JOURNAL OF AUTOMATIC CONTROL, UNIVERSITY OF BELGRADE, VOL 16:37-40, 2006 ©
Low-Frequency Noise Of A Dual-Gate Mosfet In
Linear Region
Mirjana Videnović-Mišić, Milan Jevtić and Laslo Nađ
Abstract – This paper presents results of low frequency noise
measurements for a Dual-Gate MOSFET (DGMOSFET) in
linear region. DGMOSFET working conditions are chosen in
order to set both inner transistors in linear regime. Results are
discussed with the use of the unified 1/f noise model.
Index Terms – linear region , 1/f noise, unified model
I. INTRODUCTION
This research was supported by the Serbian Ministry of Science and
Environment Protection (contracts TR-6151B and TR-6116B).
Mirjana Videnović-Mišić* and Laslo Nađ are with the Department of
Electronics, Faculty of Technical Sciences, University of Novi Sad, Trg
Dositeja Obradovica 6, 21000 Novi Sad, Serbia, E-mail*:
mirjam@uns.ns.ac.yu
Milan Jevtić is with the Department of Appl. and Techn. Phys., Institute
of Physics, Pregrevica 118, 11000 Beograd, Serbia, E-mail:
mjevt@phy.bg.ac.yu
S
+
n
G1
G2
D
L1
L2
n
+
p
ΔL
(a)
ID[mA]
0,014
VG2=1V
VG1=0.4V
VDSsat2=1,78V
0,012
VG1=0.2V
0,010
0,008
(N)L-(N)L
(N)L-S
VG1=0V
0,006
depletion
The simplified diagram of an n-channel depletion-type
DGMOSFET together with the Philips BF988 typical drain
characteristic is shown in Fig.1. It can be seen from Fig. 1b)
that drain characteristics of a depletion-type DGMOSFET
and a single-gate MOSFET are quite similar. The linear
region from the current-saturation region can be clearly
distinguished. Moreover, operating mode of a DGMOSFET
depends on the application. A DGMOSFET in a mixer will
operate in the region that exhibits strong non-linear
behaviour [5]. On the other hand, non-linear behaviour of a
DGMOSFET has to be reduced in an oscillator or an
The purpose of this study is to shed more light on
DGMOSFET LF noise in the linear region.
enhancement
Dual gate MOSFET (DGMOSFET) structures are
widely used in MOS integrated circuits where electronic
gain control, low feedback parameters, low noise, cross
modulation or reduction of short channel effects are
required [1]. They are widely used in oscillators [2], mixers
[3] and amplifiers [4], the devices that are building blocks
of transceiver front-end. These devices usually operate in
large-signal quasi-periodic conditions where low-frequency
(LF) noise, important RF design constraint [5,6,7], changes
in the rhythm of the operating point variation [8,9]. Nonlinear and time-varying nature of the front-end trasnceiver
devices cause frequency up-conversion of LF noise into the
proximity of the carrier and increase of the bandwidth of
the transmitted signal. Since DGMOSFET, as an active
component of the device, is the main contributor to overall
LF noise, better understanding of its LF noise under
different bias conditions is necessary. Therefore, the focus
of our recent work has been LF noise of the DGMOSFET
in Colpitts oscillator [9] and modelling of DGMOSFET 1/f
noise under different bias conditions [10]. High sensitivity
of the transistor LF and oscillator phase noise to the
DGMOSFET working conditions has been noticed.
amplifier [5]. Moreover, under appropriate bias conditions,
a DGMOSFET can be roughly approximated to the cascode
connection of two single-gate MOSFETs, M1 and M2.
When a DGMOSFET operates in the linear region,
transistors M1 and M2 can work in either linear (L), or nonlinear (NL) regions [1, 10]. Therefore, not only
DGMOSFET application, but also operating modes of M1
and M2 transistors have to be taken into consideration
during DGMOSFET LF noise modelling [10].
