advances in aging compact model for hot carrier ... · •for power performances, designers require...

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

[email protected]

WS-01 Recent advances in SiGe BiCMOS: technologies, modelling & circuits for 5G, radar & imaging

mailto:[email protected]

- 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


• 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


• 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.


• 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.


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


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


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


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.


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.


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


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)


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


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)


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


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)


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


advances in aging compact model for hot carrier ... · •for power performances, designers require...

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