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Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 135
CHAPTER CHAPTER CHAPTER CHAPTER 5555
Small Signal Intrinsic Equivalent Circuit Model of Small Signal Intrinsic Equivalent Circuit Model of Small Signal Intrinsic Equivalent Circuit Model of Small Signal Intrinsic Equivalent Circuit Model of
Cylindrical/Surrounded Gate MOSFET for Cylindrical/Surrounded Gate MOSFET for Cylindrical/Surrounded Gate MOSFET for Cylindrical/Surrounded Gate MOSFET for
Microwave Frequency ApplicationsMicrowave Frequency ApplicationsMicrowave Frequency ApplicationsMicrowave Frequency Applications
5.1. INTRODUCTION
Advancement in radio frequency integrated circuits (RFICs) in the last decade has
been driving a huge market for communications in various forms. These developments
have created a rapid expanding market for RFICs, which were previously dominated by
slow growing military and cable television industries [Lai07]. The technical requirements
imposed on these transceiver components were truly challenging. At the same time, the
consumer’s demand on low-cost, low-power and high-volume radio frequency devices
that were formerly implemented using bulky, expensive, and power-hungry hybrid
components were very large. Drawing an analogy to digital integrated circuit technology,
it appeared that the optimum technology choice for RFIC applications might follow the
same path that digital IC implementations followed towards the CMOS devices with the
costs dropping dramatically as the level of integration increases [Schmitz91]. The
MOSFETs used in digital CMOS have been successfully miniaturized to achieve higher
speed operation. Moreover, with scaling of the device dimensions into the sub-50 nm
regime, the transistors have achieved cut-off frequencies in the GHz regime, making
CMOS technology suitable for wireless communication and other RF applications
[Kilchytska03, Larson03, Saito98 & Yang02].
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 136
The designing of analog and digital integrated circuits requires an authentic high
speed device model, which is an important tool to carry out high-speed digital
applications. A large-signal model [Collantes95 & Ho97] should be used which will describe
the active device over the whole operating frequency range. The most suitable method to
examine a MOSFET at high frequencies involves S-parameter measurements [Curtice84].
For the characterization of the broadband behaviour of a device, measurements have to be
performed at different bias, as the electrical properties of a MOSFET strongly depend on
the applied gate bias and drain to source bias and also the frequency range of interest over
which it measured. Using an equivalent circuit consisting of different intrinsic circuit
elements, S-parameters were evaluated in-terms of fifteen frequency impendent variables.
Several commercially available programs such as MATLAB, MATHCAD, numerical
methods, simulated methods etc. were present to optimize some of or all of these
parameters [Nagatomo93]. Although in general the measured S-parameter approximated by
these methods and the resulting element values may differ considerably from their actual
physical values [Curtice84, Nagatomo93 & Lin94]. The analytical methods [Rorsman96,
Dambrine98, Berroth90 & Minasian77] on the other hand allow to extract the equivalent
circuit parameters in a straightforward manner. The most favourable extraction method
was originally proposed by Minasian [Minasian77] and was later modified by Dambrine
et.al [Dambrine98], and Berroth & Bosch [Berroth90]. In this method the series and shunt
parasitic elements of the device were first extracted by measuring the S-parameters under
suitable passive modes of its operation. Once these parasitic elements are carefully
determined, the S-parameters are then measured under active mode of device operation.
These are then successively transformed into Z (Impedance) parameters and Y
(Admittance) parameters.
In the analysis presented in this chapter, a similar equivalent circuit model has been
applied for CGT/SGT MOSFET [Ghosh12a & Auth97] then Y parameters are analytically
calculated from the equivalent circuit and then the (Scattering) S-parameters are
extracted. The advantage of CGT/SGT MOSFET is that it allows excellent control of the
charges over the channel thus minimizing the scaling limitations caused due to the short
channel effects (SCEs), thereby, increasing the device performances. In CGT/SGT
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 137
MOSFET the source, drain and gate are arranged vertically and the sidewalls of the pillar
are used as the channel region due to which the structure has a large effective channel
width even in a small-occupied area. As a result, the channel length can be adjusted
without changing the occupied area of the MOSFET resulting in high packing density
Due to high packing density and immunity against short channel effects the CGT/SGT
MOSFET has become the main point of interest in this analysis for studying CGT/SGT
MOSFET behaviour at broad frequency range.
Admittance parameters (Y-parameters) of CGT/SGT MOSFET were evaluated
using the analysis of small signal equivalent circuit. Scattering parameters (S-parameters)
and power gains such as maximum stable gain, unilateral power gain and maximum
unilateral transducer power gain [Ghosh12b] were then evaluated over the frequency range
of interest. The different power gains of CGT/SGT MOSFET were compared with bulk
MOSFET and it was found that CGT/SGT MOSFET were better as compared to bulk
MOSFET due to its cylindrical profile; hence the CGT/SGT MOSFET had better
efficiency. A good agreement is obtained between model and simulated data which
validate the theoretical analysis.
