MOS Model, level 40 - NXP Semiconductors · 2015. 11. 2. · For both TOX and TBOX less than or equal to zero, the pinch off voltage Vp = 0. When VP ≤0 only equations 1.24, 1.41,

July 2011 MOS Model, level 40

1 MOS Model, level 40

© NXP 1992-2011 1TOC Index Quitfile

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MOS Model, level 40 July 2011

1.1 Introduction

The Silicon On Isolator (SOI) Field-Effect Transistor (FET) is a semiconductor device whoseoperation is achieved by modulation of the resistance of a thin silicon layer (channel). Themodulation of the resistance is controlled by the gate voltage and handle wafer (box) voltage.These devices are often used as a load in high voltage MOS devices. This long channel SOIFET model is special developed to describe the drift region of LDMOS and EPMOS devices.When the n-channel FET transistor equations are used for p-channel FET transistors, the signof the terminal potentials, terminal currents and terminal charges must be changed.

1.1.1 Survey of modeled effects

• Accumulation/depletion at the surface

• Accumulation/depletion at the box

• Pinch off mode

• Velocity saturation in the channel

• Gate charge model

• Self-heating

• Box charge model

• Different temperature scaling for RON and VSAT

• Include temperature scaling for RSAT.

Not included in the model

• Short channel effects

• Subthreshold currents

• Inversion at the surface at high negative gate voltages

• Inversion at the box at high negative box voltages

• Noise model.

2 © NXP 1992-2011 TOC Index Quitfile

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1.2 Parameters and constants

1.2.1 Parameters and clipping

Parameter list

The parameters are listed below.

Parameter Units Description

LEVEL - Model level, must be set to 40

PARAMCHK - Level of clip warning info *)

RON Ω Ohmic resistance at zero biasRSAT Ω Space charge resistance at zero biasVSAT V Critical drain-source voltage for hot carriers

PSAT − Velocity saturation coefficientVP V Pinch off voltage at zero gate and handle wafer voltages

VP ≤ 0 no depletion and/or accumulation in the channelTOX m Gate oxide thickness

TOX > 0 SOI FET deviceTOX ≤ 0 No depletion/accumulation at the gate

DCH m-3 Doping level channel

TBOX mBox oxide thickness

No depletion/accumulation at the box

CGATE F Gate capacitance at zero bias

CBOX F Handle wafer capacitance at zero bias

TAUSC s Space charge transit time of the channel

ACH − Temperature coefficient restivity of the channelACHMOD − Parameter to switch to extended temperature scalingACHRON − Temperature coefficient of ohmic resistance at zero biasACHVSAT − Temperature coefficient of critical drain-source voltage

for hot carriers

ACHRSAT − Temperature coefficient of space charge resistance atzero bias

TREF °C Reference temperature

TBOX 0≤


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*) See Appendix D for the definition of PARAMCHK.

The additional parameters for the model including self-heating are listed below.

Parameter MULTThis parameter may be used to put several devices in parallel. The following parameters aremultiplied by MULT :

Divided by MULT are:

Default and clipping values

The default values and clipping values as used for the MOS level 40 model are listed below.

DTA °C Temperature offset to the ambient temperatureMULT − Multiplication factorPRINT-SCALED

− Flag to add scaled parameters to the OP output


RTH oC/W Thermal resistance

CTH J/oC Thermal capacitance

ATH − Thermal coefficient of the thermal resistance

CGATE CBOX CTH

RON RSAT RTH

Parametername Units Default Clip low Clip high

LEVEL - 40 - -

PARAMCHK - 0 - -

RON Ω 1.00 1e-2 -RSAT Ω 1.00 1e-2 -

VSAT V 10.00 1.00 ×10-6 -PSAT − 1.00 0.1 -



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The default values and clipping values of the additional parameters for the model includingself-heating (see section 1.4) are listed below.

1.2.2 Model constants

VP V -1.00 -1.0 -

TOX m -1.00 -1.0 0.0001

DCH m-3 1.00 ×1021 1.00 ×1011 1.00 ×1029

TBOX m -1.00 -1.00 0.0001

CGATE F 0.00 0.0 -

CBOX F 0.00 0.0 -

TAUSC s 0.00 0.0 -

ACH − 0.00 - -ACHMOD − 0.00 0 1ACHRON − 0.00 - -ACHVSAT − 0.00 - -ACHRSAT − 0.00 - -TREF °C 25 -273.0 -DTA °C 0.00 - -MULT − 1.00 0.0 -PRINT-SCALED − 0 - -

ParameterName

Units Default Clip low Clip high

RTH oC/W 300.0 0.000 -

CTH J/oC 3.0×10−9 0.000 -

ATH − 0.0 - -

Parametername Units Default Clip low Clip high

q 1.6021918 10 19– C⋅=


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The default reference temperature TREF for parameter determination is 25 °C.

εsi 1.036 1010–

C V⁄ m⋅⋅=

εox 3.453 1011–

C V⁄ m⋅⋅=

kq---

0.86171 10 4– V K⁄×=

δv 108–

=

δq 102–

=

V 0 103–

=


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1.3 Model equations

1.3.1 Equivalent circuit and equations

A full description of the long channel SOI FET model is given below.

Figure 1: Equivalent Circuit of an SOI FET

1.3.2 Temperature effects

The actual simulation temperature is denoted by TEMP (in oC). The temperature at which the

parameters are determined is TREF (in oC).

• Conversions to Kelvins

Gate

Qgd

Drain

Qbd

Ids

Qds

Qbs

Source

Qgs

Substrate


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(1.1)

(1.2)

(1.3)

(1.4)

• Thermal Voltage

(1.5)

• On resistance and saturation voltage

(1.6)

(1.7)

(1.8)

• Thermal resistance

(1.9)

T K TEMP DTA 273.15 V dT+ + +=

T amb TEMP DTA 273.15+ +=

T RK TREF 273.15+=

T NT K

T RK----------=

V Tkq---

T K⋅=

RON T RON TACHRON⋅=

VSAT T VSAT TACHVSAT⋅=

RSAT T RSAT TACHRSAT⋅=

RTH T RTHT ambT RK------------

ATH⋅=


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1.3.3 Model preprocessing

• Parameter dependent constants DC part

For both TOX and TBOX less than or equal to zero, the pinch off voltage Vp = 0.

