Aufinger, K

Celi, D.

Couret, M

Fischer, G,

Jaoul, M

Maneux, C.

Marc, F.

Mukherjee, C

Zimmer, T.

English

Archive Ouverte en Sciences de l'Information et de la Communication

Advances in Aging Compact Model for Hot Carrier 
Degradation in SiGe HBTs under Dynamic Operating 
conditions for reliability-aware circuit design 
C. Mukherjee1, F. Marc1, M. Couret1, G. G. Fischer2, M. Jaoul1, D. Céli3, K. 
Aufinger4, T. Zimmer1 and C. Maneux1
1University of Bordeaux; 2IHP; 3STmicroelectronics; 4Infineon
cristell.maneux@u-bordeaux.fr
WS-01 
Recent advances in SiGe BiCMOS: technologies, modelling & circuits for 5G, radar & imaging
- 2 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
• Purpose
• Aging experimental results
• TCAD investigations
• Modeling of the aging
• Results
• Conclusion
Outline
- 3 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
• SiGe HBTs dynamic performance 
enhancement has led to low 
breakdown voltages 
• Since open base is rarely 
encountered for in circuit situation, 
BVCEO can be exceeded up to the 
open-emitter breakdown voltage 
BVCBO
• For power performances, designers 
require to use HBTs beyond BVCEO
Purpose 1/2
M. Jaoul, C. Maneux, D. Céli, M. Schröter and T. Zimmer, "A Compact Formulation for Avalanche Multiplication in SiGe HBTs at high injection
levels," Transactions on Electron Devices, Volume: 66, Issue: 1, pp.264-270, Jan. 2019
f T
[G
H
z]
0 5 10 15 20
0
50
100
150
200
250
300
350
HS
MV
HV
BVCEO [V]
BVCBO [V]
2 6 10 14 18
HV
Performances of STMicroelectronics and Thomson 
Semiconductor bipolar technologies
- 4 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
• Circuit reliably improvement
• Reduce time and cost by limiting the aging tests at circuit level
• Use a short loop to evaluate the circuit performances
• Integrate aging laws in device compact model
Purpose 2/2
Process 
Development
Technology 
Qualification
Device 
Performance 
Process Design Kit 
(PDK)
Circuit 
Design
Circuit 
Tests
Electro - thermal
Characterizations
Aging Tests
Compact
Model
Aging laws
Defects 
location
Aging Tests
Months Weeks Weeks
C. Mukherjee, B. Ardouin, J. Y. Dupuy, V. Nodjiadjim, M. Riet, T. Zimmer, F. Marc, and C. Maneux, "Reliability-Aware Circuit Design Methodology for Beyond-5G 
Communication Systems," IEEE Trans. Device Mater. Rel. vol. 17, no. 3, pp. 490-506, Sept. 2017, DOI: 10.1109/TDMR.2017.2710303.
- 5 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
• SOA edges defined by 
• Strong avalanche regime
• Self-heating 
• Current pinch-in effect (current crowding 
at the center of the emitter)
• Failure mechanism activation depends 
on various accelerating factors
• Temperature
• Electric field
• Current density 
• Stress time
Aging tests: Mixed mode at the SOA edges
Marine Couret, Gerhard Fischer, Iria Garcia Lopez, Magali De Matos, François Marc, Cristell Maneux, "Impact of SiGe HBT Hot-Carrier Degradation on the 
Broadband Amplifier Output Supply Current", IEEE Proceedings of ESSDERC 2019, Cracow, Poland, 23-26 Sept 2019.
- 6 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
Aging tests: Dynamic mixed mode at the SOA edges
Marine Couret, Gerhard Fischer, Iria Garcia Lopez, Magali De Matos, François Marc, Cristell Maneux, "Impact of SiGe HBT Hot-Carrier Degradation on the 
Broadband Amplifier Output Supply Current", IEEE Proceedings of ESSDERC 2019, Cracow, Poland, 23-26 Sept 2019.
0 10 20 30 40 50 60 70
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
t
2
Stress 2
V
BE
=0.88V
V
CE
=1.5V
Stress 1
V
BE
=0.88V
V
CE
=2.5V
 Measurements
 HiCuM-AL V2
 HiCuM-AL V1
 
