DYNAMICS AND FLUCTUATIONS DURING MBE ON VICINAL SURFACES - I - FORMALISM AND RESULTS OF LINEAR-THEORY

We develop a full nonlinear theory including fluctuations for the stud y of dynamics of vicinal surfaces during molecular beam epitaxy. We co nsider the situation where the surface grows through step flow. The mo del is based on the Burton-Cabrera-Frank one, in which kinetic attachm ents, elastic interactions, and statistical fluctuations, through Lang evin forces, are incorporated. Green's functions techniques are used. The step dynamics are governed in the general case by nonlinear and no nlocal coupled equations. At equilibrium we recover known results and some of them are revisited. For example, we find that the step meander behaves at equilibrium as w similar to l(alpha)[ln(L)](1/2) (I is the mean interstep distance and L the lateral step extent). The quantity alpha=1/2 or 1 depending on whether the elastic interaction is In(l) o r 1/l(2). During step flow growth the steps repel each other via the d iffusion field. This repulsion prevails over the elastic one. It leads to an exponent 1/4; w similar to l(1/4). Because the diffusive repuls ion is much bigger than the elastic one, nonequilibrium conditions sho uld first result in a drastic reduction of the vicinal surface fluctua tion (steps wandering and terrace width fluctuations). However, on fur ther increase of the incoming flux F, the steps become morphologically unstable. This instability is driven by adatom diffusion. It is of de terministic origin and must be distinguished from purely statistical f luctuations. At the instability threshold and in the linear regime, th e roughness behaves as w similar to epsilon(-1/2)L(1/2) (epsilon is th e distance from the instability threshold) for an isolated step and w similar to epsilon(-1/4)[ln(.L)](1/2) for a train of steps. The expone nt 1/4 is a direct consequence of step-step interaction. At the instab ility point nonlinear terms become relevant. The nonlinear regime is d iscussed in detail in the following paper.