When VP ≤ 0 only equations 1.24, 1.41, 1.43, 1.54, 1.55, 1.107 and 1.108 are used. In thiscase the charges Qb and Qg are equal zero.

if :

if :

if & :

: (1.10)

:

: (1.11)

:

(1.12)

(1.13)

(1.14)

(1.15)

(1.16)

TBOX 0≤ CBOX 0=

TOX 0≤ CGATE 0=

TOX 0≤ TBOX 0≤ VP 0=

TBOX 0> kb 2 εsi q DCH⋅ ⋅ ⋅=

TBOX 0≤ kb 0=

TOX 0> kg 2 εsi q DCH⋅ ⋅ ⋅=

TOX 0≤ kg 0=

kox 2 εsi q DCH⋅ ⋅ ⋅=

V boxεsi q DCH⋅ ⋅

2-------------------------------- TBOX

εox----------------

2⋅=

V oxεsi q DCH⋅ ⋅

2-------------------------------- TOX

εox------------

2⋅=

Qbpkb VP⋅

VP V box+ V box+----------------------------------------------------=

Qgpkg VP⋅

VP V ox+ V ox+-----------------------------------------------=


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(1.17)

: (1.18)

:

: (1.19)

:

(1.20)

(1.21)

(1.22)

(1.23)

(1.24)

Qsoi Qbp Qgp+=

TOX 0> Coxεox

TOX------------=

TOX 0≤ Cox 0=

TBOX 0> Cboxεox

TBOX----------------=

TBOX 0≤ Cbox 0=

Csoiεsi q DCH⋅ ⋅

Qsoi--------------------------------=

V m VP V box+ VP V ox++( )2

=

V gswQsoikox----------

Qsoikox---------- 2 V box⋅+

⋅=

V bswQsoikox----------

Qsoikox---------- 2 V ox⋅+

⋅=

VRsat VSAT TRSAT TRON T------------------⋅=


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1.3.4 Model evaluation

Drain and source voltage

• Pinch-off voltage

:

:

: (1.25)

: (1.26)

, (1.27)

& :

:

(1.28)

(1.29)

V d V s≥ sign 1=

V d1 V d=

V s1 V s=

V d V s< sign 1–=

V d1 V s=

V s1 V d=

TBOX 0≤ V p VP V g+=

TOX 0≤ V p VP V b+=

TBOX 0≤ TOX 0≤ VP 0=

TOX 0> TBOX 0>

• V g V b– V gSW>

agCox

2 Cbox⋅------------------

2=

bg 1CoxCbox-----------

CoxCsoi---------- ag

2 V g⋅V box--------------⋅+ + +

=


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(1.30)

(1.31)

:

(1.32)

(1.33)

(1.34)

(1.35)

& :

(1.36)

(1.37)

(1.38)

cg2 Cbox⋅

Csoi------------------

CboxCsoi-----------

2 CoxCbox-----------

CoxCsoi----------+

V gV box-----------+⋅+ +=

Cox2 Cbox⋅------------------

V gV box-----------⋅

2 V bV box-----------+

V p V box2 cg⋅

bg bg2 4 ag cg⋅ ⋅–+

---------------------------------------------------⋅=

• V g V b– V– bSW<

abCbox

2 Cox⋅----------------

2=

bb 1CboxCox-----------

CboxCsoi----------- ab

2 V b⋅V ox

--------------⋅+ + + =

cb2 Cox⋅

Csoi----------------

CoxCsoi----------

2 CboxCox-----------

CboxCsoi-----------+

V bV ox---------+⋅+ +=

Cbox2 Cox⋅----------------

V bV ox---------⋅

2 V gV ox---------+

V p V ox2 cb⋅

bb bb2 4 ab cb⋅ ⋅–+

--------------------------------------------------⋅=

• V g V b– V bsw–≥ V g V b– V gsw≤

V bb V b V box–=

V gg V g V ox–=

V pV gg V bb–( )

2 2 V m V gg V bb+( )⋅ ⋅ V m2

+ +

4 V m⋅------------------------------------------------------------------------------------------------------=


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• Source and drain voltage including pinch-off and velocity saturation

• Integration boundary voltages

if & : (1.39)

if & : (1.40)

: (1.41)

: (1.42)

: (1.43)

(1.44)

: :

:

:

: :

:

V P 0> V p 0≤ V sp12--- V s1 V p V s1 V p–( )

2 δv+–+

⋅=

V P 0> V p 0> V sp12---

4 V s1 V p δv–⋅ ⋅

V s1 V p V s1 V p–( )2 δv++ +

------------------------------------------------------------------------

⋅=

V P 0≤ V sp V s1=

V P 0> V c VSAT T V p V sp– VSAT T2

V p V sp–( )2

+–+=

V P 0≤ V c VSAT T=

V dp V spV d1 V s1–( ) V c⋅

V d1 V s1–( )PSAT V c

PSAT+PSAT----------------------------------------------------------------------------+=

V sp V b< V dp V b< V ab V dp=

V dp V b≥ V ab V b=

V sp V b≥ V ab V sp=

V sp V g< V dp V g< V ag V dp=

V dp V g≥ V ag V g=


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• Current increase due to accumulation at the handle wafer

• Current reduction due to depletion at the handle wafer

• Current increase due to accumulation at the gate

:

:

(1.45)

:

: (1.46)

(1.47)

(1.48)

:

: (1.49)

:

V sp V g≥ V ag V sp=

V sp V b<I b1

12--- V b V sp–( )

2V b V ab–( )

2–{ }

CboxQsoi RON T⋅-------------------------------⋅=

V sp V b≥ I b1 0=

V dp V b≥ Y dpbV dp V b–( ) V box⁄

1 1 V dp V b–( ) V box⁄++-----------------------------------------------------------------=

Y abbV ab V b–( ) V box⁄

1 1 V ab V b–( ) V box⁄++-----------------------------------------------------------------=

