Elementary crystal growth mechanisms in solution and vapor growths are discussed taking semiconductor as a model material. Solution growth mechanism is argued at first taking liquid phase epitaxy (LPE) as a model system. On the surface of the LPE layer, macrosteps are often generated as a result of step bunching. By studying the behavior of the macrosteps using photoluminescence image and chemical etching of the cleaved cross section, it was found that the shape of the macrostep is governed by bulk diffusion and growth kinetics. This has been confirmed by space experiments. It is concluded that the growth on the macrostep terrace is conducted by steps generated at screw dislocations. A technique, which is called microchannel epitaxy, was developed to realize macrostep-free and dislocation-free layers. Vapor growth mechanism is discussed next taking molecular beam epitaxy of III-V compound as a model system. Here, the mechanism of inter-surface diffusion is investigated. The surface diffusion of group-III elements between facets was studied by changing group-V pressure. It was found that the direction of the inter-surface diffusion is reversed twice as the group-V pressure is increased. This has been attributed to the different group-V pressure dependence of group-III ad-atom lifetime on different facet. It was concluded that in MBE the growth on the facet is conducted by birth and spread of two-dimensional nuclei and by mass transports from next facet and from effusion cell. (c) 2004 Elsevier B.V. All rights reserved.