5.2. ANALYTICAL MODELING
5.2.1. Unified Charge Control Model
The structure of CGT/SGT MOSFET considered in the analysis is shown in the Fig. 5.01.
Better electrostatic control has been obtained in CGT/SGT MOSFET due to which the
short channel effects associated to gradual channel approximation can be neglected.
Hence, the electrostatic behaviour of the CGT/SGT MOSFET has been described by 1D
Poisson’s equation in the radial direction.
In a lightly doped CGT/SGT MOSFET, using Poisson’s equation the potential
distribution in the silicon pillar takes the form as
2
2
( )1
Vqd d k T k Te
R d r qd r
ψψ ψ
δ
−
+ =
(5.01)
where
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 138
2
( )
q ni
kTsi
δε
= (5.02)
q (1.6 x 10-19
C) is the electronic charge, R is the radius of the cylinder, in (1.45 x 1016
cm-3
) is the intrinsic carrier concentration, siε (11.7εo) is the relative permitivity of silicon
(εo=8.85x 10-12
), V is the electron quasi fermi potential, k is the Boltzman s’ constant.
Fig. 5.01 Cross sectional view of Cylindrical/Surrounded gate MOSFET. tox = 2.5nm, R=10nm, L=50nm,
Фm=4.8eV, ND+=5 x 10
19 cm
-3, NA=10
16 cm
-3, Vgs=0.5V & 1V and Vds=0.5V unless stated otherwise.
Equation (5.01) is solved subjected to the following boundary conditions:[Jiménez04b]
( 0) 0d
rdr
ψ= =
(5.03)
( ) sr Rψ ψ= = (5.04)
where R is the radius of the device and s
ψ is the surface potential.
The well known solution for the differential equation (5.01) is [Jiménez04a]
2 1( ) 2 ln
Brr A kT
qψ
+= −
(5.05)
where A and B are the constants and are related as, [Jiménez04a]
8ln
BkT
Aq
δ
− = (5.06)
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 139
substituting (5.06) in (5.05) the electrostatic potential ( )rψ in radial direction is obtained
as
( )2
2
8( ) ln
1
kT Br
q Brψ
δ
− =
+
(5.07)
Consider the current flow in the channel direction only. V, electron quasi fermi potential
is assumed to be constant along the radial direction, thus (5.07) becomes
( )2
2
8( ) ln
1
kT Br V
q Brψ
δ
− = +
+
(5.08)
The mobile sheet charge density controlled by gate electrode is given as:
( )ox gs m sQ C V φ ψ= − ∆ − (5.09)
where
ln 1
oxox
ox
Ct
RR
ε=
+
(5.10)
mφ∆ is the workfunction difference between the gate electrode and intrinsic silicon.
Gauss s’ Law at r=R is expressed as,
si
r R
dQ
dr
ψε
=
= (5.11)
differentiating (5.08) and using (5.11) the mobile sheet charge can also be expressed as,
2
4
( 1)
sikTBR
Qq BR
ε−=
+ (5.12)
Thus equating (5.09) and (5.12)
( )2
gs m s
q BRV
kT
ηφ ψ
β
−− ∆ − = (5.13)
where
4si
oxC R
εη = and (5.14)
21 BRβ = + (5.15)
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 140
also, at r=R (5.08) becomes
2
8lns
kT BV
qψ
δβ
−= +
(5.16)
substituting (5.16) in (5.13)
( ) ( ) ( )( )2
2
18ln ln 1 ln
gs m
qV V
kT R
βφ β β η
δ β
− − ∆ − − = − − +
(5.17)
β can be solved from (5.17) as a function of V. Where V is the channel potential, varies
V=0 at the source end to V=Vds at the drain end.
Rewriting (5.12), Q in terms of β is expressed as,
0
1Q Q
β
β
−=
(5.18)
where 0
4si
kTQ
qRε= (5.19)
The drain current in SGT/CGT MOSFET is calculated using unified charge model
[Iñiguez05] given below
2ds
dVI R Q
dzπ µ= (5.20)
where µ the effective mobility of the electrons,
integrating (5.20) and taking the limits from 0 to Vds
2dsI dz R QdVπ µ=∫ ∫ (5.21)
Drain current in terms of β is obtained as
( )2( )
D
Sds
R dVI Q d
L d
β
β
π µβ β
β
=
∫ (5.22)
where L is the channel length, Sβ and Dβ are values of β at the source end and the drain
end respectively.
