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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
Hz]
0 5 10 15 200
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 60 700.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25t2
Stress 2
VBE
=0.88V
VCE
=1.5V
Stress 1
VBE
=0.88V
VCE
=2.5V
Measurements
HiCuM-AL V2
HiCuM-AL V1
Stress time [h]
I RE
PS [
fA]
Stress 1
VBE
=0.88V
VCE
=2.5V
t1
- 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
8x1010
1x1011
2x1011
3x1011
6x1011
Meas. @0sMeas. @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 =𝑑𝑁𝑇𝑑𝑡
= 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 (cm3s-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
gTgT
CT
NTT
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, valuesof 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 oxide𝐿 → ∞;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 = 𝑅1𝛼𝑅𝑛−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/μm2 and VCE = 3V, JC =1
mA/μm2, respectively)
10-1
100
101
102
103
10-16
10-15
10-14
10-13
P3 condition
I RE
pS [
A]
Aging Time [h]
Extracted
HiCuM-AL V2
P2 condition
0.5 0.6 0.7 0.8 0.9 1.010
-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
P2 condition
I C,
I B [
A]
VBE
[V]
Time=0, 1, 3, 7, 72, 1000 H
Ic
IB
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 [
mA
/µm
2]
305K310K
325K335K
350K 375K 400K
JE = -8mA/µm2
JE = -6mA/µm2
JE = -4mA/µm2
JE = -2mA/µm2
JE = -1mA/µm2
VCE [V]
10-1
100
101
102
10-1
100
101
102
103
Measurement
I B
(t)
= [
I B(t
) -
I B(0
)]/I
B(0
)
Aging Time [h]
HiCuM-AL V2
VBE
=0.6V
VBE
=0.5V
0.4 0.5 0.6 0.7 0.8 0.9 1.010
-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
VBE
[V]
I B, I C
[A
]
Ic
IB
Aging time=0, 1, 12, 48, 96, 144 h
Measurement
HiCuM-AL V2
JE,stress
= 8 mA/m2
VCB
=1.5V
0.2 x 5 m2
10-2
10-1
100
101
102
10-16
10-15
10-14
I RE
pS [
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 [
mA
/µm
2]
305K310K
325K335K 350K 375K 400K
JE = -12.0mA/µm2
JE = -6.00mA/µm2
JE = -1.20mA/µm2
JE = -0.60mA/µm2
JE = -0.12mA/µm2
VCE [V]
0
10-1
100
101
102
103
10-17
10-16
10-15
10-14
10-13
Extracted
JE,stress
=0.12 mA/m2
VCB
=2.5, 2.75, 3.25 V
HiCuM-AL V2
I RE
pS (
A)
Aging Time (h)
10-1
100
101
102
103
10-1
100
101
Aging Time [h]
(b)
Measurement
I B
(t)
=[
I B (
t)-
I B (
0)]
/I B
(0) HiCuM-AL V2
Extracted @VBE
=0.7V
@JE,stress
= 0.12 mA/µm²
@VCB,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
MM
Str
ess
Rec
over
y
I B
/IB
0[%
]
HiCuM-AL V2
Stress time [s]
Dynamic mixed-mode stress
MM stress: VCB
= 3V, IE= - 0.13 mA
Recovery: VCB
= 0V, IE= - 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 3.210
-5
10-4
10-3
10-1
100
101
@JE,stress
= 0.12 mA/m2
@JE,stress
= 12 mA/m2
KF [
s-1]
VCB
[V]
JE,stress
[mA/m2]
@VCB
=2.75V
2.2 2.4 2.6 2.8 3.0 3.2 3.410
6
107
108
109
1010
KR0
=1012
KR0
=1011
IHP HBTs
KR [
cm
A-1
s-1]
1000/T [K-1]
E0=0.24 eV
Infineon HBTs
KR=K
R0exp(-E
0/k
BT)
(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
DH
[cm
2s-1
]
1000/Tj [K]
D0= 0.01 cm
2s
-1
E0=0.48 eV
DH= D
0exp(-E
0/k
BT
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 SiGeHBTs based ono 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'sECSEL Joint Undertaking under grant agreement n° 737454 - project TARANTO - and therespective 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
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