Determination of the collector resistance R CX of bipolar transistor

STMicroelectronics

Determination of the collector resistance RCX of bipolar transistor

N. Kauffmann, C. Raya, F. Pourchon, S. Ortolland, D. Celi

5th European HICUM Workshop

N. Kauffmann - 5th European HICUM Workshop 2/236/6/2005

Outline

HICUM Collector Resistance RCX

Sinker and contact resistance

Buried layer resistance

Practical Implementation

Conclusion


HICUM main parameters

Emitter (N+)

Buried layer (N+)

Ep

ita

xy

(N

) Base (P+)

Substrate (P)

Sin

ke

r (N

+)

PW

EL

L (

P+

)

B CE S

CSU

RSU

QJS

S’

ISCISC

QDS

RE

RCX

RBX

CBCX1

CE0X

B’’

RBI

CRBI

IBET

IBEP

IBCI

QJEP

CBCX2

TJ

CTH RTHP

IAVL

C’

E’

ITB’

QDC

QDC

IBCI QJCI

IBEI QJEI


RCX: HICUM External Collector ResistanceRCX is a 3D resistance, which includes

- Sinker and Contact resistance- Buried layer resistance only (but not epi resistance)

RCX is an important parameter:

- Set the internal Collector voltage (C’ node)

- Affect the extraction of the highly critical F and all high injection model

parameters

Main issues: - Difficult to extract. No efficient method so far

- Poor RCX extraction makes HICUM model not scalable

Objective:

- Determine a scalable expression for RCX


Proposed solution for a scalable RCX

C

RSK

RBL

E

RCX is divided in two components: RCX = RBL+ RSK

- RSK (sinker + contact resistance) is extracted using test structures

- RBL (buried layer resistance) is extracted / obtained from analytical formulas

The buried layer sheet resistance is uniform: RBL = rBL Rsq

- Rsq (buried layer sheet resistance) is extracted from test structures

- rBL is computed analytically, function of the transistor geometry

V = Cst

V = CstBuried layer (top view) Transistor (cross section)

IT

IT


Outline





Conclusion


Test structure: Buried layer with 4 sinker wells ( A B C D ) of dimensions LSK × WSK

- RBL = VBC / IAD

- RSK = [ VBC/IBC –(1 – WSK/ WBC) × RBL] / 2

New test structure will use real transistors with 2 separate collector contacts

RSK - Sinker Resistance

D

RSK

RBL

Test structure (top view) Test structure (cross section)

A B C D

RSK

WBC

LSK

A B C

WSK

RSK RSK

LBL


Multi-geometry extraction

- RBL = 22.24 × WBC / (LBL - 1.00) Rsq = 22.4

- RSK = 19.39 / [WSK × (LSK + 0.28)] SK = 19.39 m2

Fit requires effective Sinker and buried layer dimensions

RSK - Sinker Resistance1

/ R

BL

LBL = LSK + 0.8 m LSK

1 /

RS

K


Outline





Conclusion


RBL - Buried Layer Resistance7 contact configurations investigated, any number NE of emitter stripes

Emitter stripes parallel to contacts

Emitter stripes perpendicular to contacts

Surrounding and U-Shaped collectors


RBL - Principle and main assumptions:Main assumptions:

- The collector current IC is uniformly distributed among the NE emitter stripes

- The current density is assumed to be constant within each stripe

- Each sinker is replaced by a reference plan of constant voltage

- The buried layer sheet resistance is assumed to be constant

Power dissipation approach:

2C

CBL I

PR dxdyVV

IRR

BL

BL

BL

BL

L

L

W

WYX

CsqBL

2

2

2

2

22

22

1

- WBL, LBL : Buried layer dimensions

- PC : Power dissipated in the buried layer

- V(x,y) Voltage within the buried layer

- V(x,y) is obtained by solving Poisson Equation in the Fourier Space


RBL - Formula (1/3)

