4.4 Bulk Mobility of Strained Ge

In Ge the conduction band minima consist of four degenerate pairs of -valleys located along the directions. Application of strain lifts the degeneracy of the valleys. The valley splitting for the valley-pair can be calculated using (3.42) and the mobility tensor can be expressed as

(4.83) |

Here the scaled inverse mass tensors given by

(4.84) |

The masses are and and the transformation matrices are given as,

(4.85) | |

(4.86) |

For uniaxial compressive strain along the direction, the valley pairs located along the direction () are lowered in energy, while the remaining three valley pairs (, , ) move up in energy and remain degenerate. By this effect, the transport mass in the (111) plane is lowered and inter-valley phonon scattering is reduced, which results in a mobility enhancement.

The temperature dependence of the mobility for the strained case can be fit using a power law expression.

Here is the bulk mobility at 300K and is a parameter. The temperature dependence is introduced into the analytical model through the enhancement factor as

where is the mobility enhancement in unstrained Ge at 300K. The lattice temperature also affects the mobility through the inter-valley scattering rate (4.61) and the valley populations (4.39).

S. Dhar: Analytical Mobility Modeling for Strained Silicon-Based Devices