dV
dβis obtained by differentiating (5.17)
2
1 2
1
dV kT
d q
η
β β β β
= + +
− (5.23)
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 141
Putting (5.23) and (5.18) in (5.22), drain current is obtained as
( ) ( )
( ) ( )
2 22
2 2
4 12 1 ln4 2 2
D Ssi D S Sds
D S DD S
kTIL q
β βπµε β β βη η
β β ββ β
− − = + − +
………………………………...(5.24)
5.2.2. Capacitance Model
The total charge is obtained by integrating the mobile charge sheet density over the
channel length
20
L
Q R Q d zT o l π= − ∫ (5.25)
Electric field is represented as dV
Edz
=
(5.20) becomes,
2
ds
R QdVdz
I
π µ= (5.26)
replacing dz in (5.25) and changing the limits of integration from 0-L to 0-Vds
2 2(2 )
0
ds
ds
VQ R Q dV
Tol I
µπ= − ∫ (5.27)
QTol in terms of β can be obtained using (5.23) as,
2 2
2
1 2(2 ) ( )
1
D
dsS
kTQ R Q d
Tol qI
β ηµπ β β
β β ββ
= − + +∫
− (5.28)
Integrating (5.28),
3 2 3 2
3 1 3 1
3 3D S
D SD D S S
QTol
η η η η η ηα β β
β ββ β β β
− + − += − + + − + − −
(5.29)
Where α
2 2 3 3
3
64 si
ds
k T
I q
π ε µα
−=
(5.30)
Now, the total gate charge is given by
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 142
g Tol oxQ Q Q= − − (5.31)
where oxQ is the total oxide fixed charge. Neglecting oxQ in comparison to TolQ ,
3 2 3 2
3 1 3 1
3 3g D S
D SD D S S
Qη η η η η η
α β ββ ββ β β β
− + − += − − + + − + − −
(5.32)
The intrinsic capacitances Cgs and Cgd are defined respectively as [Liu09]
g
gs
s
dQC
dV= − (5.33)
and
g
gd
d
dQC
dV= − (5.34)
From (5.33)
g sgs
s s
dQ dC
d dV
β
β= − (5.35)
from (5.23) s
s
d
dV
β at the source is given as,
2
1 2
1
s
s s s s
dV kT
d q
η
β β β β
= + +
− (5.36)
differentiating (5.32) with respect tos
β ,
( )2 3 4
2 11 3g
s s s s s
dQ
d
ηη ηα
β β β β β
− −= + + +
(5.37)
combining (5.36) and (5.37) gs
C is obtained as,
( ) ( )2 3 4
1 2
21
3 2 11gs
kTs s s s
qs s s
Cη
β β β
η ηα η
β β β β + + −
− − = − + + −
(5.38)
In exactly similar way using (5.23), (5.32) and (5.34), gate drain capacitance gd
C is
obtained as,
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 143
( )2 3 4
1 2
21
2 11 3gd
kTd d d d
qd d d
Cη
β β β
ηα η η
β β β β + + −
− −= + + +
(5.39)
5.3. MODEL FORMULATION
5.3.1. Admittance Parameters
The intrinsic small signal equivalent circuit of CGT/SGT MOSFET used in the analysis
is shown in Fig. 5.02 comprised of intrinsic elements. Using network analysis
techniques, the Y parameters for the simplified circuit model can be derived and
expressed in terms of intrinsic small signal parameters [Berroth90]
Fig. 5.02. Small signal equivalent circuit of Cylindrical/Surrounded gate MOSFET.
Using nodal analysis the current I1 at input port and current I2 at output port are evaluated
as fellows
211 iiI += (5.40)
2 5 4 3 2I i i i i= + + − (5.41)
therefore, I1 can be obtained as,
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 144
( )1 211
1 1i gd
gs gd
V VVI
R Rj C j Cω ω
−= +
+ +
(5.42)
where 2 fω π= ; f is the frequency of operation.
Further rationalizing (5.42)
( ) ( )( )1 1 2
1( 1) (1 )
gs gd gd
gs i gd gd
V j C V V j C RI
j C R j C R
ω ω
ω ω
−= +
+ + (5.43)
similarly I2 can be obtained as,
( )1 222 21 1d m
gddsgd
V VVI V g Y
Rj Cj C
ωω
−= + + −
+ (5.44)
where, exp( )m gs mY V g jωτ= − (5.45)
Vgs is the voltage drop at Cgs.
