mosfet threshold voltage: definition, extraction, … linear region to minimize series resistances...
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MOSFET Threshold Voltage:
Definition, Extraction, and
Applications
Federal University of Santa Catarina
Brazil
WCM, June 2011
M. B. Machado , O. F. Siebel, M. C. Schneider, and C. Galup-Montoro
2
Contents
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1 – Classical and current-based threshold definition
2 – The gds/ID procedure
3 – Comparison of the different current-based
extraction methods
4 – Applications
5 - Conclusions
3
Classical threshold voltage (VT) definition
33
Classical (surface potential based) definition of threshold:
CFS V 2Where :S - surface potential for VG=VT
F - Fermi potential in the substrate
VC - channel potential
In principle the direct determination of the threshold voltage is possible
1) calculate the saturation drain current IDTh for
2) inject IDTh into the transistor and measure VG = VT
Drawbacks
- geometrical (W, L) and technological parameters ( mobility,
oxide thickness,.. ) are needed to calculate IDTh
- the transistor operates in the saturation region where several
secondary effects are relevant
CFS V 2
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444
Current-based Threshold definition.
Threshold voltage is defined as the gate voltage at which
the condition Idrift = Idiff holds.
VDS=t/2=13mV
VG = VT
130 nm (tox=2.2nm ), W/L= 720 nm /180 nm
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Classical vs. current-based definitions
555
Classical
Current
based
x
Physical MeaningValue of at
threshold
Value of at
threshold
Difference in VT
relative to the
classical definition
Surface concentration of
electrons= bulk
concentration of holes
Drift component = Diffusion
component of drain current
IQ
toxCn )1(
1ln2
n
nV tCF toxCn
1ln1
n
nnt
CF V2 0
n is the slope factor given by
where
is the oxide capacitance per unit area
is the depletion capacitance per unit area
ox
GBb
C
VCn
'
)('1
s
oxC
bC
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‘Ideal’ threshold voltage extraction procedure
666
• No parameters are needed to calculate the
threshold current
• The transistor operates at low current levels and in
the linear region to minimize series resistances and
short channel effects
• Fixed VGB to avoid variation in the slope factor
gds
/ID
procedure
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The gds
/ID
procedure
77
Direct determination of MOSFET parameters from
the ID vs VS curve at low VDS (linear region)
DmdSmsD VgVgI
VDS
=t/2=13mV
VG=0.42V
TSMC 0.35 µm, W/L= 12 µm /0.5 µm
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The gds
/ID
methodology – extraction of VT
and IS
88
From transistor model
if = 3
VDS = t /2
112
)()( rf
t
Sdms i
Ig
rfSD iiII L
WnCI t
OXS2
'
2
11ln21 )()(
)(
rfrf
t
DSPii
VV
rftS
D
DD
ds
iidV
dI
II
g
11
21
VP = VS
TSMC 0.35 µm, W/L= 12 µm /0.5 µm
VP=VS
and
VT0 = VG
IS = 1.14*ID
when VP = 0
When
tD
ds
I
g
1
max
tDI
gds
1*53.0
tDI
gds
1*53.0
VG = VT0 !
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Automatic VT
-extractor circuit - based on gds
/ID
procedure
11ln21 )()(
)(
rfrf
t
DSPii
VV
VG = VT0
Biasing condition
VDS = t /2
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VDS = t /2 (linear region)
if = 3ir = 2.12
SrfSD IiiII 88.0
Automatic VT -extractor circuit
VP = 0
From transistor model
9
10
gds
/ID
x gm
/ID
methods
1010
gm/ID
gds/ID
TSMC 0.35 µm, W/L= 125, BSIM3v3
gds/ID is independent of slope factor (n).
rftD
ds
iiI
g
11
2
D
ds
D
m
I
g
nI
g 1
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Constant current (CC) method
1111
11ln21 )()()( rfrftDSP iiVV
For a saturated transistor biased with ID=3*IS, we have VG=VT for VS=0.
n
VVV TG
P
From transistor model
if = 3
VS = 0VP=0
For
VG=VTand
The CC method was used in a previous VT -extractor circuit for tracking the VT
variation as a function of a specific parameter, e.g. temperature or ionizing
radiation.
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TSMC 0.18 µm, W/L= 100
MethodOperating
region
gm/ID Linear
gds/ID Linear
CC Saturation
Measured VT
values vs. Lmask
for different extraction methods
These methods present similar behaviors, especially for gm/ID and gds/ID methods.
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• technology characterization
• aging evaluation
• matching assessment
• temperature and radiation sensors
The threshold voltage is a fundamental electrical
parameter that can be used in:
Applications
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Example of application:
TSMC 0.35 µm, W/L= 12 µm /0.5 µm VT average values:
gm/ID 629mV
CC 611.5mV
Relative standard deviation
gm/ID 0.59%
CC 0.55%
Matching assesment
Both methods present similar behavior and almost the same relative standard deviation.
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In this example, the CC method is used for tracking the VT variation as a function of a specific
parameter (temperature).
Example of application:
TSMC 0.35 µm, W/L= 12 µm /0.5 µm
VT variation vs. temperature
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Conclusions
• A new procedure for the direct determination of the thresholdvoltage with minimum influence of second order effects isintroduced
• The threshold voltage is determined at a constant gate-to-substrate voltage, at a low drain-to-source voltage and withtransistor operation in the weak and moderate inversionregions.
• Under these operating conditions the effects of seriesresistances, mobility and slope factor variations, and channellength modulation are practically negligible, allowing a directdetermination of the threshold voltage.
• The current-based extraction in weak-moderate inversionallows the design of low power VT -extractor circuits.
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