Surface-Roughness-Scattering in Non-Planar Channels – the Role of Band Anisotropy

Non-planar transistor channels used in tri-gate [1] or gateall-around (GAA) [2] device architectures offer superior electrostatic control, which reduces short-channel effects. The limiting factor in these devices is surface-roughness scattering (SRS) as it is more pronounced in these devices than in planar technologies, which has two reasons: one is that there are more surfaces to scatter off and the other is that sidewall roughness or line-edge-roughness (LER) are harder to control in the fabrication process. Being of such importance it is surprising to find that a thorough perturbative treatment of SRS is missing in literature. Most low-field mobility calculations for non-planar channels employ phenomenological descriptions or extensions of SRS models for planar structures. Commonly, tri-gate channels are modeled as three separate non-interacting planar channels at the top and each sidewall, and the scattering rate in GAA channels is assumed to be proportional to d, with d being the diameter. The latter is based on an analysis of quantum wells in Ref. [3]. The only work known to us that rigorously treats SRS for a one-dimensional electron gas (1DEG) is Ref. [4]. The authors calculate the electron mobilities of gated silicon nanowires taking into account both axial and angular interaction of electrons with the rough nanowire surface. The calculations, however, rely on cylindrical symmetry of both real and kspace; this means that first, the model cannot be extended to non-cylindrical geometries, and second, that band anisotropy is completely neglected. The authors approximate the effective masses of 〈100〉-oriented nanowires as isotropic in the crosssection, which is questionable in itself and fails to capture the effect of channel orientation. Channel orientation is likely to play an important role in SRS as experimental data from [5] indicates. This raises the following issues and questions: • Rotational symmetry even of cylindrical GAA channels is not likely to be valid and must be dropped. • The d-approximation is only valid in very narrow channels with very low electric fields in the cross-section. • How to define a “diameter” for a tri-gate device, especially in the presence of electrostatic confinement? • How can SRS theory for planar and cylindrical geometries be extended to more general surfaces, that don’t even need to be closed shapes? In this work, we investigate the effect of band structure anisotropy and channel orientation on SRS in non-planar channels such as tri-gate and GAA structures. A new formalism is introduced for calculating SRS rates for non-planar structures. Rough barrier: