stmicroelectronics computing transit time components from a regional analysis: a practical...

STMicroelectronics

Computing transit time components from a regional analysis:

A practical implementation

6th European HICUM WorkshopJune 12,13, 2006 - Heilbronn

N. Kauffmann

N.KAUFFMANN - 6th European HICUM Workshop, Heilbronn 2006 2

The regional approach

• Bipolar transistor divided into neutral (WE , WB , WC) and SCR (WBE , WBC ) regions

Detection of an hole injection layer (WI) in the collector

• Decomposition based on DC and quasi-static analysis, in 1D only

• Transit time components computed from the above decomposition: TF = TE + TBE + TB + TBC + TC

Importance of the regional approach

• Educational purpose, better understanding of bipolar physics

• Device optimization

• First order model parameters extraction

Practical Test

• Database of 1D NPN SiGe simulations

• DEVICE Simulator (Drift-Diffusion only)

• Regional data computed and checked for all members of the database

• Note : 1D simulation only available so far (no 2D/3D effects) and S Node not Available

Introduction


Introduction

0 0.03 0.08 0.18 0.28 0.38 0.48 0.58 0.68 0.810

15

1016

1017

1018

1019

1020

1021

X, m

NA

-ND

, cm

-3

Doping Profile

0

10

20

30

40

50

Ge

Con

cent

ratio

n, %

0 10 20 30 40 50 60 70 80 90 10010

16

1017

1018

1019

1020

1021

X, nm

NA

-ND

, cm

-3

Doping and Ge Profile

WC

WEPI WTBL

WB

WE

NC

NEPI

NB

NE

Region xi (nm) xi+1 (nm) N (cm-3)

E 0 30 2.1020

B 30 80 2.1019

C-EPI 80 580 2.1016

C-TBL 580 680

C-BL 680 800 2.1019

Simulation database : validation of the regional approach

2 case studies :

Low / Medium injection : VBE = 0.8 V, VBC = 0 V

High injection : VBE = 0.9 V, VBC = 0 V

Examples of computed regional data used in these slides:

• NEPI = { 1.1016, 2.1016, 5.1016, 1.1017 }


Introduction

Regional approach

Examples

Conclusion

Outline


Regional Approach - Definitions1. Transit times

• TF : Forward transit time (BC Short)

• TR : Reverse transit time (BE Short)

• TFF : Total transit time from CE Short, = 1 / (2FT)

2. Transit time components

• TE : Transit time of minority carriers in the neutral emitter

• TBE : Transit time of minority carriers in the BE SCR

• TB : Transit time of minority carriers in the neutral base and BC SCR (electrons)

• TC : Transit time of minority carriers in the neutral collector and BC SCR (holes)

• TBC : Recharging time of the BC SCR (transport of majority carriers – electrons)

3. Charges

• Qm : Minority charge Qm = { QN if |QN| < |QP| , QP otherwise }

• QC : Uncompensated charge QC = QP - QN


Regional Approach - Overview

DC Analysis

QUAS-E Analysis

gmF, dn(x), dp(x)

QUAS-B Analysis

gm, dn(x), dp(x)

QUAS-C Analysis

gmR, dn(x), dp(x)

Regional analysis : Qm = min(qp,qn), Qc = (qp-qn)

E XMIN XMAX QmE QcE

B XMIN XMAX QmB QcB

C XMIN XMAX QmC QcC

Regional analysis : Qm = min(qp,qn), Qc = (qp-qn)

E XMIN XMAX QmE QcE

B XMIN XMAX QmB QcB

C XMIN XMAX QmC QcC

BE SCR analysis :

BE XMIN XMAX QmEB QmBE

BC SCR analysis :

BC XMIN XMAX QmBC QmCB

WE, WBE WC, WBC , WIWB

TF = (QmE+QmB+QmC+QcC) / gmF

TE = (QmE-QmEB) / gmF

TBE = (QmEB+QmBE) / gmF

TBC = QcC / gmF

TB = (QmB-QmBE) / gmF

TC = QmC / gmF

CBE = QcE

CBC = QcC

TR = (Qm+QcE) / gmR

dqN(x), dqP(x)

dqN(x), dqP(x)

dqN(x), dqP(x)

