6.3 Electron Inversion Layer Mobility of Strained Si

The inversion layer mobility was calculated by means of a Monte Carlo method taking into account the subband structure calculated from a Schrödinger-Poisson solver (see Chapter 4). Phonon scattering and screened surface roughness scattering were taken into account. Depending on the substrate orientation, the sixfold degeneracy of the $\Delta$-valley is lifted and up to three different subband ladders are formed. While for (001) substrate the subbands of the lowest subband ladder (unprimed ladder) are circular and the ladder is two-fold degenerate, for (110) substrate the subbands are elliptical and the unprimed ladder is fourfold degenerate. The higher density of states and larger transport masses for (110) substrate yield a lower inversion layer mobility as compared to (001) substrate. In Figure 6.18 simulation results are compared to experimental data [Uchida03,Tsutsui05].

Figure: Simulated effective electron mobility $\mu_\mathrm{eff}$ for substrate orientation (001) and (110) compared to measurements [Uchida03,Tsutsui05] (symbols). The anisotropic mobility for the (110) substrate is given along [001] and $[1\bar{1}0]$.

In the following the origin of the electron mobility enhancement induced by uniaxial stress of the 2DEG is discussed. To demonstrate the influence of the substrate orientation, subband MC simulations are performed for (001) and (110) oriented substrates. It is shown that uniaxial stress leads to a pronounced anisotropy of the in-plane mobility for both substrate orientations. While for (110) substrate this effect stems from the anisotropic transport mass of the lowest subband ladder, the effective mass change induced by stress in [110] direction is responsible for the anisotropic electron mobility on (001) oriented substrate.

The stress-induced change of the effective mass of electrons is incorporated in the subband MC simulations. In Figure 6.19 the mobility components parallel and perpendicular to stress direction [110] are compared to the unstrained mobility for two tensile stress levels. Tensile stress along [110] has two beneficial effects on the parallel mobility component: the splitting between the unprimed and primed ladders is increased, and the transport mass in direction of stress is reduced with respect to the unstrained case. From these two effects one can understand the mobility enhancement parallel to the stress direction for all inversion layer densities. Perpendicular to stress, the effective mass is increased, which leads to a smaller mobility enhancement in this direction. strained Si,

To enhance the mobility for (110) substrate a uniaxial tensile stress along [001] is applied, as this stress condition increases the splitting between the primed and unprimed ladders. From EPM calculations only a negligible change of the effective transport masses in the subband ladders is observed. Stress increases the component of $\mu_\mathrm{eff}$ parallel to the stress direction, whereas the perpendicular mobility is smaller as compared to the unstressed case as shown in Figure 6.20. Since the effective masses are not changed, the mobility change is expected to saturate at larger stress ($\sim$ 1 GPa), as soon as the primed ladder becomes depopulated. These results are in good agreement with experimental data for the anisotropic mobility enhancement for (001) and (110) oriented substrates [Irie04].

Figure: Mobility components parallel (closed symbols) and perpendicular (open symbols) to stress direction [110] without stress (circles), 0.1 GPa (squares), and 1 GPa stress (diamonds).

Figure: Mobility components parallel (closed symbols) and perpendicular (open symbols) to stress direction [001] without stress (circles), 0.1 GPa (squares), and 1 GPa stress (diamonds).

Subsections

• 6.3.1 Channel Mobility in UTB MOSFETs for (001) and (110) Substrates
• 6.3.2 Degeneracy Effects on Inversion Layer Mobility

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