© M. Schroter 1

Latest developments of HICUM/L2

for mm-wave applications

Michael Schroter1,2, Andreas Pawlak1, Julia Krause1, Paulius Sakalas1,3

1CEDIC, TU Dresden, Dresden, Germany2ECE Dept., UC San Diego, La Jolla, USA3FRL Semic. Phys. Inst., Vilnius, Lithuania

BCTM Open Workshop, Bordeaux (France)Oct. 3, 2013

© M. Schroter 2

Outline

• Introduction

• HICUM/Level2 extensions

• Model verification

• Summary

© M. Schroter 3

Introduction

IntroductionMajor challenge for mm-wave and THz operation:

generating sufficient output power

=> need to exploit process limits by careful device and circuit optimization=> need accurate compact models for active and passive devices

electronics photonics

solid-state THz sources (CW)

© M. Schroter 4

Introduction

HBT modeling challenges ... to be addressed for mm-wave and THz circuit design

• self-heating => thermal stability, reliability

• breakdown => reliability, stability

• high-current effects & quasi-saturation => PAE, operating frequency

• substrate effects => PAE, jitter, operating frequency

• large-signal operation => distortion

• distributed effects: high-frequency, breakdown, thermal, substrate

• gm drop (technology dependent) => drive capability/circuit speed

ALSO: model verification issues ...

• process development is outpacing measurement equipment availability => how to verify large-signal modeling at multi-100 GHz? (incl. distortion!!)

© M. Schroter 5

Introduction

Modeling approaches

Goal: cover large variety of applications & circuit optimization (bias, T, f)=> Physics-based model (cuts design cycle, supports process dev.)

Criteria Behavioral, X-par. Physics-basedaccuracy high (within narrow ranges) moderate to high over wide

rangenumerical stability compromised outside fitting

rangeshigh (for standard models)

fabricated devices need every possible layoutused in circuits

only few devices (6 HF trs, 6 test structures)

measurement effort moderate to high moderate to lowpar. extraction effort moderate to low (per device)

very high for librarymoderate to low (per device)very low for library

geometry scaling inconsistent (typically) consistentpredictive capability none moderate to highstatistical modeling none (very high effort) good to excellent

© M. Schroter 6

Introduction

Physics-based compact model... definition

each spatial region is represented by corresp. equivalent circuit element

• each EC element value is a function of bias, T, structural and physicalparameters

ijBCx

QjS

ijSC

RE

B

RCx

E

C

CEpar

QdS

QjEpijBEp

iTS

S

QBCx, QBCx

,,

Csu

Rsu

RBx

S’

Ti

iBEt E’

B*C

E

BB

© M. Schroter 7

Introduction

Physics-based compact model... definition

each spatial region is represented by corresp. equivalent circuit element • each EC element value is a function of bias, T, structural & physical parameters

=> realized in HICUM/Level2 (from the beginning)=> supports circuit optimization, statistical modeling, process development

ijBCx

QjS

ijSC

RE

B

RCx

E

C

CEpar

QdS

QjEpijBEp

iTS

S

QBCx, QBCx

,,

Csu

Rsu

RBx

S’

Ti

iBEt E’

B*C

E

BB

© M. Schroter 8

HICUM/Level2 extensions

HICUM/Level2 extensions... recent development work during DOT5, DOT7, RF2THz

• transfer current and gm drop (technology dependent) • bias dependence of reverse Early effect => gm degradation at low injection• weight factor for low-current mobile charge => gm degradation at medium injection • temperature dependence of weight factors

• explicit formulation of BC barrier effect

• flexible CE voltage dependence of critical current

• temperature dependence of thermal resistance

• simplification of AC emitter current crowding implementation

• exact implementation of correlated HF noise (verified up to at least 500GHz)

• simplification of input NQS effect description (and verification)

... and: reliable model parameter extraction methods

© M. Schroter 9

HICUM/Level2 extensions

Complete HICUM/L2 equivalent circuit

ijBCx

iBEtp

ijSC

iT

RE

B

ijBCi

RCx

E

C

ijBEi

C’

B’

E’

iAVL

CBEpar2

B*

ijBEp

QjCi

iTS

S

CrBi

ΔTj

CthRthP

Csu

Rsu

RBx

S’

intrinsic transistor

T

thermal networkQr

QjEi Qf

QBCx QdS

QjS

QjEp

,,QBCx,

Rbi*

Inb= 2qIjBEi

Vnb

1S.Vnb

Inc= 2qIT

Vnc

1S.Vnc

1S.VncTb2VncTb1Vnb

Tb1=1+jωτf Bf(2αqf -αIT)