TFF = dqP / gm

FT = 1 / 2TFF

NA(x), ND(x)

N(x), P(x) QN(x), QP(x) QP = QP(x)

1i

i

x

x

n dndQ

1i

i

x

x

p dpdQ

Forward

Reverse

CE Short


1. Quasi-static analysis: dVE = -1 (dVBE = 1 ) induces :

• Change in charge density : dQp and dQn

• Change in current (Forward transconductance) : gmF = 7.0259 mS / um2

Regional Approach (Low injection)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-100

0

100

200

300

400

500

600

X, um

min

(dN

,dP

), f

C/u

m3

Minority Carrier [Entire structure]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-2000

-1500

-1000

-500

0

500

1000

1500

X, um

dP-d

N,

fC/u

m3

Compensated Carrier [Entire structure]

• Minority charge dQm = min (dQn , dQp ) ,

• Uncompensated charge dQC = dQp - dQn

E B C E B C

un


2. Regional analysis : transistor divided in elementary regions [x i xi+1] where dQN>dQP or dQN>dQP

• Decomposition in minority (Qm) and uncompensated (QC) carriers

• Use of DC metallurgical junctions to separate the 3 regions


Region Maj xi (um) xi+1 (um) dQp (fC) dQn (fC) dQm (fC) dQC (fC)

1 (E) N - 0 0.0309 2.0543 11.5544 2.0543 -9.5001

2 (B) P + 0.0309 0.0849 30.5211 8.5579 8.5579 21.9633

3 (C) N - 0.0849 0.3753 0.2600 16.7993 0.2600 -16.5392

3 (C) N + 0.3753 0.8000 0.0000 -4.0566 0.0000 4.0566


3. BE Space-Charge-Region analysis :

• From quasi-static analysis [ dVE = -1 ]

• Limits defined at 50 % of the transferred uncompensated charge


0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-2000

-1500

-1000

-500

0

500

1000

1500

X, um

dP-d

N,

fC/u

m3

Compensated Carrier [BE SCR]

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080

100

200

300

400

500

600

X, um

min

(dN

,dP

), f

C/u

m3

Minority Carrier [BE SCR]

Region xi (um) xi+1 (um) QmEB (fC) QmBE (fC)

BE 0.0257 0.0361 1.2578 1.6206

50%Qn

50%(Qp-QpC)

50%Qn

QpC

50%(Qp-QpC)

QmBEQmEB

E B E B


4. BC Space-Charge-Region analysis :

• From quasi-static analysis [ dVC = -1 ]



0.1 0.2 0.3 0.4 0.5 0.6 0.7-5

0

5

10

15

20

25

30

35

X, um

dP-d

N,

fC/u

m3

Compensated Carrier [BC SCR]

0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

X, um

min

(dN

,dP

), f

C/u

m3

Minority Carrier [BC SCR]

Region xi (um) xi+1 (um) QmBC (fC) QmCB (fC)

BC 0.0729 0.2928 0.0206 0.0374 0.0729 < 0.0800 : No injection layer

B C B C



C = dQC / dVBE

= dQ / gmF

5. Computations :

Region xi (um) xi+1 (um) Qm (fC) QC (fC)

E 0 0.0309 2.0543 9.5001

B 0.0309 0.0849 8.5579 21.9633

C 0.0849 0.800 0.2600 12.4826


BE 0.0257 0.0361 1.2578 1.6206

Region xi (um) xi+1 (um) QmBC (fC) QmCB (fC)

BC 0.0729 0.2928 0.0206 0.0374

Region xi (um) xi+1 (um) Qm (fC) QC (fC) ps

E 0.0000 0.0257 0.7965 0.1134

BE 0.0257 0.0361 2.8784 0.4097

B 0.0361 0.0729 6.9373 0.9874

BC 0.0729 0.2928 12.4826 1.7767

C 0.2928 0.8000 0.2600 0.0370

Total 0.0000 0.8000 10.8722 12.4826 3.3241

WE (um) WBE (um) WB (um) WI (um) WBC(um) WC (um)

