A method of forming a crystalline semiconductor material on the basis of a very thin semiconductor base material and an amorphous semiconductor material deposited thereon is disclosed. Radiation-based anneal process techniques may be applied by using appropriate radiation wavelengths, for instance, below 380 nm, in order to efficiently restrict energy deposition to the surface-near area. A solid and crystalline bottom portion of the semiconductor base material may be reliably preserved, thereby achieving crystallization of the overlying material portions and, in particular, of the previously deposited amorphous semiconductor material. Extremely thin channel regions of fully depleted SOI transistor elements may be used as a semiconductor base material, upon which raised drain and source regions may be formed in a later manufacturing stage, thereby substantially avoiding any process irregularities, which are conventionally associated with the epitaxial growth of a semiconductor material on a very thin semiconductor base material.