08 Antonio Cerdeira

Training Courses on Compact Modeling

Tarragona, June 30-July 1, 2010

DC PARAMETER EXTRACTION METHODS FOR MOSFETS

Antonio Cerdeira AltuzarraSection of Solid State Electronics, CINVESTAV, México, D.F.

[email protected]

DC Parameter Extraction Methods 2

Circuit simulation MOSFET models in SPICE simulator Model Parameters

Individual extraction methods (DC)Threshold voltage extraction methods:

Constant current (CC) Extrapolation in linear region (ELR) Second derivative (SD) Extrapolation in saturation region (ESR)

Subthreshold slopeEffective channel length and series resistance:

Hu method

Mathematical extraction methods (optimization).

Examples.

OUTLINE



In the process of development of new semiconductor devices,different types of simulations are required:• Semiconductor Process Simulation

Virtual fabrication of semiconductor devices.

• Semiconductor Device simulation.Electrical behavior of semiconductor devices.

• Circuit simulation (SPICE type).Behavior of an electrical circuit with different devices

interconnected.

All these simulations require models, and all models requireparameters

SIMULATION IN SEMICONDUCTOR DEVICE DEVELOPMENT

Training Courses onCompact Modeling


The Spice-type circuit simulators calculates the current-voltagecharacteristics of the devices to conform a circuit net, wherecurrents in each branch, and voltages at each node, aredetermined.

The behavior of each semiconductor device is described byequations that we know as device model.

Each model has a set of parameters that must be defined. Someof them are technological, others are electrical and others are justadjusting parameters.

Models used in circuit simulators must provide: accuracy in thereproduction of I-V characteristics and low CPU timeconsumption.

CIRCUIT SIMULATION



At the beginning, the main goal was to develop analytical modelsto provide a simple description of the MOSFET, looking tounderstand its behavior, rather than to provide a precise modelfor circuit simulation.

As device dimensions reduced, MOSFET modeling shifted fromthe physically based analytical description to a more complicated,but precise representation that could provide efficient circuitsimulation.

The Spice-type MOSFET models can be grouped in:

Threshold voltage models

Compact models

Analytical models.

MOSFET MODELS IN SPICE SIMULATOR



Threshold voltage models

The I-V characteristics are divided into several parts or regions,with different sets of equations for each region: e.g. subthreshold;above threshold; linear and saturation regions.

Examples of these first models are SPICE LEVEL 1, LEVEL 2,LEVEL 3 and the first BSIM models. They have a problem ofdiscontinuity of functions or their derivatives at the point of transitionfrom one region to the other.

Compact models

Currents are obtained from only one equation that works in differentoperation regions. They are based either the calculation of mobilecharge or surface potential. Examples are the BSIM4, PSP, HiSim,EKV and SDDGM. Numerical calculation can be used.




Analytical models

All magnitudes are described by analytical equations, so numericalcalculation is not needed.

Each transistor model has a set of parameters which must bedetermined in order to use it.

There are three types of model parameters:

1. “Technological parameters” as transistor dimensions, thickness of different layers, impurity concentrations;

2. “Electrical parameters” as threshold voltage and mobility;

3. “Adjusting parameters” used for fitting the model to the experimental data.




The process of determination of the value of modelparameters is known as “parameter extraction”.

There are two ways for obtaining these parameters:“the individual method” – where parameters areextracted one by one, both DC or RF methods can beused;

“the optimization method” - where all the parametersare determined at the same time.

PARAMETERS OF THE MODELS



Individual extraction method.

Useful when it is necessary to study one physicalparameter as function of technology or operatingconditions to characterize the device, as e.g. VT, ormobility reduction, or effective channel length, Leff.

Drawbacks: sometimes complexity and time consuming.

In the following sections we will review several DCmethods of extractions of the following parameters forMOS transistors: VT, S, Leff and series resistance, Rs.


INDIVIDUAL PARAMETER EXTRACTION METHODS


THRESHOLD VOLTAGE (VT) EXTRACTION

The threshold voltage extraction:

VT is a fundamental parameter for MOSFET modeling andcharacterization, which represents the onset of significantdrain current flow. It has been given several definitions, but itmay be essentially understood as the gate voltage value atwhich the transition between weak and strong inversiontakes place in the channel of the inversion-type MOSFET.

A review of MOSFET threshold voltage extraction methodscan be found in [*], some of which will be mentioned below.

