the direct determination of mosfet parameters from the id ... · * from yannis tsividis, operation...

The direct determination of The direct determination of MOSFET parameters from the IMOSFET parameters from the IDD

versus Vversus VSS curve at low Vcurve at low VDSDS

Carlos Galup-Montoro, Márcio Bender Machado,

Thiago de Oliveira, Márcio Cherem Schneider Thiago de Oliveira, Márcio Cherem Schneider

Federal University of Santa CatarinaBrazil

MOSMOS--AK Workshop, AK Workshop, DecemberDecember 20102010

ContentsContents

11 - Threshold Voltage definitions

22 - Determination of MOSFET parameters from ID

x VS

curve, (channel_conductance)/Id method

33 - Comparison with gm/Id method

222MOS-AK Workshop, December 2010

44 - Applications of the threshold voltage

determinations

55 - Conclusions

Near the threshold condition ( moderate inversion), both the drift and

diffusion transport mechanisms are important.

Threshold voltage (VT)Threshold voltage (VT)


IDS1= Drift component

IDS2= Diffusion component

* from Yannis Tsividis, Operation and Modeling of The MOS transistor, MCGraw-Hill

No critical point can be directly identified

ClassicalClassical threshold voltage (VT) definitionthreshold voltage (VT) definition

Classical (surface potential based) definition of threshold:Classical (surface potential based) definition of threshold:

CFS V+= φφ 2Where :φφφφS - surface potential for VG=VT

φφφφF - Fermi potential in the substrate

VC - channel potential

In principle the direct determination of the threshold voltage

is possible


is possible

1)1) calculate the saturation drain current IDTh

for

22)) inject IDTh

in the transistor and measure VG

= VT

DrawbacksDrawbacks

- 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+= φφ 2

For a MOSFET the current defined threshold corresponds to an

inversion charge density equal to the thermal charge density ( the

effective channel capacitance per unit area times the thermal voltage).

diffdrift II =

Current based threshold definition Current based threshold definition


where n is the slope factor

tOXI nCQ φ'' −=For a bulk MOSFET

Relationship between threshold voltages Relationship between threshold voltages


‘Ideal’ threshold voltage extraction ‘Ideal’ threshold voltage extraction procedureprocedure

• No parameters are needed to calculate the

threshold current

• The transistor operates at low current levels

and in the linear region to minimize series and in the linear region to minimize series

resistances and short channel effects

gm/Id curve in the linear regiongm/Id curve in the linear region


VT determination from gm/Id VT determination from gm/Id curve in the linear regioncurve in the linear region

• Transconductance-to-current ratio for VDS

≅ ϕt/2 and V

S=0.

Threshold gm

/ID

≅≅≅≅ 0.5 (gm

/ID)

max

Drawback (gm/ID)max

has some dependence on VG


The new (channel conductance GThe new (channel conductance Gn0n0/Id) /Id) methodologymethodology

Direct determination of MOSFET parameters from the ID

versus VS curve at low VDS

VDS=ϕ

t/2

2

x 10-4

x 10-4

[A]


XDS VVV ∆=∆=∆

nomdmsX

D GggV

I=+−=

∂∂

VG

VX

0 0.1 0.2 0.3 0.4 0.5 0.6

0

1

VX [V]

I D [A

]

VX

[V]I D[A]

The Gn0/Id methodologyThe Gn0/Id methodology

Transistor operation:Transistor operation:

• low VDS

• weak and moderate inversion

• fixed VG

Negligible effects of :Negligible effects of :


Negligible effects of :Negligible effects of :

• series resistances

• field dependent mobility

• slope factor variation

• channel length modulation

The Gn0/Id methodology The Gn0/Id methodology –– extract Vextract VTT and Iand ISS

When if =3 → VP=VS=VX

From transistor model

From UICM

( ) ( )rfD

n

rftD

n

iiI

G

iiI

G

+++

=

+++−=

11

2

11

2

min

00

φ

( )112

)()( −+= dft

Sdms i

Ig

φ

( )rfSD iiII −=L

WnCI t

OXS 2'

