236
8 Transport
Fig. 8.11 Piezoresistive coefficient for current parallel (perpendicular) to the stress π l as blue lines (π t , red lines) for
uniaxially stressed Si (001) at room temperature, a for p-type Si, b for n-type Si. The upper (lower) halves of the graphs
show positive (negative) values of the piezoresistive coefficient, i.e. resistivity increases (decreases) with tensile stress.
The solid circle indicates the value of |π| = 10 −9 Pa −1 , the dashed circle half that value. Adapted from [752]
Table 8.3 Piezoresistivity coefficients (in 10 −11 Pa −1 ) for Si, Ge and GaAs at room temperature
Material
ρ (Ω cm)
π 11
π 12
π 44
References
p-Si
7.8
6.6
−1.1
138.1
[749]
n-Si
11.7
−102.2
53.4
−13.6
[749]
p-Ge (Ge:Ga)
15.0
−10.6
5.0
98.6
[749]
n-Ge (Ge:As)
9.9
−4.7
−5.0
−137.9
[749]
p-GaAs
∼10 −3
−12.0
−0.6
46
[753]
n-GaAs
∼10 −3
−3.2
−5.4
−2.5
[753, 754]
π =
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
π 11 π 12 π 12 0 0 0
π 12 π 11 π 12 0 0 0
π 12 π 12 π 11 0 0 0
0 0 0 π 44 0 0
0 0 0 0 π 44 0
0 0 0 0 0 π 44
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
.
(8.28)
Values for the piezoelectric coefficients are given in Table 8.3 for Si, Ge and GaAs.
The piezoelectric effect has been discussed in detail [750] and modeled for p-type Si [751]. We shall
only give a simple example which is particularly relevant for advanced CMOS design (Sect. 24.5.5); the
directional dependence of the piezoresistive coefficient of silicon is shown for uniaxial stress within
in the (001) plane in Fig. 8.11. Uniaxial tensile stress increases hole resistivity along 110 stress
directions, compressive stress thus increases hole conductivity.
8.4 High-Field Transport
In the case of small electric fields the scattering events are elastic. The drift velocity is linearly proportional to the electric field. The average thermal energy is close to its thermal value 3kT /2 and
the carriers are close to their band edges (Fig. 8.12a). The scattering efficiency, however, is reduced
8 Transport
Fig. 8.11 Piezoresistive coefficient for current parallel (perpendicular) to the stress π l as blue lines (π t , red lines) for
uniaxially stressed Si (001) at room temperature, a for p-type Si, b for n-type Si. The upper (lower) halves of the graphs
show positive (negative) values of the piezoresistive coefficient, i.e. resistivity increases (decreases) with tensile stress.
The solid circle indicates the value of |π| = 10 −9 Pa −1 , the dashed circle half that value. Adapted from [752]
Table 8.3 Piezoresistivity coefficients (in 10 −11 Pa −1 ) for Si, Ge and GaAs at room temperature
Material
ρ (Ω cm)
π 11
π 12
π 44
References
p-Si
7.8
6.6
−1.1
138.1
[749]
n-Si
11.7
−102.2
53.4
−13.6
[749]
p-Ge (Ge:Ga)
15.0
−10.6
5.0
98.6
[749]
n-Ge (Ge:As)
9.9
−4.7
−5.0
−137.9
[749]
p-GaAs
∼10 −3
−12.0
−0.6
46
[753]
n-GaAs
∼10 −3
−3.2
−5.4
−2.5
[753, 754]
π =
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎝
π 11 π 12 π 12 0 0 0
π 12 π 11 π 12 0 0 0
π 12 π 12 π 11 0 0 0
0 0 0 π 44 0 0
0 0 0 0 π 44 0
0 0 0 0 0 π 44
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎠
.
(8.28)
Values for the piezoelectric coefficients are given in Table 8.3 for Si, Ge and GaAs.
The piezoelectric effect has been discussed in detail [750] and modeled for p-type Si [751]. We shall
only give a simple example which is particularly relevant for advanced CMOS design (Sect. 24.5.5); the
directional dependence of the piezoresistive coefficient of silicon is shown for uniaxial stress within
in the (001) plane in Fig. 8.11. Uniaxial tensile stress increases hole resistivity along 110 stress
directions, compressive stress thus increases hole conductivity.
8.4 High-Field Transport
In the case of small electric fields the scattering events are elastic. The drift velocity is linearly proportional to the electric field. The average thermal energy is close to its thermal value 3kT /2 and
the carriers are close to their band edges (Fig. 8.12a). The scattering efficiency, however, is reduced