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