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
jC be
z bc  R bc ||
1
jC bc
Cceo
gm=g mo e-jd
Re
z bcx  R bcx ||
1
jC 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=4.7m2
Wc=0.13m
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=4.7m2
Wc=0.13m
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  ReZ11  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  jR be (C be  C bc ))
1  jR 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
Re1 /(Z11  Z12 )  
R bi
 C bcx  C bci 




C
bci


Im1 /(Z 22  Z 21)   (C bcx  C bci )
Wc  0.130m
 r  12.56
A e  3.9m 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