0.0257 0.0105 0.0368 0 0.2199 0.5072

Transit times

Widths

CBE = 9.5 fF /um2


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-1

0

1

2

3

4

5x 10

4

X, um

min

(dN

,dP

), f

C/u

m3

Minority Carrier [Entire structure]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-1500

-1000

-500

0

500

1000

X, um

dP-d

N,

fC/u

m3

Compensated Carrier [Entire structure]

1. Quasi-static analysis: dVE = -1 (dVBE = 1 ) induces :

• Change in charge density : dQp and dQn

• Change in current (Forward transconductance) : gmF = 12.4907 mS / um2

Regional Approach (High injection)

• Minority charge dQm = min (dQn , dQp ) ,

• Uncompensated charge dQC = dQp - dQn

E B C E B C


2. Regional analysis : transistor divided in elementary regions [x i xi+1] where dQN>dQP or dQN>dQP

• Decomposition in minority (Qm) and uncompensated (QC) carriers

• Use of DC metallurgical junctions to separate the 3 regions


Region Maj xi (um) xi+1 (um) dQp (fC) dQn (fC) dQm (fC) dQC (fC)

1 (E) N - 0 0.0304 49.1264 56.6213 49.1264 -7.4949

2 (B) P + 0.0304 0.0591 455.4927 445.7501 445.7501 9.7426

2 (B) N - 0.0591 0.0776 548.6740 551.3355 548.6740 -2.6615

2 (B) P + 0.0776 0.0854 56.5979 54.3917 54.3917 2.2062

3 (C) N - 0.0854 0.0991 19.5639 21.7840 19.5639 -2.2201

3 (C) P+ 0.0091 0.4731 295.3405 289.3333 289.3333 6.0073

3 (C) N- 0.4731 0.6150 2.5532 17.3802 2.5532 -14.8270

3 (C) N- 0.6150 0.6178 -0.0000 0.2817 -0.0000 -0.2817

3 (C) N + 0.6178 0.8000 -0.0000 -9.4951 -0.0000 9.4951

Injection layer


0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.080

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

4

X, um

min

(dN

,dP

), f

C/u

m3

Minority Carrier [BE SCR]

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-1500

-1000

-500

0

500

1000

X, um

dP-d

N,

fC/u

m3

Uncompensated Carrier [BE SCR]

3. BE Space-Charge-Region analysis :

• From quasi-static analysis [ dVE = -1 ]




BE 0.0246 0.0356 17.9075 21.1445

50%Qn

50%(Qp-QpC)

50%Qn QpC

50%(Qp-QpC)

QmBEQmEB

E B E B


0.1 0.2 0.3 0.4 0.5 0.6 0.7-5

0

5

10

15

20

25

30

35

40

X, um

min

(dN

,dP

), f

C/u

m3

Minority Carrier [BC SCR]

0.1 0.2 0.3 0.4 0.5 0.6 0.7-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

X, um

dP-d

N,

fC/u

m3

Uncompensated Carrier [BC SCR]

4. BC Space-Charge-Region analysis :

• From quasi-static analysis [ dVC = -1 ]



Region xi (um) xi+1 (um) QmBC (fC)

BC 0.4597 0.6297 0.0749 0.4597 > 0.0800 : Injection layer

B C B C

QmBC



C = dQC / dVBE

= dQ / gmF

5. Computations :

Region xi (um) xi+1 (um) Qm (fC) QC (fC)

E 0 0.0304 49.1 7.4949

B 0.0304 0.0854 1048.8 9.2872

C 0.0854 0.8000 311.5 1.8264


BE 0.0246 0.0356 17.9075 21.1445

Region xi (um) xi+1 (um) QmBC (fC)

BC 0.4597 0.6297 0.0749

Region xi (um) xi+1 (um) Qm (fC) QC (fC) ps

E 0.0000 0.0246 31.2 2.50

BE 0.0246 0.0356 39.1 3.13

B 0.0356 0.0800 1027.4 82.49

BC 0.4597 0.6297 1.8264 0.15

C+WI 0.0800 0.8000 311.5 25.42

Total 0.0000 0.8000 10.8722 1.8264 113.68

WE (um) WBE (um) WB (um) WI (um) WBC(um) WC (um)

