and Large-Signal Modeling for Submicron InP/InGaAs - MOS-AK
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Transcript and Large-Signal Modeling for Submicron InP/InGaAs - MOS-AK
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 Denmark
DK-2800 Kgs. Lyngby
Denmark
**III-V Lab,
F-91461 Marcoussis
France
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
2
The ”InP/InGaAs DHBT” Device
• 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
6
BVceo (V)
5
4
HBT SiGe IBM
HBT SiGe IBM Cryo
HBT InP UIUC
HBT InP EHTZ
HBT InP UCSB
HBT InP ALTH
HEMT
Indicated in red are the 1.5µm and
0.7µm InP/InGaAs DHBT technologies
developed at the III-V Lab.
3
2
1
100
500
fT (GHz)
1000
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:
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
• An InP DHBT large-signal model must
predict the frequency characteristic
dependence on bias and on geometry
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:
1D BJT cross-section:
Base Current
Reverse
Operation
Base Current
Net Transport
Forward
Current
Operation
The transport current in a npn transistor
depends directly on the hole charge!
Vbc
Vbe
qVT A e VT
I cc
e VT
e
p
Hole
X c p( x )
p
dx
2
Xe n ni
concentraction
The Gummel-Poon model for BJTs
Gummel-Poon model formulation:
I
I cc s
qb
Vbc
Vbe
V
V
e T e T
Normalized base charge:
Q B Q BO Q Ej (Vbe ) Q Cj(Vbc ) Q F Q R
QB
q
q
qb
q1 2 q b 1
Q BO
qb
2
Is : saturation current
q b : normalized base hole charge
q12
q2
4
V
V
q1 1 q Ej q Cj 1 BE BC
V
VF
R
Models the Early effect
VBC
VBC
VBE
VBE
I
Is
Is
Is
V
V
V
q 2 F s e VT 1 R
e T 1
e T 1
e T 1
Q BO
Q BO
I KF
I KR
Models the Webster effect
Extended GP model for HBTs
Energy band diagram for abrupt DHBT:
HBT modeling approach:
≈1 in HBTs
q
qb 1
2
I
I cc s
qb
Vbc
Vbe
N V
N V
e F T e R T
Vbe
Vbc
2
q1
I
I
q 2 s e N A VT s e N BVT
4
ISA
ISB
• 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)
Forward Gummel-plot for InP DHBT device
Nf=1.14
•Base current in UCSD HBT model:
VBE
VBE
Is N FVT
I BE
1 ISE e N E VT 1
e
q b F
Ideal
Non ideal
Forward Gummel-plot for InP DHBT device
•Nf=1.14
•Base current in Agilent HBT model:
VBE
VBE
N V
N V
I BE ISH e H T 1 ISE e E T 1
Ideal
Non ideal
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:
ec
Qdiff (Vbe , Vbc ) T ranscapacitances in the
small - signal model
dQ be
dI cc
Vce
dQ bc
dI cc
Vce
C je C bc
gm
Qbe
Q je
Fex Qdiff
depletion charge diffusion charge
Qbc
Q jc
(1 Fex )Qdiff
depletion charge diffusion charge
b c
• Diffusion charge partitionen with Fex
Transit time formulation
Analytical transit-times:
2
WB
WB
b
2D n v exit
c
Wc
2vc
Velocity-field diagram for InP:
Base thickness
(assumed constant)
(varies with bias)
Collector thickness
Typ. c b in III - V HBTs!
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
Transit time formulation: Full depletion
Collector transit-time model:
Slowness of electrons in InP:
Wc
Wc2
k1
k1
Tc k 0
(V j c Vbci )
( N dc 2n )
2
2
2
12 0 r
Conv. delay Av. field increase Velocity profile m odulation
Ic
n
qv( av )A e
Av. electrondensity
Base-collector capacitance model:
Cbci
0 r Ae
Wc
Ic
Tc
A Ik
kIW
Cbci 0 r e c 1 1 1 c c
Vbci
Wc
2 6 0 r Ae
• Formulation used in UCSD HBT model
1 / v(E) k 0 k1E
Inclusion of self-heating
Self-Heating formulation:
d
delT
Q th
dt
R th
d
0 delT I th R th R th
Q th
dt
I th
delT: Tempeture rise
Thermal network
I th : P owerdissipatio
n
R th : Thermal resistance
Q th C th delT: Thermal charge
• The thermal network provides an 1.order estimate of the temperture
rise (delT) in the device with dissipated power (Ith).
InP HBT self-heating characteristic
I c
I c E g
T I const
T kT
b
• Self-heating in HBT devices manifests itself with the downward sloping
Ic-Vce characteristic for fixed Ib levels.