By applying voltage divider rule at Cgs
1
1
1
1 1
gs
gs
i gsi
gs
Vj C V
VR j C
Rj C
ω
ωω
= =++
(5.46)
substituting (5.45) and (5.46) in (5.43),
( )( )( )1 21
2 2 2 exp1 1
gd
ds d mgs i gd gd
V V j CVI V j C V g g j
j C R j C R
ωω ωτ
ω ω
−= + + − −
+ + (5.47)
The different Y- parameters can now be evaluated as follows:
(A) Y11, is the input admittance parameter, which is the ratio of the current at input
port to the voltage at input port when the output port is short circuited
2
111
1 0V
IY
V=
= (5.48)
From (5.43) making V2=0
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 145
1
1 (1 ) (1 )
gs gd gd
gs i gd gd
j C j C RI
V j C R j C R
ω ω
ω ω= +
+ + (5.49)
rationalizing (5.49)
2 2 2 2 2
11gs gs i gd gd gdj C C R C R j C
YD D
ω ω ω ω+ += +
′ (5.50)
where,
2 2 21 i gsD R Cω= + (5.51)
2 2 21 gd gdD R Cω′ = + (5.52)
since gdR is very small (5.50) can be simplified as,
2 2
11gs i gs
gd
C R CY j C
D D
ωω
= + +
(5.53)
(B) Y12, is the reverse transfer admittance parameter, which is the ratio of current at
input port to the voltage at output port when input port is short circuited
1
112
2 0V
IY
V=
= (5.54)
putting V1=0 in (5.43)
( )12
(1 )
gd gd
gd gd
j C RY
j C R
ω
ω= −
+ (5.55)
rationalizing (5.55)
2 2
12gd gd gdj C C R
YD D
ω ω−= −
′ ′ (5.56)
neglecting gdR , Y12 becomes,
12 gdY j Cω= − (5.57)
(C) Y21, is the forward transfer admittance parameter, which is the ratio of current
at the output port to the voltage at input port when output port is short circuited
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 146
2
221
1 0V
IY
V=
= (5.58)
substituting V2=0 in (5.47)
21
exp( )
1 1
gdm
gs i gd gd
j Cg jY
j C R j R C
ωωτ
ω ω
−= −
+ + (5.59)
neglecting Rgd, Y21 becomes
21
exp( )
1
mgd
gs i
g jY j C
j C R
ωτω
ω
−= −
+ (5.60)
(D) Y22, is the output admittance parameter, which is the ratio of current at the
output port to the voltage at output port when the input port is short circuited
1 0
222
2 V
IY
V=
= (5.61)
substituting V1=0 in (5.47)
( ) ( )
2 2
22 2 2 2 2 2 21 1
gd gd gdds d
gd gd gd gd
j C C RY j C g
C R C R
ω ωω
ω ω= + + +
+ + (5.62)
which on simplification gives,
2 2
22gd gd gd
d ds
C C RY g j C
D D
ωω
= + + + ′ ′
(5.63)
on neglecting Rgd the Y22 becomes
22 ( )d ds gdY g j C Cω= + + (5.64)
Fig. 5.03, Fig. 5.04, Fig 5.05 and Fig. 5.06 show the variation of real and imaginary part
of input admittance Y11, the reverse transfer admittance Y12, forward transfer admittance
Y21 and output admittance Y22 respectively as a function of frequency evaluated using
above proposed model for CGT/SGT MOSFET. The results shown are also compared
with the work by Cho et.al. [Cho11] and found to be in good agreement.
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 147
0
2
4
6
8
10
12
14
0 50 100 150 200Frequency (GHz)
Y11 (
uS
)
Imaginary Y11
∆ Real Y11
Line =Model
Symbol=[Cho11]
Fig. 5.03. Real and Imaginary part of Y11 of CGT/SGT MOSFET as a function of frequency at Vgs=1V,
Vds=0.5V, L=30nm, R=5nm and tox=3.5nm.
-2.5
-2
-1.5
-1
-0.5
0
0.5
0 50 100 150 200Frequency (GHz)
Y12(u
S)
Imaginary Y12
∆ Real Y12
Line= Model
Symbol=[Cho11]
Fig. 5.04. Real and Imaginary part of Y12 of CGT/SGT MOSFET as a function of frequency at Vgs=1V,
Vds=0.5V, L=30nm, R=5nm and tox=3.5nm.
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 148
-10
10
30
50
0 50 100 150 200Frequency (GHz)
Y21 (u
S)
Imaginary Y21
∆ Real Y21
Line =Model
Symbol=[Cho11]
Fig. 5.05. Real and Imaginary part of Y21 of CGT/SGT MOSFET as a function of frequency at Vgs=1V
and Vds=0.5V. L=30nm, R=5nm and tox=3.5nm.
0
5
10
15
20
25
0 50 100 150 200Frequency (GHz)
Y22 (
uS
) ImaginaryY22
∆ Real Y22
Line =Model
Symbol=[Cho11]
Fig. 5.06. Real and Imaginary part of Y22 of CGT/SGT MOSFET as a function of frequency at Vgs=1V
and Vds=0.5V. L=30nm, R=5nm and tox=3.5nm.
5.3.2. Transconductance and Drain Conductance
The transconductance gm and drain conductance gd are defined as
constantds
dsm
gsV
dIg
dV=
=
(5.65)
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 149
constantgs
dsd
gdV
dIg
dV=
=
(5.66)
Unity gain frequency (cut-off frequency) ft is the figure of merit which is defined as the
frequency at which the current gain of the device becomes unity (0dB). The value of fT is
approximated as
( )2
mT
gs gd
gf
C Cπ=
+ (5.67)
The transit time,τ is defined as the time taken by the electrons to cross the channel
length in the velocity-saturated region and it determines the speed of the device [Chen94],
is given by
1
2t
fτ
π= (5.68)
5.3.3. Scattering Parameters
Scattering implies causing something to separate into different components, and
scattering parameters provide a measure of the degree of separation and the magnitudes
of the different components. At low frequencies, the Z (open circuit impedance
parameter), Y (short circuit admittance parameter), h (hybrid parameter) and ABCD
(cascade) parameters are used to describe input output relation of two-port networks.