0.0246 0.0111 0.0444 0.3796 0.2199 0.5072

Transit times

Widths

CBE = 7.49 fF /um2


Introduction

Regional approach

Examples

Conclusion

Outline


WBE vs. VBE

• Plot of WBE vs. VBE in the Off (Left) and Forward (Right) region

-1 -0.75 -0.5 -0.25 0 0.25 0.515

16

17

18

19

20

21

22

23

24

25

WB

E [nm

]

VBE

[V]

WBE

vs. VBE

[OFF Region, VCE

= 0]

WBE

oSi

/ CBE

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

40

45

50

55

60

WB

E [nm

]

VBE

[V]

WBE

vs. VBE

[Forward Region, VBC

= 0]

W

BE

oSi

/ CBE

WBE is also compared to the theoretical width of the CBE capacitance assuming it is a pure plate capacitance.

Conclusion : Very good match when operating at low current injection. However, either WBE or CBE are underestimated in the high injection region.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WB

C

[um

]

WBC vs. IC

WBC, NEPI = 1e+016 , VBC = -2

WBC, NEPI = 2e+016 , VBC = -2

WBC, NEPI = 5e+016 , VBC = -2

WBC, NEPI = 1e+017 , VBC = -2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.810

14

1015

1016

1017

1018

1019

1020

1021

1022

x, um

D =

|NA

- N

D| [

cm-3

]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

5

x, um

Ele

ctric

Fie

ld,

V/c

m

Electric Field

0.2 um

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.810

14

1015

1016

1017

1018

1019

1020

1021

1022

x, um

D =

|NA

- N

D| [

cm-3

]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

5

x, um

Ele

ctric

Fie

ld,

V/c

m

Electric Field

0.28 um

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WB

C

[um

]

WBC vs. IC

WBC, NEPI = 1e+016 , VBC = -2

WBC, NEPI = 2e+016 , VBC = -2

WBC, NEPI = 5e+016 , VBC = -2

WBC, NEPI = 1e+017 , VBC = -2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.810

14

1015

1016

1017

1018

1019

1020

1021

1022

x, um

D =

|NA

- N

D| [

cm-3

]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

5

x, um

Ele

ctric

Fie

ld,

V/c

m

Electric Field

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WB

C

[um

]

WBC vs. IC

WBC, NEPI = 1e+016 , VBC = -2

WBC, NEPI = 2e+016 , VBC = -2

WBC, NEPI = 5e+016 , VBC = -2

WBC, NEPI = 1e+017 , VBC = -2

0.43 um

WBC vs. IC @ VBC = -2 V

• Plot of WBC vs. IC for NEPI = { 1.1016, 2.1016, 5.1016, 1.1017 }

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WB

C

[um

]

WBC vs. IC

WBC, NEPI = 1e+016 , VBC = -2

WBC, NEPI = 2e+016 , VBC = -2

WBC, NEPI = 5e+016 , VBC = -2

WBC, NEPI = 1e+017 , VBC = -2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.810

14

1015

1016

1017

1018

1019

1020

1021

1022

x, um

D =

|NA

- N

D| [

cm-3

]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

5

x, um

Ele

ctric

Fie

ld,

V/c

m

Electric Field

0.54 um

The simulated DC electric field of the current operating point (red dot) is plotted in the right figure, allowing a crude evaluation of the BC SCR width. WBC appears to be very close to the width of the BC SCR defined by the electric field. The maximum value of WBC is 0.55 mm, close from the theory (WBC≈ WEPI)

Note that when the doping concentration of the epitaxy layer is very low, WBC does not enter the buried layer and its value is therefore shorter than what is estimated by the electric field.


