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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