These parameters cannot be measured accurately at higher frequencies as the required
short-and open-circuit tests are difficult to achieve over a broadband range of microwave
frequencies. A set of parameters that is very useful in microwave range are the scattering
parameters (S parameters) [Guy98 & Lee00]. These parameters are defined in terms of
traveling waves and completely characterize the behavior of two-port networks at
microwave frequencies [Liao87].
The scattering concept is more difficult to visualize when the incident and reflected
component do not actually exist and is true for a transistor connected to its load through a
lumped matching network [Carson75 & Vendlin82]. Therefore it is necessary to define what
is meant by incident and reflected components because they cannot be identified. When
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 150
the scattering concept is applied to lumped circuits, the actual currents and voltages can
be separated into scattered components.
Therefore
1 1 1i rV V V= + (5.69)
2 2 2i rV V V= + (5.70)
At this point new variables are defined as follows
1 11 1
0 0
i rV V
a bZ Z
= = (5.71)
2 22 2
0 0
i rV V
a bZ Z
= = (5.72)
where 0Z (50Ω) is the characteristics impedance of the transmission line. At port 1
1a represents the incident wave and 1b the reflected wave. Similarly, at port 2, 2a
represents the incident wave and 2b the reflected wave. The S parameters can now be
defined by the following relationship among these new variables [Vendlin82]
1 11 1 12 2b S a S a= + (5.73)
2 21 1 22 2b S a S a= + (5.74)
or in the matrix form,
1 11 12 1
2 21 22 2
b S S a
b S S a
=
(5.75)
where
Two Port Network
Input port Output Port
Port 1 Port 2
a1 a2
b1 b2
Fig. 5.07. Two Port Network
V1 V2
+ +
- -
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 151
2
111
1 0a
bS
a=
= is the input reflection coefficient with the output matched
1
112
2 0a
bS
a=
= is the reverse transmission coefficient with the input matched
2
221
1 0a
bS
a=
= is the forward transmission coefficient with the output matched
1
222
2 0a
bS
a=
= is the output reflection coefficient with the input matched
Input or output ports are considered to be matched when it is terminated by the
characteristics impedance, Zo.
These are called scattering parameters as the reflected wave “b” can be thought of as
being “scattered” by the device from the incoming wave “a”.
The analysis of CGT/SGT MOSFET has been carried out for a channel length L=50 nm,
device radius R=10 nm, oxide thickness tox=2.5 nm, uniformly doped source/drain region,
ND+ with doping density of 5x10
19 cm
−3, p type substrate, NA with a doping density of
1016
cm−3
, the metal gate work function (Фm) is 4.8 eV and drain-to-source voltage
Vds=0.5V unless stated otherwise. The analytical results are compared with the simulated
results of ATLAS 3D device simulator [ATLAS10] at various gate biases and then
compared with the bulk MOSFET at channel length L=50 nm, width W=1µm and gate
oxide thickness tox=2.5 nm.
The S-parameters have been evaluated in terms of intrinsic Y-parameters by using
transformation given in [Ramo93] and are given below
The S-parameters, thus evaluated and expressed as
• The input reflection scattering coefficient ( 11S ) is obtained as
211 22 12 21
11
(1 )(1 )o o oZ Y Z Y Z Y YS
− + +=
∇ (5.76)
• The reverse transmission scattering coefficient ( 12S ) is obtained as
1212
2( )oZ YS
−=
∇ (5.77)
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 152
• The forward transmission scattering coefficient ( 21S ) is obtained as
2121
2( )oZ YS
−=
∇ (5.78)
• The output reflection scattering coefficient ( 22S ) is obtained as
211 22 12 21
22
(1 )(1 )o o oZ Y Z Y Z Y YS
+ − +=
∇ (5.79)
where 211 22 12 21(1 )(1 )o o oZ Y Z Y Z Y Y∇ = + + − (5.80)
and oZ characteristics impedance at each port is assumed to be 50 Ω. 50 Ω impedance
was selected from a trade off between the lowest loss and maximum power handling
capabilities in microwave devices [Golio08].
0.9
1
1.1
1 10 100 1000Frequency (GHz)
Re (
S11)
0.5V
1V
Vds=0.5V
Vgs
Lines Model
Symbols Simulated
Fig. 5.08. Real part of input reflection coefficient Re [S11] as a function of frequency for CGT/SGT
MOSFET.
Fig.5.08 to Fig.5.23 show the variations of S-parameters (S11 Input reflection coefficient,
S12 Reverse transmission Coefficient, S21 Forward transmission Coefficient and S22 output
reflection coefficient) both in real and imaginary form as a function of frequency ranging
from 1 GHz to 1000 GHz range. These parameters which have been evaluated
analytically using intrinsic equivalent circuit model are then compared with the results
obtained from 3-D device simulation at low gate bias of Vgs=0.5V & a high gate bias of
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 153
Vgs=1V and at a drain bias of Vds=0.5V. A good agreement is obtained between the
simulated and analytical results for both the gate bias.
