is a union of Lipschitz Jordan curves of finite total length.     

Soap films and covering spaces

A new mathematical model of soap films is proposed, called the “covering space model.” The two sides of a film are modeled as currents on different sheets of a covering space branching along the film boundary. Hence a film may be seen as the minimal cut separating one sheet of the covering space from the others. The film is thus the oriented boundary of one sheet, which represents the exterior of the film. As oriented boundaries, films may be calibrated with differential forms on the covering space, a version of the min-cut, max-flow duality of network theory. This model applies to unoriented films, films with singularities, films touching only part of a knotted curve, films that deformation retract to their boundaries, and other examples that have proved troublesome for previous soap film models. Communicated by Frederick Almgren     

Phenomenological theory of surface effects in ferroelectrics and its relationship with transverse Ising model

The relationship between the transverse field Ising model and the Landau phenomenological theory for ferroelectrics is analyzed, and the Landau free energy expression for ferroelectrics having surfaces is derived. It is pointed out that the traditional expression in which the surface integral has only a term of the square polarization is valid only for special cases, in general a term of the polarization to the four should be included as well. By use of the newly derived free energy expression, the thickness-dependence of the spontaneous polarization and Curie temperature of ferroelectric films is calculated; thereby some experimental results incompatible with the traditional phenomenological theory are successfully explained.     

Blister Patterns and Energy Minimization in Compressed Thin Films on Compliant Substrates

This paper is motivated by the complex blister patterns sometimes seen in thin elastic films on thick, compliant substrates. These patterns are often induced by an elastic misfit that compresses the film. Blistering permits the film to expand locally, reducing the elastic energy of the system. It is therefore natural to ask: what is the minimum elastic energy achievable by blistering on a fixed area fraction of the substrate? This is a variational problem involving both the elastic deformation of the film and substrate and the geometry of the blistered region. It involves three small parameters: the nondimensionalized thickness of the film, the compliance ratio of the film/substrate pair, and the mismatch strain. In formulating the problem, we use a small‐slope (Föppl–von Kármán) approximation for the elastic energy of the film, and a local approximation for the elastic energy of the substrate. For a one‐dimensional version of the problem, we obtain “matching” upper and lower bounds on the minimum energy, in the sense that both bounds have the same scaling behavior with respect to the small parameters. The upper bound is straightforward and familiar: it is achieved by periodic blistering on a specific length scale. The lower bound is more subtle, since it must be proved without any assumption on the geometry of the blistered region. For a two‐dimensional version of the problem, our results are less complete. Our upper and lower bounds only “match” in their scaling with respect to the nondimensionalized thickness, not in the dependence on the compliance ratio and the mismatch strain. The lower bound is an easy consequence of our one‐dimensional analysis. The upper bound considers a two‐dimensional lattice of blisters and uses ideas from the literature on the folding or “crumpling” of a confined elastic sheet. Our main two‐dimensional result is that in a certain parameter regime, the elastic energy of this lattice is significantly lower than that of a few large blisters. © 2015 Wiley Periodicals, Inc.