Model of Growth of Heusler-Alloy Epitaxial Films

The experimentally studied surface morphology of films of the Heusler alloy Fe2CoAl is compared to the theory of the formation of the fractal surface of films. This theory is based on the Cauchy problem for the simplified Kardar–Parisi–Zhang equation. It is shown that for the initial fractal shape of the film it can be solved immediately by applying the Oleinik–Lax principle (a weak solution to the problem). Within the framework of the exhaustive search method, numerical implementation of the Oleinik–Lax principle is proposed. A vector criterion of the quality of surface growth of the studied film is introduced. As the components of this criterion, the following functionals are tested: the norm of the spectral density of the autocorrelation function of the film surface in Hilbert space, Shannon information, and fractal dimension of the film surface. All these functionals are calculated over the shape of the film surface at each moment of time. A procedure for obtaining samples of the Fe2CoAl Heusler alloy is described.