0,004
VG1=-0.2V
0,002
S-(N)L
S-S
VG1=-0.4V
0,000
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
VDS[V]
4,0
4,5
5,0
5,5
6,0
(b)
Fig. 1. (a) The simplified diagram of an n-channel
depletion-type DGMOSFET (b) The Philips BF988 drain
characteristic for VG2=1V and VG1 changing the value from
-0.4V to 0.4V with the 0.2V step measured with the
Tektronix curve tracer type 576.
II. DGMOSFET DRAIN CHARACTERISTICS AND OPERATING
MODES OF DGMOSFET TRAN-SISTORS
In contrast to the cascode-type MOS tetrode, the drain
of the first DGMOSFET gate is actually the layer under the
second gate, as can be seen in Fig. 1a). Since a
DGMOSFET has no intermediate island, the proper
38
VIDENOVIĆ-MIŠIĆ M., JEVTIĆ M., NAĐ L., LOW-FREQUENCY NOISE OF A DUAL-GATE MOSFET IN LINEAR REGION
coupling can be achieved only if separation between the
adjacent gates is small enough. Consequently, the point
between two transistors is inaccessible. Therefore, the drain
voltage (VDS1) of the M1, gate (VGS2) and drain (VDS2)
voltages of the M2 together with some other transistors
parameters cannot be directly measured. They can be
assessed by using results of experimental measurements and
the implicit device current model [1]. After extracting
internal parameters, operational modes of M1 and M2
transistors can be estimated. Generally, the transistors can
work in off or on states. The off state corresponds to the
sub-threshold region (ST), VGS<VTH, while in the on state,
transistors can work in linear (L), VDS<<VGS-VTH, VGS≥VTH,
non-linear (NL), VDS≤VGS-VTH, VGS≥VTH, or saturation (S),
VDS≥VGS-VTH, VGS≥VTH, regions.
For a qualitative first-order approximation we use a
simple analytical model of a DGMOSFET and ignore the
body effect. Under the condition of the same current
flowing through both transistors (ID1 = ID2 = ID) and the
grounded source (VS=0), boundaries between NL and S
operational modes of M1 and M2 transistors can be
expressed as:
VDSsat1=V2-[(V2-V1)2-(V12/m)]1/2,
(1)
VDSsat2=V2,
(2)
where V2=VG2-VTH, V1=VG1-VTH, m=L1/L2, VTH threshold
voltage, L1 and L2 channel lengths of M1 and M2,
respectively. VDSsat1 and VDSsat2 are DGMOSFET drain to
source voltages at which M1 and M2 channels are pinchedoff, respectively. It can be seen from the equation (1) that
VDSsat1 can have a real or complex value. If the VDSsat1
1/ 2
value is complex or V2<(1+ 1 / m )V1, M1 operates in
either L or NL regions, otherwise it operates in the S region.
Operating modes of DGMOSFET transistors and
corresponding conditions in ON states are summarised in
the Table 1.
importance. With the change of a single gate transistor
operating mode not only its LF noise mechanism and model
is changed, but also its contribution to overall noise [10].
III. EXPERIMENT
Low-frequency noise measurements have been
performed with the measurement set shown in Fig. 2. The
implemented set consists of the amplifying section
(Keithley 103A amplifier), current-to-voltage convertor
(made in our laboratory), data acquisition and processing
unit (Dynamic Signal Analyzer HP3562A) and the
DGMOSFET bias circuit. Keithley 103A, as a critical part
of the measurement set, has its own power-supply system
Keithley 1024, which minimises supply noise. Dynamic
Signal Analyzer HP3562A sets the limit on the
measurement set bandwidth from 10Hz to 100kHz.
Keithley 1024
VGG2 VGG1
G2
DG
current to
voltage
convertor
Keithley 103A
HP3562A
G1
Fig.2. Measurement set for LF noise measurements
The current to voltage convertor, shown in Fig. 3,
enables fine-tuning of the VDS voltage and selection of the
DGMOSFET operating point. In order to decrease the noise
level in the most sensitive part of the measurement set, the
low-noise TLE2027 operational amplifier, metal film
resistors and batteries as power-supplies have been used.
