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Layer epitaxial growth attracts much attention due to its important technological implications. In this paper, a detailed analysis of the growth mode in this regime, using kinetic model based on the rate equations for adatom and 2D island density and coverage in successive layers combined with a feeding zone allowing taking into account the interlayer mass transport in the presence of the Ehrlich-Schwoebel (ES) barrier at an island edge is presented. The numerical integration of the rate equations shows that increasing of the ES barrier height leads to the crossover of the homoepitaxial growth from a smooth layer-by-layer (LL) growth to a rough multilayer growth. For more reliable registration the transition from a smooth LL to a rough growth when the roughness starts to diverge the model is extended to large times and by exploring the growth kinetics up to fifty monolayers an accurate phase diagram of the homoepitaxial growth mode in the space of the growth parameters characterizing the surface diffusivity of adatoms and the ES barrier is constructed. An analytic form for the first layer coverage kinetics with taking into account the second growing layer, up to the third layer nucleation is derived for the first time. It is shown that a critical coverage for the next layer nucleation is a more appropriate parameter than a widely used critical island radius because it does not depend on the island density and uniquely determines the growth mode transition and its scaling behaviour with the main growth parameters (the ratio of the surface diffusivity to the deposition flux and the ES barrier height) is obtained. From the calculated temperature dependence of the critical coverage at different values of the activation energy for adatom surface diffusion and the ES barrier height the growth mode behaviour with substrate temperature was found. The model predictions are compared with published Monte Carlo simulations and experimental data. The results obtained enable experimental data to be examined quantitatively and in greater detail than has previously been reported. |