Tb2=jωτf αIT

2 noiselessintrinsic

transistor

noise correlation Qf,nqs

R=τf

Qf,qsτf

αIT

VC1 iT,nqs=VC2

R=τf

VC2τf

iT,qsτf

VC1τf

αQf

αIT3

vertical NQS effects

CBEpar1

iBEti

(Verilog-A implementation)

© M. Schroter 10

HICUM/Level2 extensions

Model features

• large-signal model => small-signal, noise, distortion follow automatically!!

• includes all relevant SiGe HBT related effects(e.g. Ge dependence, BC barrier)

• physics-based => geometry scalable, predictive (statistical simulation) capability

• available in all mainstream simulators (ADS, ELDO, MWO, SPECTRE ...)• vs. "special" models available in only a single simulator

• applied to every Si BJT and SiGe HBT process node since early eighties => spans 90(55)nm to 1μm lithography, 10 to 400 GHz transit frequency

=> continuous model development and improvement

© M. Schroter 11

HICUM/Level2 extensions

Transfer current

=> gm degradation difficult to capture accurately with existing models

10−5

10−3

10−10.7

0.75

0.8

0.85

0.9

0.95

1

JC

(mA/µm2)

g m*V

T/I C

A−1

A0

B−3

B−2

B−1

B0

C−1

C0

HICUM/L2 2.24

10−2

10−1

100

101

10210

−3

10−2

10−1

100

JC

(mA/µm2)

g mR

E

A−1

A0

B−1

B0

C−1

C0

• gm degrades at low-injec-tion for some technologies

• degradation is not related toprocess generations

• not caused by emitter resistance

• not caused by BGN or quantum effects

© M. Schroter 12

HICUM/Level2 extensions

Transconductance

10−4

10−2

1000.75

0.8

0.85

0.9

0.95

1

JC

(mA/µm2)

gm

iVT/I

C

no GeBox GeWeak Ge gradientStrong Ge gradient

0.5 0.6 0.7 0.80

1

2

3

4

5

6

VBE

(V)

h jEi

gradbox

NBNE

p(x)

VBE

x

N (log)Ge (lin)

Ge

VBE=0 V

xjE xpe0xpexpe-dx

ΔVGe

Δw

similar trend observed from device simulationfor graded Ge profile in BE SCR

=> Ge grading causes bias dependence of GICCR weight factor hjEi for BE depletion

charge QjEi:

ITc10

Qp0 hjEiQjEi+------------------------------------

VB'E'VT

----------- exp

VB'C'VT

----------- exp–=

© M. Schroter 13

HICUM/Level2 extensions

Transconductance

=> very accurate modeling of transconductance

10−3

10−2

10−1

100

10110

−3

10−1

101

103

105

Qm

in, Q

min

,T (

fC)

JC

(mA/µm2)

0

100

200

300

400

f T (

GH

z)

grad, Qmin

grad, Qmin,T

box, Qmin

box, Qmin,T

10−5

10−3

10−10.7

0.75

0.8

0.85

0.9

0.95

1

JC

(mA/µm2)g m

*VT/I C

A−1

A0

B−3

B−2

B−1

B0

C−1

C0

HICUM/L2 2.32

• hjEi voltage dependence

with

• hf0: weight factor for mobile charge • graded Ge causes shift in weighted

mobile charge center of gravity in base region

hjEi VB'E'( ) hjEi0u( ) 1–expu

--------------------------=

u ahjEi 1 VB'E' VDEi⁄–=

graded

IT c10

VB'E'VT

----------- exp

VB'C'VT

----------- exp–

Qp0 hjEi VB'E'( )QjEi hf0Qf0+ +---------------------------------------------------------------------------==>

© M. Schroter 14

HICUM/Level2 extensions

AC emitter current crowding (Lateral NQS effect)Issue: generates 2.3MB of code for derivatives!

• gm overestimation by iTf/VT partially compensated by using τf0 instead of τf => reduces code size (ADMS) to 0.3 MB(2.31)

• AC analysis by using

• Previous calculations of diffusion capacitances

and

=> calculated using ddx-operator

• Simplification avoiding ddx operator

and .

