EPFL HEMT Compact Model Model s Documentation

(1)

EPFL HEMT Compact

Model

Model’s Documentation

Technical Report

EPFL HEMT Model Version: V2.2

Developed

By

Farzan Jazaeri and Jean-Michel Sallese

Ecole polytechnique fédérale de Lausanne (EPFL), Lausanne, Switzerland

Coding, Implementation, and Testing

By

Dr. Majid Shalchian, Amirkabir University

Dr. Matthias Bucher

Nikolaos Makris,

University of Crete (TUC), Chania, Crete, Greece.

August 07, 2019

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Chapter 1 List of Parameters:

Table 1- Instance Parameters

Parameter Default Value Unit Short Description

T 300 K Temperature

L 10u m Gate’s Length

W 10u m Gate’s Width

M 1 - Number of Devices in Parallel

NS 1 - Number of Fingers

AD 0.0 𝑚2 _{Drain’s Area}

AS 0.0 𝑚2 Source’s Area

PD 0.0 m Drain’s Perimeter

PS 0.0 m Source’s Perimeter

Table 2- Matching Parameters

AVTO 0 - Matching Parameter for Threshold Voltage AKP 0 - Matching Parameter for Mobility AGAMMA 0 - Matching Parameter for Body Factor(Gamma)

(5)

Table 3- GaN/AlGaN and Gate Related Parameters

Parameter Default Value Unit Short Description

𝐶_𝑏 0.0025 𝑭

𝒎𝟐

AlGaN Capacitance per Unit Area

𝑥_𝑗 20n m Depth of junction (source and drain)

𝑁_𝐴 𝟏𝟎𝟐𝟐 - Doping of GaN Layer

𝑁𝐷 𝟔 × 𝟏𝟎𝟐𝟐 Doping of AlGaN Layer

xx 0.3 - Percentage of Al in AlxxGa(1-xx)N

𝜎_𝑝𝑜𝑙 (sigma_pol) 0 Polarization Charge Density in AlGaN/Gan Interface

ϕ_B (Phi_B) 0 V Gate Schottky Barrier

𝑥₁ -30n AlGaN Layer Thickness

𝑉𝑇𝑂 -0.9 V Threshold Voltage

TCV 1e-3 V/K Temperature Coefficient of VTO

gu 0.2p - Experimentally Determined Parameter

𝜙 (PHI) 0.45 V Fermi Bulk Potential

VBI 0.0 V Built-in Voltage Drop-off

Table 4- Mobility Parameters – Long Channel

KP 500e-6 𝑨

𝑽 ∗ 𝑽

Mobility(Multiply by 𝑪_𝒃) Parameter

BEX −𝟏. 𝟓 - Mobility temperature exponent THETA 𝟎 𝟏/𝑽 Mobility reduction coefficient

(6)

Table 5- Threshold voltage Short/Narrow/Reverse Short Channel

LETA 0.0 - Short-channel effect coefficient WETA 0.0 - Narrow-channel effect coefficient

Q0 0.0 Reverse short channel effect peak charge density LK 0.4e-6 m Reverse short channel effect characteristic length

Table 6- Process Geometrical Scaling Factor

DL -10n m Difference between effective and drawn gate length

DW -10n m Difference between effective and drawn gate width

WDL 0.0 𝒎𝟐 Width Scaling for narrow devices of Effective

Length

LDW 0.0 𝒎𝟐 Length Scaling for short devices of Effective

Width

DLC 0.0 m Tuning the difference of effective gate length between current and capacitance behaviour

DWC 0.0 m Tuning the difference of effective gate width between current and capacitance behaviour

(7)

Table 7- Velocity Saturation and CLM Related Parameters

UCRIT 2e6 𝐕

𝒎 Longitudinal critical field

USEX 0.8 - Longitudinal critical field temperature exponent

𝝀 0.8

-Depletion length coefficient (channel length modulation)

Table 8- Substrate Current Parameter

IBA 5e7 𝟏

𝒎 First impact ionization coefficient

IBB 4e8 𝐕

𝒎 Second impact ionization coefficient

𝑰𝑩𝑩𝑻 9e-4 𝟏

𝑲 Temperature coefficient for IBB IBN 1 - Saturation voltage factor for impact ionization

Table 9- Series Resistance

Parameter Default Value Unit Short Description HDIF 0.0u m Half Length of the Active Area

RSH 0.0 𝛀

(8)