BLBLnm

BLBL

nY

mX

EEE

Csq

L

yn

W

xm

Ln

Wm

HH

LWN

IRyxV

12cos

2cos

)12(2),(

,

2

2

2

22

)()(),( yHxHLWN

IRyxV YX

EEE

Csq

Example : Buried layer with 2 perpendicular contacts (blue)

Hm and Hn are the Fourier coefficients of H(x) and H(y)

Equation and solution for V(x,y)

NE = 3 Stripes

WE, LE = 0.2×0.8 um2

HX(x)

HY(y)


RBL - Formula (2/3)Example : Buried layer with 2 perpendicular contacts (blue)

Gm and Gn are the Fourier coefficients of G(x) and G(y)

Solution for RBL

nm

BLBL

nY

mX

EEE

sqBL

L

n

W

m

GG

LWN

RR

,

2

2

2

2

2

)12(2

1

2

NE = 3 Stripes

WE, LE = 0.2×0.8 um2

GY(y)

GX(x)


RBL - Formula (3/3)Example : Buried layer with 2 perpendicular contacts (blue)

NE = 3 Stripes

WE, LE = 0.2×0.8 um2

),

2(

202

2

BL

E

BL

BL

m

mX

EEE

BLBL L

L

W

LmK

m

G

LWN

WLS

Srrr YXBL

BL

E

BLY W

L

W

Lr

12

1

2

1 1

EBLE

IXXIEXXXXEX LWN

WWWWNWWWWNr

8

))(1()(2 2222

2

WX2WX

WI

L1

L1/ WBL

L1/ WBL

(LE/ WBL)/12

rX

rY

mm

mmmK

cosh

21sinhsinh),(

LBL

WBL


RBL – Comparison with numerical results

M. Schröter: DEVICE, User’s Guide to version 1.8 – July 2004

# terms RBL/ Rsq Error (%)

0 0.212 60

1 0.212 60

2 0.142 6.96

5 0.139 5.08

10 0.133 0.72

25 0.132 0.08

50 0.132 0

# terms RBL/ Rsq Error (%)

0 0.223 0.4

1 0.223 0.4

2 0.222 0.03

5 0.222 0.02

10 0.222 0

25 0.222 0

50 0.222 0

WE, LE = 0.2×0.8 um2

WE, LE = 0.2×10 um2

NE = 3

NE = 3


RBL – Results (Potential V)

NE = 3 Stripes

WE, LE = 0.2×0.8 um2

NE = 3 Stripes

WE, LE = 0.2×10 um2

2 perpendicular contacts



RBL – Results (Current)

NE = 3 Stripes

WE, LE = 0.2×0.8 um2

NE = 3 Stripes

WE, LE = 0.2×10 um2




RBL – Close-form approximations

Three approximations of the Kernel K: [Complex, Basic and intermediate] vs. exact Fourier series

21

0

)(1

)(),(

mm C

CK

Kernel Simplification:

3 levels of approximation:

Basic (WBL >> LBL only )

Interm. (WBL >> LBL & WBL << LBL)

Complex (1st, 2nd term exact)


Outline





Conclusion


RBL : Matlab Form

Contact configuration

Input geometry

RBL from Fourier

Display Features

DEVICE

Main Window


RSK , Rsq : ICCAP Toolkit

Load Files

Single extraction

Process Data

Multi-extraction

Statistics


Outline





Conclusion


Conclusion

Scalable RCX available using both extraction and analytical methods

- RSK Rsq, resistances are extracted from test structure

- RBL computed from analytical formulas for 7 contact configurations

Practical implementation with Matlab and ICCAP- New, more accurate test structures coming soon

- Formulas to be implemented in model libraries for full extraction and validation

Still, many assumptions need to be carefully checked:

- 3D RCX divided into 2D RBL and RSK

- Approximated boundary conditions with constant voltage- Uniform current injection between stripes, spatially uniform current

- Power dissipation approach: effect of current crowding

Determination of the collector resistance R CX of bipolar transistor

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