Introduction to PSP MOSFET Model

Introduction to PSP Introduction to PSP MOSFET ModelMOSFET Model

G. Gildenblat, X. Li, H. Wang, W. WuDepartment of Electrical EngineeringThe Pennsylvania State University, USA

and

R. van Langevelde, A.J. Scholten, G.D.J. Smit and D.B.M. KlaassenPhilips Research Laboratories, The Netherlands

OUTLINEOUTLINE

Origin and General Features of PSP ProjectTechnical DetailsFitting ExamplesNQSSimulation ExamplesConclusions

Key Objectives of PSP ProjectKey Objectives of PSP Project

Merge the best features of the two most advanced Surface-Potential-Based Models (SPBM): SP and MM11Provide the modeling capabilities down to 65nm node and beyond (in the nearest future)Strengthen the infrastructure of the SPBM

What Makes PSP Project PossibleWhat Makes PSP Project Possible

Similar approach to compact modeling at PSU and Philips ResearchSimilar modular structure of SP and MM11Extension of Symmetric Linearization Method beyond SP and MM11

Structure of PSP ModelStructure of PSP Model

Glo

bal P

aram

eter

Set

Loca

l Par

amet

er S

et

Intrinsic

Extrinsic

JUNCAP

NQS

Support Modules

Core

PSP

Worth NotingWorth Noting

PSP is far more than mixture of the best SPand MM11 modules. For example, thefollowing PSP submodels go beyond both SPand MM11 versions.

NQSGate current

General Features of PSP (I)General Features of PSP (I)Physical surface-potential-based formulation in both intrinsic and extrinsic model modules Physical and accurate description of the accumulation region Inclusion of all relevant small-geometry effects Modeling of the halo implant effects, including the output conductance degradation in long devices Coulomb scattering and non-universality in the mobility model Non-singular velocity-field relation enabling the modeling of RF distortions including intermodulationeffects.Complete Gummel symmetry

General Features of PSP (II)General Features of PSP (II)Mid-point bias linearization enabling accurate modeling of the ratio-based circuits (e.g. R2R circuits)Quantum-mechanical correctionsCorrection for the polysilicon depletion effectsGIDL/GISL modelSurface-potential-based noise model including channel thermal noise, flicker noise and channel-induced gate noise.Advanced junction model including trap-assisted tunneling, band-to-band tunneling and avalanche breakdownSpline-collocation-based NQS model including all terminal currentsStress model

OUTLINEOUTLINE

Origin and General Features of PSPTechnical DetailsFitting ExamplesNQSSimulation ExamplesConclusions

Surface Potential without Minority Carriers Surface Potential without Minority Carriers (for use in S/D overlap regions)(for use in S/D overlap regions)

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-0.3

-0.2

-0.1

0.0

0.1

Vgs (V)

Surf

ace

Pote

ntia

l (V)

-40

-20

0

20

40

Numerical Solution Analytical Approximation

Erro

r (pV

)

PSP: PSP: ψψss calculationcalculation

with FPSP(u)

VSB=1V

Accuracy of Accuracy of ψψs s approximationapproximation

MobilityMobility

PSP uses SP mobility model. It includes “universal” dependence on the vertical effective field Eeff and the deviations from the universality associated with theCoulomb scattering.

( )( )

2THEMU

2

MU0CS1 MUE

x

bmeff

bm im

qEq q

µµ ⋅=

⋅+ ⋅ +

+

PSP uses MM11 drift velocity model that is conducive to the highly accurate description of saturation region including high order drain conductances.

This form also assures compliance with Gummel symmetry test and non-singular model behavior at Vds= 0.

Drift VelocityDrift Velocity

( )21 cy

yd

EE

EV

+=

µ

No need for correction factors used in older SPBMs to reproduce proper behavior for small Vds

Subthreshold region is accurately modeled through

Velocity saturation is introduced in such a way that its effects automatically vanish in subthreshold.

