35
Review of Basic Device Physics
From Equation 2.37, it is found that when L = W, the diffused layer
becomes a square with R = ρ sh . Thus, the total resistance of a diffusion
line is simply ρ sh times the number of squares in the path of current and
is expressed in units of Ω per square (Ω/□). The process parameters that
determine the sheet resistance of a layer are the resistivity and thickness t
of the layer. Since the resistivity is a function of carrier concentration and
mobility, both of which are functions of temperature, ρ sh is temperature
dependent.
2.2.5.4 Velocity Saturation
The field versus velocity linear relationship, given by Equation 2.28 in
Section 2.2.5.1, is valid only for low electric field (<1 × 10 4 V cm –1 ) and carriers are in equilibrium with the lattice. At higher electric fields, the average
carrier energy increases and carriers lose their energy by optical-phonon
emission nearly as fast as they gain it from the field. This causes a decrease
in μ from its low field value as the field increases until finally the drift velocity reaches a limiting value v sat , referred to as the saturation velocity. This
phenomenon is called the velocity saturation. For silicon, a typical value of
v sat = 1.07 × 10 7 cm sec –1 for electrons and occurs at an electric field of about
2 × 10 4 V cm –1 . The corresponding values for holes are v sat = 8.34 × 10 6 cm
sec –1 and E ≅ 5.0 × 10 4 V cm –1 .
It is found that the measured value of drift velocity for electrons and holes
in silicon is a function of the applied field E and can be approximated by the
following expression
v
v
E E
E E
d
s at
c
c
=
+ ( )
/
/
/
1
1
β
β
(2.38)
where:
E c is the critical electric field at which carrier velocity saturates
The parameters v sat , E c , and β in Equation 2.38 are given in Table 2.2.
Figure 2.7 shows the simulated value of drift velocity for electrons and
holes at 300° K in silicon as a function of the applied field E obtained by
Equation 2.38. It is observed from Figure 2.7 that at low fields, the carrier
TABLE 2.2
Parameters for Field Dependence of Drift Velocity for Silicon at 300 K
Parameter
v sat (cm sec –1 )
E c (V cm –1 )
β
Electrons
1.07 × 10 7
6.91 × 10 3
1.11
Holes
8.34 × 10 6
1.45 × 10 4
2.637
Review of Basic Device Physics
From Equation 2.37, it is found that when L = W, the diffused layer
becomes a square with R = ρ sh . Thus, the total resistance of a diffusion
line is simply ρ sh times the number of squares in the path of current and
is expressed in units of Ω per square (Ω/□). The process parameters that
determine the sheet resistance of a layer are the resistivity and thickness t
of the layer. Since the resistivity is a function of carrier concentration and
mobility, both of which are functions of temperature, ρ sh is temperature
dependent.
2.2.5.4 Velocity Saturation
The field versus velocity linear relationship, given by Equation 2.28 in
Section 2.2.5.1, is valid only for low electric field (<1 × 10 4 V cm –1 ) and carriers are in equilibrium with the lattice. At higher electric fields, the average
carrier energy increases and carriers lose their energy by optical-phonon
emission nearly as fast as they gain it from the field. This causes a decrease
in μ from its low field value as the field increases until finally the drift velocity reaches a limiting value v sat , referred to as the saturation velocity. This
phenomenon is called the velocity saturation. For silicon, a typical value of
v sat = 1.07 × 10 7 cm sec –1 for electrons and occurs at an electric field of about
2 × 10 4 V cm –1 . The corresponding values for holes are v sat = 8.34 × 10 6 cm
sec –1 and E ≅ 5.0 × 10 4 V cm –1 .
It is found that the measured value of drift velocity for electrons and holes
in silicon is a function of the applied field E and can be approximated by the
following expression
v
v
E E
E E
d
s at
c
c
=
+ ( )
/
/
/
1
1
β
β
(2.38)
where:
E c is the critical electric field at which carrier velocity saturates
The parameters v sat , E c , and β in Equation 2.38 are given in Table 2.2.
Figure 2.7 shows the simulated value of drift velocity for electrons and
holes at 300° K in silicon as a function of the applied field E obtained by
Equation 2.38. It is observed from Figure 2.7 that at low fields, the carrier
TABLE 2.2
Parameters for Field Dependence of Drift Velocity for Silicon at 300 K
Parameter
v sat (cm sec –1 )
E c (V cm –1 )
β
Electrons
1.07 × 10 7
6.91 × 10 3
1.11
Holes
8.34 × 10 6
1.45 × 10 4
2.637