Structure Below the Growing Surface

– In recent years there has been a growing interest in the statistical properties of surfaces growing under deposition of material. Yet it is clear that a theory describing the evolution of a surface should at the same time describe the properties of the bulk buried underneath. Clearly, the structure of the bulk is relevant for many practical purposes, such as the transport of electric current in devices, transport of fluids in geological formations and stress transmission in granular systems. The present paper demonstrates explicitly how models describing deposition can provide us with information on the structure of the bulk. Comparison of an analytic model with a simulation of a discrete growth model reveals an interesting long range tail in the density-density correlation in the direction of deposition. The study of the statistical properties of surfaces growing under the deposition of material has attracted many researchers over the last two decades. The systems under consideration vary from heaps of sand or other assemblies of granular matter, to devices manufactured by the bombardment of atoms on a growing target. The theoretical description of such systems is given by a number of discrete and continuous models that belong mainly to three categories. The first is the Edwards Wilkinson category [1] which was constructed to describe a situation of slow deposition under gravity where each deposited particle has the time to find its lowest possible gravitational potential energy in the presence of the existing surface. The second category is that of KPZ [2] in which lateral growth is important. This can be a result of sticking or just the geometry of growth perpendicular to the surface as explained in ref. [2]. The third category is the MBE (Molecular Beam Epitaxy) [3] which was constructed to describe processes of device fabrication in which the physics should produce under a wide range of parameters flat surfaces. The focus of interest in those studies was the statistical characterization of the growing surface. This is achieved by obtaining the roughness exponent of the steady state surface, the growth exponent [4–20] and the scaling functions associated with the steady state evolution of the surface [21–24]. It is easy to envisage many practical applications c EDP Sciences