6. Simulation Results

In this chapter the results of band structure calculations and of electron mobility simulations for Si under general strain conditions are presented. Special emphasis is put on shear strain arising from stress along $\langle110\rangle$ because of its high relevance from a technological point of view.

The chapter is organized as follows: In Section 6.1 results from band structure calculations using the empirical pseudopotential method are presented. Especially the impact of strain on the $\Delta$-valleys of the lowest conduction band is analyzed as the electron mobility is mainly determined by electrons residing in these valleys. Band structure calculations are compared to the analytical expressions derived using a degenerate k$\cdot$p-theory at the zone boundary $X$ point. The effective mass change of electrons predicted by the calculations is verified by comparison with experimental data. Next, the effect of strain on the subband structure of Si inversion layers as obtained from the Schrödinger-Poisson solver is examined.

In Section 6.2 the Si bulk electron mobility is analyzed for various strain conditions. The impact of the strain-induced valley shifts and the strain-induced effective mass change on the mobility is evaluated. Section 6.3 contains the simulation results of the effective mobility in Si inversion layers. Again, focus is put on substrate orientations and strain configurations that are of technological relevance. Finally, the influence of degeneracy effects on the inversion layer mobility is analyzed and simulation results are compared to experimental data.

Subsections

• 6.1 Bandstructure Calculations
  • 6.1.1 Strain-Induced Shift of the Conduction Band Minimum
  • 6.1.2 Strain-Induced Change of the Shape of the Conduction Band Edge
  • 6.1.3 Subband Structure
  
  
• 6.2 Bulk Electron Mobility of Strained Si
• 6.3 Electron Inversion Layer Mobility of Strained Si
  • 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