Table 10- Drain –Bulk and Source-Bulk Junction Capacitance and Current

xd_n 1.0 - xd_js 1.0E-09 - xd_jsw 1.0E-12 - xd_jswg 1.0E-12 - xd_mj 0.900 - xd_mjsw 0.700 - xd_mjswg 0.700 - xd_pb 0.800 - xd_pbsw 0.600 - xd_pbswg 0.600 - xd_cj 1.0E-09 - xd_cjsw 1.0E-12 - xd_cjswg 1.0E-12 - xd_gmin 0.0 - xd_xjbv 0.0 - xd_bv 10.0 - xd_njts 1.0 - xd_njtssw 1.0 - xd_njtsswg 1.0 -

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xd_vts 0.0 - xd_vtssw 0.0 - xd_vtsswg 0.0 - tp_xti 3.0 - tp_cj 0.0 - tp_cjsw 0.0 - tp_cjswg 0.0 - tp_pb 0.0 - tp_pbsw 0.0 - tp_pbswg 0.0 - tp_njts 0.0 - tp_njtssw 0.0 - tp_njtsswg 0.0 -

Table 11- Physical Parameter

epsilon0 8.854e-12 𝑭/𝒎 Vacuum Permittivity

KB 1.38e-23 𝑱/𝑲 Boltzmann Constant

eGaN 8.9epsilon0 𝑭/𝒎 GaN Permitivity

Eg AlGaN 3.9727 eV Bandgap AlGaN (T=300 K)

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Chapter 2 Equations:

General Equations

0.0259*

T NOM

T

U

T



2.1

Physical Equations

𝐃𝐎𝐒

_𝟐𝐃

=

𝟎. 𝟐𝐦

𝐞

(

𝟏 _𝐪

𝟏. 𝟎𝟓𝟒𝟓𝟗𝟏𝟎

−𝟑𝟒

₎

𝟐 2.2

8.5 8.9*(1

)

AlGaN

xx









2.3 GaN GaN b

t

C





2.4

0.7[

_AlGaN _GaN

]

Ec

Eg

 



2.5 C GaN j

L



T

x

2.6

.

C C

L

_



L Lambda

2.7 ,

3

GAN W GAN

T

 

T



WETA

2.8 , GAN L GAN

T



T



LETA

2.9 1

2 . 2.

.

GaN A GaN A

N q

x

Gamma

N q

C

t







2.10

(11)

Thermal variation of Parameters

( )

.(

_NOM

)

VTO T



VTO TCV T T



2.11 .

( )

UCEX crit crit NOM

T

U

T

U

T







_

_





2.12

( )

BEX NOM

T

KP T

KP

T







_

_





2.13

( )

*(1

*(

_NOM

))

IBB T



IBB



IBBT

T T



2.14

Effective geometry

eff

WDL

L

DL

W





2.15 eff

LDW

W

DW

L





2.16 , eff C eff

L



L



DLC

2.17 , eff C eff

W



W



DWC

2.18

(12)

Matching

6 , .10 . a eff NF eff AGAMMA GAMMA GAMMA W L   2.19 6 , 0.10 0 0 . a eff NF eff AVT VT VT W L   2.20 6 , . .10 . A eff NF eff AKP KP KP KP W L   2.21

Reverse Short Channel Effect





0 2 2 1 1 1 2 RSCE b Q V C _C 



   _ _ _      2.22 2.23

0.28 (

L

eff

0.1)

LK









,

C



=4x(22x10

-3

)

2

Offset Voltage, Pinch-off Voltage and Gamma

2 1 1

2

C D A B pol AlGaN AlGaN

E

qN

V

x

q









 





2.24 ' G G RSCE a

(13)

Current and Charges

Qspec= −2nqCbUT 2.32 ( ) ( ) 0

(

)

s d P S D

n

V

y

F

n

UT





2.33 2 ( ) 1

_{( ) ln(exp( ) 1)}

3 P S D

V

F

y

UT









 



2.34 ( ) ( ) s d s d spec

qn

q

Q





2.35 2 s s f

i



q



q

2.36 2 r d d

i



q



q

2.37 2 ' ' 0

2

a a P G a G

GAMMA

V



V



PHI GAMMA







V





_



_



















2.26





2 ' 2 ( ) ( ) ( )

1

16

2

S D S D S D

V





_

V



PHI



V



PHI



UT



_





2.27 0 ' ' 0

1

3. .

(

)

a s d p eff eff

LETA

WETA

GAMMA

V

PHI

TGAN

L

W









_









_





2.28



2



'

1

0 0

_0.1

2 UT













2.29 2 ' ' ' ' '

2

P G G

V

PHI



V





_{ }













_{ }





_{ }







2.30

1

2

4

a q P

GAMMA

n

V

PHI

UT

 



2.31

(14)

Velocity Saturation

.

C eff

V



UCRIT NS L

2.38

1

1 .