-120
-100
-80
-60
-40
-20
0
1 10 100 1000Frequency (GHz)
Im (
S11)
X 1
0-5
0.5V
1V
Lines Model
Symbols Simulated
Vgs
Fig. 5.09. Imaginary part of input reflection coefficient Im [S11] as a function of frequency for
CGT/SGT MOSFET
0.84
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1 10 100 1000Frequency (GHz)
Re
(S
11)
MOSFET="0.5V"
CGT/SGT="0.5V"
MOSFET="1V"
CGT/SGT="1V"
Vgs
Vds=0.5V
Fig. 5.10. Real part of input reflection coefficient Re [S11] as a function of frequency for CGT/SGT and
a comparison with Bulk MOSFET.
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 154
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
1 10 100 1000Frequency (GHz)
Im (
S 11)
MOSFET="0.5V"MOSFET="1V"
CGT/SGT="0.5V"CGT/SGT="1V"
Vgs
Vds
=0.5V
Fig. 5.11. Imaginary part of input reflection coefficient Im [S11] as a function of frequency for
CGT/SGT MOSFET and a comparison with Bulk MOSFET.
Fig.5.08 and Fig.5.09 show the variation of real and imaginary part of input reflection
coefficient as a function of frequency respectively for CGT/SGT MOSFET. And Fig.5.10
and Fig.5.11 shows the comparison between the bulk-MOSFET and CGT/SGT MOSFET
in terms of real and imaginary input reflection coefficients.
0
300
600
900
1200
1500
1800
1 10 100 1000Frequency (GHz)
Re (
S12)
x 1
0-8
0.5V
1VVgs
Vds=0.5V
Lines Model
Symbols Simulated
Fig. 5.12. Real part of Reverse transmission coefficient Re[S12] as a function of frequency for
CGT/SGT MOSFET.
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 155
0
5
10
15
20
25
1 10 100 1000Frequency (GHz)
Im (
S12)
x 1
0-5
0.5V
1V
Lines Model
Symbols
Simulated
Vds=0.5V
Vgs
Fig. 5.13. Imaginary part of reverse transmission coefficient Im [S12 ] as a function of frequency for
CGT/SGT MOSFET.
0
0.005
0.01
0.015
0 250 500 750 1000
Frequency (GHz)
MO
SF
ET
Re
(S
12)
0
400
800
1200
1600
2000
CG
T/S
GT
Re
(S12 ) x
10
-8
MOSFET
MOSFET
CGT/SGT
CGT/SGT
Vgs=1V
Vgs=0.5V
Vds=0.5V
Fig. 5.14. Real part of Reverse transmission coefficient Re[S12] as a function of frequency for CGT/SGT
MOSFET and a comparison with Bulk MOSFET.
Fig. 5.12 and Fig. 5.13 show the variation of real and imaginary part of Reverse
transmission coefficient as a function of frequency for CGT/SGT MOSFET. A
comparison between the bulk-MOSFET and CGT/SGT MOSFET in terms of real and
imaginary reverse transmission coefficients is also shown in Fig.5.14 and Fig.5.15. From
the figure it is analyzed that both real and imaginary reverse transmission coefficient for
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 156
CGT/SGT MOSFET is very less as compared to bulk one, which is more desirable for
better device performances because of better power gain. And a good matching between
the analytical and simulated data validates the model.
0
1
2
3
4
5
6
7
0 500 1000Frequency (GHz)
MO
SF
ET
Im
(S
12)x
10
-2
0
5
10
15
20
25
CG
T/S
GT
Im (S
12 ) x
10
-5
/∆ Vgs=1V
/ Vgs=0.5V
Fig. 5.15. Imaginary part of reverse transmission coefficient Im [S12] as a function of frequency for
CGT/SGT MOSFET and a comparison with Bulk MOSFET.
-50
-40
-30
-20
-10
0
1 10 100 1000Frequency (GHz)
Re
(S21)
x 1
0-5
0.5V
1V
Vgs
Lines Model
Symbols
Simulated
Vds=0.5V
Fig. 5.16. Real part of forward transmission coefficient Re [S21] as a function of frequency for CGT/SGT
MOSFET.
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 157
0
10
20
30
40
50
60
1 10 100 1000
Frequency (GHz)
Im (
S21)
x 1
0-5
0.5V
1V
Lines Model
Symbols Simulated
Vds=0.5V
Vgs
Fig. 5.17. Imaginary part of forward transmission coefficient Im[S21] as a function of frequency for
CGT/SGT MOSFET.
-15
-12
-9
-6
-3
0
1 10 100 1000Frequency (GHz)
MO
SF
ET
R
e (S
21)x
10
-2
-47
-32
-17
-2
13
CG
T/S
GT
Re (S
21 )x
10
-5
Vgs=0.5V
Vgs=1V
∆ / CGT/SGT MOSFET
/ MOSFET
Vds=0.5V
Fig. 5.18. Real part of forward transmission coefficient Re [S21] as a function of frequency for CGT/SGT
MOSFET and a comparison with Bulk MOSFET.