* A. Ortiz-Conde, F.J.García-Sánchez, J.J. Liou, A. Cerdeira, M. Estrada, Y. Yue, “A review of recent MOSFET threshold voltage extraction method” Microelectronics Reliability, 42, pag. 583-596, 2002.




VT extraction methods in MOSFETs biased in the linear region:

1) Constant Current (CC) method.

Defines VT as the gate voltage, VG, corresponding to a certainpredefined practical constant drain current ID;

2) Extrapolation of the Linear Region (ELR) method:

Determines the gate voltage axis intercept of the linear extrapolationof the ID-VG characteristic at the maximum slope;

3) Transconductance Linear Extrapolation (GMLE) method:

Determines the gate voltage axis intercept of the linear extrapolationof the gm-VG characteristic at the maximum slope.




VT extraction methods in MOSFETs biased in the linear region(cont):

4) Second Derivative (SD) method:

Determines VT as the gate voltage corresponding to the maximumof the second derivative of the ID - VG characteristic;

5) Ratio method (RM):

Determines the gate voltage axis intercept of the ratio of the draincurrent to the square root of the transconductance vs. VG;

6) Second Derivative Logarithmic (SDL) method:

Determines VT as the gate voltage corresponding to the minimumof the second derivative of log(ID) – VG .



VT extraction methods in MOSFETs biased in the saturationregion:

Extrapolation in the Saturation Region (ESR) method:

Determines the gate voltage axis intercept of the linearextrapolation of the ID0.5-VG characteristics at maximum slope.




Fully Depleted (FD) SOI MOSFET

W= 20 µm;tox = 30 nm; tSi = 80 nm; tbox= 400 nm; Poligate; Na= 5x1017 cm-3.

0.0 0.5 1.0 1.50.0

0.1

0.2

0.3

0.4

0.5

0.6 L (µm)

0.1 0.12 0.15 0.2 0.3 0.5 1

I D (m

A)

VG (V)

FD SOIVD= 50 mV

Measured atVD = 50 mV

VT - LINEAR REGION


Experimental data


0.0 0.5 1.0 1.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

I D (m

A)

VG (V)

experimental linear regresion constant current =(W/L)10-7A

FD SOI L=100 nm Lef= 78 nm

VD= 50 mV

VTconst= -0.03 VVTlin = 0.017 V

VTconst

VTlin-nVD

Arbitrary constant draincurrent

IDarb=(Wm/ Lm)0.1 [µA]

Wm and Lm are the maskchannel width and length,respectively.

This method is widelyused in industry becauseof its simplicity for go/no-go probers.

Advantage: simplicity

Drawback: It is totally dependent on the arbitrarily chosen IDarbIDarb -green line

VT-> intercept with the exp data

VT – CONSTANT CURRENT METHOD (CC)



0.0 0.5 1.0 1.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

I D (m

A)

VG (V)

experimental linear regresion constant current =(W/L)10-7A

FD SOI L=100 nm Lef= 78 nm

VD= 50 mV

VTconst= -0.03 VVTlin = 0.017 V

VTconst

VTlin-nVD

Extrapolation line– blue lineVT=Vintercept+VD/2 Maximum slope at VG0

Most popular: find thegate-voltage axis intercept(ID = 0) of the linearextrapolation of the ID-VGcurve at the point ofmaximum gm,.

Add Vd/2 to the resultinggate-voltage axis intercept.

Main drawback: maximumslope point might beuncertain, because the ID-VG can deviate from idealstraight line behavior atgate voltages even slightlyabove VT , due to mobilitydegradation effects and tothe presence of significantsource and drain seriesparasitic resistances.

VT – EXTRAPOLATION OF LINEAR REGION (ELR)



Rs effect on the extrapolation line: VT=Vintercept+VD/2

Effect of Rs on theslope andintercept pointvalues.

Rs at source anddrain decrease theslope in the linearregion changingthe intercept pointto lower values,and so affectingthe value ofextracted VT.


0.0 0.7 1.40.0

0.2

0.4

0.6

I D (m

A)

VG (V)

experimental lineal regretion: R=65 Ω R= 0 Ω

R=0 R=65 Ω

-0.009 0.055

VT – EXTRAPOLATION OF LINEAR REGION (ELR)


Developed to avoid the dependence of VT by the series resistances,

VT is the voltage at the maximum of the transconductance

(dgm/dVG = d2ID/dVG2) .

The shift of VT with the channel length is clearly seen.