4

2

DSS C f C

UT

V

i

V







_





_





2.39 '

_.

1

3 _{ln( )}

1 _ln

_0.6

4

2

C DSS C f f C

V

UT

V

i

UT

V

UT



_

_



_

_

_

_







_



_







_

_

_



_





















2.40

Channel Length Modulation

1

4 .

64

DSS f

V

UT LAMBDA

i

UT





 

_



_







2.41

2

d s ds

V





2.42





2 2 2 2 ip DSS ds DSS

V



V

 

V



V



V

 

V

2.43

. .ln 1

ds ip C C

V

L LAMBDA L

L UCRIT







 

_



_





2.44

Equivalent Channel Length including Velocity Saturation and

Channel Length Modulation

' ds ip eff

V

L

UCRIT





  

2.45

(15)

min

.

eff

/10

L



NS L

2.46



' 2 2



min

1 '

2

eq

L



L



L



L

2.47

Reverse Normalized Current Scaling





2 ' 2 2 ' 2 ' P ds s Dss ds DSS d

V

q

F

UT



_

_{ }

_

_

_{ }







 











2.48 ' ' 2 ' r d d

i



q



q

2.49 p D d

V

q

F

UT







 







2.50 2 r d d

i



q



q

2.51

Transconductance Factor and Mobility Reduction due to

Vertical Field

0

.

_eff a eq

NPW

KP

L





2.52 0 B a

q



GAMMA

PHI

2.53 ' 0 0 0 0

1

b B GaN

C

q

E











_



_





2.54 ' 0 1 0

1

b

0.5

B I GAN

C

UT q

q

E









2.55

Specific Current

(16)

2 2

2

SP

I



n UT



2.56 '

.(

)

DS SP f r

I



I

i



i

2.57

Transconductance

Fs= q Cbnq 2.58 Fd= qUT q_dQ_spec+_Cq bnq 2.59 g_m= −I_spec× ((2qs+ 1)q n_qQ_specF_s − (2qd+ 1)q n_qQ_specF_d) 2.60 g_ds= I_spec×qd U_T 2.61

Transcapacitance

ETA = −W × L × Qspec (I_f− I_r+ 10−19₎2 2.62 Q_md= ETA × (If(0.667 × qd3+ 0.5 × qd2) − (0.4 × qd5+ 0.75 × qd4) − I_f(0.667 × q_s3_{+ 0.5 × q} s2) − (0.4 × qs5+ 0.75 × qs4)) 2.63 Q_ms= ETA × (I_r(0.667 × q_d3_{+ 0.5 × q} d2) − (0.4 × qd5+ 0.75 × qd4) − I_r(0.667 × q_s3_{+ 0.5 × q} s2) − (0.4 × qs5+ 0.75 × qs4)) 2.64 Diff_gs= −q n_qQ_spec b₂+ q C_bn_q + b3 2.65 F_d∗= (I_f− q2_d− q_d)(2q2_d+ q_d) 2.66 G_s∗= (I_r− q2_s_{− q} s)(2q2s+ qs) 2.67

CDG = ETA × (DiffgdFd∗− DiffgsGs∗) + ETA

× (2q_s+ 1)(Diff_gs)((0.667 × q_d3+ 0.5 × q_d2) − (0.667 × q_s3_{+ 0.5 × q} s2))

− (2Qmd

i₂ )(Diffgs(2qs+ 1) − Diffgd(2qd+ 1))

(17)

C_SG= ETA × (Diff_gdF_d∗− Diff_gsG_s∗) + ETA × (2q_d+ 1)(Diff_gd)((0.667 × q_d3_{+ 0.5 × q} d2) − (0.667 × qs3+ 0.5 × qs2)) − (2Qms i₂ )(Diffgs(2qs+ 1) − Diffgd(2qd+ 1)) 2.69 C_G = −(C_DG+ C_SG) 2.70

External Resistances

RS =Hdif × RSH Weff− DW , Symmetric model 2.71 RD =Hdif × RSH Weff− DW , Symmetric model 2.72 ,

1 .

.

