Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s

‘Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**

*DTU Electrical Engineering, Electromagnetic Systems Group, Technical University of DenmarkDK-2800 Kgs. LyngbyDenmark

**III-V Lab,F-91461 MarcoussisFrance

2

Outline

• The ”InP/InGaAs DHBT” device

• Specific modeling issues for III-V HBT devices:

-The integral charge control relation (ICCR) for HBT modelling

-Charge and transit-time modelling in III-V HBT devices

-Temperature effects and self-heating

• Small-signal modellng: Direct parameter extraction

• Scalable large-signal model verification

• Summary

• The introduction of an wide-gap emitter and collector to form a

Double Heterojunction Bipolar Transistor (DHBT) offers several

advantages over Homojunction Bipolar Transistors:

- Higher fT and fmax characteristic

- increased breakdown voltage

- better performance under saturation operation

The ”InP/InGaAs DHBT” Device

100 500 1000

1

2

3

4

5

6

BV ce

o(V

)

fT (GHz)

HBT SiGe IBMHBT SiGe IBM CryoHBT InP UIUCHBT InP EHTZHBT InP UCSBHBT InP ALTHHEMT

100 500 1000

1

2

3

4

5

6

100 500 1000

1

2

3

4

5

6

BV ce

o(V

)

fT (GHz)

HBT SiGe IBMHBT SiGe IBM CryoHBT InP UIUCHBT InP EHTZHBT InP UCSBHBT InP ALTHHEMT

Indicated in red are the 1.5µm and

0.7µm InP/InGaAs DHBT technologies

developed at the III-V Lab.

The ”InP/InGaAs DHBT” Device

• InP/InGaAs DHBT allows simultaneously high output power and

high frequency:

- mm-Wave power amplifiers

- VCOs for PLLs

- Electronic laser drivers and transimpedance amplifiers for

ultra-high bit rate optoelectronics (>100Gbit/s operation)

III-V Lab’s 0.7µm InP/InGaAs DHBT:

Emitter

Base plug

Collector

InP DHBT Frequency Performance

Geometrical parameters:

• An InP DHBT large-signal model must

predict the frequency characteristic

dependence on bias and on geometry

Frequency characteristic:

Device Lein [um] Ae [um2] Ac [um2]

T5B3H7 5.0 2.7 8.6

T7B3H7 7.0 3.9 10.9

T10B3H7 10.0 5.7 14.3

HBT large-signal model topology

Circuit diagram of HBT model: Agilent ADS SDD implementation:

• The large-signal topology is nearly identical for the various HBT models

(UCSD HBT model, Agilent HBT model, FBH HBT model)

The integral charge control relation

DC model of bipolar transistor:

TVbcV

eTVbeV

ep

eATqVccI

cX

eXdx

2inn

)x(pp

The transport current in a npn transistor

depends directly on the hole charge!

Hole

concentraction

1D BJT cross-section:

Base Current

Forward

Operation

Net Transport

Current

Base Current

Reverse

Operation

The Gummel-Poon model for BJTs

Gummel-Poon model formulation: Normalized base charge:

TVbcV

eTVbeV

ebqsI

ccI

current saturation :sI

charge hole base normalized :bq

RQFQ)bcV(CjQ)beV(EjQBOQBQ

2q4

21q

21q

bqbq2q

1qBOQBQ

bq

effectEarly theModels

FVBCV

RVBEV

1CjqEjq11q

effect Webster theModels

1TVBCV

eKRI

sI1TVBEV

eKFIsI1TV

BCV

eBOQsI

R1TVBEV

eBOQsI

F2q

Extended GP model for HBTs

Energy band diagram for abrupt DHBT: HBT modeling approach:

TVBNbcV

eSBIsITVAN

beV

eSAIsI

2q4

21q

21q

bq

• In an abrupt DHBT additional transport mechanisms such as

thermionic emission over the barrier and tunneling through it

tend to drag the ideality factor away from unity (NF>1).