WBC vs. IC @ VBC = -0.5 V


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WB

C

[um

]

WBC vs. IC

WBC, NEPI = 1e+016 , VBC = -0.5

WBC, NEPI = 2e+016 , VBC = -0.5

WBC, NEPI = 5e+016 , VBC = -0.5

WBC, NEPI = 1e+017 , VBC = -0.5

0.1 0.2 0.3 0.4 0.5 0.6 0.7-15

-10

-5

0

5

10

15

20

25

X, um

dP-d

N,

fC/u

m3

Uncompensated Carriers [BC SCR] - VBE = 0.755 V

0.1 0.2 0.3 0.4 0.5 0.6 0.7-15

-10

-5

0

5

10

15

20

25

X, um

dP-d

N,

fC/u

m3


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WB

C

[um

]

WBC vs. IC

WBC, NEPI = 1e+016 , VBC = -0.5

WBC, NEPI = 2e+016 , VBC = -0.5

WBC, NEPI = 5e+016 , VBC = -0.5

WBC, NEPI = 1e+017 , VBC = -0.5

0.1 0.2 0.3 0.4 0.5 0.6 0.7-15

-10

-5

0

5

10

15

20

25

X, um

dP-d

N,

fC/u

m3


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WB

C

[um

]

WBC vs. IC

WBC, NEPI = 1e+016 , VBC = -0.5

WBC, NEPI = 2e+016 , VBC = -0.5

WBC, NEPI = 5e+016 , VBC = -0.5

WBC, NEPI = 1e+017 , VBC = -0.5

0.1 0.2 0.3 0.4 0.5 0.6 0.7-15

-10

-5

0

5

10

15

20

25

X, um

dP-d

N,

fC/u

m3


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WB

C

[um

]

WBC vs. IC

WBC, NEPI = 1e+016 , VBC = -0.5

WBC, NEPI = 2e+016 , VBC = -0.5

WBC, NEPI = 5e+016 , VBC = -0.5

WBC, NEPI = 1e+017 , VBC = -0.5

0.1 0.2 0.3 0.4 0.5 0.6 0.7-15

-10

-5

0

5

10

15

20

25

X, um

dP-d

N,

fC/u

m3


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WB

C

[um

]

WBC vs. IC

WBC, NEPI = 1e+016 , VBC = -0.5

WBC, NEPI = 2e+016 , VBC = -0.5

WBC, NEPI = 5e+016 , VBC = -0.5

WBC, NEPI = 1e+017 , VBC = -0.5

0.1 0.2 0.3 0.4 0.5 0.6 0.7-15

-10

-5

0

5

10

15

20

25

X, um

dP-d

N,

fC/u

m3


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WB

C

[um

]

WBC vs. IC

WBC, NEPI = 1e+016 , VBC = -0.5

WBC, NEPI = 2e+016 , VBC = -0.5

WBC, NEPI = 5e+016 , VBC = -0.5

WBC, NEPI = 1e+017 , VBC = -0.5

B C

At VBC = -0.5 V, WBC does not behave as expected by the theory, going down to a value close to 0 for some points or ‘glitches’. In the right figure, the uncompensated carriers of the BC region are plotted while going through one of this glitch (moving red dot) . At some point, the electronic charge in the BC SCR splits, generating two peaks at the boundaries of the epitaxy layer.

The splitting of the charge is most likely induced by the Ge concentration at the BC interface.


WBC vs. IC @ VBC = 0.4 V


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WB

C

[um

]

WBC vs. IC

WBC, NEPI = 1e+016 , VBC = 0.2

WBC, NEPI = 2e+016 , VBC = 0.2

WBC, NEPI = 5e+016 , VBC = 0.2

WBC, NEPI = 1e+017 , VBC = 0.2

0.1 0.2 0.3 0.4 0.5 0.6 0.7-40

-30

-20

-10

0

10

20

30

40

50

60

X, um

dP-d

N,

fC/u

m3


B C

0 0.05 0.1 0.15 0.2 0.25-40

-30

-20

-10

0

10

20

30

40

50

60

X, um

dP-d

N,

fC/u

m3


B C

At VBC = 0.4 V, the BC SCR must vanish as the transfer current increases (quasi-saturation region). As expected, WBC decreases with IC , going down to a small but non-zero value: 30 nm. In the right figure, the uncompensated carriers of the BC region are plotted at the minimum of WBC (red dot) . Both boundaries of the BC SCR are probably not optimal, due to the shape of the peaks


WI vs. IC

• Plot of WI vs. IC for NEPI = 1.1016 (left) & 1.1017 (right) and VBC = {-2V, -1V, -0.5V, 0V, 0.2V, 0.4V, 0.6V}