This method is recommended for actual nanometric devices (d2φS/dVG

2 )

VT extracted from the maximum of the second derivative of ID - VG

-0.2 0.0 0.2 0.4 0.6-1

0

1

2

3

4

5

6 L (µm) VT2D(V)

0.1 0.024 0.12 0.054 0.15 0.096 0.2 0.135 0.3 0.17 0.5 0.2 1 0.2

VG (V)

FD SOISECOND DERIVATIVE

VT – SECOND DERIVATIVE METHOD (SD)



VT EXTRACTION METHODS: COMPARISON

VT extracted from CC; ELR and SD as function of the L. The roll-off effect is shown.

0.0 0.2 0.4 0.6 0.8 1.0

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

V T (V)

Channel length (µm)

SECOND DERIVATIVE CONSTANT CURRENT EXTRAPOLATION LR

FD SOI VT ROLL-OFF



Currents in the linear region for the FD SOI MOSFET can be described by the following equations (VT model):

Drain current( )

( )

+−−

+

+−−

=

DTGeffox

DDTGeffoxD

VVVCL

WR

VVVVC

LWI

δµ

δ

µ

211

21 2

δ - Equivalent body factor

Effective mobility ( )TGeff VVg −+

=θ

µµ1

0

I-V LINEAR REGION


( )boxSiox

SiboxCCC

CC+

=δ


The current expression for very low VD is equal to:

Drain current( )

[ ]( )TG

DTGDlin VVRKg

VVVKI−++

−=

θ1 0µoxCL

WK =

I-V LINEAR REGION


Extracting the maximum slope, VT; R and ∆L, the mobility degradation factor θg and maximum mobility µ0 can be calculated as:

TGGmeasured

Dg VV

RVI

VK−

−

−=

00

1)(

θ ( )( )TG

Dox

slope VVgV

LWC

P−+= 00 1 θµ

And the maximum slope is equal to: ( )( )TG

oxslope VVg

CL

WP−++

=0

0

11 θµ


Drain current can be written in the following form:

( )( ) DTG

TGox

oxDlin VVVVVC

LWRg

CL

WI −

−

++

=

0

0

1 µθ

µ

I-V LINEAR REGION


Mobility degradation and series resistance have the sameeffect in the current and it is difficult to separate one effectfrom the other.

It is important to remark that series resistance does notaffect mobility, it only affects the amplitude of the appliedvoltage.


VT EXTRACTION IN SATURATION

To extract the saturation threshold voltage VTsat the draincurrent must be measured as a function of gate voltage withthe drain connected to the gate, to guarantee that the deviceis operating in the saturation regime.

Normally the VTsat obtained in saturation is less that the VTobtained in the linear region.

( )( )

( )( )

+−

+

+−

=

δµ

δµ

121

12

2

TGeffox

TG

effoxsatD VVCL

WR

VV

CL

WI ( )TGDsat VVI −∝



Intercept of the IDsat0.5-VG characteristics linearly extrapolated

at its maximum first derivative (slope) point.

-0.5 0.0 0.5 1.0 1.5

0.00

0.02

0.04

0.06

0.08

0.10

0.12

( ID )

0.5

VG (V)

FinFETL= 50 nmVD= 1 V

VT= -0.41 VVTSD= -0.22 V

0.0 0.5 1.0 1.5

0.000

0.002

0.004

0.006

0.008

( ID )

0.5

VG (V)

FinFETL= 10µmVD= 1 V

VT= -0.08 V VTSD= -0.05 V

EXAMPLE OF VT EXTRACTION IN SATURATION



EXTRACTION OF SUBTHRESHOLD SLOPE S


decadeV

IIVVS

1)log()log( 12

12 ∆=

−−

=

-0.5 0.0 0.5 1.010-10

10-8

10-6

10-4

10-2

100

L (µm) 0.1 0.12 0.15 0.2 0.3 0.5 1

I D (m

A)

VG (V)

FD SOIVD= 50 mV

S

Ioff

Ion

∆V

Subthreshold slope definition

L (nm) S (mV/dec)100 220300 62

The effect of leakage gate current is important in subthreshold


EFFECTIVE CHANNEL LENGTH ANDSERIES RESISTANCE EXTRACTION METHODS

We define different channel length:In the mask; in the gate; metallurgical and effective.

From the external node of voltages to the internal point at thebeginning of the channel there is a resistance that we defineas series resistance.

These both parameters can be voltage depended too.



There are different definitionsof channel length.Lmask - Mask length

Lgate - Gate length. It is thephysical dimension of thegate and is a processmonitoring parameter.