I b22– kb V box

3 2⁄⋅ ⋅Qsoi RON T⋅--------------------------------

Y dpb2

Y abb2

–

2-----------------------------

Y dpb3

Y abb3

–

3-----------------------------+

⋅=

V dp V b< I b2 0=

V sp V g< I g112--- V g V sp–( )

2V g V ag–( )

2–{ }

CboxQsoi RON T⋅-------------------------------⋅=

V sp V g≥ I g1 0=


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• Current reduction due to depletion at the gate

• Total ohmic current

• Total current including velocity saturation

(1.55)

: (1.50)

(1.51)

(1.52)

:

: (1.53)

: (1.54)

V dp V g≥ Y dpgV dp V g–( ) V ox⁄

1 1 V dp V g–( ) V ox⁄++---------------------------------------------------------------=

Y aggV ag V g–( ) V ox⁄

1 1 V ag V g–( ) V ox⁄++---------------------------------------------------------------=

I g22– kg V ox

3 2⁄⋅ ⋅Qsoi RON T⋅--------------------------------

Y dpg2

Y agg2

–

2-----------------------------

Y dpg3

Y agg3

–

3-----------------------------+

⋅=

V dp V g< I g2 0=

VP 0> I ohmV dp V sp–

RON T------------------------ I b1 I b2 I g1 I g2+ + + +=

VP 0≤ I ohmV dp V sp–

RON T------------------------=

I ds sign I ohm 1V d1 V dp–

VRsat------------------------+

⋅ ⋅=


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1.3.5 Substrate charge model

If then

:

:

:

:

:

:

:

accumulation part

depletion part

accumulation part

depletion part

accumulation part times accumulation part

depletion part times accumulation part

depletion part times depletion part

(1.56)

: (1.57)

(1.58)

:

: (1.59)

(1.60)

TBOX 0≤ V b1 V b2 V b3 V b4 V b5 V b6 V b7 0= = = = = = =

V b1V b2V b3V b4V b5V b6V b7

qbqb

qb2

qb2

qb qgqb qgqb qg

FcV p V sp–( )

4

V p V sp–( )4

VP 100⁄( )4+---------------------------------------------------------------

V dp V sp–

V 0 V dp V sp–+-------------------------------------⋅=

V sp V b< V b11

I ohm RON T⋅-------------------------------- 1

2--- V b V sp–( )

2V b V ab–( )

2–{ }⋅=

V b3C– box

3 Qsoi I ohm RON T⋅ ⋅ ⋅------------------------------------------------------ V b V ab–( )

3V b V sp–( )

3–{ }⋅=

V sp V b≥ V b1 0;= V b3 0=

V dp V b≥ V b22– kb T box V box

3 2⁄⋅ ⋅ ⋅εox I ohm RON T⋅ ⋅

------------------------------------------------Y dpb

2Y abb

2–

2-----------------------------

Y dpb3

Y abb3

–

3-----------------------------+

⋅=

V b42 kb

2T box V box

2⋅ ⋅ ⋅Qsoi εox I ohm RON T⋅ ⋅ ⋅-----------------------------------------------------------

Y dpb3

Y abb3

–

3-----------------------------

Y dpb4

Y abb4

–

4-----------------------------+

⋅=


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:

& > :

(1.61)

or :

& & :

(1.62)

(1.63)

& & :

(1.64)

V dp V b< V b2 0=

V b4 0=

V g V b V sp V g V b:< V ai V ag=

V g V b:≥ V ai V ab=

V b5C– ox

Qsoi I ohm RON T⋅ ⋅-----------------------------------------------

V g V b–( )V b V ai–( )

2V b V sp–( )

2–

2---------------------------------------------------------------⋅ +

V b V ai–( )3

V b V sp–( )3

–

3---------------------------------------------------------------

⋅=

V g V b V≤ sp V b5 0=

V dp V b≥ V sp V< g V b V< g

Y agbV ag V b–( ) V box⁄

1 1 V ag V b–( ) V box⁄++-----------------------------------------------------------------=

V b62– kb Cox T box V box

5 2⁄⋅ ⋅ ⋅ ⋅Qsoi εox I ohm RON T⋅ ⋅ ⋅-------------------------------------------------------------

V g V b–

V box-------------------

Y agb2

Y abb2

–

2-----------------------------

Y agb3

Y abb3

–

3-----------------------------+

⋅ –

⋅=

2Y agb

3Y abb

3–

3-----------------------------⋅ 3

Y agb4

Y abb4

–

4-----------------------------⋅

Y agb5

Y abb5

–

5-----------------------------+ +

V dp V g≥ V sp V< b V g V< b

Y abgV ab V g–( ) V ox⁄

1 1 V ab V g–( ) V ox⁄++---------------------------------------------------------------=


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(1.65)

& or & :

& < :

(1.66)

(1.67)

(1.68)

V b62 kg V ox

5 2⁄⋅ ⋅Qsoi I ohm RON T⋅ ⋅-----------------------------------------------

V b V g–

V ox-------------------

Y agg2

Y abg2

–

2-----------------------------

Y agg3

Y abg3

–

3-----------------------------+

⋅ –

⋅=

2Y agg

3Y abg

3–

3-----------------------------⋅ 3

Y agg4

Y abg4

–

4-----------------------------⋅

Y agg5

Y abg5

–

5-----------------------------+ +

V g V b V< sp V g V b V dp> V b6 0=

V g V b V dp V g V b> V ad V ag=

V g V b≤ V ad V ab=

Y adbV ad V b–( ) V box⁄

1 1 V ad V b–( ) V box⁄++-----------------------------------------------------------------=

Y adgV ad V g–( ) V ox⁄

1 1 V ad V g–( ) V ox⁄++---------------------------------------------------------------=

Z0V g V b– V ox– V box+

2----------------------------------------------------=


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(1.69)

(1.70)

Vb7exact

kg kb T box⋅ ⋅Qsoi RON T Cbox I ohm⋅ ⋅ ⋅---------------------------------------------------------------- ⋅