The convertor impedance is set to 5k Ω in order to satisfy
Keithley 103A demand for its beter noise characteristic.
Table 1 Operating modes of DGMOSFET transistors
Transistor M1
operating mode
Transistor
M2
operating mode
Condition
VDS>V2=VDSsat2
S
S
V2>(1+ 1 / m
1/ 2
)V1
VDSsat1<VDS
S
L or NL
VDS<V2
Keithley
103A
VDS>V2
L or NL
S
L or NL
L or NL
V2<(1+ 1 / m
1/ 2
)V1
otherwise
Boundaries between M1 and M2 operating modes are
superimposed as broken lines on the BF988 drain
characteristic, shown in Fig. 1b).
For DGMOSFET LF noise modelling, detection of the
M1 and M2 operating modes is the matter of the utmost
Fig. 3 Current-to-voltage convertor
IV. EXPERIMENTAL RESULTS AND DISCUSSION
DGMOSFET LF noise has been measured in three
different operating points (OPs). They were carefully
selected not only to set DGMOSFET OPs into the linear
region, but also to set transistors M1 and M2 into the L-L
operating mode. The measured drain current noise power
spectral densities have been shown in Fig. 4. The measured
JOURNAL OF AUTOMATIC CONTROL, UNIVERSITY OF BELGRADE
current noise spectrum can be described by the empirical
relation
S id ( f ) = A +
C jτ j
B
1
+∑
, (3)
, τj =
γ
2 2
f
2πf j
j 1+ ω τ j
39
Table 2 Noise parameters
Fig. 4. Current noise spectra obtained by curve fitting and
measurements for three different DGMOSFET OPs
2
-10
B0/ID
10
-11
10
-12
10
where A, (B,γ) and (Cj, τj) are the parameters of white, 1/f
and noise with Lorentzian spectra, respectively.
Normalized 1/f noise
Vds = 0.2623V
-13
10
-14
10
-0,4
The frequency fj is the characteristic frequency of the
Lorentzian spectrum. Noise parameters, presented in the
Table 2, were found using the least square fitting method,
while fitting the experimental results to the empirical
relation. In order to better understand DGMOSFET LF
noise behaviour in the L region, it is necessary to recognize
underlying physical mechanisms in transistors M1 and M2.
For that reason we have examined 1/f noise components in
OPs under consideration. The normalized 1/f noise
parameter B0/ID2 as a function of the bias voltage VG1 is
shown in Fig. 5. It can be seen that the VG1 decrease results
in the normalized 1/f noise parameter increase.
-17
10
-18
10
VG1 = 0.273V
VG1 = 0.273V
VG1 = 0.6169V
VG1 = 0.6169V
-19
10
-20
10
-21
10
Symbol - Experimental results
Line - Fitting results
VDS=0,2623V
VG2=1,85V
-22
10
1
10
2
10
3
10
Frequency [Hz]
4
10
5
10
VG1 [V]
0,2
0,4
0,6
In order to analyse agreement between obtained
experimental data and theoretical predictions, we have used
the unified 1/f noise model for a single MOS transistor [11].
