223
Compact Models for Small Geometry MOSFETs
represent the halo doping, model V th for nonuniform lateral channel
doping. Given L = channel length, and L y = halo spread inside L at
the source/drain ends:
a. Derive an expression for the average channel doping concentration to account for the halo doping in the channel. Clearly define
all parameters and explain any assumptions you make.
b. Show the expressions for model parameters from your work in
part (a).
c. How would you extract the model parameters obtained in part (b)?
d. Compare the model parameters in part (b) with that derived
using box-shaped profiles given by Equation 5.12. Explain.
5.4 In order to derive an effective inversion carrier mobility model, it is
shown that the effective channel electrical field, E eff = [0.5Q inv + Q b ]/ε si ,
where Q inv and Q b are the inversion charge and bulk (depletion) charge
under the gate, respectively, and ε si is the dielectric constant of silicon.
The dependence of surface mobility μ s on process parameters such as T ox
and N sub and the terminal voltages are lumped in E eff . Assume V gs > V th
and small V ds :
a. Show that E eff ≅ (V gs + V th )/6T ox .
b. If the effective mobility is modeled by: μ eff = μ 0 /[1 + E eff /E 0 )] ν ,
where μ s = μ 0 @ V gs = 0 and E 0 and ν are parameters determined
from the measured data. Use the expression for E eff in part (a) to
show that:
µ
µ
eff
a
g s
t h
o x
b
gs
th
ox
U V V T
U V V T
=
+
+
(
)
+
+
(
)
0
2
1
where:
U a and U b are the model parameters that are determined
experimentally from I–V data of MOSFET devices
Clearly state any assumptions you make.
5.5 An nMOSFET device is designed with a gate oxide thickness of 5 nm
and a uniformly doped substrate with N a = 5 × 10 17 cm −3 . Assuming
that the “ON” state of this device is characterized by f s = 2f B and
the “OFF” state by f s = f B , estimate the ratio of ON to OFF currents
flowing in the device.
5.6 Complete the mathematical steps to show that the MOSFET drain
current expression in the linear region is given by Equation 5.74.
5.7 Complete the mathematical steps to show that the general expression for MOSFET saturation drain voltage is given by Equation 5.79.
Compact Models for Small Geometry MOSFETs
represent the halo doping, model V th for nonuniform lateral channel
doping. Given L = channel length, and L y = halo spread inside L at
the source/drain ends:
a. Derive an expression for the average channel doping concentration to account for the halo doping in the channel. Clearly define
all parameters and explain any assumptions you make.
b. Show the expressions for model parameters from your work in
part (a).
c. How would you extract the model parameters obtained in part (b)?
d. Compare the model parameters in part (b) with that derived
using box-shaped profiles given by Equation 5.12. Explain.
5.4 In order to derive an effective inversion carrier mobility model, it is
shown that the effective channel electrical field, E eff = [0.5Q inv + Q b ]/ε si ,
where Q inv and Q b are the inversion charge and bulk (depletion) charge
under the gate, respectively, and ε si is the dielectric constant of silicon.
The dependence of surface mobility μ s on process parameters such as T ox
and N sub and the terminal voltages are lumped in E eff . Assume V gs > V th
and small V ds :
a. Show that E eff ≅ (V gs + V th )/6T ox .
b. If the effective mobility is modeled by: μ eff = μ 0 /[1 + E eff /E 0 )] ν ,
where μ s = μ 0 @ V gs = 0 and E 0 and ν are parameters determined
from the measured data. Use the expression for E eff in part (a) to
show that:
µ
µ
eff
a
g s
t h
o x
b
gs
th
ox
U V V T
U V V T
=
+
+
(
)
+
+
(
)
0
2
1
where:
U a and U b are the model parameters that are determined
experimentally from I–V data of MOSFET devices
Clearly state any assumptions you make.
5.5 An nMOSFET device is designed with a gate oxide thickness of 5 nm
and a uniformly doped substrate with N a = 5 × 10 17 cm −3 . Assuming
that the “ON” state of this device is characterized by f s = 2f B and
the “OFF” state by f s = f B , estimate the ratio of ON to OFF currents
flowing in the device.
5.6 Complete the mathematical steps to show that the MOSFET drain
current expression in the linear region is given by Equation 5.74.
5.7 Complete the mathematical steps to show that the general expression for MOSFET saturation drain voltage is given by Equation 5.79.