• The collector blocking leads to earlier saturation at high collector

voltages (the so-called ”soft knee” effect)

TVRNbcV

eTVFNbeV

ebqsI

ccI≈1 in HBTs

Forward Gummel-plot for InP DHBT device

Nf=1.14

•Base current in UCSD HBT model:

idealNon

1TVENBEV

eSEI

Ideal

1TVFNBEV

eFbq

sIBEI

•Nf=1.14

idealNon

1TVENBEV

eSEI

Ideal

1TVHNBEV

eSHIBEI

Forward Gummel-plot for InP DHBT device

•Base current in Agilent HBT model:

Charge modeling in III-V HBT

• In any transistor a change in bias requires charge movement which

takes time:

- built up depletion layers in the device

- redistribution of minority carriers

AC model of bipolar transistor: Total emitter-collector delay:

model signal-small

in the itancesTranscapac)bcV,beV(diffQ

cbm

bcje

Vcc

bc

Vcc

beec g

CC

dI

dQ

dI

dQ

cece

charge diffusion

diffQexF

chargedepletion

jeQbeQ

charge diffusion

diffQ)exF1(

chargedepletion

jcQbcQ

• Diffusion charge partitionen with Fex

exitvBW

nD2

2BW

b

cv2cW

c

Transit time formulation

Analytical transit-times: Velocity-field diagram for InP:

Velocity modulation effects in collector:

• Collector transit-time c increase with electrical field

• Collector transit-time c decrease with current due to modulation of

the electrical field with the electron charge (velocity profile modulation)

• Intrinsic base-collector capacitance Cbci decrease with current

(assumed constant)

(varies with bias)

HBTs! V-IIIin bc .Typ

Base thickness

Collector thickness

modulation profileVelocity

r0

2c

dc1

increase field Av.

bcijc1

delay Conv.

c0c 12

W)n2N(

2

k)VV(

2

k

2

WkT

er

ccc

c

erbci

bci

cc

c

erbci A

WIkkI

W

AC

V

TI

W

AC

0

1100

61

2

Transit time formulation: Full depletion

Collector transit-time model:

densityelectron Av.

eav

cA)(qv

In

Base-collector capacitance model:

Slowness of electrons in InP:

Ekk)E(v/1 10

• Formulation used in UCSD HBT model

Inclusion of self-heating

• The thermal network provides an 1.order estimate of the temperture

rise (delT) in the device with dissipated power (Ith).

Thermal network

thththth

ththth

Qdt

dRRIdelT0

R

delTQ

dt

dI

charge Thermal :delTCQ

resistance Thermal :R

ndissipatioPower :I

rise Tempeture :delT

thth

th

th

Self-Heating formulation:

InP HBT self-heating characteristic

• Self-heating in HBT devices manifests itself with the downward sloping

Ic-Vce characteristic for fixed Ib levels.

kT

gE

TcI

constbITcI

bebebe Cj

1||Rz

bcbcbc Cj

1||Rz

bcxbcxbcx Cj

1||Rz

ebxbembcxbccibi

bcbi

bcxbccibi

bcxcibi

bem

be11 RR

)Zg1)(ZZRR(

ZR

ZZRR

)ZR(R

Zg1

Zz

ebembcxbccibi

bcbi

bcxbccibi

cibi

bem

be12 R

)Zg1)(ZZRR(

ZR

ZZRR

RR

Zg1

Zz

eR)beZmg1)(bcxZbcZciRbiR(

beZbcxZbcZmgbcZbiR

bcxZbcZciRbiRciRbiR

beZmg1beZ

21z

ecxbembcxbccibi

bcxbibc

bcxbccibi

bcxbici

bem

be22 RR

)Zg1)(ZZRR(

)ZR(Z

ZZRR

)ZR(R

Zg1

Zz

Small-signal modeling

_

Cbcx

C

Cceo

Rbci

Rbcx

gmVbeVbe

+

Rbx RbiB

Cbe Rbe

Re

Cbci Rci Rcx

gm=gmoe-jd

bbx1211 Ifor R)ZZRe(

Resistance Extraction: Standard method

Open-Collector Method: HBT base current flow:

•Rbx underestimated due to shunting

effect from forward biased external

base-collector diode!

Saturated HBT device:

bIfor ciR||biReR)12ZRe(

bIfor cxR)12Z22ZRe(

•Re overestimated due to the intrinsic

collector resistance!

Standard method only good for Rcx extraction

c

factor Correction

Ifor ebcxbci

bcxbi12 R

)1)(CC(

CR)0)(ZRe(

Emitter resistance extraction

Forward biased HBT device:

Re can be accurately determined if correction is employed

Notice: Rbi extracted assuming

uncorrected Re value.

Circuit diagram of HBT model:

• Correct extraction of the extrinsic base resistance is important as it

influence the distribution of the base-collector capacitance

fmax modeling!

