4. Quantum Confinement and Subband Structure

Charge transport in the MOSFET channel is different from the bulk transport since the carriers interact with the Si-SiO$_2$ interface. Furthermore, a large electric field normal to the Si-SiO$_2$ interface causes the formation of a potential well, which confines charge carriers to a region close to the Si-SiO$_2$ interface. In the potential well a quasi two dimensional electron gas (2DEG) or hole gas (2DHG) is formed. Carriers are free to move parallel to the interface, but are tightly confined in the direction normal to the interface. This confinement leads to quantized energy levels, thus the conduction or valence bands are split into subbands.

The calculations of the energy levels of carriers confined in a quantum well are commonly based on three approximations:

• The Hartree approximation, stating that each electron moves in the average potential produced by all other electrons, thus neglecting many-body effects.
• In the semiconductor, the effective mass approximation (EMA) is applied [Bastard81].

• For the calculation of the energy levels it can also be assumed that the barrier between the insulator and the semiconductor is large enough that the envelope wave functions vanish at the semiconductor-insulator interface which is reasonable for the Si-SiO$_2$ interface [Ando82].

While the bulk band structure and its modification under the influence of mechanical strain was discussed in the previous chapter, this chapter is devoted to the subband structure of electrons in the MOS inversion layer. The influence of strain on the subband structure is shown for various orientations of the Si-SiO$_2$ interface.

Subsections

• 4.1 Electron Confinement at the Semiconductor-Oxide Interface
  • 4.1.1 The Si-SiO$_2$ Interface
  • 4.1.2 Substrate Orientation (001)
  • 4.1.3 Substrate Orientation (110)
  • 4.1.4 Substrate Orientation (111)
  
  
• 4.2 Strain Effects
  • 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