6.3.1 Channel Mobility in UTB MOSFETs for (001) and (110) Substrates

The influence of stress on the effective electron mobility enhancement in UTB MOSFETs is analyzed. For (001) oriented substrate it was shown before that a stress in the [110] direction induces two beneficial effects for the electron mobility in the [110] direction, namely (i) stress-induced valley splitting and (ii) stress-induced effective mass change. At relatively large body thicknesses like $T_\mathrm{si}=$ 20 nm, the mobility enhancement $\Delta \mu_\mathrm{eff}$ can be understood from a combination of these two effects yielding an anisotropic $\mu_\mathrm{eff}$ as compared to the unstressed system (see Figure 6.21). In ultra-thin Si bodies, however, the strong geometrical quantum confinement induces a large intrinsic valley splitting, thus the additional stress-induced valley shifts have a negligible effect on the mobility. At $T_\mathrm{si}$=2.4 nm, the larger component $\mu_\mathrm{eff\vert\vert}$ parallel and the smaller component $\mu_\mathrm{eff\perp}$ perpendicular to the stress direction result from the effective mass change only, which is in good agreement with experimental data [Uchida05].

Figure: Simulated effective mobility for substrate orientation (001), two channel orientations and two body thicknesses of unstressed Si (solid lines) and with 1 GPa stress along (a) [110] and (b) along [100] (dashed lines). The mobilities are plotted parallel (closed symbols) and perpendicular (open symbols) to the stress direction.

[stress along [110]] [stress along [100]]

Figure: Effective mobility for substrate orientation (110) of unstressed (solid lines) and 1 GPa stressed (dashed lines) Si for two body thicknesses. The mobility components are plotted parallel (closed symbols) and perpendicular (open symbols) to stress direction [001].

In Figure 6.21 the effect of uniaxial stress along channels in [100] direction is shown. Stress in direction [100] lifts the degeneracy of the fourfold degenerate, primed ladder. Since no effective mass change occurs, $\Delta \mu_\mathrm{eff}$ occurring at large $T_\mathrm{si}$ is a result of subband ladder repopulation only. As the body thickness is decreased, the population of the higher subband ladders inevitably decreases, and strain cannot further decrease the population. Therefore, in Si films with a thickness of $T_\mathrm{si}=2.4$ nm even stress at a level of 1 GPa does not induce a mobility enhancement.

Stress-induced $\Delta \mu_\mathrm{eff}$ for (110) oriented substrates can be understood from similar arguments. Tensile stress along [001], which increases the bulk- and inversion layer mobility parallel to stress (see Figure 6.16 and Figure 6.20), does not alter the mobilities at small $T_\mathrm{si}$, because it does not change the effective masses, but merely increases the splitting between the primed and unprimed subband ladders. Figure 6.22 shows how the stress-induced mobility enhancement, that can be observed at $T_\mathrm{si}=20$ nm, vanishes at $T_\mathrm{si}=3.7$ nm.

E. Ungersboeck: Advanced Modelling Aspects of Modern Strained CMOS Technology