 
Stress time [h]
I R
E
P
S
 [
fA
]
Stress 1 
V
BE
=0.88V
V
CE
=2.5V
t
1
- 7 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
Aging tests: Failure mechanism origin investigation
M. Jaoul, D. Ney, D. Céli, Cristell Maneux and T. Zimmer, “Analysis of a failure mechanism occurring in SiGe HBTs under mixed-mode stress conditions”, IEEE 
ICMTS, 18-21 Mar. 2019, Fukuoka, Japan.
• TCAD simulations 
• Trap density have been added at the EB spacer interface
• Increasing the trap density increases the base recombination current 
• Follows the same behavior as observed on measurements at 25°C (symbols)
• IREPS : HICUM parameter associated with peripheral base recombination current
10
-12
10
-10
10
-8
10
-6
10
-4
10
-2
0.4 0.5 0.6 0.7 0.8 0.9 1
I B
, 
I C
[A
]
VBE [V]
NT=0
8x10
10
1x10
11
2x10
11
3x10
11
6x10
11
Meas.  @0s
Meas. @122h
- 8 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
Aging tests: Failure mechanism equations
• The rate of bond dissociation is governed by a chemical interaction between 
the carriers and the passivated Si-H bond through generation and annihilation 
of traps. 
• When a Si–H breaks, every dangling Si bond is associated with a free H atom in 
the oxide.
• In the oxide volume, the flow 
of hydrogen is related to the 
density by Fick’s diffusion law
• Adding the hydrogen conservation law when x>0, Fick’s second law reads
Collector
Poly-base Emitter
Spacer
Base
𝑔𝑇 𝑡 = 𝐾𝐹 𝑁𝐹 − 𝑁𝑇 𝑡 − 𝐾𝑅𝑁𝑇 𝑡 𝑁𝐻 0, 𝑡
𝑔𝑇 𝑡 =
𝑑𝑁𝑇
𝑑𝑡
= 𝛷𝐻 0, 𝑡
𝛷𝐻 𝑥, 𝑡 = −𝐷𝐻
𝜕𝑁𝐻 𝑥, 𝑡
𝜕𝑥
𝜕𝑁𝐻 𝑥, 𝑡
𝜕𝑡
− 𝐷𝐻
𝜕2𝑁𝐻 𝑥, 𝑡
𝜕𝑥2
= 0
- 9 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
Implementation of the R-D Model
• In order to introduce in the compact model the time-invariance property and 
the memory effect necessary for dynamic stress simulation, we introduce a 
new structure of the compact model compared to HiCUM_AL V1*
• Aging model implemented in HiCuM compact model => HiCuM_AL V2
• through recombination current parameter in the periphery, IREpS
• similar evolution as the trap density NT (x, t). 
• KF (s
-1), KR (cm
3s-1) are represented by their corresponding compact model parameters 
KF,I (s
-1), KR,I (cm.A
-1.s-1), respectively, and NF by IF (A) which is the final value of ΔIREpS, (A).
D0 NH0
diffusion model
gnd
gTgTCT
NT T
equ. (1)
*C. Mukherjee, T. Jacquet, G. G. Fischer, T. Zimmer, and C. Maneux, " Hot Carrier Degradation in SiGeHBTs: A Physical and Versatile Aging Compact Model," IEEE 
Transactions on Electron Devices, vol. 64, no. 12, pp. 4861-4867, Dec. 2017.DOI: 10.1109/TED.2017.2766457.
- 10 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
Implementation in a Spice-like circuit simulator
• To simulate the diffusion model in a Spice-like circuit simulator
=> organized around a finite set of nodes or variables. 
• To obtain a time-invariant model
=> the time does not appear explicitly in the equations but only in time 
derivatives. 
=> the distributed partial derivative equations are replaced by a finite 
set of first order differential equations implemented by a resistor-capacitor (R-C) 
network. 
=> As the physical system can only be considered for one dimension, an 
R-C ladder network is used. 
GCN
DNRNRN-1
C2 CN-1
R2
C1
R1
I1 IN-1 INI0
gnd
gT
D0 DN-1
R-C ladder network representing Hydrogen diffusion model.
- 11 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
Verilog-A model
• Hydrogen flow density is presented as currents IN (ensuring conservation law)
• Hydrogen density as potential VN at node DN
• Voltage at D0 is 𝑉0= 𝑁𝐻 0, 𝑡 , Input current is 𝐼0 = 𝛷𝐻 0, 𝑡 = 𝑔𝑇 𝑡 .
• In frequency representation, introducing admittances ෨𝑌𝑛 = Τ෩𝐼𝑁 ෪𝑉𝑁, we have the 
recurrence:
• To reduce model parameter number, values
of 𝑅𝑛 and 𝐶𝑛 follow geometrical sequences
• Sequence identified to a finite difference approximation along the x axis, 
considering a geometrically increasing sequence of x. 
=> One dimensional system =>  same common ratio 𝛼𝑅= 𝛼𝐶 . 
=> Identification of the diffusion compact model parameters => diffusion 
model equations => Fick’s second law translated into the frequency domain 
Limit conditions ෨𝑌 𝑓 = ෪𝛷𝐻 Τ0, 𝑓 ෪𝑁𝐻 0, 𝑓
Very thick oxide
𝐿 → ∞;𝐴𝐻
= 0
1 + 𝑗 𝜋𝑓𝐷𝐻
Finite thickness: 
Hydrogen barrier 
at 𝐿
𝛷𝐻 𝐿, 𝑡 = 0 1 + 𝑗 𝜋𝑓𝐷𝐻𝑡𝑎𝑛ℎ 1+ 𝑗 𝜋𝑓/𝐷𝐻𝐿
Finite thickness: 
Free hydrogen at 
𝐿
𝑁𝐻 𝐿, 𝑡 = 0 1 + 𝑗 𝜋𝑓𝐷𝐻𝑐𝑜𝑡ℎ 1 + 𝑗 𝜋𝑓/𝐷𝐻𝐿
෨𝑌𝑁 = 𝐺
෨𝑌𝑛−1 =
1
𝑅𝑛 +
1
𝑗2𝜋𝑓𝐶𝑛 + ෨𝑌𝑛
; 𝑛 = 1. . 𝑁
𝑅𝑛 = 𝑅1𝛼𝑅
𝑛−1, 𝐶𝑛= 𝐶1𝛼𝐶
𝑛−1 LIMIT CONDITIONS FOR
HYDROGEN DIFFUSION MODEL
- 12 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
Results : Infineon technology
• Aging-tests were performed on SiGe NPN HBTs from Infineon Technologies. 
• DUTs of drawn emitter dimension 0.2×10 μm2 exhibit peak fT/fMAX of 240/380 GHz and 
a BVCE0 of 1.3V. 
• Stress conditions P2 and P3 (above BVCE0 with VCE = 2V, JC =5 mA/μm
2 and VCE = 3V, JC =1 
mA/μm2, respectively)
10
-1
10
0
10
1
10
2
10
3
10
-16
10
-15
10
-14
10
-13
P3 condition
 