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WI

[um

]

WI vs. IC

WI, NEPI = 1e+016 , VBC = -2

WI, NEPI = 1e+016 , VBC = -1

WI, NEPI = 1e+016 , VBC = -0.5

WI, NEPI = 1e+016 , VBC = 0

WI, NEPI = 1e+016 , VBC = 0.2

WI, NEPI = 1e+016 , VBC = 0.4

WI, NEPI = 1e+016 , VBC = 0.6

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

IC [mA/um2]

WI

[um

]

WI vs. IC

WI, NEPI = 1e+017 , VBC = -2

WI, NEPI = 1e+017 , VBC = -1

WI, NEPI = 1e+017 , VBC = -0.5

WI, NEPI = 1e+017 , VBC = 0

WI, NEPI = 1e+017 , VBC = 0.2

WI, NEPI = 1e+017 , VBC = 0.4

WI, NEPI = 1e+017 , VBC = 0.6

The injection width WI behaves as expected: WI = 0 before the high-injection regime starts and then increases sharply up to a maximum value close to WEPI. When the doping of the epitaxy is high (right figure), the curves at VBC<0 are affected by the avalanche current.

The shape of the WI curves is strongly technology dependant, although it is only modeled by the HICUM parameter Ick (The HICUM parameter ahc is not supposed to have a physical meaning) .


Transit times

• Transit times vs. IC @ VBC = -0.5 V (Left) & VBC = 0.4 V (Right)

The transit-time components are plotted vs. IC for two different values of VBC and NEPI = 1.1016 cm-3. In both cases, TBC is the major contribution to TF at low injection due to the very wide BC SCR. TBE is entirely responsible of the increase in TF at very low injection but decreases sharply with IC. However, it remains greater than TE in the high injection region leading to a possible overestimation of WBE . As expected TB and TC become predominant at very high injection.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

10-2

10-1

100

101

102

IC [mA/m2]

T F, T E,

T BE,

T B,

T BC,

T C

[ps]

TF, T

E, T

BE, T

B, T

BC, T

C vs. I

C

TF, NEPI = 1e+016 , VBC = -0.5

TE, NEPI = 1e+016 , VBC = -0.5

TC, NEPI = 1e+016 , VBC = -0.5

TBE, NEPI = 1e+016 , VBC = -0.5

TBC, NEPI = 1e+016 , VBC = -0.5

TB, NEPI = 1e+016 , VBC = -0.5

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

10-2

10-1

100

101

102

IC [mA/m2]

T F, T E,

T BE,

T B,

T BC,

T C

[ps]

TF, T

E, T

BE, T

B, T

BC, T

C vs. I

C

TF, NEPI = 1e+016 , VBC = 0.4

TE, NEPI = 1e+016 , VBC = 0.4

TC, NEPI = 1e+016 , VBC = 0.4

TBE, NEPI = 1e+016 , VBC = 0.4

TBC, NEPI = 1e+016 , VBC = 0.4

TB, NEPI = 1e+016 , VBC = 0.4


Introduction

Regional approach

Examples

Conclusion

Outline


Conclusion 1. Regional Approach implementation

• Bipolar transistor structure divided in neutral and SCR regions using DC & quasi-static information

• Region assignment based on quasi-static data and DC metallurgical boundaries

• Definition of SCR Boundaries : 50% of the SCR quasi-static electron / hole charge displaced

• So far, no transit time component for BC SCR minority carriers – majority carriers only

2. Test & qualitative results

• Database of 1D TCAD simulations of NPN-SiGe transistors – DEVICE Simulator used (Drift/diffusion)

• Very smooth and robust results over the entire database

• Results physically consistent : Transit times, region widths behave as expected

3. Quantitative results

• Quasi-static charge distribution probably affected by Ge content leading to more complex peak structures

• Results are usually very good but in some cases, they may not be fully optimal.

• AC simulations required to validate the variations of the BE and BC capacitances with IC

4. Perspectives

• Extraction of a first order set of HICUM parameters

• 2D extension, S node

stmicroelectronics computing transit time components from a regional analysis: a practical...

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