Lmet - Metallurgical channellength. Distance between thetwo P-N junctions of thesource and drain diffusions atthe silicon surface. Can beextracted only with 2D TCADprograms.

EFFECTIVE CHANNEL LENGTH (Leff)



Leff - Effective channel length.

It is defined through electricalcharacteristics of the MOSFETand is not strictly a physicalparameter. It is a key parameterin CMOS technology used fortransistor models, short-channeldesign and process monitoring. Asimple model is necessary.

The physical interpretation of Leffis an open question.




Simulated SOI FD MOSFET Lm= 1 um (NO-LDD and LDD)



Another important effect to take into consideration is the dispersionof the gate channel length obtained in the technological process. Inthis case Leff can change from one transistor to another in thesame chip.

With the introduction of the HALOdiffusion in submicrometrictechnology and retrogradedjunctions, the definition of Leff isless and less associated withsome real physical dimension.

Gate

Source Drain

Body/Halo Doping




Rs or Rd = contact resistance + n+ path + n- path. R=Rs+Rd

Rs is a real physical parameter. The introduction of the LDD processincreases RS and increases the gate dependence of this parameter.

SERIES RESISTANCES (R) IN MOSFETS



Leff and R EXTRACTION METHODS

The extraction of effective channel length Leff and theseries resistance R are normally made with the sameprocedure.

From the 70th different method were proposed. SomeDC and another RF methods.

Nowadays the most used DC methods are the methodof Hu and Shift and Ratio Method.

Considering the complexity of the S&R method, we willdescribe the Hu Method.



For SOI FD MOSFET in the linear region ID can be expressed as:

Lm channel length in mask; ∆L channel length reduction; θG, θD gate and drain bias mobility degradation factors, respectively;C01,C02, Cs thin oxide, thick oxide and semiconductor capacitances respectively.

0100 CLWKeff

µ=

TGGT VVV −=

( )0201

02

CCCCC

S

S+

=δ

[ ]DDGTG

DDGTD VV

nVVVKIθθ ++−

=1

20

where:

21 δ+

=nLLL meff ∆−=

HU METHOD



DGT

DDGTG

o

m

D

DchannelStot nVV

VVK

LLIVRRR

−++∆−

==+=θθ1

( ) ( ) ( )DGT

DGTGSGm

DGTo

DDGTGmGTtot nVV

VnVVRVLLnVVK

VVLVR−−

+∆−⋅

−++

=32)()(1),( θθ

In the linear region (triode region), the total resistance Rtot is equal to:

After some rearrangements:

Rtot(Lm) is a linear function of Lm for constant VGS. and VDS.

Plotting Rtot vs. Lm will show an interception point that provides information about Rs and Leff.

HU METHOD



HU METHOD

Plotting Rtot vs. Lm at different VG will show an interception pointthat provides information about Rs and Leff.

Rtot is calculated for two close VGT values (V1 and V2), for whichRS an Leff remain constant:

R(V1)=R(V2)=Ro and ∆L(V1)=∆L(V2)= ∆Lo ,

V1= VGT1+∆V/2 , V2= VGT2-∆V/2 and VGT=(V1+V2)/2

),()(

)()(1

)()()(

GTmodrainsourceGTo

GToDGD

GTooDGoGTmo

VLRRRVR

VLVn

VRKnVVLVL

=+=

∆≈++

+∆=θθ

From previous equation:

HU METHOD



Measured Data SOI FD LDD

0 5 10 15 20

0

2

4

6

8

10

12

14

Vgs=(V1+V2)/2 = 1.7 VRt

(kΩ

)

Lm (µm)

V1 = 1.8 V V2 = 1.6 V

HU METHOD



Measured Data SOI FD LDD near the intercept point

0.0 0.1 0.2 0.3 0.40.0

0.1

0.2

0.3

Lmo= 0.19 µmRso= 153 Ω

Vgs=(V1+V2)/2 = 1.7 VRt

(kΩ

)

Lm (µm)

V1 = 1.8 V V2 = 1.6 V

HU METHOD



0.5 1.0 1.5 2.00

100

200

300

400

500

600

700

800

900

1000DATA FROM MARCELO

Rs [Ω

]

Vgs [V]

sin LDD 0.1 sin LDD 0.2 con LDD 0.1 con LDD 0.2

0.5 1.0 1.5 2.0

0.2

0.3

0.4

0.5

0.6

0.7

DATA FROM MARCELO

∆L [µm

]

