4.2.1 Substrate Orientation (001)

On (001) substrate the energy difference between the lowest subband of the unprimed ladder and the lowest subband of the primed ladder stems from the different quantization masses. The larger quantization mass of the unprimed ladder ( $m_\mathrm{l}$=0.916 $\ensuremath{\mathrm{m}}_0$) as compared to the small quantization mass of the primed ladder ( $m_\mathrm{t}$=0.19 $\ensuremath{\mathrm{m}}_0$) yields a smaller splitting between the subband energies of the unprimed ladder than that of the unprimed ladder.

Electron transport in the inversion layer on (001) substrate can be improved by preferentially populating the twofold degenerate unprimed ladder and depopulating the primed ladder which is fourfold degenerate. A repopulation has two consequences for electron transport:

• A higher fraction of electrons has the smaller transport mass of the unprimed ladder.
• Additionally, by shifting the subbands of the primed ladder up in energy with respect to the unprimed ladder, the scattering rate to this subband ladder is decreased. This also contributes to the mobility increase.

The intrinsic splitting between unprimed and primed subband ladder can be increased by applying

• compressive stress along the interface normal,
• biaxial in-plane tensile strain (e.g. from epitaxially growing Si on Si$_{1-x}$Ge$_{x}$).
• tensile stress along the in-plane $\langle110\rangle$ direction.

Under the first two conditions the strain tensor only contains non-zero diagonal components ( ${\ensuremath{\varepsilon_{xx}}} = {\ensuremath{\varepsilon_{yy}}} \neq {\ensuremath{\varepsilon_{zz}}}$). In the third case, where stress is applied along the $\langle110\rangle$ direction, additionally ${\ensuremath {\varepsilon _{xy}}}$ is non-zero and an effective mass change occurs. Under the strain conditions listed above the degeneracy of the subband ladders is not changed. Thus, the unprimed ladder is still twofold degenerate, and the primed ladder remains fourfold degenerate.

Figure: On the left the projection of constant-energy surfaces onto the (001) plane is plotted. The concentric circles indicate the twofold degeneracy of the unprimed ladder. Constant-energy lines of the primed ladder have ellipsoidal shape. On the right the effect of shear strain $\varepsilon_{xy}$ on the subband dispersion is visualized: the effective masses of the unprimed subband ladder change.

Using linear deformation potential theory the splitting of the unprimed subband ladders can be calculated from (3.47). Under shear strain the additional shift between the primed and unprimed subband ladder given in (3.54) and the effective mass change (see equations (3.98), (3.99), and (3.94)) of electrons in the unprimed ladder has to be accounted for. As depicted in Figure 4.6, the energy dispersion of electrons in the unprimed subband ladder is not longer isotropic in the (001) plane and transport characteristics depends on the direction of transport.

Recent experiments suggest an enhancement of electron mobility if tensile stress is applied in the [100] direction [Irie04]. Under such stress conditions ${\ensuremath{\varepsilon_{xx}}} \neq {\ensuremath{\varepsilon_{yy}}}$, thus the fourfold degeneracy of the primed subbands is lifted and three sets of twofold degenerate ladders are formed (compare Figure 4.5).

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