Disclaimer: This course was prepared, in its entirety, by Adam Teman. Many materials were copied from sources freely available on the internet. When possible, these sources have been cited;

however, some references may have been cited incorrectly or overlooked. If you feel that a picture, graph, or code example has been copied from you and either needs to be cited or removed,

please feel free to email adam.teman@biu.ac.il and I will address this as soon as possible.

Digital Integrated Circuits(83-313)

Lecture 11:

MOSFET ModelingSemester B, 2016-17

Lecturer: Dr. Adam Teman

TAs: Itamar Levi, Robert Giterman

18 June 2017

MOSFET Current Modeling

• In Digital Electronic Circuits, we used the Shockley Model

for hand-analysis of circuit operation.

• However, there are many models with varying levels of

accuracy to estimate the I-V curves of a MOSFET.

• In this section, we will overview several models that will

come in use throughout this course and your future.

2

Lecture Content

3

Basic MOS Models

4

• The most simple MOSFET model is the Switch Model.

Switch Model

5

VGS

IDS

VT

VDS

IDS

1/Ron

The Switch Model

VGS > VT

S D

Ron

The Piece-Wise Linear Model

• As we know, when the channel pinches off,

the current saturates.

• This can be depicted with the simple

Piece-Wise Linear Switch Model

6

VDS

IDS

1/Ron

IDSAT

VGT

linear saturation

The Piece-wise Linear Model

The Switch Model

Adding Channel Length Modulation

• Channel Length Modulation modeled as a finite output

resistance, causes a saturation current dependence on VDS.

7

VDS

IDS

1/Ron

IDSAT

VGT

Channel

Length

Modulation

λIDSAT

-1/λ

IDSAT

1/λ

I DS

AT

D

S

VDS

IDS

The Piece-wise Linear Model

The Switch Model

Square Law (Shockley) Model

• To get a more accurate model, we already are familiar

with the Shockley or Square Law Model.

• Current is just charge times velocity, so at any point, x,

along the channel:

• We found that charge can be approximated as:

• And the velocity is the mobility times the electrical field:

8

DI x x Q x Wdx

ox GS CS TQ x C V V x V

n

dVx E x

dx

The Piece-wise Linear Model

The Switch Model

The Square Law Model

Square Law (Shockley) Model

• So we get:

• And integrating from source to drain, we get

• At pinch-off (VDS=VGS-VT), the voltage over the channel is constant, so we get:

• This is where the “Square-Law” name comes from.

9

D n ox GS TI dx C W V V V dV

0 0

1

2

DSL V

DS D n ox GS T n ox DS GS T DS

WI I dx C W V V V dV C V V V V

L

2

2DSAT n ox GS T

WI C V V

L

The Piece-wise Linear Model

The Switch Model

The Square Law Model

Square Law (Shockley) Model

• Replacing VDS with VDSeff=min(VGS-VT, VDS) we get:

10

2

12

DSeff

DS n ox GS T DSeff DS

VWI C V V V V

L

The Piece-wise Linear Model

The Switch Model

The Square Law Model

The Velocity Saturation Model

• However, when looking at a short channel device,

we see a linear dependence on VGS.

• This can be attributed to Velocity Saturation.

11

510satm

s

The Piece-wise Linear Model

The Switch Model

The Square Law Model

The V-Sat Model

The Velocity Saturation Model

• A good approximation of the mobility curve is:

• For continuity:

• After integration, we get:

12

1crit

crit

sat crit

2 satcrit

2

21

n ox DSDS GS T DS

DS

crit

C VWI V V V

V LL

The Piece-wise Linear Model

The Switch Model

The Square Law Model

The V-Sat Model

The Velocity Saturation Model

• This is hard to use, but we can reach an important

conclusion.

