Effect of band warping and wafer orientation on NMOS mobility under arbitrary applied stress

Abstract

We have developed a novel simulation approach to model electron mobility in the inversion layer which encompasses all the important effects of arbitrary wafer and applied stress orientations, such as carrier re-population, band warping, and scattering, going beyond the separate treatments of band warping and inversion anisotropy that have been demonstrated. Our model predicts an important consequence of electron band warping in retaining the increase of stress gain at high stress levels in the presence of shear stress at strong inversion.

Modeling the effects of applied stress and wafer orientation in silicon devices: from long channel mobility physics to short channel performance

“…With increased doping level, electron mobility stress gains decrease [19,27]. These dependencies are simulated at a fixed 1.5 MV/cm effective field in Fig.…”

“…We emphasize that the off-diagonal terms in the effective mass tensors describe band warping effects which are present under shear stresses [27]. The procedure of our solution for electrons has been discussed by us in [27,36].…”

“…The procedure of our solution for electrons has been discussed by us in [27,36]. Schrödinger equations for the X, Y , and Z valleys are solved self-consistently with the Poisson equation to obtain the confined bandstructure in the inversion layer.…”

“…1 and 2 are used unchanged for all wafer/channel orientations and stresses throughout all results presented in the paper. Stress modifies conduction bands by splitting valleys and warping the bands in the presence of shear stresses [27]. Valley splitting leads to carrier repopulation and reduced scattering.…”

“…Recent extensive modeling has been able to successfully explain long channel mobility changes with wafer/channel orientations for electrons and holes [3,4,[26][27][28][29]. Smaller PMOS stress responses were predicted on a (110) wafer under confinement [2,26].…”