171
Large Geometry MOSFET Compact Models
inversion region [25]. However, for most of the digital applications this
error is not significant due to the low magnitude of the current in this
region. There are other approaches reported, which could be used to
achieve better simulation results [30]. However, the improvement is not
significant.
4.5 Summary
In this chapter we have introduced the four terminal MOSFET devices.
The basic features of MOSFETs are described. A number of simplified
assumptions are used to derive threshold voltage model for long channel
devices. The fundamental Pao-Sah double-integral model and Brews chargesheet model are derived to characterize MOSFET devices. We have discussed
that the Pao-Sah and Brews models are computationally intensive to use for
VLSI circuit analysis with billions of transistors in an IC chip. We have used
simplified assumptions to derive the first-generation SPICE models for long
channel devices. In these basic models, we have discussed how different
equations for different regions of device operation are pieced together using
smoothing functions.
The advantages of the simplified regional models include easy implementation of physical effects using empirical relations and fast computation time.
On the other hand, the disadvantages include assumption of a constant f s
(=2f B ) in strong inversion, resulting in an inaccurate modeling of moderate
inversion, particularly, capacitances; and the model ignores inversion layer
thickness and small geometry effects. However, the basic model is widely
used for intuitive analysis of device performance.
Exercises
4.1 Pao-Sah model:
a. Complete the mathematical steps to derive Pao-Sah model given
by Equation 4.36. Clearly define all parameters and explain.
b. To calculate MOSFET drain current using Pao-Sah model from
Equation 4.36, the surface potential is numerically calculated
from Equation 4.37. However, Equation 4.37 is derived assuming strong inversion only. Derive an accurate expression similar to Equation 4.37, which is valid in all regions of MOSFET
operation.
Large Geometry MOSFET Compact Models
inversion region [25]. However, for most of the digital applications this
error is not significant due to the low magnitude of the current in this
region. There are other approaches reported, which could be used to
achieve better simulation results [30]. However, the improvement is not
significant.
4.5 Summary
In this chapter we have introduced the four terminal MOSFET devices.
The basic features of MOSFETs are described. A number of simplified
assumptions are used to derive threshold voltage model for long channel
devices. The fundamental Pao-Sah double-integral model and Brews chargesheet model are derived to characterize MOSFET devices. We have discussed
that the Pao-Sah and Brews models are computationally intensive to use for
VLSI circuit analysis with billions of transistors in an IC chip. We have used
simplified assumptions to derive the first-generation SPICE models for long
channel devices. In these basic models, we have discussed how different
equations for different regions of device operation are pieced together using
smoothing functions.
The advantages of the simplified regional models include easy implementation of physical effects using empirical relations and fast computation time.
On the other hand, the disadvantages include assumption of a constant f s
(=2f B ) in strong inversion, resulting in an inaccurate modeling of moderate
inversion, particularly, capacitances; and the model ignores inversion layer
thickness and small geometry effects. However, the basic model is widely
used for intuitive analysis of device performance.
Exercises
4.1 Pao-Sah model:
a. Complete the mathematical steps to derive Pao-Sah model given
by Equation 4.36. Clearly define all parameters and explain.
b. To calculate MOSFET drain current using Pao-Sah model from
Equation 4.36, the surface potential is numerically calculated
from Equation 4.37. However, Equation 4.37 is derived assuming strong inversion only. Derive an accurate expression similar to Equation 4.37, which is valid in all regions of MOSFET
operation.