• We found that:

• And we know that for a velocity saturated device:

• Equating, we get:

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GS T crit

DSAT

GS T crit

V V LV

V V L

2

21

n ox DSDS GS T DS

DS

crit

C VWI V V V

V LL

DS ox GS DSAT T satI WC V V V

DSAT crit GT GS TV L V V V pinchoff

DSAT crit GT critV L V L vel sat

The Piece-wise Linear Model

The Switch Model

The Square Law Model

The V-Sat Model

The Unified Model for Hand Analysis

• A few simple estimations will make the V-Sat model

more user-friendly:• The mobility is piecewise linear, saturating at ξ>ξcrit/2

• VDSAT is piecewise linear, saturating at VDSAT=ξcritL/2,

when VGT>ξcritL/2

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The Piece-wise Linear Model

The Switch Model

The Square Law Model

The V-Sat Model

The Unified Model

The Unified Model for Hand Analysis

• This brings us to the Unified Model:

15

2

12

DSeff

DS n ox GS T DSeff DS

VWI C V V V V

L

min , ,DSeff GS T DS DSATV V V V V

2

critDSAT

LV

2 satcrit

The Piece-wise Linear Model

The Switch Model

The Square Law Model

The V-Sat Model

The Unified Model

Advanced MOS Models

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VT* Model

• Sometimes we want to use a really simple model.

• We can assume that if the transistor is on,

it’s velocity saturated.

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*

2

2

2

T

DSATDS n GS T DSAT

DSATn GS T DSAT

V

VI k V V V

Vk V V V

*

* *

0 GS T

DS

n GS T DSAT GS T

V VI

k V V V V V

The VT* Model

The Piece-wise Linear Model

The Switch Model

The Square Law Model

The V-Sat Model

The Unified Model

The Alpha Power Law Model

• Sakurai found that by changing the exponent of the square

law, a better fit can be found with simple calculations.

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The VT* Model

The Alpha Power Law Model

The Piece-wise Linear Model

The Switch Model

The Square Law Model

The V-Sat Model

The Unified Model

2

DSAT n ox GS T

WI C V V

L

Shockley (α=2) Alpha (α=1.3)

BSIM

• The main model used by simulators today is the BSIM4

model. This model uses hundreds of parameters to

achieve a good fit.

• This model takes into

account all known

physical effects, as

well as many fitting

parameters.

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The VT* Model

The Alpha Power Law Model

BSIM

The Piece-wise Linear Model

The Switch Model

The Square Law Model

The V-Sat Model

The Unified Model

Newer Models

• BSIM Group Webpage:

http://www-device.eecs.berkeley.edu/bsim/

• Compact Model Coalition (CMC) Webpage:

https://www.si2.org/cmc_index.php

• Newer BSIM Models:• BSIM6 – Bulk CMOS

• BSIMSOI - SoI model standardized in 2001 (built on BSIM3.3)

• BSIM-CMG – multi-gate FETs (FinFet, Nanowire) – written in Verilog-A

• BSIM-IMG – Independent Multi-Gate – for UTBB-SoI

• EKV Model: http://ekv.epfl.ch/• Developed in 1995 to provide accuracy even in subthreshold

• PSP: http://psp.ewi.tudelft.nl/• Standard for current bulk CMOS

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The VT* Model

The Alpha Power Law Model

BSIM

And more…

The Piece-wise Linear Model

The Switch Model

The Square Law Model

The V-Sat Model

The Unified Model

Threshold Voltage Revisited

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Energy Band Diagrams

• To understand the threshold voltage and other secondary effects of

the MOS device, we often use energy band diagrams.

• The first approach is looking in from the gate:

22

Energy Band Diagrams

• The second approach is looking from the source to the drain.

23

Threshold Voltage - Basic Theory

• The basic definition of threshold voltage is

the gate voltage (VG) required to invert the channel

24

0 2depOX

T MS F

ox ox

QQV

C C

2 2dep A si FQ qN

ln AF T

i

N

n

T

kT

q

Basic Theory

Body Effect

• The appearance of a voltage difference between the

source and body (VSB) is known as “The Body Effect”

• This can be modeled by the additional

charge that needs to be depleted.

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2 2dep A si F SBQ qN V

0 2 2T T F SB FV V V

2 si A

ox

q N

C

0

0 2depox

T MS F

ox ox

QQV

C C

Classic Body Effect

Basic Theory

Modern Body Effect

• A different approach is to look at

the capacitive voltage divider

between the gate and body (CGB)

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0

0

max

31 1

inv oxe GS CS T dep SB CS

dep oxeoxe GS CS T

oxe d

Q C V V V C V V

C TC V nV V n

C W

maxd

sdep

WC

Classic Body Effect

Basic Theory

Modern Body Effect

VGG

C

B

S

Coxe

Cdep

VS

VB

Modern Body Effect

• This can be shown to redefine VT as:

• In modern technologies, Cdep/Coxe is a constant,

so VT is linearly dependent on VSB!