14--- V box V ox⋅⋅

V ox V box–( ) Y dpb Y dpg–( ) Y adb Y adg–( )– ][⋅

V box Y dpb Y dpb 1 Y dpb+( )⋅ Y dpg 3 3 Y dpb⋅ Y dpb2

+ +( )⋅+[ ]⋅ ⋅+

V box Y adb Y adb 1 Y adb+( )⋅ Y adg 3 3 Y adb⋅ Y adb2

+ +( )⋅+[ ]⋅ ⋅–

V ox Y dpg Y dpg 1 Y dpg+( )⋅ Y dpb 3 3 Y dpg⋅ Y dpg2

+ +( )⋅+[ ]⋅ ⋅+

V ox Y adg Y adg 1 Y adg+( )⋅ Y adb 3 3 Y adg⋅ Y adg2

+ +( )⋅+[ ]⋅ ⋅–

⋅

z02

lnV box 1 Y dpb+( )⋅ V ox 1 Y dpg+( )⋅+

V box 1 Y adb+( )⋅ V ox 1 Y adg+( )⋅+-------------------------------------------------------------------------------------------------⋅–

2 V box3 2⁄

V oxY dpb

2Y adb

2–

2-----------------------------

Y dpb3

Y adb3

–

3-----------------------------+

⋅ ⋅ ⋅–

2 V ox3 2⁄

V boxY dpg

2Y adg

2–

2------------------------------

Y dpg3

Y adg3

–

3------------------------------+

⋅ ⋅ ⋅–

=

Vb7appro

kg kb T box⋅ ⋅εox Qsoi RON T I ohm⋅ ⋅ ⋅------------------------------------------------------------ ⋅

1

4 V box V ox⋅⋅------------------------------------- V dp V ad–( ) V b V g⋅[ ]⋅

V dp2

V ad2

–

2------------------------- V g V b+[ ]⋅–

V dp3

V ad3

–

3-------------------------+

⋅ +

1

16 V box V ox⋅( )3 2⁄⋅

-------------------------------------------------

V dp V ad–( ) V b V g V g V box⋅ V b V ox⋅+( )⋅ ⋅[ ]⋅ –

V dp2

V ad2

–

2------------------------- V g

2V box⋅ V b

2V ox⋅ 2 V b V g V box V ox+( )⋅ ⋅ ⋅+ +[ ]⋅ +

V dp3

V ad3

–

3------------------------- V g 2 V box⋅ V ox+( )⋅ V b V box 2 V ox⋅+( )⋅+[ ]⋅ –

V dp4

V ad4

–

4------------------------- V box V ox+[ ]⋅

⋅

=


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(1.71)

(1.72)

(1.79)

: (1.73)

: (1.74)

& : (1.75)

or :

(1.76)

: (1.77)

:

(1.78)

Y swV box Y dpb

2Y adb

2+( )⋅ V ox Y dpg

2Y adg

2+( )⋅+

V 02

V box V ox+( )⋅--------------------------------------------------------------------------------------------------------=

Sw1 2 V o⋅+( ) Y sw

2⋅

1 Y sw2

+------------------------------------------ V o–=

Sw 1> V b7 Vb7exact

=

Sw 0< V b7 Vb7appr

=

Sw 0≥ Sw 1≤ Vb7 Sw Vb7exact⋅ 1 Sw–( ) Vb7

appr⋅+=

V g V b V dp≥ Vb7 0=

Qbx CBOX V b1 V b2 V b3 V b4 V b5 V b6 V b7+ + + + + +( )⋅=

TBO X 0:≤ Qby 0=

TBO X 0>

V• bV sp V dp+

2------------------------

≥ Qby CBOX V bV sp V dp+

2------------------------

– ⋅=

V• bV sp V dp+

2------------------------

< QbyCBOX– kb⋅

Cbox------------------------------

V sp V dp+

2------------------------ V b–

V sp V dp+

2------------------------ V b– V box+ V box+

----------------------------------------------------------------------------------⋅=

Cb fix 0.01 CBOX⋅ MULT 1017–⋅+=


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(1.80)

If or then (1.81)

else if then (1.82)

else if then (1.83)

(1.84)

(1.85)

1.3.6 gate charge model

If then

If and :

: (1.86)

(1.87)

Qb 0.99 Qbz⋅ Cb fix V b V d V s+( ) 2⁄–{ }⋅+=

Fc 0≤ V dp V sp–( ) 1.0e 4–≤ Qbz Qby=

Fc 1≥ Qbz Qbx=

Fc 1< Qbz Qby= Fc Qbx Qby–( )+

Qbs 0.5 Qb⋅=

Qbd 0.5 Qb⋅=

TOX 0≤ V g1 V g2 V g3 V g4 V g5 V g6 V g7 0= = = = = = =

V dp V sp–( ) 1.0e 4–> Fc 0>

V sp V g< V g1V g V sp–( )

2V g V ag–( )

2–

2 I ohm RON T⋅ ⋅-----------------------------------------------------------------=

V g3Cox

Qsoi I ohm RON T⋅ ⋅-----------------------------------------------

V g V sp–( )3

V g V ag–( )3

–

3-----------------------------------------------------------------⋅=


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(1.91)

:

: (1.88)

(1.89)

:

If and

otherwise (1.90)

V sp V g≥( )m

V g1 0=

V g3 0=

V dp V g≥ V g22– kg T ox V ox

3 2⁄⋅ ⋅ ⋅εox I ohm RON T⋅ ⋅----------------------------------------------

Y dpg2

Y agg2

–

2-----------------------------

Y dpg3

Y agg3

–

3-----------------------------+

⋅=

V g4V ox

2 2 kg2

T ox⋅ ⋅ ⋅Qsoi εox I ohm RON T⋅ ⋅ ⋅-----------------------------------------------------------

Y dpg3

Y agg3

–

3-----------------------------

Y dpg4

Y agg4

–

4-----------------------------+

⋅=

V dp V g< V g2 0=

V g4 0=

Cbox 0>( Cox 0> )

V g5CboxCox----------- V b5 V b6 V b7+ +( )=

V g5 0=

Qgx CGATE V g1 V g2 V g3 V g4 V g5+ + + +( )⋅=

T O X 0:≤ Qgy 0=


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:

: (1.92)

:

(1.93)

(1.94)

(1.95)

If or then (1.96)

else if then (1.97)

else if then (1.98)

(1.99)

(1.100)

TO X 0>

V• gV sp V dp+

2------------------------

≥ Qg y CGATE–V sp V dp+

2------------------------ V g–

⋅=

V g•V sp V dp+

2------------------------

< Qg yCGATE– kg⋅

Cox---------------------------------

V sp V dp+

2------------------------ V g–

V sp V dp+

2------------------------ V g– V ox+ V ox+

-----------------------------------------------------------------------------⋅=

Cg fix 0.01 CGATE MULT 1017–⋅+⋅=

Qg 0.99 Qgz Cg fix V g V d V s+( ) 2⁄–{ }⋅+⋅=

Fc 0≤ V dp V sp–( ) 1.0e 4–≤ Qgz Qg y=

Fc 1≥ Qgz Q= gx

Fc 1< Qgz Qg y= Fc Qgx Qg y–( )+

Qgs 0.5 Qg⋅=


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1.3.7 Space charge in the channel

• Critical current for hot-carriers

:

: (1.101)

: (1.102)

: (1.103)

: (1.104)

(1.105)

(1.106)

:

(1.107)

Qgd 0.5 Qg⋅=( )m

VP 0>

V g V sp≥ Qgs Cox V g V sp–( )⋅=

V g V sp< Qgs k– gV sp V g–

V sp V g– V ox+ V ox+-------------------------------------------------------------⋅=

V b V sp≥ Qbs Cbox V b V sp–( )⋅=

V b V sp< Qbs k– bV sp V b–

V sp V b– V box+ V box+------------------------------------------------------------------⋅=

Qspx 1 Qgs Qbs+( ) Qsoi⁄+=

I hcVSAT TRON T------------------

Qspx Qspx2 δq++

2--------------------------------------------⋅=

VP 0≤

I hc VSAT T RON T⁄=


ttt

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(1.108)

(1.109)

(1.110)

Qds sign TAUSC I hc 1I dsI hc----------

2 PSAT⋅+

1 2 PSAT⋅( )⁄

1–⋅ ⋅=

Qd12--- Qb Qg+( ) Qds+–=

Qs12--- Qb Qg+( ) Qds––=


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Numerical Adaptations

To implement SOI FET Model, level 40 in a circuit simulator, care must be taken of thenumerical stability of the simulation program. The functions as well as their derivativesshould be continuous at any bias condition that may occur during the iteration cycle.

Numerical Problems and Solutions

Fc must be set to zero when Iohm gets close to zero or even negative. This prevents divisionsby zero in the substrate charge model.

1.3.8 Numerical Adaptation

To implement the model in a circuit simulator, care must be taken of the numerical stabilityof the simulation program. A non-existent conductance, Gmin, is connected between the

nodes DS. The value of the conductance is 10-15 [1/Ω].


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1.4 Self-heating

1.4.1 Equivalent circuit

Self-heating is part of the model. It is defined in the usual way by adding a self-heating net-work (see figure 2) containing a current source describing the dissipated power and both athermal resistance RTH and a thermal capacitance CTH.

Figure 2: On the left, the self-heating network, where the node voltage VdT is used in thetemperature scaling relations. Note that for increased flexibility the node dT isavailable to the user. On the right are parameter values that can be used for Ath.

The resistance and capacitance are both connected between ground and the temperature nodedT. The value of the voltage VdT at the temperature node gives the increase in local tempera-ture, which is included in the calculation of the temperature scaling relation (1.1), see section1.3.2 on page 8.

For the value of Ath we recommend using values from literature that describe the temperaturescaling of the thermal conductivity. For the most important materials, the values are given infigure 2, which is largely based on Ref. [ 1], see also [ 2].

For example, if the value of VdT is 0.5V, the increase in temperature is 0.5 degrees Celsius.

Material

SiGeGaAsAlAsInAsInPGaPSiO2

ATH

1.31.251.251.371.11.41.40.7

dT

PdissRTHT CTH


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1.4.2 Model equations

The total dissipated power is a sum of the dissipated power of each branch of the equivalentcircuit and is given by:

The total dissipation applies for the geometrical model (mnt1, mpt2, mos40t3).

1.4.3 Usage

Below a Pstar example is given to illustrate how self-heating works.

q Example

Title: example self-heating 40;

circuit;mnt_1(Vd, Vg, Vs, 0, dt) level=40, Rth=1e6,Cth=1e-9;R_1 ( Vdd, Vd) 100;R_2 ( Vgg, Vg) 1k;R_3 ( Vs, 0) 100;e_SRC_2 (Vgg ,net101) 5;e_SRC_1 ( Vdd, 0) 1;e_SRC_3 ( net101, 0) 0;end;

dc;print: vn(dt), op(pdiss.mnt_1);end; run;

result:DC Analysis.VN(DT) = 24.764E+00Pdiss.MNT_1 = 24.764E-06

The voltage on node dT is 24.764e+0 V, which means that the local temperature is increased

by 24.764e+0 oC.

1.Pstar model name.2.Pstar model name.3.Spectre/ADS model name.

Pdiss I DS V DS⋅=


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1.5 DC operating point output

The DC operating point output facility gives information on the state of a device at its opera-tion point. Besides terminal currents and voltages, the magnitudes of linearized internal ele-ments are given. In some cases meaningful quantities can be derived which are then alsogiven (e.g. u). The objective of the DCOP-facility is twofold:

• Calculate small-signal equivalent circuit element values.

• Open a window on the internal bias conditions of the device and its basic capabilities (e.g.u).

Below the printed items are described. Cx(y) indicates the derivate of the charge Q at terminalx to the voltage at terminal y, when all other terminals remain constant.