CRBi fCRBi CjEi CjCi CdEi CdCi+ + +( )=

CdEidQdEidVBE--------------

VBC

= CdCidQjCidVBC--------------

VBE

=

CdEidQdEidiTf

--------------diTf

dVBE------------- τf0

iTfVT------≈= CdCi τr

iTrVT------≈

B* B’RBi

CRBi

VRBi

© M. Schroter 15

HICUM/Level2 extensions

Temperature dependence of thermal resistance• For potential numerical stability reasons, modeling of Rth(T) was

changed from nonlinear to linear formulation:

to

• For backward compatibility, the present implementation reads

where the previous term and parameter have still been kept• Setting

- αRth = 0 and ζRth > 0 recovers the previous formulation- αRth > 0 and ζRth = 0 gives the new formulation

• Planned: no further support for previous implementation (and parameterζRth) but requires to add prevention of negative Rth

Rth T( ) Rth T0( ) TT0----- ζRth= Rth T( ) Rth T0( ) 1 αRthΔT+( )=

Rth T( ) Rth T0( ) 1 αRthΔT+( ) TT0----- ζRth=

Thermal and emitter resistance

Thermal and emitter resistance... from a joint extraction

• Scaling of thermal resistance was changed from

to

to give better results for width scaled devices

• Emitter resistance scaling almost ideally linear

Rth4lE bE⁄( )lnlE

----------------------------rth= RthRth0

1 arthbbE arthllE+ +-------------------------------------------------=

0 2 4 6 80

5

10

15

20

25

1/AE0

(µm−2)

RE (

Ω)

0 2 4 60

2

4

6

8

1/AE (µm2)

Rth

(K/m

W)

ExtractionOrig modelGeneral model

lE

bE

lE

bE

© M. Schroter 1

© M. Schroter 16

HICUM/Level2 extensions

Correlated noise• New formulation for correlated noise modeling

• modeling at the transistor input, not output• flag flcono turns correl. noise on (1) and off (0)• conditional statement for calculation of square root

IF =>

otherwise =>

• no use of nested ddt operators anymore• default values of αQf (alqf) & αiT (alit) have been

changed to physically meaningful values• Range of alqf & alit modified from [0:1] to (0:1]

• Generic method for constructing corre-lated noise networks see:• J. Herricht et al., "Systematic compact modeling

of correlated noise in bipolar transistor", acceptedin IEEE Trans. MTT, 2012.

2αQf αiT> τb1 1 jωτf 2αQf αiT2–+=

τb1 1=

InC= 2qIT InB= 2qIjBEi1S*VnC

VnC

1S*VnB

VnB

noiseless

intrinsic

transistor

τB1VnB τB2VnC VnC

τB1=1+jωτf Bf(2αQf-αiT)2

τB2=jωτfαIT

InC= 2qIT InB= 2qIjBEi1S*VnC

VnC

1S*VnB

VnB

noiseless

intrinsic

transistor

VnB τC2VnB

τC2=-jωβfτfαIT

τC1VnB

τC1=1-0.5*ω2τf2 BfαiT

2

© M. Schroter 17

Model verification

Model verification• standard characteristics: DC, small-signal y-parameters

occasionally noise (often limited 26 GHz), sometimes load-pull & harmonics

=> typically in (foundry) characterization labs=> issues for mm-wave & THz technologies

• need (large) arrays for achieving suitable impedances => impact of interconnect parasitics• distortion/harmonics, load-pull: coupler & passive tuners limit frequency to below 50...75GHz• on-wafer S-parameter measurement: limited to 110GHz in foundries, rarely 220GHz, none at

higher frequencies; pulsed AC difficult (bias Tees, meas. interval)• severe self-heating limits usable bias region for parameter extraction

=> how to verify compact models beyond equipment limitations?• device simulation: small-signal, noise, large-signal characteristics

=> limited to basic 1D or 2D device structure without major parasitic regions• use in-band distortion from two-tone load-pull => limited to magnitude

=> use physics-based models for extrapolating beyond equipment limits=> Really needed:

pulsed mag & phase (or time domain) measurement capability up to 1THz

© M. Schroter 18

Model verification

High-performance SiGe HBT (cont’d)B7HF500 (IFX) high-performance BEC transistor with AE0=2x0.1x4.88μm²

transit frequency output vs. input power

=> excellent agreement up to high input power and third harmonics

VCB\V = -0.5, -0.3, 0, 0.3, 0.5

10−1

100

101

1020

50

100

150

200

250

JC

(mA/µm2)

f T (

GH

z)

measmodel

−50 −40 −30 −20 −10 0−100

−80

−60

−40

−20

0

Pin

(dBm)P

ou

t (dB

m)

measmodel

(VBE, VCE) = (0.8, 0.8) V

10

f/GHz

30

50peak JCat Pin=-10dBm

self-biasing (even harmon.)

