4.2 Strain Effects

In this section the effect of strain on the subband structure of Si inversion layers is analyzed. For this purpose we assume that the energy shifts of the individual subband ladders can be calculated using the deformation potential theory. Furthermore it is assumed that the effective mass change induced by shear strain in bulk Si is reflected in the subband structure as well.

Both strain and confinement breaks the cubic symmetry of bulk Si. As a result the degeneracy among different pairs of valleys is lifted, while each of these pairs retain their twofold valley degeneracy (Kramers degeneracy) [Ashcroft76].

The effect of strain on the subband structure is illustrated in Figure 4.5c. If strain is present, the energetic position of the subband ladders with respect to each other is not completely determined from their quantization masses. An additional shift of each subband ladder has to be considered according to (3.47). Since this shift depends on the valley orientation, it may be different for each valley and consequently the degeneracy between the subband ladders can be lifted.

Electron mobility in the inversion layer can be improved by preferentially populating the subband ladder with smallest transport mass. This can be achieved by shifting ladders with larger transport mass up in energy resulting not only in a smaller net effective transport mass, but also in a reduction of intervalley scattering. However, since the density of states is reduced by pushing subband ladders with large transport mass up in energy, the Fermi level accommodates at higher values and the electron gas experiences more pronounced degeneracy effects. These effects are crucial in the determination of the electron mobility and will be discussed in greater detail in Section 5.4.

Figure 4.5: Energy lineups of the conduction subbands in unstrained Si for (a) substrate orientation (001), (110), and (b) substrate orientation (111). (c) Strain changes the lineup of the energies and thus is able to remove the degeneracy of subband ladders.

Subsections

• 4.2.1 Substrate Orientation (001)
• 4.2.2 Substrate Orientation (110)
• 4.2.3 Substrate Orientation (111)

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