Quantity Equation Description

Level 40 Model level

Ids Ids Drain Source current

Vds Drain Source voltage

Vgs Gate Source voltage

Vbs Bulk Source voltage

Vp Vp Channel pinch-off voltage

gm dIds/dVg Transconductance

gmb dIds/dVb Bulk transconductance

gds dIds/dVd Output conductance

Qg Gate charge

Cgd -dQg/dVd Gate charge dependence on drain voltage

Cgg dQg/dVg Gate charge dependence on gate voltage

Cgs -dQs/dVs Gate charge dependence on source voltage

Cgb -dQg/dVb Gate charge dependence on bulk voltage

Qb Bulk charge


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The additional operating point output for the model including self-heating (see section 1.4),is listed in the table below.

Cbd -dQb/dVd Bulk charge dependence on drain voltage

Cbg -dQb/dVg Bulk charge dependence on gate voltage

Cbs -dQb/dVs Bulk charge dependence on source voltage

Cbb +dQb/dVb Bulk charge dependence on bulk voltage

Qd Drain charge

Cdd +dQd/dVd Drain charge dependence on drain voltage

Cdg -dQd/dVg Drain charge dependence on gate voltage

Cds -dQd/dVs Drain charge dependence on source voltage

Cdb -dQd/dVb Drain charge dependence on bulk voltage

Qs Source charge

Csd -dQs/dVd Source charge dependence on drain voltage

Csg -dQs/dVg Source charge dependence on gate voltage

Css +dQs/dVs Source charge dependence on source voltage

Csb -dQs/dVb Source charge dependence on bulk voltage

u gm/gds Transistor gain

Rout 1/gds Small signal output resistance

Vearly Ids /gds Equivalent Early voltage

Iohm Iohm Drain source current excluding velocity saturation

Ihc Ihc Critical current for velocity saturation

Quantity Equation Description

Tk Tk Actual temperature including self-heating

Pdiss Pdiss Power dissipation


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When the parameter PRINTSCALED is set to 1, the device parameter set after geometricaland temperature scaling is added to the OP output:

Remarks:

• When Vds



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1.6 Simulator specific items

1.6.1 Pstar syntax

n channel : mn_n (d,g,s,b) level=40, p channel : mp_n (d,g,s,b) level=40, n channel self-heating : mnt_n (d,g,s,b,dt) level=40, p channel self-heating : mpt_n (d,g,s,b,dt) level=40,

n : occurrence indicator : list of model parameters

d,g,s,b and dt are drain, gate, source, bulk and self-heating terminals respectively.

1.6.2 Spectre syntax

n channel : model modelname mos40 type=n componentname d g s b modelname

p channel : model modelname mos40 type=p componentname d g s b modelname

n channel self-heating : model modelname mos40t type=n componentname d g s b dt modelname

p channel self-heating : model modelname mos40t type=p componentname d g s b dt modelname

modelname : name of model, user definedcomponentname : occurrence indicator : list of model parameters : list of instance parameters


Note3Warning! In Spectre, use only the parameter statements type=n or type=p. Using any otherstring and/or numbers will result in unpredictable and possibly erroneous results.


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1.6.3 ADS syntax

n channel : model modelname mos40 gender=1 modelname:componentname d g s b

p channel : model modelname mos40 gender=0 modelname:componentname d g s b

n channel self-heating : model modelname mos40t gender=1 modelname:componentname d g s b dt

p channel self-heating : model modelname mos40t gender=0 modelname:componentname d g s b dt

modelname : name of model, user definedcomponentname : occurrence indicator : list of model parameters : list of instance parameters


1.6.4 The ON/OFF condition for Pstar

The solution for a circuit involves a process of successive calculations. The calculations arestarted from a set of ‘initial guesses’ for the electrical quantities of the nonlinear elements. Asimplified DCAPPROX mechanism for devices using ON/OFF keywords is mentioned in [3].By default the devices start in the default state.Nu

n-channel p-channel

Default ON OFF Default ON OFF

VDS 2.0 2.0 2.0 VDS -2.0 -2.0 -2.0

VGS -2.0 -2.0 -4.0 VGS 2.0 2.0 4.0

VSB 0.0 0.0 -2.0 VSB 0.0 0.0 +2.0


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1.6.5 The ON/OFF condition for Spectre Nu

Nu

1.6.6 The ON/OFF condition for ADS

n-channel

OFF Triode Saturation Subthreshold Reverse Forward Breakdown

VDS 0.0 0.75 1.25 0.0 0 0 0

VGS 0.0 2.0 1.25 0.0 0 0 0

VSB 0.0 0.0 0.0 0.0 0 0 0

p-channel

OFF Triode Saturation Subthreshold Reverse Forward Breakdown

VDS 0.0 -0.75 -1.25 0.0 0 0 0

VGS 0.0 -2.0 -1.25 0.0 0 0 0

VSB 0.0 0.0 -1.25 0.0 0 0 0

n-channel p-channel

Default Default

VDS 0 VDS 0

VGS 0 VGS 0

VSB 0 VSB 0


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1.7 References

[1] V. Palankovski R. Schultheis and S. Selberherr, Modelling of power hetero-junction bipolar transistor on gallium arsenide,IEEE Trans. Elec. Dev., vol 48, pp.1264-1269, 2001. Note: the paper uses = 1.65 for Si, but = 1.3 goves a better fit:also, k300 for GaAs is closer to 40 than to the published value of 46 (Palankovski,personal communication).

[2] Sze, S.M., Physics of semiconductor devices, 2nd edition, John Wiley & Sons,Inc., New York, 1981

[3] Pstar User Manual.