Fig.5.16 and Fig.5.17 show the variation of real and imaginary part of forward
transmission coefficient with respect to frequency for CGT/SGT MOSFET. A
comparison between the bulk-MOSFET and CGT/SGT MOSFET in terms of real and
imaginary forward transmission coefficient as a function of frequency is also shown in
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 158
Fig.5.18 and Fig.5.19. From the figure reasonably good matching between the model and
simulated data is observed which validates the model.
0
5
10
15
20
1 10 100 1000Frequency (GHz)
MO
SFE
T Im
(S
21)x
10
-2
0
20
40
60
CG
T/S
GT Im
(S21 ) x
10
-5
/ MOSFET
/∆ CGT/SGT
Vgs=0.5V
Vgs=1V
Fig. 5.19. Imaginary part of forward transmission coefficient Im[S21] as a function of frequency for
CGT/SGT MOSFET and a comparison with Bulk MOSFET.
0.99
1
1.01
1 10 100 1000Frequency (GHz)
Re
(S
22)
0.5V
1VVgs
Vds=0.5V Lines Model
Symbols Simulated
Fig. 5.20. Real part of output reflection coefficient Re[S22] as a function of frequency for CGT/SGT
MOSFET.
Fig.5.20 and Fig.5.21 show the variation of real and imaginary part of output reflection
coefficient as a function of frequency for CGT/SGT MOSFET. A comparison between
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 159
the bulk-MOSFET and CGT/SGT MOSFET in terms of real and imaginary output
reflection coefficient is also shown in Fig.5.22 and Fig.5.23.
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
1 10 100 1000Frequency (GHz)
Im (
S22)
x 1
0-5
0.5V
1VVgs
Lines Model
Symbols Simulated
Vds=0.5V
Fig. 5.21. Imaginary part of output reflection coefficient Im[S22] as a function of frequency for
CGT/SGT MOSFET.
0.96
0.97
0.98
0.99
1
1.01
1 10 100 1000Frequency (GHz)
Re
(S
22)
0.5V0.5V1V1V
CGT/SGT MOSFET
Vgs
MOSFET
Vds=0.5V
Fig. 5.22. Real part of output reflection coefficient Re[S22] as a function of frequency for CGT/SGT
MOSFET and a comparison with Bulk MOSFET.
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 160
-9
-7
-5
-3
-10 300 600 900
Im (
S22)
x 1
0-2
-30
-20
-10
Frequency (GHz)
Im (S
22 ) x
10
-5
/ 0.5V
/∆ 1V
MOSFET
CGT/SGT
Fig. 5.23. Imaginary part of output reflection coefficient Im[S22] as a function of frequency for
CGT/SGT MOSFET and a comparison with Bulk MOSFET.
5.4. Power gains
Power gains play an important role in design of an amplifier in microwave frequency
range. Several definitions of power gains are important for the design of amplifiers.
5.4.1. Unilateral Power gain (UT)
Unilateral Power Gain (UT ) is the only device characteristic that is invariant under
lossless reciprocal embeddings and can be used as a figure of merit to compare any three-
terminal, active device. If UT is greater than one, the two-port device is active; otherwise,
that device is passive. This is especially relevant to microwave engineers since UT is
usually slightly greater than or equal to unity, in the microwave frequency range. It is the
highest possible gain that an active port can achieve. Unilateral power gain determines
the high power and high gain capability of the device.
Unilateral power Gain (UT) is expressed as [Ladbrooke89].
21
12
21 21
12 12
212
1
Re
S
S
T S S
S S
UK
−=
−
(5.81)
where K is stability factor defined as
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 161
2 2 2
11 22
12 21
1
2
S SK
S S
+ ∆ − −= (5.82)
where
11 22 12 21S S S S∆ = − (5.83)
-10
0
10
20
30
40
50
60
70
0 200 400 600 800 1000Frequency(GHz)
Un
ila
tera
l P
ow
er
Ga
in (
dB
)0.5V
1V
Vgs
Lines Model
Symbols
Simulated
Vds=0.5V
Fig. 5.24. Variation of Unilateral Power gain (UT) (in dB) as a function of frequency for CGT/SGT
MOSFET.
K is the stability factor which determines the stability of the device or its resistance to
oscillations. K>1 and ∆ <1 forms the primary condition for the device to be stable.
Higher is the frequency upto which the device is stable (i.e. K>1), greater is suitability of
the device for RF and Low noise amplifier devices. The frequency at which the unilateral
power gain becomes unity (0dB) is known as maximum frequency of oscillation.
Fig. 5.24 shows the variation of Unilateral power gain (UT) as a function of frequency for
CGT/SGT MOSFET at channel length L=50 nm. At a constant drain bias Vds=0.5V and
gate bias of Vgs=0.5V & Vgs=1V. Unilateral power gain is obtained using (5.81). From the
figure, it is observed that there is an exponential decrease in the unilateral power gain as
the frequency increases. By extrapolating the curve of unilateral power gain fmax is
obtained, which comes out to be around 700 GHz. A good matching between the
simulated results with the analytical data validates the model.