Vgs [V]

sin LDD 0.1 sin LDD 0.2 con LDD 0.1 con LDD 0.2

Extracted Rs(VGS) V1-V2= 0.2 , 0.1 V Extracted ∆L(VGS)

Voltage dependence of Rs and ∆L

HU METHOD



Adjust to a fixed function:

)253.0(82.51122.0

)519.0(0116.0176.27

−+=∆

−+=

GS

GS

VL

VRs

)413.0(43.2

)413.0(39.4

58.0215.0

45.141475.98−

−−

+=∆

+=GS

GS

V

V

eL

eRs

F1 -> Shu,Hu,Ko,Hsu, 1984 F2 -> Reydezel, Murphy, 2002

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

100

200

300

400

500

Rs [Ω

]

Vgs [V]

Rs F-1 F-2

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

∆L [µm

]Vgs [V]

∆L F 1 F 2

HU METHOD



PROBLEMS WITH THE TOTAL RESISTANCE EXTRACTION METHODS

-1 0 1 2 3 4 5 6 7

0

2000

4000

6000

8000

Vg= 1V Vg= 1.2 V Vg= 1.5 V

Tota

l res

istan

ce (Ω)

Channel length (µm)0.00 0.05 0.10 0.15

50

100

150

200

Vg= 1V Vg= 1.2 V Vg= 1.5 V

Tota

l res

istan

ce (Ω)

Channel length (µm)

For some devices Rtotal can no longer be considered to vary linearlywith Lm. For FinFETs with channel length down to 40 nm non-linearitycan be significant .



In large channel transistors with very thin gate dielectric, includingstacks, gate tunneling current can be very large and the values of drainand source currents are affected.

EFFECT OF THE GATE CURRENT

-1.0 -0.5 0.0 0.5 1.0 1.5-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

curre

nt [u

A]

Vgs

IG ID IS IG/2 ID+IG/2 IS-IG/2

L= 10 umVds= 0.05 V

FinFET with EOT= 2 nm

In this case, it isimportant to measure IGcurrent in order to besure that the currentregion used forparameter extraction isnot affected by the gatecurrent.



Individual extraction methods are not the best solution in thefollowing cases:

1. The model has too many parameters. (Some models have morethan hundred parameters).

2. The equations of the model do not have a direct dependence onexternal voltages. They can depend on charges or electric fields, inwhich cases it is not possible to obtain explicit equations.

3. The volume of data is too big, you need a very precise devicedescription or you are dealing with different types of transistors inthe circuit.

In these cases the parameter extraction must be done using amathematical algorithm, known as optimization.


INDIVIDUAL PARAMETER EXTRACTION METHODS


When you have a current-voltage data for onetransistor, you can use the well-known mathematicalmethod, optimization or minimization, in order to extractthe model parameter.

Levenberg-Marquardt algorithm is the best for thispurpose.

PARAMETER EXTRACTION : THE OPTIMIZATION METHOD



Current-voltage equation (model).

Vector of N variables (parameters) X

M measured points, pairs of current

and voltage

An objective function F(Vi,X) is

defined. It must be normalized.∑=

−=

=

=

M

iimeas

imeasi

iimeas

N

IIVXIXF

VfI

xxxX

VXI

1

2

21

),()(

)(

),...,,(

),(

OPTIMIZATION METHOD: DESCRIPTION

Levenberg-Marquard algorithm is implemented in the following way:



Like other numerical minimization algorithms, this is aniterative procedure. An initial guess for the parameter vectorX is required .

In each step of iteration, the parameter vector Xk is replacedby a new one Xk+1.

[ ] ),()(11

ikT

kkTkiik

Tk

kk VXIJJJJJXX ⋅⋅+⋅⋅−=−+ λ

The iterations stop when the difference is less than ε;

ε<−+ )()( 1 kk XFXF

OPTIMIZATION METHOD: DESCRIPTION

Constrains are introduced to define the specified range for the variation of parameters.


46

A way to solve the parameter extraction is the solution of asystem of equations, using an algorithm of optimization(minimization) in the following steps:

• Model definition

• Definition of N current-voltage equations at N measuredpoints.

• M –number of unknown parameters, N ≥ M.

Iterative solution steps stops when the measuredcharacteristics can be described using a parameter vector Xwith a fixed error.

The solutions of this system of equations by the optimizationmethod can be done using any of the known mathematicalpackages like Mathcad, Mathlab or Mathematica.