α α


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December 2009 Hyp functions

A Hyp functions

39TOC Index Quitfile

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Hyp functions December 2009

Figure 3:

Figure 4:

0 X

ε

hyp1

hyp1 x ε;( )12--- x x2 4 ε2⋅++( )⋅=

0

ε

hyp2

x0

x0 x

hyp2 x x0; ε;( ) x hyp1 x x0– ε;( )–=

40 TOC Index Quitfile

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December 2009 Hyp functions

Figure 5:

Figure 6:

0 x0 x

hyp3

εxo+hyp1(-xo;ε)

hyp3 x x0; ε;( ) hyp2 x x0; ε;( ) hyp2 0 x0; ε;( )–= for ε ε x0( )=

0

x

hyp4

ε

-hyp1(-xo;ε) xo

hyp4 x x0; ε;( ) hyp1 x x0– ε;( ) hyp1 x0– ε;( )–=


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Hyp functions December 2009

Figure 7:

The hypm-function:

(1.111)

setlength{unitlength}{0.40900pt} begin{picture}(1500,900)(0,0) enrm hinlines drawline[-50](264,158)(1436,158) hinlines drawline[-50](264,158)(264,787) hicklines path(264,158)(264,178)hicklines path(264,787)(264,767) put(264,113){makebox(0,0){0}} hicklines path(264,158)(1436,158)(1436,787)(264,787)(264,158) put(45,472){makebox(0,0)[l]{shortstack{hyp

0

x0ε

xo

hyp5

x

hyp5 x x0; ε;( ) x0 hyp1 x0 xε2

x0-----–– ε,

–= for ε ε x0( )=

hypm x, y;m[ ] x y⋅

x2 m⋅

y2 m⋅

+( )1 2 m⋅( )⁄-----------------------------------------------------=


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December 2009 Spectre Specific Information

B Spectre Specific Information


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Spectre Specific Information December 2009

Imax, Imelt, Jmelt parameters

IntroductionImax, Imelt and Jmelt are Spectre-specific parameters used to help convergence and to pre-vent numerical problems. We refer in this text only to the use of Imax model parameter inSpectre with SiMKit devices since the other two parameters, Imelt and Jmelt, are not part ofthe SiMKit code. For information on Imelt and Jmelt refer to Cadence documentation.

Imax model parameterImax is a model parameter present in the following SiMKit models:– juncap and juncap2– psp and pspnqs (since they contain juncap models)

In Mextram 504 (bjt504) and Modella (bjt500) SiMKit models, Imax is an internal parameterand its value is set through the adapter via the Spectre-specific parameter Imax.The default value of the Imax model parameter is 1000A. Imax should be set to a value whichis large enough so it does not affect the extraction procedure.

In models that contain junctions, the junction current can be expressed as:

(1.112)

The exponential formula is used until the junction current reaches a maximum (explosion)current Imax.

(1.113)

The corresponding voltage for which this happens is called Vexpl (explosion voltage). Thevoltage explosion expression can be derived from (1):

(1.114)

For the following linear expression is used for the junction current:

I I sV

N φTD⋅------------------ 1–

exp=

I max I sV lexp

N φTD⋅------------------ 1–

exp=

V lexp N φTDI max

I s----------

1+log⋅=

V V lexp>


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(1.115)

Region parameter

Region is an Spectre-specific model parameter used as a convergence aid and gives an esti-mated DC operating region. The possible values of region depend on the model:

– For Bipolar models:– subth: Cut-off or sub-threshold mode– fwd: Forward– rev: Reverse– sat: Saturation.– off1

–– For MOS models:

– subth: Cut-off or sub-threshold mode;– triode: Triode or linear region;– sat: Saturation– off1

For PSP and PSPNQS all regions are allowed, as the PSP(NQS) models both have a MOSpart and a juncap (diode). Not all regions are valid for each part, but when e.g. region=for-ward is set, the initial guesses for the MOS will be set to zero. The same holds for setting aregion that is not valid for the JUNCAP.

– For diode models:– fwd: Forward– rev: Reverse– brk: Breakdown– off1

Model parameters for device reference temperature in Spectre

This text describes the use of the tnom, tref and tr model parameters in Spectre with SiMKitdevices to set the device reference temperature.

1.Off is not an electrical region, it just states that the user does not know in what state thedevice is operating

I I max V V lexp–( )+I s

N φTD⋅------------------

V lexpN φTD⋅------------------

exp=


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A Simkit device in Spectre has three model parameter aliases for the model reference temper-ature, tnom, tref and tr. These three parameters can only be used in a model definition, not asinstance parameters.

There is no difference in setting tnom, tref or tr. All three parameters have exactly the sameeffect. The following three lines are therefore completely equivalent:

model nmos11020 mos11020 type=n tnom=30 model nmos11020 mos11020 type=n tref=30 model nmos11020 mos11020 type=n tr=30

All three lines set the reference temperature for the mos11020 device to 30 C.

Specifying combinations of tnom, tref and tr in the model definition has no use, only thevalue of the last parameter in the model definition will be used. E.g.:

model nmos11020 mos11020 type=n tnom=30 tref=34

will result in the reference temperature for the mos11020 device being set to 34 C, tnom=30will be overridden by tref=34 which comes after it.

When there is no reference temperature set in the model definition (so no tnom, tref or tr isset), the reference temperature of the model will be set to the value of tnom in the optionsstatement in the Spectre input file. So setting:

options1 options tnom=23 gmin=1e-15 reltol=1e-12 \ vabstol=1e-12 iabstol=1e-16 model nmos11020 mos11020 type=n

will set the reference temperature of the mos11020 device to 23 C.

When no tnom is specified in the options statement and no reference temperature is set in themodel definition, the default reference temperature is set to 27 C.So the lines:

options1 options gmin=1e-15 reltol=1e-12 vabstol=1e-12 \ iabstol=1e-16 model nmos11020 mos11020 type=n

will set the reference temperature of the mos11020 device to 27 C.


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The default reference temperature set in the SiMKit device itself is in the Spectre simulatornever used. It will always be overwritten by either the default "options tnom", an explicitlyset option tnom or by a tnom, tref or tr parameter in the model definition.


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June 2010 OvervoltageSpecification

C OvervoltageSpecification


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OvervoltageSpecification June 2010

Overvoltage warnings in SiMKit

IntroductionOvervoltage flagging is signalling that a (terminal) voltage is outside a specified safe range.A warning will be given when the conditions for giving a warning are fulfilled.

Simple checks for overvoltage have been added to the following models: mos903, mos1100,mos1101, mos1102, mos2002, mos2003, mos3100, mos4000, psp102, psp103.The checks are done on terminal voltages of the models.

There are many ways to define overvoltage. For a general overvoltage flagging solution Ver-ilog-A should be used.

