a self consistent joint extraction of 0 and rcx for hicum 6th european hicum workshop 12-13 june...
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A Self Consistent Joint Extraction of 0 and RCX
for HICUM6th European Hicum Workshop
12-13 June 05, ATMEL in Heilbronn
Zoltan Huszka austriamicrosystems AG
Purpose
• Proposal for a new 0 & RCX extraction
• Demonstration of the results
• Lowlights and Highlights
Outline
• Former RCX extraction methods
• Overview of the existing 0 extraction methods
• Theory of joint extraction for both parameters
• Extraction procedure
• Extraction results
• Summary
A Few Known RCX Extraction Methods
• Forced beta (Logan_1971)
• Isub (Berkner_1994)
• Solution of Parasitic pnp (Paasschens_2001)
• Special test structures (Schroeter_1991)
• Modified forced beta (Wu_2004)
• 2D numerical calculations (Kaufmann_ 2005)
• Corrected Inverse FT vs. VT/Ic (Schroeter_1991)
• Refined Inverse FT vs. VT/Ic (Ardouin_2001)
• Inverse FT vs. 1/gm (Malorny_2002)
• 3-variate linear regression (Fregonese_2006)
0 Extraction Methods
Existing Concept of 0 Extraction
T
cjcxjc
jcxjcBE
Tf V
IgmCCRERCX
gm
CCC :ionapproximat);()(
1
0 is the zero intercept for infinite Ic
• Key model parameters must be formerly known• Correct magnitude of RCX is critical• Internal collector time constant is omitted• The formula is approximative only
A Novel Concept
rbx rbi rc i rcxcjc
cjep
rpicpi
ro
re
cjcp
rs
gm*vbeivbei
1
3
2
34
B C
E E
• Extract intrinsic FT of block#1 with nonzero rci
• Apply result to HICUM
Block Transformations (1)
Unilateralized (UL) two-port parameters:
22
21
11
2121
1111
1221211212212112
~
~
~
~~~1~
~~~~
z
z
y
yh
yh
zzzzzzyyyyyy iiiiiiii
Consequently: )2(21
)3(21
)2(11
)3(11
~~~~ yyyy
With :
Dividing :
)1()1()1()1(
)1(21)2(
21)1()1(
)1()1(11)2(
11
~~~
YZYZYZ
Y
gmyy
rciyy b
bb
b0)1(12 by
)1(1)1(
~1
)1(21
)1(22
)1(11
)1()1(11
)3(21
rcicjcjhgm
yrciy
gm
rciy
h b
bb
b
Y
)1(1
~1
)1(21
)3(21
rcicjcjhh bb
Block Transformations (2)
Starting from the outside:
RELATION OF RAW AND INTRINSIC UL BETA
)4(12
)4(21
)3(12
)3(22
)4(12
)4(21
)4(12
)4(22
)4(21
~1
bb
bb
bb
bb
b zz
RCXzz
zz
zz
h
)4(
21)3(
21)4(
21~~
1~
1
bbb z
RCX
hh
)4(21
)1(21
)1(21
)4(21
~1
~1
bbbb z
RCX
h
rcicjcj
hh
The intrinsic transistor has a single pole ac beta:
)1()1()1(021
)1(21
111
TTbb
jjhh
Determining RCX
RCX can be expressed from the first equation
)4(21
)1(2
)4(21
)4(21
)1()4(21
~1
1~1
~11
~1
bTb
bTb
zRCX
cjcrci
h
zRCXcjcrci
h
)4(21
)1(21
)1(21
)4(21
~1
~1
bbbb z
RCX
h
rcicjcj
hh
)4(21
)1()4(21
~11
1~
11
b
Tb
z
cjcrcih
RCX
Unknown in numerator will be obtained by regression
Determining the Time Constants (1)
Canceling RCX yields the regression equation
)4(21
)4(21
)4(21
)4(21
)4(21
)4(21
~1
~1
~1
~1
~1
~1
b
b
b
bbb
z
zxxrf
z
zzconj
hyyrf
with variables
xxrfcjcrci
cjcrciyyrfTT
)1()1(
1
The zero intercept allows for the computation of RCX
Determining the Time Constants (2)
can be computed by deembedding raw data with the known RCX. The coefficients with the
time constants are obtained by regression from
)3(21
~eh
)1(2
)1(021
)3(21
)1()3()3(21
~1
~1
1~1
~11
Tee
TTe
cjcrci
hh
cjcrcih
)1(TQuadratic for and then regression povides 0
cjcrci
