141
Large Geometry MOSFET Compact Models
2D numerical analysis shows that the GCA is valid for most of the
channel length except near the drain end of the channel region.
Near the drain end of the channel, the longitudinal electric field E y
is comparable to the transverse electric field E x even for long channel devices and GCA breaks down. In spite of its failure near the
drain end, the GCA is used as it reduces the system to a 1D current
flow problem. The fact that we have to solve only a 1D Poisson’s
equation means that the charge expressions developed in Chapter 3
for an MOS capacitor system could be used for an MOS transistor,
with the modification that charge and potential will now be position
dependent in the y direction.
Assumption 2: Assume that only minority carriers contribute to I ds ;
for example, for an nMOSFET device, the hole current can be
neglected. In nMOSFETs, the majority carrier holes are created by
impact ionization and become important in describing the device
characteristics in the avalanche or breakdown regime. However,
in the normal operation range of MOSFET devices, the drain
current does not include breakdown regime, and therefore, the
assumption that the current in MOSFETs is due to the minority
carriers is valid under the normal biasing conditions, for example,
for nMOSFETs V ds ≥ 0 and V bs ≤ 0. Thus, the drain current model
needs to consider only the minority carrier current density, J n , for
nMOSFET devices.
Assumption 3: Assume there are no generation and recombination of carriers, that is, for an nMOSFET device R n = 0 = G n . Then considering
only the static characteristics of the device, the continuity equation
4.18 becomes
∇
=
⋅ J n 0
(4.20)
This implies that the total drain current I ds is a constant at any point
along the channel of the device.
Assumption 4: Assume that the current flows in the y direction along
the channel only, that is, df n /dx = 0. Thus, the electron quasi-Fermi
potential, f n , is a constant in the x direction. Then from Equation 4.17,
the electron current density is given by
J x y
qn x y
x y y
n
n
n
( , )
( , ) ( , )
= −
∂
∂
µ
φ
(4.21)
Since the cross-sectional area of the channel in which the current
flows is the channel width, W, times the channel length, L, integrating Equation 4.21 across the depth x and width z, we get I ds at any
point y in the channel as
Large Geometry MOSFET Compact Models
2D numerical analysis shows that the GCA is valid for most of the
channel length except near the drain end of the channel region.
Near the drain end of the channel, the longitudinal electric field E y
is comparable to the transverse electric field E x even for long channel devices and GCA breaks down. In spite of its failure near the
drain end, the GCA is used as it reduces the system to a 1D current
flow problem. The fact that we have to solve only a 1D Poisson’s
equation means that the charge expressions developed in Chapter 3
for an MOS capacitor system could be used for an MOS transistor,
with the modification that charge and potential will now be position
dependent in the y direction.
Assumption 2: Assume that only minority carriers contribute to I ds ;
for example, for an nMOSFET device, the hole current can be
neglected. In nMOSFETs, the majority carrier holes are created by
impact ionization and become important in describing the device
characteristics in the avalanche or breakdown regime. However,
in the normal operation range of MOSFET devices, the drain
current does not include breakdown regime, and therefore, the
assumption that the current in MOSFETs is due to the minority
carriers is valid under the normal biasing conditions, for example,
for nMOSFETs V ds ≥ 0 and V bs ≤ 0. Thus, the drain current model
needs to consider only the minority carrier current density, J n , for
nMOSFET devices.
Assumption 3: Assume there are no generation and recombination of carriers, that is, for an nMOSFET device R n = 0 = G n . Then considering
only the static characteristics of the device, the continuity equation
4.18 becomes
∇
=
⋅ J n 0
(4.20)
This implies that the total drain current I ds is a constant at any point
along the channel of the device.
Assumption 4: Assume that the current flows in the y direction along
the channel only, that is, df n /dx = 0. Thus, the electron quasi-Fermi
potential, f n , is a constant in the x direction. Then from Equation 4.17,
the electron current density is given by
J x y
qn x y
x y y
n
n
n
( , )
( , ) ( , )
= −
∂
∂
µ
φ
(4.21)
Since the cross-sectional area of the channel in which the current
flows is the channel width, W, times the channel length, L, integrating Equation 4.21 across the depth x and width z, we get I ds at any
point y in the channel as