Extra parameters for overvoltage flaggingA set of extra parameters has been added to the mos models mos903, mos1100, mos1101,mos1102, mos2002, mos2003, mos3100, mos4000, psp102, psp103.

For mos models the safe region is: and and

Table 1:

Name Unit Default Description

VBOX V 0.0 Oxide breakdown voltage.Checking will be done if

VBDS V 0.0 Drain-source breakdown voltageChecking will be done if

TMIN s 0.0 Ovcheck tmin value

VBOX 0>

VBDS 0>

V gs VBOX< V gd VBOX< V ds VBDS

June 2010 OvervoltageSpecification

Ovcheck: two terminal dummy modelA (dummy) two-terminal model ovcheck has been implemented that can be used to check ifthe voltage between the two terminals is within or without a so called safe region.The model parameters are:

For the ovcheck model the safe region is:, where t1 is the first and t2 is the second terminal.

Functionality

In Spectre and PstarAt the end of a DC analysis or in a transient analysis after each time step a check wil be doneif the device is inside or outside the safe region.A warning is given whenever the device enters or leaves the safe region.

Name Unit Default Description

VLOW V 0.0 Lower bound of safe region

VHIGH V 0.0 Upper bound of safe regionChecking will be done when

TMIN s 0.0 Ovcheck tmin value

VBOX

leave msg

enter msg

VHIGH VLOW>

VLOW V t1 V t2– VHIGH≤ ≤


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OvervoltageSpecification June 2010

In Spectre onlyTo prevent too many warnings in a Spectre transient analysis the model parameter TMIN hasbeen introduced. If the time between leaving and entering the safe region is less than theTMIN value no warning is given.Because of the TMIN parameter a warning cannot be issued when leaving the safe region. Awarning is given when the device enters the safe region again. This warning includes the timeand the voltage when the safe region was exited.At the end of the transient warnings aregiven for devices that are still out of the safe range.In Pstar TMIN may be specified as a model parameter, but it will be ignored.


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July 2011 Parameter PARAMCHK

D Parameter PARAMCHK


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Parameter PARAMCHK July 2011

Parameter PARAMCHK

IntroductionAll models have the parameter PARAMCHK. It is not related to the model behavior, but hasbeen introduced control the clip warning messages. Various situations may call for variouslevels of warnings. This is made possible by setting this parameter.

PARAMCHK model parameterThis model parameter has been added to control the amount of clip warnings.

PARAMCHK 0 No clip warnings

PARAMCHK 0 Clip warnings for instance parameters (default)

PARAMCHK 1 Clip warnings for model parameters

PARAMCHK 2 Clip warnings for electrical parameters at initialisation

PARAMCHK 3 Clip warnings for electrical parameters during evaluation.This highest level is of interest only for selfheating jobs,where electrical parameters may change dependent ontemperature.

<

≥

≥

≥

≥


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April 2008 Bibliography

E Bibliography


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Bibliography April 2008

[1] Sze, S.M., Physics of semiconductor devices, 2nd edition, John Wiley & Sons,Inc., New York, 1981

[2] Muller, R.S. and Kamins, T.I., Device electronics for integrated circuits, 2nd

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[14] K.A. Sakallah, Yao-Tsung Yen, S. Greenberg, The Meyer model revisited:explaining and correcting the charge nonconservation problem, Proceedings IEEEICCAD, 1987

[15] P.B.L. Meijer, Meijer model for Meyer model

[16] SPICE version 2G6 source code, Dep. Elec. Eng. and Comput. Sci., Univ. ofCalifornia Berkeley, March 15, 1983.


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[17] Klaassen, F.M., Compact models for circuit simulation, Springer, Vienna,chapter 7: Models for the enhancement - type MOSFET (1989)

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internet: http://www.semiconductors.philips.com/Philips_Models.

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[56] A.J. Scholten, R. Duffy, R. van Langevelde and D.B.M. Klaassen, CompactModelling of Pocket-Implanted MOSFETs, in Proceedings ESSDERC 2001, pp.311-314, 2001.

[57] R. van Langevelde et al., Gate Current: Modeling, Extraction and Impacton RF Performance, IEDM 2001 Tech. Digest, pp. 289-292, 2001.

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1101, Nat.Lab Unclassified Report, NL-UR 2002/802

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[60] N. D' Halleweyn, Modelling and Characterisation of Silicon-On-InsulatorLateral Double Diffused MOSFETs for Analogue Circuit Simulation, Ph.D. The-sis, University of Southampton, August 2001

[61] R. van Langevelde and F.M. Klaassen, An Explicit Surface-Potential BasedMOSFET Model for Circuit Simulation, Solid-State Electronics, Vol 44, 2000, pp.409-418

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[70] MOSModel 9:http://www.nxp.com/models/


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1 MOS Model, level 401.1 Introduction1.1.1 Survey of modeled effects

1.2 Parameters and constants1.2.1 Parameters and clipping1.2.2 Model constants

1.3 Model equations1.3.1 Equivalent circuit and equations1.3.2 Temperature effects1.3.3 Model preprocessing1.3.4 Model evaluation1.3.5 Substrate charge model1.3.6 gate charge model1.3.7 Space charge in the channel1.3.8 Numerical Adaptation

1.4 Self-heating1.4.1 Equivalent circuit1.4.2 Model equations1.4.3 Usage

1.5 DC operating point output1.6 Simulator specific items1.6.1 Pstar syntax1.6.2 Spectre syntax1.6.3 ADS syntax1.6.4 The ON/OFF condition for Pstar1.6.5 The ON/OFF condition for Spectre1.6.6 The ON/OFF condition for ADS

1.7 References

A Hyp functionsB Spectre Specific InformationImax, Imelt, Jmelt parametersRegion parameterModel parameters for device reference temperature in Spectre

C OvervoltageSpecificationOvervoltage warnings in SiMKit

D Parameter PARAMCHKParameter PARAMCHK

E Bibliography

Documents

MOS Model, level 40 - NXP Semiconductors · 2015. 11. 2. · For both TOX and TBOX less than or equal to zero, the pinch off voltage Vp = 0. When VP ≤0 only equations 1.24, 1.41,