DS old DS S D

I

gms R

gds R





Extrinsic Diodes

Temperature Dependence

, , · · g nom T nom NOM t D E _Eg _T XTI U UT T Jss Jss exp N    2. 73 , , · · g nom T nom NOM t D E Eg T XTI U UT T Jssws Jssws exp N    2.74 , , · · g nom T nom NOM t D E Eg T XTI U UT T Jsswgs Jsswgs exp N    2. 75 , ,

·

g nom T nom NOM t JD

E

Eg

T

XTI

U

UT

T

Jsd

Jsd exp

N







2. 76

(18)

, ,

·

· E

_Eg

_T

XTI

U

UT

T

Jsswd

Jsswd exp

N







2. 77 , ,

·

· E

_Eg

_T

XTI

U

UT

T

Jsswgd

Jsswgd exp

N







2. 78









js· 1 · t NOM Cjs  C  TCj T  T 2. 79









jsws· 1 · t NOM Cjsws  C  TCjsw T  T 2. 80









jswgs· 1 · t NOM Cjswgs  C  TCjswg T  T 2. 81









jd· 1 · t NOM Cjd  C  TCj T  T 2. 82









jswd· 1 · t NOM Cjswd  C  TCjdw T  T 2. 83









jswgd· 1 · t NOM Cjswgd  C  TCjswg T  T 2. 84









PBS· 1 · t NOM Pbs   TPB T  T 2. 85









PBSWS· 1 · t NOM Pbsws   TPBSW T  T 2. 86









PBSWGS· 1 · t NOM Pbswgs   TPBSWG T  T 2. 87









PBD· 1 · t NOM Pbd   TPB T  T 2. 88









PBSWD· 1 · t NOM Pbswd   TPBSW T  T 2. 89









PBSWGD· 1 · t NOM Pbswgd   TPBSWG T  T 2. 90 ,

·

_{g nom} _T

· · " 1

##

JTSt



JTS exp E

U

XTS



T TNOM

2. 91 , · g nom . · 1-t T NOM E T JTss JTss exp XTI U T     _  _     2. 92 , · g nom . · 1-t T NOM E T JTssws JTssws exp XTI U T     __ _ ___     2. 93 , · g nom . · 1-t T NOM E T JTsswgs JTsswgs exp XTI U T     _  _     2. 94 , · g nom . · 1-t T NOM E T JTsd JTsd exp XTI U T     _  _     2. 95 , · g nom . · 1-t T NOM E T JTsswd JTsswd exp XTI U T     __ _ ___     2. 96

(19)

, · g nom . · 1-t T NOM E T JTsswgd JTsswgd exp XTI U T     _  _     2. 97 · 1 T 1 · Njtsst NJTSS TNJTSS TNOM       _ _ _  _ __       2. 98 · 1 T 1 · Njtsswst NJTSSWS TNJTSSWS TNOM       _ _ _  _ __       2. 99 · 1 T 1 · Njtsswgst NJTSSWGS TNJTSSWGS TNOM       _ _ _  _ __       2.100 · 1 T 1 · Njtsdt NJTSD TNJTSD TNOM       _ _ _  _ __       2.101 · 1 T 1 · Njtswdt NJTSWD TNJTSWD TNOM       _ _ _  _ __       2.102 · 1 T 1 · Njtswgdt NJTSWGD TNJTSWGD TNOM       _ _ _  _ __       2.103

Area and Perimeter





. eff. 1 as hdif W NF if NF is odd 2.104





. eff. 2 as hdif W NF if NF is even 2.105









2. . 1 eff ps hdif NF W if NF is odd 2.106









2. . 2 eff ps hdif NF W if NF is even 2.107





. eff. 1 ad hdif W NF if NF is odd 2.108





. eff. 2 ad hdif W NF if NF is even 2.109









2. . 1 _eff pd  hdif NF W if NF is odd 2.110

(20)









2. . 2 eff pd  hdif NF W if NF is even 2.111

Junction Current

Source Side

,

·

S S t t t

I



JTss as



JTssws ps



JTsswgs Weff NF

2.112

 

,

1

·

breakdown s T NOM

V di b

BV

f

XJBV exp

U ND T









 

_



_





2.113









( , ).

,

. .

· exp

·

1 · ·

,

( , ).

· · exp

·

1 · ·

,

t eff t T t t T

V di b T

VTSSWGS

ISB tun W NF JTsswgs

TNOM U NJTSSWGS

VTSSWGS

V di b

V di b T

VTSSWS

ps JTssws

TNOM U NJTSSWS

VTSSWS

V di b







_



_





_

_













_

_









_

_

















· · exp

( , ).

· _

_

1 · ·

,

t t T

V di b T

VTSS

as JTss

TNOM U NJTSS

VTSS

V di b



_

_





_



_





_

_











2.114

 

_

_

, ,

,

. 1

.

, ·

·

S S breakdown s T NOM

V di b

BV

ISBJ

I

exp

f

V di b

GMIN

U

ND T













_









_











2.115

Drain Side

,

·

S D t t t

I



JTsd ad



JTsswd pd



JTsswgd Weff NF

2.116





, , 1 · · · breakdown d T NOM V di b BV f XJBV exp U ND T       _ _   2.117

EPFL HEMT Compact Model Model s Documentation