a self consistent joint extraction of 0 and rcx for hicum 6th european hicum workshop 12-13 june...
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![Page 1: A Self Consistent Joint Extraction of 0 and RCX for HICUM 6th European Hicum Workshop 12-13 June 05, ATMEL in Heilbronn Zoltan Huszka austriamicrosystems](https://reader035.vdocuments.mx/reader035/viewer/2022070412/5697bf761a28abf838c810f2/html5/thumbnails/1.jpg)
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
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Purpose
• Proposal for a new 0 & RCX extraction
• Demonstration of the results
• Lowlights and Highlights
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Outline
• Former RCX extraction methods
• Overview of the existing 0 extraction methods
• Theory of joint extraction for both parameters
• Extraction procedure
• Extraction results
• Summary
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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)
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• 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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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!
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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
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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
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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
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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
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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!
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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
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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