gives correct transit time in full bias range
)3(21
~eh
Example: main regression
0 1 2 3 4 5 6 7
x 1011
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1x 10
-10
yyrf
[s]
xxrf [s]
f1dd06 meas.: tau1+tci & tau1*tci extraction: Vce=7.001V
Vbe= 0.750VVbe= 0.755VVbe= 0.760VVbe= 0.765VVbe= 0.770VVbe= 0.775VVbe= 0.780VVbe= 0.785VVbe= 0.790VVbe= 0.795VVbe= 0.800V
The high linearity is confirming the concept
Example: Averaging RCX
0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.820
100
200
300
400
500
600
Vbe [V]
RC
X [o
hms*
um]
f1ddo8 meas. RCX
RCX= 78ohms*um
Vce= 7.00VVce= 10.00V
0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.820
100
200
300
400
500
600
Vbe [V]R
CX
[ohm
s*um
]
f1dd24 meas. RCX
RCX= 496ohms*um
Vce= 7.00VVce= 10.00V
RCX of a short (Le=0.8um) and a long (Le=24um) device
Example: RCX from parasitic PNP
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.310
-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
VBC [V]
ISU
B [A
/um
]
Regressed ISUB : n221_0.8
ISP= 1.401e-17 NFP= 1.0000 IKP= 1.026e-05 RBX= 102.6 RCX= 60.4
IS_FGPIS_RG
A perfect fit to measurements
Example: RF and DC Comparision
0 5 10 15 20 2550
100
150
200
250
300
350
400
450
500
Le [um]
RC
X_R
F, R
CX
_DC
[ohm
s*um
]
RCX extracted by RF and DC, on double collector, single base transistors
RCX_RFRBX_DC
Only a part of RCX is in the Isub current path
The difference may be particularly critical for HICUM!
Example: Time constants (1)
0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.820.8
1
1.2
1.4
1.6
1.8
2
2.2x 10
-11
tau1
+tci
[s]
Vbe [V]
f1dd06 meas. tau1+tci
Vce= 7.00VVce= 10.00V
Transit time of unilateralized Block#3
Example: Time constants (2)
0.75 0.755 0.76 0.765 0.77 0.775 0.784
6
8
10
12
14
16
18
(1
) , rci
*cjc
[ps]
Vbe [V]
f1ddu6 meas. transit time components (Vce= 7.00V)
(1)
rci*cjc
Intrinsic and collector time constants from quadratic
Example: Extraction of 0
0 500 1000 15000
5
10
15
20
25
Vt/Ic [ohms*um]
1/
(1) , 1
/(4
) [ps]
f1ddu6 meas. low current transit times (Vce= 7.00V)
0(1)= 0.79ps
0(4)= 7.29ps
1/(1)
1/(4)
Raw and intrinsic low current transit times
Lowlights
• The method mines data from the full depth of the model: high quality low noise RF data is reqired
• The quadratic may provide complex roots at higher biases: not critical since a few points are enough for 0 regression
Highlights
• The method is unprecedented as to jointly extract RBX with the intrinsic low-bias time constant
• No former model parameters are needed
• Self-consistency is insured by using one single data
• HICUM preference is met by extracting critical parameters from RF measurements
• The firm theoretical basis may provide confidence in customers and modeling engineers
Correct transit times in full bias range from one single raw s-parameter set!
Suggestion to the Model Developers
• Revive the discussion of the low-bias collector time constant in the model documentation
• Advise a proper way how to merge the collector time-constant in the present model structure
Acknowledgement
The author is grateful to
for the careful measurement of the samples and designing the setup & codes for a noiseless substrate
current acquisition.
Dr. Bishwanat Senapati