 
I R
E
p
S
 [
A
]
Aging Time [h]
 Extracted
 HiCuM-AL V2
P2 condition
0.5 0.6 0.7 0.8 0.9 1.0
10
-9
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
P2 condition
 
 
I C
, 
I B
 [
A
]
V
BE
 [V]
Time=0, 1, 3, 7, 72, 1000 H
I
c
I
B
 Measurement
  HiCuM-AL V2
(a) (b)
- 13 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
Results : STMicroelectronics technology
0
2
4
6
8
10
12
0 0.5 1 1.5 2 2.5 3 3.5
J C
 [
m
A
/µ
m
2
]
305K
310K
325K
335K
350K 375K 400K
JE = -8mA/µm
2
JE = -6mA/µm
2
JE = -4mA/µm
2
JE = -2mA/µm
2
JE = -1mA/µm
2
VCE [V]
10
-1
10
0
10
1
10
2
10
-1
10
0
10
1
10
2
10
3
 Measurement

I B
 (
t)
 =
 [
I B
(t
) 
- 
I B
(0
)]
/I
B
(0
) 
Aging Time [h]
 HiCuM-AL V2
V
BE
=0.6V
V
BE
=0.5V
0.4 0.5 0.6 0.7 0.8 0.9 1.0
10
-11
10
-10
10
-9
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
V
BE
 [V]
I B
, 
I C
 [
A
]
I
c
I
B
Aging time=0, 1, 12, 48, 96, 144 h
 Measurement
 HiCuM-AL V2
J
E,stress
= 8 mA/m
2
V
CB
=1.5V
0.2 x 5 m
2
10
-2
10
-1
10
0
10
1
10
2
10
-16
10
-15
10
-14
I R
E
p
S
 [
A
]
Aging Time [h]
 Extracted
 HiCuM-AL V2
(a)
(b)
(c)
(d)
NPN SiGe HBTs based on an advanced BICMOS 55nm technology from STMicroelectronics 
featuring devices with a drawn emitter size of 0.2×5 μm² in CBEBC configuration
- 14 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
Results : IHP technology 1/2
• Aging model validated on SG13S IHP technology featuring transistors in BEC 
configuration with an effective emitter area of 8×0.16×0.52 µm2. 
• Aging tests were performed under various mixed-mode stress conditions.
• Very large spectrum of aging tests allowing analysis of hot-carrier degradation 
governed by the two accelerating factors: VCB and JE.
• In all cases, aging tests were performed up to 1000h of stress time.
0
5
10
15
20
0.5 1 1.5 2 2.5 3 3.5 4 4.5
J C
 [
m
A
/µ
m
2
]
305K
310K
325K
335K 350K 375K 400K
JE = -12.0mA/µm
2
JE = -6.00mA/µm
2
JE = -1.20mA/µm
2
JE = -0.60mA/µm
2
JE = -0.12mA/µm
2
VCE [V]
0
10
-1
10
0
10
1
10
2
10
3
10
-17
10
-16
10
-15
10
-14
10
-13
 Extracted
J
E,stress
=0.12 mA/m
2
V
CB
=2.5, 2.75, 3.25 V
 
