88
Strain-Engineered MOSFETs
hole mobility enhancement under biaxial tensile strain is mainly due to the
large reduction of hole intervalley scattering from energy splitting between
light-hole (LH) and heavy-hole (HH) bands, especially for stress higher than
1 GPa. However, this energy splitting between LH and HH bands decreases
at high vertical electric field (E eff ) due to the quantum mechanical confinement effect.
Uniaxial strain along the silicon channel has been also widely used to
enhance both electron and hole mobilities. Similar to biaxial tensile strain,
uniaxial tensile strain improves electron mobility by reducing the net inplane conductivity effective mass by band repopulation; i.e., electrons preferentially occupy the four lower energy valleys (unstrained valleys) with
small in-plane effective mass. Intervalley scattering is also suppressed by
the energy splitting between strained valleys (two in-plane valleys) and
unstrained valleys (two in-plane and two out-of-plane valleys), but this is
smaller than that for biaxial strain, giving an advantageously small n-MOSFET V th shift. The reduction of hole intervalley scattering from energy splitting between light-hole (LH) and heavy-hole (HH) bands also improves hole
mobility. In particular, the band splitting is maintained even at high E eff due
to anisotropic out-of-plane hole effective masses of top (LH) and second
(HH) bands. On the other hand, uniaxial compressive strain improves hole
mobility more effectively than biaxial tensile strain. Under uniaxial compressive strain, the net in-plane hole conductivity effective mass becomes
much smaller due to reduced in-plane hole conductivity effective mass
of the top (LH) band, while biaxial tensile strain shows the opposite top
band curvature.
Uniaxial tensile strain also enhances electron mobility by reducing effective mass and suppressing intervalley scattering. However, the energy splitting between strained valleys and unstrained valleys is smaller than that of
biaxial strain. In this chapter, the basic physical definitions, such as the strain
and stress tensors, are introduced and it is shown how they are related.
Different methods of calculating the effect of strain on the band structure are
presented. Since carrier mobility is a key parameter for the simulation of the
electrical characteristics of semiconductor devices, several analytical models
have been developed capturing the dependence of mobility on temperature,
doping, and electric field [3–7]. All these models are developed for unstrained
Si. For device simulation of strained-Si MOSFETs, different types of strainrelated mobility models need to be developed [8, 9]. A simple piezoresistance
model is introduced to quantify strain-induced mobility enhancement. The
piezoresistance coefficients with arbitrary crystallographic orientations can
be obtained by an appropriate coordinate transformation.
Strain-Engineered MOSFETs
hole mobility enhancement under biaxial tensile strain is mainly due to the
large reduction of hole intervalley scattering from energy splitting between
light-hole (LH) and heavy-hole (HH) bands, especially for stress higher than
1 GPa. However, this energy splitting between LH and HH bands decreases
at high vertical electric field (E eff ) due to the quantum mechanical confinement effect.
Uniaxial strain along the silicon channel has been also widely used to
enhance both electron and hole mobilities. Similar to biaxial tensile strain,
uniaxial tensile strain improves electron mobility by reducing the net inplane conductivity effective mass by band repopulation; i.e., electrons preferentially occupy the four lower energy valleys (unstrained valleys) with
small in-plane effective mass. Intervalley scattering is also suppressed by
the energy splitting between strained valleys (two in-plane valleys) and
unstrained valleys (two in-plane and two out-of-plane valleys), but this is
smaller than that for biaxial strain, giving an advantageously small n-MOSFET V th shift. The reduction of hole intervalley scattering from energy splitting between light-hole (LH) and heavy-hole (HH) bands also improves hole
mobility. In particular, the band splitting is maintained even at high E eff due
to anisotropic out-of-plane hole effective masses of top (LH) and second
(HH) bands. On the other hand, uniaxial compressive strain improves hole
mobility more effectively than biaxial tensile strain. Under uniaxial compressive strain, the net in-plane hole conductivity effective mass becomes
much smaller due to reduced in-plane hole conductivity effective mass
of the top (LH) band, while biaxial tensile strain shows the opposite top
band curvature.
Uniaxial tensile strain also enhances electron mobility by reducing effective mass and suppressing intervalley scattering. However, the energy splitting between strained valleys and unstrained valleys is smaller than that of
biaxial strain. In this chapter, the basic physical definitions, such as the strain
and stress tensors, are introduced and it is shown how they are related.
Different methods of calculating the effect of strain on the band structure are
presented. Since carrier mobility is a key parameter for the simulation of the
electrical characteristics of semiconductor devices, several analytical models
have been developed capturing the dependence of mobility on temperature,
doping, and electric field [3–7]. All these models are developed for unstrained
Si. For device simulation of strained-Si MOSFETs, different types of strainrelated mobility models need to be developed [8, 9]. A simple piezoresistance
model is introduced to quantify strain-induced mobility enhancement. The
piezoresistance coefficients with arbitrary crystallographic orientations can
be obtained by an appropriate coordinate transformation.