Determination of the collector
resistance RCX of bipolar transistor
5th European HICUM Workshop
N. Kauffmann, C. Raya, F. Pourchon, S. Ortolland, D. Celi
STMicroelectronics
Outline
HICUM Collector Resistance RCX
Sinker and contact resistance
Buried layer resistance
Practical Implementation
Conclusion
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
2/23
HICUM main parameters
B
E
C
S
RE
Emitter (N+)
E’
X
IBET
X
B’’ QJEP IBEP
Q CBCX2 IBCI
B’
DS
Epitaxy (N)
CBCX
CRBI
IBEI QJEI
IBCI QJCI
Base (P+)
1
IAVL
Buried layer (N+)
ISC
QJS
RC
X
DTJ
S’
CTH
QDC
C’
ISC
P
IT
PWELL (P+)
RB
QDC
RBI
Sinker (N+)
CE0
Substrate (P)
RSU
RTH
CSU
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
3/23
RCX: HICUM External Collector Resistance
RCX 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 tF 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:
-
6/6/2005
Determine a scalable expression for RCX
N. Kauffmann - 5th European HICUM Workshop
4/23
Proposed solution for a scalable RCX
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
C
E
V = Cst
RSK
IT
IT
RBL
V = Cst
Buried layer (top view)
6/6/2005
Transistor (cross section)
N. Kauffmann - 5th European HICUM Workshop
5/23
Outline
HICUM Collector Resistance RCX
Sinker and contact resistance
Buried layer resistance
Practical Implementation
Conclusion
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
6/23
RSK - Sinker Resistance
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
A
A
B
C
B
D
RSK
LBL
D
C
RSK
RSK
RSK
WBC
LSK
RBL
WSK
Test structure (top view)
6/6/2005
Test structure (cross section)
N. Kauffmann - 5th European HICUM Workshop
7/23
RSK - Sinker Resistance
Multi-geometry extraction
- RBL = 22.24 × WBC / (LBL - 1.00)
- RSK = 19.39 / [WSK × (LSK + 0.28)]
Rsq
rSK
= 22.4 W
= 19.39 W mm2
1 / RBL
1 / RSK
Fit requires effective Sinker and buried layer dimensions
LBL = LSK + 0.8 mm
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
LSK
8/23
Outline
HICUM Collector Resistance RCX
Sinker and contact resistance
Buried layer resistance
Practical Implementation
Conclusion
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
9/23
RBL - Buried Layer Resistance
7 contact configurations investigated, any number NE of emitter stripes
Emitter stripes parallel to contacts
Emitter stripes perpendicular to contacts
Surrounding and U-Shaped collectors
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
10/23
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:
RBL 
PC
I C2
RBL 
1
Rsq2 I C2
LBL
2
WBL
2
    V    V  dxdy
2
X

2
Y
LBL WBL

2
2
-
WBL, LBL :
PC :
V(x,y)
-
V(x,y) is obtained by solving Poisson Equation in the Fourier Space
6/6/2005
Buried layer dimensions
Power dissipated in the buried layer
Voltage within the buried layer
N. Kauffmann - 5th European HICUM Workshop
11/23
RBL - Formula (1/3)
HX(x)
Example : Buried layer with 2 perpendicular contacts (blue)
NE = 3 Stripes
WE, LE = 0.2×0.8 um2
HY(y)
Equation and solution for V(x,y)
DV ( x, y ) 
V ( x, y ) 
Rsq I C
N EWE LE
Rsq I C
 N EWE LE
2
 H X ( x)  H Y ( y )

m,n
 2mx 
 2n  1y 

cos

cos




 2m 2 (2n  1) 2 
 WBL 
 LBL 
 2 

2
W
L
BL
BL


H Xm  H Yn
Hm and Hn are the Fourier coefficients of H(x) and H(y)
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
12/23
RBL - Formula (2/3)
GX(x)
Example : Buried layer with 2 perpendicular contacts (blue)
NE = 3 Stripes
WE, LE = 0.2×0.8 um2
GY(y)
Solution for RBL
2
RBL
Rsq 

1
GXm  GYn


 
2   N EWE LE  m,n  2m2 (2n  1) 2 
 2 

L2BL 
 WBL
Gm and Gn are the Fourier coefficients of G(x) and G(y)
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
13/23
RBL - Formula (3/3)
rY
Example : Buried layer with 2 perpendicular contacts (blue)
NE = 3 Stripes
WBL
WX
L1/ WBL
(LE/ WBL)/12
WE, LE = 0.2×0.8 um2
WI
WX2
L1/ WBL
L1
LBL
rX
K ( m ,  ) 
rBL  rX  rY  S
rY 
sinh  m  sinh  m 1  2 
 m cosh  m
1 L1
1 LE


2 WBL 12 WBL
2 N E (WX2  WX2 2  WX WX 2 )  ( N E  1)(WI  WX 2  WX )WI
rX 
8 N EWBL  LE
2
 WBL

G Xm
m LBL LE
S  LBL 

K
(
,
)
 
2

N
W
L
2
W
L
m  0 2m 
E E E 
BL
BL

6/6/2005
N. Kauffmann - 5th European HICUM Workshop
14/23
RBL – Comparison with numerical results
WE, LE = 0.2×0.8 um2
NE = 3
# 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
WE, LE = 0.2×10 um2
NE = 3
# 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
M. Schröter: DEVICE, User’s Guide to version 1.8 – July 2004
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
15/23
RBL – Results (Potential V)
NE = 3 Stripes
WE, LE = 0.2×0.8 um2
2 perpendicular contacts
NE = 3 Stripes
WE, LE = 0.2×10 um2
2 perpendicular contacts
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
16/23
RBL – Results (Current)
NE = 3 Stripes
WE, LE = 0.2×0.8 um2
2 perpendicular contacts
NE = 3 Stripes
WE, LE = 0.2×10 um2
2 perpendicular contacts
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
17/23
RBL – Close-form approximations
Kernel Simplification:
C0 ( )
K ( m ,  ) 
1  C1 ( )   m2
3 levels of approximation:
Basic (WBL >> LBL only )
Interm. (WBL >> LBL & WBL << LBL)
Complex (1st, 2nd term exact)
Three approximations of the Kernel K: [Complex, Basic and intermediate] vs. exact Fourier series
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
18/23
Outline
HICUM Collector Resistance RCX
Sinker and contact resistance
Buried layer resistance
Practical Implementation
Conclusion
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
19/23
RBL : Matlab Form
Contact configuration
Input geometry
Main Window
RBL from Fourier
Display Features
DEVICE
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
20/23
RSK , Rsq : ICCAP Toolkit
Load Files
Single extraction
Process Data
Multi-extraction
Statistics
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
21/23
Outline
HICUM Collector Resistance RCX
Sinker and contact resistance
Buried layer resistance
Practical Implementation
Conclusion
6/6/2005
N. Kauffmann - 5th European HICUM Workshop
22/23
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
-
6/6/2005
Power dissipation approach: effect of current crowding
N. Kauffmann - 5th European HICUM Workshop
23/23