Drain CurrentDrain Current

ψ∆

( )( )( )2

2;

1 1 2im t

d

c

W L qI

E L

µ αφ ψ

ψ

+ ∆=

+ + ∆sd ssψ ψ ψ∆ = −

Lateral Field GradientLateral Field Gradient

Most SPBMs use GCA:HiSIM: SP, PSP:

( )( )2 21 s sub sf qN yε ψ= − ∂ ∂

1f =

( )gs sb dsL, W, V , V , Vf f=( )L,Wf f=

Symmetric Linearization (I)Symmetric Linearization (I)

( )mi simqq ψψα −−=

( ) ( )

−

∆−−+= myy

HLHy m

ψψψ 211

∆+=

HLym 4

12

ψ

These equations are the same in SP and PSP

Variable H in PSP is defined differently than in SP

Without velocity saturation:

In SP:

In PSP:

Symmetric Linearization (II)Symmetric Linearization (II)

( ) ( )1 1

2 2 2PSP 0

1 1 11 ; 1 22 2 2

H hH h hξ ξ−

= + = + +

( )0 im tH q α φ= +

( ) 1SP 0 01 ; = cH H E Lδ ξ ξ ψ−= + ∆

Normalized QuasiNormalized Quasi--Static ChargesStatic Charges

∆−

∆−

∆+= 2

PSP

2

2021

122 PSP HHqQ im

Dψψψα

PSP12

2

HqQ imI

ψα∆−=

PSP12

2

HVQ oxmG

ψ∆−=

DIS QQQ −= IGB QQQ −=

Using Ward-Dutton partition

Vds = 2V, Vbs= 0 V, Vfb=-1V

Verification of Symmetric Verification of Symmetric LinearizationLinearization

-1 0 1 2 3 40.0

0.3

0.6

0.9 Linearized CSM Original CSM

Cdg

Cbg

Csg

Cgg

Nor

mal

ized

Tra

nsca

paci

tanc

es

Vgs (V)

PSP Noise ModelPSP Noise ModelIncludes thermal channel noise, 1/f noise, channel-induced gate noise and shot-noise in the gate-current

Thermal channel noise automatically becomes shot noise below threshold, so it is not necessary to model this phenomena separately

Rigorously includes fluctuations in the velocity saturation term. Based on MM11 formulation

Takes advantage of symmetric linearization to simplify expressions for the spectral densities

Experimentally verified

ExampleExample

Drain (Sid) and gate (Sig) current noise spectral densities

Gate Current ModelGate Current Model

Based on Tsu-Esaki formulation, includes supply function

Includes contributions from both the channel and the overlap regions. Automatic scaling (no scaling parameters)

SP model extended MM11 formulation of Igate by including supply function. PSP version is based on SPbut is further developed

Experimentally verified using several processes from four different production facilities

Vsb=0V, Vds=0.025, 0.042, 0.61 and 1V

ExampleExample

OUTLINEOUTLINE

Origin and General Features of PSP Technical DetailsFitting Examples (Global fit, no binning)NQSSimulation ExamplesConclusions

IIDD--VVGSGS

for long/wide devicefor long/wide device

0.0 0.4 0.8 1.2

2

4

6

8

10

V GS (V)

I D (

µ A

)

V DS = 0 . 05 V

0.0 0.4 0.8 1.2 10-12 10-11

10-10

10-9

10-8

10-7

10-6

V GS (V)

I D (

A)

V DS = 0 . 05 V

Philips 90nm LP-process NMOS W/L = 10µm/10µm

VBS = 0 .. –1.2V

ggmm and gand gmm/I/IDD


0.0 0.4 0.8 1.2

5

10

15

V GS (V)

g m (

µ A

/V)

V DS = 0 . 05 V


10-12 10-11 10-10 10-9 10-8 10-7 10-6

10

20

30

40

I D (A)

g m /

I D (

1/V

) V DS = 0 . 05 V

VBS = 0 .. –1.2V

IIDD--VVDSDS


0.0 0.4 0.8 1.2

0.05

0.10

0.15

0.20

V DS (V)

I D (

mA

)

0.0 0.4 0.8 1.2 10-7

10-6

10-5

10-4

V DS (V)

g DS

(A/V

)


VGS = 0.34 .. 1.2VVBS = 0V

IIDD--VVGSGS

for short/narrow devicefor short/narrow device

Philips 90nm LP-process NMOS W/L = 110nm/100nm

0.0 0.4 0.8 1.2

1

2

3

4

5

V GS (V)

I D (

µ A

)

V DS = 0 . 05 V

0.0 0.4 0.8 1.2 10-15 10-14 10-13 10-12 10-11 10-10 10-910-810-710-6

V GS (V)

I D (

A)

V DS = 0 . 05 V

VBS = 0 .. –1.2V

ggmm and gand gmm/I/IDD



0.0 0.4 0.8 1.2

2

4

6

8

V GS (V)

g m (

µ A

/V)

V DS = 0 . 05 V

10-15 10-14 10-13 10-12 10-11 10-10 10-910-810-710-6

10

20

30

40

I D (A)

g m /

I D (

1/V

) V DS = 0 . 05 V

VBS = 0 .. –1.2V

IIDD--VVDSDS



0.0 0.4 0.8 1.2

0.02

0.04

0.06

V DS (V)

