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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
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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
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• 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.
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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
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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
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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)
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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
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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
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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
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Forward Gummel-plot for InP DHBT device
Nf=1.14
•Base current in UCSD HBT model:
idealNon
1TVENBEV
eSEI
Ideal
1TVFNBEV
eFbq
sIBEI
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•Nf=1.14
idealNon
1TVENBEV
eSEI
Ideal
1TVHNBEV
eSHIBEI
Forward Gummel-plot for InP DHBT device
•Base current in Agilent HBT model:
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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
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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
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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
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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:
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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
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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
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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
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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.
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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
![Page 21: Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e575503460f94b50591/html5/thumbnails/21.jpg)
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)
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]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)
![Page 23: Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e575503460f94b50591/html5/thumbnails/23.jpg)
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.
![Page 24: Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e575503460f94b50591/html5/thumbnails/24.jpg)
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)
![Page 25: Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e575503460f94b50591/html5/thumbnails/25.jpg)
)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
![Page 26: Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e575503460f94b50591/html5/thumbnails/26.jpg)
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
![Page 27: Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e575503460f94b50591/html5/thumbnails/27.jpg)
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
![Page 28: Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e575503460f94b50591/html5/thumbnails/28.jpg)
Scalable UCSD HBT model verification
![Page 29: Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e575503460f94b50591/html5/thumbnails/29.jpg)
Scalable Agilent HBT model verification
![Page 30: Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e575503460f94b50591/html5/thumbnails/30.jpg)
• Load pull measurements not
possible. Load and source
fixed at 50Ω.
• Lowest measurement loss at
74.4GHz
Single-finger device
Large-signal characterization setup
![Page 31: Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e575503460f94b50591/html5/thumbnails/31.jpg)
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:
![Page 32: Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e575503460f94b50591/html5/thumbnails/32.jpg)
• 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
![Page 33: Small- and Large-Signal Modeling for Submicron InP/InGaAs DHBT’s ‘ Tom K. Johansen*, Virginie Nodjiadjim**, Jean-Yves Dupuy**, Agnieszka konczykowska**](https://reader035.vdocuments.mx/reader035/viewer/2022062421/56649e575503460f94b50591/html5/thumbnails/33.jpg)
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