The 1/f noise model includes not only the effect of
fluctuation in the total number of channel carriers, but also
the mobility fluctuation caused by Coulombic scattering due
to trapped carriers. At low drain voltages (linear region), the
carrier density is uniform along the channel and is given by
qNS=Cox (VG-VTH), where Cox [F/m2] is oxide capacitance
per unit area, NS [cm-2] is the number of channel carriers
near the interface per unit area and VTH is the threshold
voltage. Consequently, the normalized parameter B0/ID2
extracted from the expression for the unified 1/f noise
model [11] can be expressed as
ID2
VG1 = -0.273V
VG1 = -0.273V
0,0
Fig. 5 Normalized 1/f noise parameter obtained by curve
fitting with respect to VG1
B0
Sid/Δf
2
[A /Hz]
-0,2
2
⎞
1 ⎛ 1
⎜⎜
=
+ αμ ⎟⎟ kTN T ( E Fn ) ,
γWL ⎝ N S
⎠
(4)
where W [m] and L[m] are, respectively, the channel width
and length, kTNT(EF) [cm-3] is the density of oxide traps per
unit volume and γ is the McWhorter tunneling parameter
typically taken to be 10-8 cm-1 for the Si/SiO2 interface [11].
As a consequence of the fact that both inner DGMOFET
transistors operate in the L region and that M1 and M2
contribution to overall noise is equal [10], the equation (4)
is used for the DGMOSFET 1/f noise analysis. Moreover, in
the L-L region, under working conditions VDS = const. and
VG2 = VDS1+VGS2 =const., the VGS1 =VG1 increase results in
the VGS2 increase. Therefore, the gate 1 change generates the
40
VIDENOVIĆ-MIŠIĆ M., JEVTIĆ M., NAĐ L., LOW-FREQUENCY NOISE OF A DUAL-GATE MOSFET IN LINEAR REGION
same effect on the normalized 1/f noise parameter for
transistors M1, M2 and DGMOSFET.
Fig. 5, two order magnitude change in B0/ID2 could only be
achieved by dominant influence of the first term.
The gate 1 bias has different impact on NS for positive
and negative VG1 polarisations. With the increase of positive
VG1 polarisation, channel carriers are pushed toward the
Si/SiO2 interface, resulting in an NS increase. For negative
gate 1 polarisation, channel carriers are pushed away from
the Si/SiO2 interface. Consequently, the number of channel
carriers near the interface per unit area is reduced. In the
first approximation we have neglected fluctuations caused
by Coulombic scattering. Therefore, the first term in
brackets in the equation (4) dominates. Consequently, the
gate 1 bias increase results in the reduction of the
normalized 1/f noise parameter, which is in agreement with
the experimental results presented in Fig. 5. In order to take
into consideration the Coulombic scattering effect on
DGMOSFET 1/f noise included into the equation (4) as the
second term in brackets, we need information on carrier
mobility behaviour. Using the Matthiessen’s rule, the
effective mobility can be expressed as [11]
From the results of the curve fitting (Table 2) can
be seen that noise sources with the Lorentzian spectra are
also present. The significant change in characteristic
frequencies with the change of VG1 from 0,273V to 0,6169V
is noticed. Understanding of the origin of these changes
demands more detailed investigation that exceeds the scope
of this paper.
1
μ
=
1
μn
+
1
μc
=
1
μn
+ αn t ,
(5)
where µc=1/α nt is the moblity limited by oxide charge
scattering and µn is the mobility limited by phonon,
interface roughness and impurities scattering. α is the
scattering parameter in Vs, and nt [cm-2] is the occupied trap
density per unit area. It has been reported [12] that the
Coulombic scattering mobility of the oxide trapped charges
is proportional to the square root of the inversion carrier
density NS and can be represented by
μ c = μ c0
NS
nt
,
(6)
where µc0=5,9 x 108 cm/Vs. Consequently, αµ expression
becomes
αμ =
μc0
μn
1
.
V. CONCLUSION
From the results obtained by fitting experimental results
to the empirical relation for DGMOSFET LF noise
operating in the linear region can be concluded that 1/f
noise and noise sources with the Lorentzian spectre are
present. 1/f noise analysis with the use of the unified 1/f
noise model has shown that dependence of 1/f noise on the
change in the VG1 voltage can be explained with the change
of the channel carriers concentration near the Si/SiO2
interface. It has been found that the first term in the
equation (4), which describes fluctuations of the channel
carrier number, significantly contributes to 1/f noise. R
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