The spectacular increase of computational speed and power of modern integrated circuits is supported by the continuing miniaturization of semiconductor devices. With scaling approaching its fundamental limits, however, the semiconductor industry is facing the challenge of introducing new innovative elements and engineering solutions and to improve performance of a Metal-Oxide-Semiconductor Field-Effect Transistor (MOSFET). A promising alternative to the electron charge degree of freedom currently used in MOSFET switches and RAM is to take into account the electron spin. The spin of an electron possesses several exciting properties suitable for future devices. It is characterized by only two projections on a chosen axis - up or down, and it can change its orientation rapidly by utilizing an amazingly small amount of energy. Employing spin as an additional degree of freedom is promising for boosting the efficiency of future low-power nanoelectronic devices, with high potential for both memory and logic applications. Silicon, the main element of microelectronics, possesses several properties attractive for spin-driven applications: it is composed of nuclei with predominantly zero spin and is characterized by small spin-orbit interaction. Due to this, the spin relaxation in silicon is relatively weak, which results in long spin life time. Spin propagation through an undoped silicon wafer of 350μm thickness has been already demonstrated. Coherent spin propagation over such long distances makes the fabrication of spin based switching devices in the near future increasingly likely. The SpinFET concept by Datta and Das employs spin-orbit interaction in the channel to modulate the current through the device. SpinFETs are composed of two ferromagnetic contacts (source and drain) that sandwich the semiconductor channel region. The ferromagnetic source contact injects spin-polarized electrons in the semiconductor region. The electron spin precesses during its propagation through the channel due to the non-zero spin-orbit interaction. Only the electrons with spin aligned to the drain magnetization can leave the channel through the drain contact, thus contributing to the current. The spin-orbit interaction is controlled electrically by applying an external gate voltage. Silicon has not been considered as a candidate for the SpinFET channel material because of the weak spin-orbit interaction in the bulk. Recently, however, it was shown that thin silicon films in SiGe/Si/SiGe heterostructures can have relatively large values of spin-orbit interaction. Interestingly, the dominant contribution to the spin-orbit interaction is of the Dresselhaus-like form. The stronger spin-orbit interaction, however, leads to increased spin relaxation. Fortunately, in quasi-one-dimensional electron structures, a substantial suppression of the spin relaxation is predicted.
We studied silicon fins of a square cross-section with (001) horizontal faces. The parabolic band approximation is not sufficient in thin and narrow silicon fins. In order to compute the subband structure in silicon fins, we employed the two-band k·p model, which is accurate up to 0.5eV above the conduction band edge. The resulting Schrödinger differential equation is discretized using the box integration method and solved for each value of the conserved momentum along the current directions using efficient numerical algorithms available through the Vienna Schrödinger-Poisson framework. Figure 1 demonstrates the dependence of the subband minima as a function of the fin thickness t, for the lowest four subbands. The fin orientation is along [110] direction. The dependence of the splitting between the unprimed subbands with decreasing t, which are perfectly degenerate in the effective mass approximation, is clearly seen. Splitting between the valleys in a [100] fin is negligible. In contrast, the dependence of the effective mass of the ground subband in [100] fins on t is more pronounced as compared to [110] fins. Results of density-functional calculations confirm the mass dependences obtained from the k·p model (Figure 2). Due to the larger effective mass, [100] fins are more suitable for practical realizations of silicon SpinFETs.