 
 HiCuM-AL V2 
I R
E
p
S
 (
A
)
Aging Time (h)
10
-1
10
0
10
1
10
2
10
3
10
-1
10
0
10
1
Aging Time [h]
(b) 
 
 
 Measurement

I B
 (
t)
=
[
I B
 (
t)
-
I B
 (
0
)]
/
I B
 (
0
)  HiCuM-AL V2
Extracted @V
BE
=0.7V
@J
E,stress
 = 0.12 mA/µm²
@V
CB,stress
= 2.5, 2.75, 3, 3.25 V
 HiCuM
(a) (b)
- 15 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
Results : IHP technology 2/2
0 1000 2000 3000 4000
0
50
100
150
200
250
300
 Measurements
M
M
 S
tr
es
s
R
ec
o
v
er
y
 
 
 

I B
/I
B
0
[%
]
 HiCuM-AL V2
Stress time [s]
Dynamic mixed-mode stress
MM stress: V
CB
= 3V, I
E
= - 0.13 mA
Recovery: V
CB
= 0V, I
E
= - 5.2 mA
DC mixed-mode stress
Evolution of excess base current for IHP technology under dynamic mixed-mode stress 
conditions comparing the measurements and HiCuM_AL V2 
- 16 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
Model parameters analysis
• Forward rate, KF,I, increases with VCB,stress following an exponential dependence while 
JE,stress is kept constant
• On the other hand, while VCB,stress is kept constant, KF,I demonstrates a peak value before 
starting to roll off. 
=> explained by a decrease in the C-B electric field at the onset of the Kirk effect at 
such high stress current densities
=> resulting in a reduction in ΔIB
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
10
-5
10
-4
10
-3
10
-1
10
0
10
1
 
 @J
E,stress
= 0.12 mA/m
2
 @J
E,stress
= 12 mA/m
2
K
F
 [
s-
1
]
V
CB
 [V]
J
E,stress
 [mA/m
2
]
 @V
CB
=2.75V
2.2 2.4 2.6 2.8 3.0 3.2 3.4
10
6
10
7
10
8
10
9
10
10
K
R0
=10
12
K
R0
=10
11
 
 
 IHP HBTs 
K
R
 [
c
m
A
-1
s-
1
]
1000/T [K
-1
]
E
0
=0.24 eV
 Infineon HBTs
K
R
=K
R0
exp(-E
0
/k
B
T)
(a) (b)
2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4
10
-10
10
-9
10
-8  IFX
 IHP
 ST
 
 
D
H
 [
cm
2
s-
1
]
1000/T
j
 [K]
D
0
= 0.01 cm
2
s
-1
  
E
0
=0.48 eV
D
H
= D
0
exp(-E
0
/k
B
T
j
)
- 17 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging
Conclusion
• A new physical and accurate aging compact model implementation for modern SiGe
HBTs based on
o the reaction-diffusion theory of hot-carrier degradation 
o a differential form of Fick’s law of diffusion. 
• The model implementation, although complex compared to its predecessor while 
employing additional transistor nodes in simulation, ensures invariance in time of the 
degradation characteristics. 
• The aging model has been compared with long-term aging tests on various SiGe HBT 
technologies, yielding very good agreement thus confirming its accuracy and versatility. 
• The proposed model formulation can easily be co-integrated with existing circuit 
design framework. 
• With its strong physical basis, the proposed model can prove to be indispensable for 
ensuring stable circuit operation close to the SOA of the technology, through prediction 
of reliability-aware circuit architectures. 
The research leading to these results has received funding from the European Commission's
ECSEL Joint Undertaking under grant agreement n° 737454 - project TARANTO - and the
respective Public Authorities of France, Austria, Germany, Greece, Italy and Belgium.
Thank you
- 18 -WS-01 - Recent advances in SiGe BiCMOS: technologies, modelling and circuits for 5G, radar and imaging


Advances in Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating conditions for reliability-aware circuit design

https://hal.archives-ouvertes.fr/hal-02386290/file/EuMW-2019_WS01_Talk_6_MANEUX.pdf

Advances in Aging Compact Model for Hot Carrier Degradation in SiGe HBTs under Dynamic Operating conditions for reliability-aware circuit design

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