267
Compact MOSFET Models for RF Applications
The basic model given by Equation 7.13 is not adequate for the characterization
of noise in advanced MOSFET devices. Therefore, in this section, the unified flicker noise model that explains most of the observed behavior of lowfrequency noise is presented.
Let us assume that y is the distance along the direction of channel length,
z is the distance along the direction of channel width, and x is the coordinate along the direction of oxide thickness perpendicular to both the y and z
directions.
For a section of channel width W eff and length Δy in a MOSFET, fluctuations
in the amount of trapped interface charge will introduce correlated fluctuations in the channel carrier concentration and mobility. The resulting fractional change in the local drain current can be expressed as [29]
δ
δ
δ
δµ
δ
δ
I
I
N
N
N
N
N
ds
ds
t
eff
t
t
=
±
⋅
1
∆
∆
∆
∆
∆
(7.14)
where:
ΔN = NW eff Δy
ΔN t = N t W eff Δy
N is the number of channel carriers per unit area
N t is the number of occupied traps per unit area
The sign in front of the mobility term in Equation 7.14 is dependent on
whether the trap is neutral or charged when filled [29]. The ratio of the fluctuations in the carrier number to the fluctuations in occupied trap number,
R n = δΔN/δΔN t , is close to unity at strong inversion but assumes smaller values at other bias conditions [30]. A general expression for R n is
R
N
N
C
C
C
C
C
n
t
inv
ox
inv
d ep
it
=
=−
+
+
+
δ
δ
∆
∆
(7.15)
where:
C inv is the inversion layer capacitance
C dep is the depletion layer capacitance
C it is the interface trap capacitance
The relationship between C inv and N can be approximated as
C
q
v
N
inv
kT
≅
(7.16)
where:
v kT is the thermal voltage
Thus, Equation 7.15 can be rewritten as,
R
N
N N
n = − + *
(7.17)
Compact MOSFET Models for RF Applications
The basic model given by Equation 7.13 is not adequate for the characterization
of noise in advanced MOSFET devices. Therefore, in this section, the unified flicker noise model that explains most of the observed behavior of lowfrequency noise is presented.
Let us assume that y is the distance along the direction of channel length,
z is the distance along the direction of channel width, and x is the coordinate along the direction of oxide thickness perpendicular to both the y and z
directions.
For a section of channel width W eff and length Δy in a MOSFET, fluctuations
in the amount of trapped interface charge will introduce correlated fluctuations in the channel carrier concentration and mobility. The resulting fractional change in the local drain current can be expressed as [29]
δ
δ
δ
δµ
δ
δ
I
I
N
N
N
N
N
ds
ds
t
eff
t
t
=
±
⋅
1
∆
∆
∆
∆
∆
(7.14)
where:
ΔN = NW eff Δy
ΔN t = N t W eff Δy
N is the number of channel carriers per unit area
N t is the number of occupied traps per unit area
The sign in front of the mobility term in Equation 7.14 is dependent on
whether the trap is neutral or charged when filled [29]. The ratio of the fluctuations in the carrier number to the fluctuations in occupied trap number,
R n = δΔN/δΔN t , is close to unity at strong inversion but assumes smaller values at other bias conditions [30]. A general expression for R n is
R
N
N
C
C
C
C
C
n
t
inv
ox
inv
d ep
it
=
=−
+
+
+
δ
δ
∆
∆
(7.15)
where:
C inv is the inversion layer capacitance
C dep is the depletion layer capacitance
C it is the interface trap capacitance
The relationship between C inv and N can be approximated as
C
q
v
N
inv
kT
≅
(7.16)
where:
v kT is the thermal voltage
Thus, Equation 7.15 can be rewritten as,
R
N
N N
n = − + *
(7.17)