4. Quantum Confinement in UTB Films

Multi-Gate FinFETs and Ultra Thin Body Silicon On Insulator (UTBSOI) FETs are considered as perfect candidates for the $22\,\mathrm{nm}$ technology node and beyond. Strong size quantization leads to a formation of quasi-two-dimensional subbands in carrier systems in thin silicon films. For analytical hole subband structure calculations a six-band k.p Hamiltonian is commonly employed. The electron subband structure consists of six equivalent minima located close to the X-points in the Brillouin zone. Close to the minimum the energy dispersion is usually described by a parabolic approximation with the transversal masses $m_\mathrm{t}$ and the longitudinal mass $m_\mathrm{l}$. Isotropic non-parabolicity takes into account deviations in the density of states at higher energies. A more general description is, however, needed in ultra-thin silicon films, especially in the presence of shear strain [178]. The two-band k.p Hamiltonian accurately describes the bulk structure up to energies of $0.5-0.8\, \mathrm{eV}$ [179]. It includes a shear strain component which is neglected in the parabolic approximation [161,170,179]. Shear strain is responsible for effective mass modification and is, therefore, an important source of the electron mobility enhancement in ultra-thin silicon films [180,178].