© M. Schroter 19

Summary

Summary

• Need for pushing process limits => accurate compact HBT modeling

• HBT compact modeling approaches (physics-based vs. behavioral models)

• HICUM/L2 latest developments• released as CMC model v2.33• available in all commercial circuit simulators and many industry PDKs

• Experimental examples for small and large-signal behavior• high-performance (low breakdown voltage) HBTs• similar results were obtained also for high-voltage (low speed) HBTs• used in industry (e.g. WCDMS, OFDMA, CD/DVD laser drivers, OC192, GSM and GPS

receiver front ends, wireless entry systems, UWB, DBS(SAT), radar, OC768...)

© M. Schroter 20

Summary

Planned extensions and improvements

• improved substrate coupling network (incl. compact geometry scaling)

• BTB, TAT in BC SCR and BTB in forward-biased BE SCR

• reliability model

• additional model verification on benchmark circuits

• CPU time reduction

© M. Schroter 21

Summary

Acknowledgments

Compact modeling• EU FP7 IP DOTFIVE (financial support; SiGe HBT technology)

• EU Catrene RF2THz(SiSoC) (financial support; SiGe HBT technology)

• German Science Foundation SFB 912 (financial support; SiGe HBT technology)

• German Science Foundation SCHR695-3 (financial support; InP HBT research)

Users and user support• IHP, Infineon, GCS, Skyworks, ST Microelectronics, TowerJazz (wafer supply)

• AWR, Cadence, Mentor Graphics (software)

• Agilent, AIST, Analog Devices, Atmel, IBM, ProPlus Solutions, Qualcomm, Renesas Electronics, RFMD, Samsung, Silvaco, SK Hynix, Synopsys, Texas Instru-ments (National), TelefunkenSemi, Toshiba, TSMC, UMC

© M. Schroter 22

Appendix

Appendix• SG13 (IHP) CBE transistor with AE0= 8 x 0.12 x 1.1μm²: DC, fT, fmax

10−1

100

101

1020

100

200

300

400

500

JC

(mA/µm2)

f max

(GH

z)

measmodel

0 0.5 1 1.5 20

5

10

15

VCE

(V)

J C (m

A/µ

m2 )

measmodel

0.8 0.9 110

−4

10−3

10−2

10−1

100

101

102

VBE

(V)

J C, J

B (m

A/µ

m2 )

measmodel

0.4 0.5 0.6 0.710

−10

10−8

10−6

10−4

10−2

100

VBE

(V)

J C, J

B (m

A/µ

m2 )

10−1

100

101

1020

50

100

150

200

250

300

JC

(mA/µm2)

f T (GH

z)

measmodel

© M. Schroter 23

Appendix

Model verification (cont’d)• SG13 (IHP) CBE HBT, AE0= 8x0.12x1.1μm²: y-parameters at peak fT

10−1

100

101

10265

70

75

80

85

90

f (GHz)

Pha

se{y

11} (

°)

measmodel

10−1

100

101

10210

−2

10−1

100

101

102

f (GHz)

Abs{

y11}

(mS/

µm2 )

measmodel

10−1

100

101

102−25

−20

−15

−10

−5

0

5

f (GHz)

Phas

e{y2

1} (°

)

measmodel

10−1

100

101

10210

1

102

f (GHz)

Abs{

y21}

(mS/

µm2 )

measmodel

© M. Schroter 24

Appendix

Model verification (cont’d)• SG13 (IHP) CBE HBT, AE0=8x0.12x1.1μm²: y-parameters at peak fT

10−1

100

101

102−100

−50

0

50

100

f (GHz)

Phas

e{y2

2} (°

)

measmodel

10−1

100

101

102−100

−95

−90

−85

−80

f (GHz)

Phas

e{y1

2} (°

)

measmodel

10−1

100

101

10210

−2

10−1

100

101

f (GHz)

Abs{

y12}

(mS/

µm2 )

measmodel

10−1

100

101

10210

−2

10−1

100

101

102

f (GHz)

Abs{

y22}

(mS/

µm2 )

measmodel