Extrinsic base resistance extraction (I)

• Distributed base lumped into a few elements

• The bias dependent intrinsic base resistance Rbi describes the active region under the emitter

• The extrinsic base resistance Rbx describes the accumulative resistance going from the base contact to the active region

er0

cc1c1

c

er0bci A6

WIk1

2

Ik

W

AC

p

c0bcibci I

I1CC

Base-collector capacitance model: Linearization of capacitance:

• Linear approximation only valid at very low collector currents.

Low current linear approximation:

10bcip k/C2I c

er00bci W

AC

Linear approx.

K1=0.35ps/V

Ae=4.7m2

Wc=0.13mPhysical model

Characteristic

current

Extrinsic base resistance extraction (II)

]I/I)X1(1[XI/IX1

]I/I1[X

C]I/I1[C

]I/I1[C

CC

CX

pc00pc0

pc0

bcxpc0bci

pc0bci

bcxbci

bci

Base-collector splitting factor: Linearization of splitting factor:

• Base collector splitting factor follows linear trend to higher currents.

Linear approx.

K1=0.35ps/V

Ae=4.7m2

Wc=0.13m

X0=0.41Physical model

cebcx0bci0bci0 A/A)CC/(CX

Zero-bias splitting factor:

Extrinsic base resistance extraction (III)

pc

bxbip

c00beff

bxbibxbibcxbci

bcibeff

II for

RRI

I)X1(1XR

RXRRRCC

CR

Improved extraction method:

• Extrinsic base resistance estimated from extrapolation in full depletion.

Effective base resistance model:

Rbx extraction method:

0

pcbxbeff X1

IIfor RR

Extrinsic base resistance extraction (IV)

1211beff ZZReR :Def.

bebe

bcbebebibe121111 CRj1

))CC(Rj1(RR)YY/(1H

bibe

bcbebi11 R

C

CCR)(H

Intrinsic base resistance extraction

Rbi in InP DHBT devices is fairly

constant versus base current

Improved Semi-impedance circle method:

(Rbx, Re, Rcx de-embedded)

)CC()ZZ/(1Im bcibcx2122

bci

bcibcx

bi1211 C

CC

R

1)ZZ/(1Re

Base-collector capacitance extraction

Base-collector capacitance modelling:

er0

cc1c1

c

er0bci A6

WIk1

2

Ik

W

AC

40.0X

V/ps44.0k

m9.3A

56.12

m130.0W

0

1

2e

r

c

1

X

1

W

AC

0c

er0bcx

•Model parameters:

•Base-collector capacitance extraction

i

12Yi11YImbeC

i

12Yi11YRe/1beR

Intrinsic element extraction

Intrinsic hybrid-pi equivalent circuit

• The influence from the elements Rbx, Rbi, Re, Rcx, Cbcx, and Cceo are

removed from the device data by de-embedding to get to the intrinsic data.

i

12YImbciC

i

12YRe/1bciR

)dcos(/i12Yi

21YRemog

i12Yi

21YRe

i12Yi

21YImtana

1d

Direct parameter extraction verification

Small-signal equivalent circuit S-Parameters

Model Parameter Value Model Parameter Value

Rbx [] 8.0 Cbcx [fF] 10.1

Rbi [] 11.1 Cbci [fF] 3.0

Rcx [] 2.6 Rbci [k] 56.0

Re [] 2.7 gmo [mS] 773

Cbe [fF] 340.8 d [pS] ≈0

Rbe [] 34.6 Cceo [fF] 6.8

Scalable UCSD HBT model verification

Scalable Agilent HBT model verification

• Load pull measurements not

possible. Load and source

fixed at 50Ω.

• Lowest measurement loss at

74.4GHz

Single-finger device

Large-signal characterization setup

Large-signal single-tone verification

• The large-signal performance at 74.4GHz of the individual single-finger devices is well predicted with the developed UCSD HBT model except for

low collector bias voltage (Vce=1.2V).

mm-wave verification!

Measurements versus UCSD HBT model:

• The large-signal performance at 74.4GHz of the individual single-finger devices is well predicted with the developed Agilent HBT model. The agreement at lower collector bias voltage is better.

Measurements versus Agilent HBT model:

mm-wave verification!

Large-signal single-tone verification

Summary

• The InP/InGaAs DHBT can be modeled accurately by an extended

Gummel-Poon formulation

- thermionic emission and tunneling

- collector blocking effect

- collector transit-time physical modeling

• Small-signal InP/InGaAs HBT modeling

-unique direct parameter extraction approach

•Scalable large-signal HBT model verfication

-RF figure-of-merits and DC characteristics

-mm-wave large-signal verification