2φµ=

( )11ln21)( −++−+=− DSP ii

VV


When if =3 → VP=VS=VX

for if = 3 and

VDS = φφφφt /2

we have ir = 2.12 VP = VX

When

min

00 *53.0

=

D

n

D

n

I

G

I

G

andVG

VDS

=ϕt/2

VX

( )11ln21 )()( −++−+= rfrft

iiφ

-30

-25

-20

-15

-10

-5

0

Gno

/I D [1

/V]

min

00 53.0

=

D

n

D

n

I

G

I

G

V = V

The Gn0/Id methodology The Gn0/Id methodology –– extract Vextract VTT and Iand ISS


0 0.1 0.2 0.3 0.4 0.5

-40

-35

VX [V]

VP

= VX

VT0 = - nVP + VG

IS = ID

When

min

00 *53.0

=

D

n

D

n

I

G

I

Gand

The Gn0/Id methodology The Gn0/Id methodology –– extract extract pinchpinch--offoff

voltage voltage VVPP

and and slope factor slope factor nnVP[V]

slopefactor(n)

BSIM simulation

0 0.1 0.2 0.3 0.4 0.50

1

2

x 10-4

vg=0.7V

vg=0.75V

vg=0.8Vvg=0.85V

vg=0.9V


measuring ID x VS for different VG values

VG

[V]VG

[V]

VX[V]

I D[A]

Gn0/Id x gm/Id methodsGn0/Id x gm/Id methods

|Gn0/I

D|

gm/I

Dgm/I

D

|Gn0/I

D||G

n0/I

D|

Transconductance

/ID[1/V]


Transconductance

ID

[A]

Gn0/Id x gm/Id methodsGn0/Id x gm/Id methods

IISS

L mask (W/L=100) 0.2 µm 0.3 µm 0.4 µm 0.5 µm 0.6 µm 0.8 µm 2.0 µm

IS

(µA) gm/ID

23.82 18.21 16.19 15.67 15.54 15.94 16.62

IS

(µA) Gn0/ID 21.47 15.21 13.27 13.53 13.41 13.72 14.65

VVT0T0

L mask (W/L=100) 0.2 µm 0.3 µm 0.4 µm 0.5 µm 0.6 µm 0.8 µm 2.0 µm

VT

(mV) gm/ID

514 499 494 488 484 478 456

VT

(mV) Gn0/ID

515 495 490 486 481 475 455

0.18 µm technology

IS

when VGS

≈VT0


0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2450

460

470

480

490

500

510

520

Lmask

[µm]

VT [m

V]

gm/Id method

Gno/Id method

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 212

14

16

18

20

22

24

Lmask

[µm]

I S [µ

A]

gm/Id method

Gno/Id method

ApplicationsApplications

•• Transistor aging (or electrical stress)

• Matching assessment

• Temperature drift characterization

Applications using VT extractionApplications using VT extraction


• Temperature drift characterization

• Radiations effects on MOS transistor


11- Extract IS and VT in a non-noisy environment using an accurate method (gm/Id or Gn0/Id)

VV −22- Extract VT in a real environment considering Id=3*Is (if =3) in a


n

VVVP TG 0−

=

VP

= 0 VG

= VT0

VP

[V]

VG[V]

VG

VS

3IS

considering Id=3*Is (if =3) in a

saturated transistor

From UICM

when if = 3, VP

= VS

Example of HCI stress measurement using VT variation


[mV]


ΔVT[m

V]

Time [Seconds]

ConclusionsConclusions

• New procedure for direct determination of the threshold voltage and some other important electrical parameters with minimum influence of second order effects.

• The threshold voltage is determined at a constant gate-to-substrate voltage, at a low drain-to-source voltage and with transistor operation in the weak and moderate inversion transistor operation in the weak and moderate inversion regions.

• Under these operating conditions the effects of series resistances, mobility and slope factor variations, and channel length modulation are practically negligible, allowing a direct determination of the threshold voltage and of the DIBL effect.


the direct determination of mosfet parameters from the id ... · * from yannis tsividis, operation...

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