I D (

mA

)

0.0 0.4 0.8 1.2 10-6

10-5

10-4

V DS (V)

g DS

(A/V

)

VGS = 0.34 .. 1.2VVBS = 0V

CV CharacteristicsCV Characteristics

W/L = 800µm/90nm, Vds=0, Vsb=0

OUTLINEOUTLINE

Origin and General Features of PSP Technical DetailsFitting ExamplesNQSSimulation ExamplesConclusions

PSP NQS ModelPSP NQS Model

Unified model for AC and transient simulationsSpline-collocation-basedConsistent with QS, includes all terminal currents, and all operation regionsVerified by comparison with experiments and channel segmentation methodIncludes all major small-geometry effectsSimilar to SP but further developed

The differential equations to be solved:

Using sub-circuit approach (for N=2):

CR CRCf1 Cf2

V1=u1 V2=u2

R is sufficiently large so that the current flow through it is negligible

SubcircuitSubcircuit--Based ImplementationBased Implementation

( )1,...,kk N

du f u udt

= −

( ) ( )1 1 1 2 2 2 1 2, , ,f f V V f f V V= =

0.0 0.2 0.4 0.6 0.8 1.0-2

-1

0

1

2

0.0 0.2 0.4 0.6 0.8 1.0-1

0

1

2

Cur

rent

s (m

A)

Time (ns)

QS NQS

IG

IB

0.6ns

-3V

3V 3V

Cur

rent

s (m

A)

Time (ns)

QS NQS

IDIS

0.6ns

-3V

3V 3V

Extended Operation RangeExtended Operation Range

Mobility Degradation EffectsMobility Degradation Effects

0.0 0.2 0.4 0.6

-0.4

0.0

0.4

0.8

1.2

1.6

Cur

rent

s (m

A)

Time (ns)

Symbols: NQS QS TCAD

constant µ field-dependent µ

0.3ns

0V

3V 3V

RF ModelingRF Modeling90-nm Philips low-power technology

Ground-signal-ground configuration; common sourcebulk; pad open-short-dedicated open de-embedding (Tiemeijer et al.)

L=3 µm; Wfing=10 µm; Nfing=6; MULT=2i.o.w. total width=120 µm

markers: measurementsdashed lines: PSP-QS solid lines: PSP-NQS

Re[YRe[Y1111]]

VDS=1.5 VVGS=0.5 VVGS=1.0 VVGS=1.5 V

PSP, SWNQS=5 PSP, SWNQS=9

MM11, 5 segments

CCgggg

VDS=1.5 VVGS=0.5 VVGS=1.0 VVGS=1.5 V

PSP, SWNQS=5 PSP, SWNQS=9

MM11, 5 segments

Vdd

A

B

Q

X

MP1

MP2

MN1MN2

The “Killer” NOR Gate

MP1 W/L=8.0/10.0um MP2, MN1, MN2 W/L=8.0/3.0um

0 50 100 150 200

0.0

0.4

0.8

1.2

1.6

Nod

e V

olta

ges

(V)

Time (ns)

V(A) V(B) V(Q) NQS V(Q) QS

PSP Default Parameter Set

0 50 100 150 200-10

-5

0

Nod

e V

olta

ge a

t X (V

)

Time (ns)

QS NQS

Generic 90nm Process Parameter Set

0 50 100 150 200

-20

-15

-10

-5

0

5

Nod

e V

olta

ge a

t X (V

)

Time (ns)

QS NQS

AcknowledgementAcknowledgement

The Authors are grateful to C. McAndrew, J. Watson, P. Bendix, D. Foty, B. Mulvaney, N. Arora, W. Grabinski, J. Victory, G. Workman and S. Veeraraghavanfor numerous stimulating discussion of the subject and toD. Gloria and S. Boret for kindly providing the 90 nm RFdata.

PSP development at PSU was supported in part by SRC, LSI Logic, Freescale Semiconductor, IBM

andby simulation tools provided by Freescale Semiconductor, Mentor Graphics and Agilent.

PSP Code and Documentation

http://www.semiconductors.philips.co/Philips_Models/mos_models/psp/index.html

documentation of the model and parameter extraction strategy Verilog-A code C-code Modules that can be directly linked to Spectre and ADS

ConclusionsConclusions

The commonality between SP and MM11 has been used to merge them into a powerful new model – PSPPSP has been extensively tested on several 90 nm nodesPSP satisfies all the requirements for a next generation compact MOSFET modelPSP-SOI is in progress

Introduction to PSP MOSFET Model

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