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dep

T SB T0 SB

oxe

( )C

V V V VC

Classic Body Effect

Basic Theory

Modern Body Effect

Poly Depletion and Channel Depth

The threshold voltage is affected by two additional

factors that we have disregarded until now:

• Polysilicon Depletion• Since polysilicon is, itself, a semiconductor,

the depletion layer into the poly effectively

increases the oxide thickness.

• Channel Depth• Since the channel is not a 2-dimensional

line along the surface, the oxide thickness

is essentially increased.

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max

31 1

dep oxe

oxe d

C Tn

C W

Classic Body Effect

Basic Theory

Modern Body Effect

Hot Carrier Effects

• Electrons can get so fast that they can tunnel into

the gate oxide and increase the threshold voltage.

• This is a reliability issue as it happens over time.

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0 2depOX

T MS F

ox ox

QQV

C C

Classic Body Effect

Basic Theory

Modern Body Effect

Hot Carriers

VT Roll Off (Short Channel Effect)

• As channel length is reduced, effective channel length is

reduced by depletion regions.

• A trapezoid is created under the gate,

dividing the channel into the region

controlled by the gates and by the drain.

• In essence, VT is reduced.30

K. Goto et

al., IEDM

2003

65nm technology.

tox=1.2nm

Vdd=1V

Classic Body Effect

Basic Theory

Modern Body Effect

VT Roll-Off

Hot Carriers

DIBL (Drain Induced Barrier Lowering)

• In short channels, the barrier of

the channel is essentially lowered,

as the drain causes the energy band

to drop closer to the source.

• This is exponentially dependent on VDS.

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dT T,long DS

oxe

0.4C

V V VC

Classic Body Effect

Basic Theory

Modern Body Effect

VT Roll-Off

Hot Carriers

DIBL

Roll Off / DIBL combined

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Classic Body Effect

Basic Theory

Modern Body Effect

VT Roll-Off

Hot Carriers

DIBL

Reverse Short Channel Effect (RSCE)

• VT actually increases at channel lengths a bit higher than

minimum…

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Classic Body Effect

Basic Theory

Modern Body Effect

VT Roll-Off

Hot Carriers

DIBL

RSCE

• There are various ways to measure VT

• One classic way takes a small VDS and sweeps VGS.

• So we can find the VGS

at which the linear part

crosses Ids=0.

VDS=50mV

How to Measure VT

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2( ) 0.5d gs t ds dsI k V V V V gs tV V

VT,gm

Classic Body Effect

Basic Theory

Modern Body Effect

VT Roll-Off

Hot Carriers

DIBL

RSCE

Measuring VT

How to Measure VT

• One of the more common ways is to find the

VGS at which IDS=100 nA x W/L.

• For VT,lin, set a low VDS (VDS=50mV)

• For VT,sat set a high VDS (VDS=VDD)

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Classic Body Effect

Basic Theory

Modern Body Effect

VT Roll-Off

Hot Carriers

DIBL

RSCE

Measuring VT

OP and MP in Spectre

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Classic Body Effect

Basic Theory

Modern Body Effect

VT Roll-Off

Hot Carriers

DIBL

RSCE

Measuring VT

Further Reading

• J. Rabaey, “Digital Integrated Circuits” 2003, Chapters 2.5, 3.3-3.5

• Weste, Harris “CMOS VLSI Design”, Chapter 7

• C. Hu, “Modern Semiconductor Devices for Integrated Circuits”, 2010, Chapters 4-7

• Tzividis, et al. “Operation and Modeling of MOS Transistor”Chapters 1-5

• E. Alon, Berkeley EE-141, Lecture 9 (Fall 2009)

• M. Alam, Purdue ECE-606 – lectures 32-38 (2009) nanohub.org

• A. B. Bhattacharyya “Compact MOSFET models for VLSI design”, 2009,

• T. Sakurai, “Alpha Power-Law MOS Model” – JSSC Newsletter Oct 2004

• Managing Process Variation in Intel’s 45nm CMOS Technology, Intel Technology Journal, 2008

• Berkeley “BSIM 4.6.4 User’s Manual”

http://www-device.eecs.berkeley.edu/~bsim/BSIM4/BSIM464/BSIM464_Manual.pdf

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