EXAMPLE

DC Parameter Extraction MethodsTraining Courses onCompact Modeling

47

In the SDDGM model (*) for double-gate transistors (FinFETs) drain current is equal to:

qs (VG,VD) and qd (VG,VD) are the normalized mobile charges at source and drain. Em (VG,VD) is the medium electric field between S and D

Known parameters: VT , W, L, kT, µ0, δ, CoxUnknown parameters: X(E1, E2, P1, P2, R)

EXAMPLE

( )

+−−+

+

+

++

−−+−

=

DTGox

Pm

Pm

bd

bsbds

dsox

D

VVVRCL

WEE

EE

qqqqqqqqq

qkTC

LW

I

δµ

µ

2121

ln22

2

0

2

2

1

1

222

0

mod


* A. Cerdeira, B. Iñiguez and M. Estrada, “Compact model for short channel symmetricdoped double-gate MOSFETs”, Solid-State Electronics, 52 (2008) 1064-1070.

48

EXAMPLE

For transfer characteristic in the linear region at fixed VDcurrents are extracted at n gate voltage points:

IDexp (VGi) where i =1,2..n

A system of n equations is obtained:

DC Parameter Extraction Methods

1),,(),,(

mod

exp =XVVIXVVI

DGiD

DGiD


49

EXAMPLE

The following FinFET transistor will be modeled:

EOT= 1.6 nm;WFIN= 30 nm;HFIN = 60 nm; W= 67.5 µm;

VD= 20 mV; T= 25 ºCMetal gate with work function of 4.6 Vµ0= 1300 cm2/VsVT=0.3 V

0.0 0.5 1.0 1.50.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

I D (m

A)

VG (V)

FinFETL= 120 nmW= 67.5 µm

VD= 20 mV

Selected points:1. 0.4 V 2. 0.6 V3. 0.8 V4. 1.2 V5. 1.5 V


EXAMPLE

Guess parameters Extracted parameters E1= 104 V/cm 12 V/cmE2= 2x106 V/cm 8.34x104 V/cmP1= 0.33 0.2P2= 1.5 1.13R= 10 Ω 0 Ω


-0.5 0.0 0.5 1.0 1.50.0

0.4

0.8

1.2

I D (m

A)

VG (V)

measured modeled

VD= 20 mVT= 25 ºC

-0.5 0.0 0.5 1.0 1.51E-91E-81E-71E-61E-51E-41E-30.010.1

110

I D (m

A)

VG (V)

measured modeled

VD= 20 mVT= 25 ºC



1. The extraction is made for all the parameters at the sametime.

2. When the program is well written, the method is fast andeasy to use.

3. The data and the resulting parameters can describe the I-V in different regions, where different models work.

OPTIMIZATION METHOD: ADVANTAGES



4. The input data can include measurements of one transistor,or measurements of different transistors of the same type,or accumulated measurements in a week, etc. That is, theextracted parameters can be the result of consideringstatistical data for one type of transistor.

5. These are the mean value parameters that the foundrygives to the user in order to simulate the integrated circuitswith SPICE MODELS.

6. This method is the best for the extraction of thoseparameters that are not depending directly on externalapplied voltages. It gives the best fitting.

OPTIMIZATION METHOD: ADVANTAGES



1. Extracted values of parameters are fitting valueswhich may not have physical meaning.

2. These parameters cannot be used in order toanalyze physical magnitudes as threshold voltageor mobility.

OPTIMIZATION METHOD: DRAWBACKS



1. Parameter extraction is a necessary step in theprocess of device modeling.

2. Extraction methods can be done using DC or RFmeasurements.

3. Two types of DC method can be used: individual andoptimization.

4. Individual extraction of VT, S, R and ∆L werepresented.

5. For VT the best method for the actual nanometrictransistors is the Second Derivative Method.

CONCLUSIONS



6. Extraction of R and ∆L is a complex process,specially for short channel devices. In some casesHu method gives a good result. Another goodapproach is by simulation.

7. The extraction by mathematical optimization(minimization) is the best method for the newMOSFETs when models have many parameters andparameters have a complex dependence on fieldsand voltages.

CONCLUSIONS



Thanks for your attention



Parameters extracted:VT= 0.024 VR= 65 Ω∆L= 22 nm

µo= 1400 cm2/Vsθg= 0.09 1/V

VD = 50 mV

0.0 0.5 1.0 1.5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

I D (m

A)

VG (V)

experimental modeled

FD SOIW= 20 µmL= 100 nm

Comparison with the experimental

I-V LINEAR REGION


08 Antonio Cerdeira

Documents

Transcript of 08 Antonio Cerdeira