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 162
5.4.2. Maximum Stable power gain (Gms) [Goswami00 & Goswami01]
Maximum stable power gain, Gms is defined as
21
12
SGms
S= (5.84)
This is the gain that can be achieved by resistively loading the two-port network such that
the stability factor (K) is unity and then simultaneously matching the input and output
ports.
Fig. 5.25 indicates the variation of Maximum stable power gain (Gms) with respect to
frequency upto 1 THz for CGT/SGT MOSFET at channel length, L=50 nm at Vds=0.5V
and gate bias of Vgs=0.5V & Vgs=1V. Maximum stable power gain, Gms is an important
parameter used for designing low noise amplifier (LNA). From the figure it is analysed
that highest Gms value is obtained at 30 dB; and even at frequency of 1000 GHz Gms
have a value above 0 dB, which is only due to the better matching at input and output
ports. Thus, a simultaneous conjugate match has been obtained in the analysis. A good
agreement between the analytical model and simulated data is obtained.
0
10
20
30
0 200 400 600 800 1000
Frequency (GHz)
Maxim
um
sta
ble
Pow
er
Gain
(G
ms)
(dB
)
0.5V
1V
Lines Model
Symbols Simulated
Vds=0.5V
Vgs
Fig. 5.25. Variation of Maximum Stable power gain (Gms) (in dB) as a function of frequency for
CGT/SGT MOSFET.
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 163
5.4.3. Maximum unilateral Transducer power gain ( maxTUG ) [Goswami00 &
Ladbrooke89]
Maximum unilateral transducer power gain is defined as
( )( )
2
21max 2 2
11 221 1TU
SG
S S=
− − (5.85)
Fig 5.26 anticipates the variation of Maximum unilateral Transducer power gain (GTUmax)
as function of frequency upto 1 THz range for CGT/SGT MOSFET at a channel length,
L=50 nm at Vds=0.5V and gate bias of Vgs=0.5V & Vgs=1V. The Maximum Unilateral
Transducer Power Gain (GTUmax) is obtained when the source reflection coefficient, sΓ is
adjusted as *11s SΓ = and the load reflection coefficient, LΓ is adjusted as *
22L SΓ = . From
the figure it is observed that at 1000 GHz maximum unilateral transducer power gain
have value above 0dB which predicts better matching between the input and output ports.
This is given by the (5.85). At lower frequencies maximum unilateral transducer power
gain is obtained at 50-70 dB. A good matching between the analytical results and
simulated values validates the model.
0
10
20
30
40
50
60
0 200 400 600 800 1000
Frequency (GHz)
Max U
nila
tera
l Tra
nsducer
Pow
er
gain
(dB
)
0.5V
1V
Lines Model
Symbols Simulated
Vds=0.5V
Vgs
Fig. 5.26. Variation of Maximum unilateral transducer power gain (GTUmax) (in dB) as a function of
Frequency CGT/SGT MOSFET.
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 164
-5
5
15
25
35
45
0 2 4 6 8 10Frequency (GHz)
Diff
ere
nt G
ain
s (
dB
)
Solid symbols= MOSFET [Gosw ami00]
Hollow Symbols=CGT/SGT MOSFET
Unilateral Power Gain
Maximum Unilateral
transducer Power Gain
♦♦♦ Maximum Stable Power Gain
Fig. 5.27. Variation of different gains with frequency for both MOSFET and CGT/SGT MOSFET at L=
0.8 µm and Vds=3V.
Fig. 5.27 predicts the variation of different gain namely unilateral power gain, maximum
unilateral transducer power gain and maximum stable gain as a function of frequency for
both MOSFET and CGT/SGT MOSFET at L=0.8 µm. From the figure, it is analyzed
that all the gains are higher for CGT/SGT MOSFET as compared to bulk MOSFET; this
is due to the better gate controllability over the channel obtained using
Cylindrical/Surrounded architecture and hence improves the efficiency. Therefore,
CGT/SGT MOSFET is a useful device for microwave frequency applications.
5.5. Conclusion
An intrinsic circuit model for CGT/SGT MOSFET has been proposed from where
microwave characteristics in terms of scattering parameters (S11 Input reflection
coefficient, S12 Reverse transmission Coefficient, S21 Forward transmission Coefficient
and S22 output reflection coefficient) and power gains in terms of unilateral power gain,
Maximum Unilateral transducer power gain and maximum stable gain have been
obtained. The results so obtained using the model are then compared with bulk MOSFET.
It is observed that CGT/SGT device has better device performance in terms of different
power gains. This can be concluded that this circuit can be used for high frequency
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 165
applications through proper designing and optimization of the structure. Improvement in
the CGT/SGT MOSFET as compared to bulk MOSFETs concluded that
cylindrical/surrounded architecture has a better gate control as compared to bulk
MOSFET.
Chapter 5: Small Signal Intrinsic...........
Pujarini Ghosh 166
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