Small-signal modeling
Rbcx
Cbcx
Rbci
Rbx
Cbci
Rbi
Rci
B
Rcx
C
+
Vbe
_
Cbe
Rbe
gmVbe
z be R be ||
1
jC be
z bc R bc ||
1
jC bc
Cceo
gm=g mo e-jd
Re
z bcx R bcx ||
1
jC bcx
z11
Z be
R bi ( R ci Z bcx )
R bi Z bc
R bx R e
1 g m Z be R bi R ci Z bc Z bcx ( R bi R ci Z bc Z bcx )(1 g m Z be )
z12
Z be
R bi R ci
R bi Z bc
Re
1 g m Z be R bi R ci Z bc Z bcx ( R bi R ci Z bc Z bcx )(1 g m Z be )
z 21
Z be
R bi R ci
R bi Z bc g m Z bc Z bcx Z be
Re
1 g m Z be R bi R ci Z bc Z bcx (R bi R ci Z bc Z bcx )(1 g m Z be )
z 22
Z be
R ci (R bi Z bcx )
Z bc (R bi Z bcx )
R cx R e
1 g m Z be R bi R ci Z bc Z bcx (R bi R ci Z bc Z bcx )(1 g m Z be )
Resistance Extraction: Standard method
Open-Collector Method:
HBT base current flow:
•Rbx underestimated due to shunting
Saturated HBT device:
effect from forward biased external
Re(Z11 Z12 ) R bx for I b
base-collector diode!
Re(Z12 ) R e R bi | | R ci for I b
Re(Z22 Z12 ) R cx for I b
•Re overestimated due to the intrinsic
collector resistance!
Standard method only good for Rcx extraction
Emitter resistance extraction
Forward biased HBT device:
Re(Z12 )( 0)
R bi C bcx
R e f orI c
(C bci C bcx )(1 )
Correctionfactor
Notice: Rbi extracted assuming
uncorrected Re value.
Re can be accurately determined if correction is employed
Extrinsic base resistance extraction (I)
Circuit diagram of HBT model:
• 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
• 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 (II)
Base-collector capacitance model:
A
k I
C bci 0 r e 1 c
Wc
2
k1I c Wc
1
6
A
0 r e
Linearization of capacitance:
K1=0.35ps/V
Ae=4.7m2
Wc=0.13m
Physical model
Low current linear approximation:
I
Cbci Cbci0 1 c
I p
Characteristic
current
A
C bci0 0 r e
Wc
Linear approx.
I p 2Cbci0 / k1
• Linear approximation only valid at very low collector currents.
Extrinsic base resistance extraction (III)
Base-collector splitting factor:
C bci0 [1 I c / I p ]
C bci
C bci C bcx C bci0 [1 I c / I p ] C bcx
X 0 [1 I c / I p ]
X 0 [1 (1 X 0 )I c / I p ]
1 X0Ic / I p
X
Linearization of splitting factor:
K1=0.35ps/V
Ae=4.7m2
Wc=0.13m
X0=0.41
Physical model
Zero-bias splitting factor:
X 0 C bci0 /(C bci0 C bcx ) A e / A c
Linear approx.
• Base collector splitting factor follows linear trend to higher currents.
Extrinsic base resistance extraction (IV)
Improved extraction method:
Effective base resistance model:
Def.: R beff ReZ11 Z12
R beff
C bci
R bi R bx XR bi R bx
C bci C bcx
I
R beff X 0 1 (1 X 0 ) c R bi R bx
I p
for I c I p
Rbx extraction method:
R beff R bx for I c
Ip
1 X0
• Extrinsic base resistance estimated from extrapolation in full depletion.
Intrinsic base resistance extraction
Improved Semi-impedance circle method:
(Rbx, Re, Rcx de-embedded)
H11 1 /(Y11 Y12 )
R be R bi (1 jR be (C be C bc ))
1 jR be C be
H11 ( ) R bi
C be C bc
R bi
C be
Rbi in InP DHBT devices is fairly
constant versus base current
Base-collector capacitance extraction
Base-collector capacitance modelling:
k1I c Wc
1
6 0 r A e
A
k I
C bci 0 r e 1 c
Wc
2
A
C bcx 0 r e
Wc
1
1
X
0
•Model parameters:
•Base-collector capacitance extraction
1
Re1 /(Z11 Z12 )
R bi
C bcx C bci
C
bci
Im1 /(Z 22 Z 21) (C bcx C bci )
Wc 0.130m
r 12.56
A e 3.9m 2
k1 0.44ps / V
X 0 0.40
Intrinsic element extraction
Intrinsic hybrid-pi equivalent circuit
i Yi
Cbe Im Y11
12
i Yi
R be 1/ Re Y11
12
i
Cbci Im Y12
i
R bci 1/ Re Y12
i Yi / cos( )
g mo Re Y21
d
12
i Yi
Im Y21
12
1
d a tan
i Yi
Re Y21
12
• 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.
Direct parameter extraction verification
Small-signal equivalent circuit
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
S-Parameters
Scalable UCSD HBT model verification
Scalable Agilent HBT model verification
Large-signal characterization setup
Single-finger device
• Load pull measurements not
possible. Load and source
fixed at 50Ω.
• Lowest measurement loss at
74.4GHz
Large-signal single-tone 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 UCSD HBT model except for
low collector bias voltage (Vce=1.2V).
mm-wave verification!
Large-signal single-tone verification
Measurements versus Agilent 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.
mm-wave 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