Download Generation of distributed electrical and electro

Generation of distributed electrical and
electro-thermal networks with TRADICA
Yves Zimmermann
CEDIC, Technical University of Dresden
4th European HICUM Workshop
June 15/16, 2004
Bordeaux, France
4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
OUTLINE
• Introduction
• Electro-thermal Characteristics
• Self-heating Networks
• Static Thermal Coupling
• Transient Thermal Coupling
• Distributed electrical networks
• Available Model Complexities
• Conclusion
• Outlook
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Introduction
• Shrinking device sizes lead to increased influence of parasitic effects on electrical
behavior.
• Deep trenches confine the heat flow resulting in higher operating temperatures.
• Multi-dimensional effects like avalanche breakdown are difficult to implement in
compact models.
• Need for accurate models for critical circuits and single devices
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Electro-thermal Characteristics
• Distinguish two different effects:
1. Self-heating (temperature rise due to power dissipation of a single heat source) and
2. Thermal coupling (temperature rise due to thermal interaction between several heat sources).
• Heat source definition:
Characteristic volume of integrated devices where heat is generated (e.g. BC-SCR of
BJTs)
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
PROBLEM-I
• Transient thermal characteristic is of complex exponential nature and varies with emitter contact configuration (CBEBC (solid), CBEBEBC (dashed), CBEBEBEC (dotted)).
BUT: Compact models use only simple thermal networks (parallel thermal
resistance Rth and capacitance Cth)!!!
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Self-heating Networks
• Common simple „built-in“ network (single RC-element):
-t
∆T(t) = P diss ⋅ R th  1 – exp  -------------------- 

 R ⋅ C 
th
Pdiss
th
Rth
Cth
∆T
• Extended network (multiple RC-elements):
Rth1
∆T(t) = P diss ⋅
n
∑i = 1
thi
Cth1
Pdiss
Yves Zimmermann, CEDIC
Rthn
..............
-t
R thi  1 – exp  ----------------------- 

 R ⋅ C 
thi
Rth2
Cth2
Cthn
∆T
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
PROBLEM-II
• Multi-emitter BJTs consist of several characteristic heat sources (one per emitter finger).
• Temperature distribution across the devices is NOT homogeneous due to thermal coupling
resulting in different operating temperatures at the fingers.
BUT: Compact models use only ONE ∆T for whole structure!!!
45%
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
PROBLEM-II
• Thermal coupling (intra- and inter-device) characteristic is NOT covered by compact models.
∆T 1
∆T 2
∆T 3
∆T 4
∆T 5
dT [K]
Heat sources for the multiple
internal base-collector junctions
10
9
8
7
6
5
4
3
2
1
14
12
10
0
1
8
2
3
x [µm]
Yves Zimmermann, CEDIC
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4
5
4
6
7
y [µm]
2
8 0
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Static Thermal Coupling
• Total temperature rises (∆T1, ∆T2) of two interacting sources can be expressed as a sum of
both self-heating contributions (∆T11, ∆T22) using thermal coupling coefficients (c21, c12):
∆T 1 = ∆T 11 + c 21 ∆T 22
∆T 2 = ∆T 22 + c 12 ∆T 11
• Representation using voltage controlled voltage sources (VCVS) [D.J.Walkey]:
∆T1
self-heating
device 1
Pdiss1
Rth1
VCVS
Yves Zimmermann, CEDIC
∆T2
∆T11
c12∆T22
∆T22
c21∆T11
Rth2
self-heating
device 2
Pdiss2
VCVS
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Transient Thermal Coupling
• Time-dependence of coupling coefficient (solid line) is of exponential nature and can be
represented using one or multiple RC-elements (dashed line).
∆T 21 ( t )
-t
------------------c 21c ( t ) =
= c 21  1 – exp  ----------------------------------- 


∆T 11 ( t )
R thc21 ⋅ C thc21 
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Transient Thermal Coupling
• Voltage controlled current sources (VCCS) drive the delay networks for the coupling coefficients. VCVSs add the coupled temperatures to the respective self-heating contributions.
•
-t
∆T 12 ( t ) = ∆T 22 ( t ) ⋅ c  1 – exp  ----------------------------------- 
R

12 
thc12 ⋅ C thc12
-t
∆T 21 ( t ) = ∆T 11 ( t ) ⋅ c  1 – exp  ----------------------------------- 
R

21 
thc21 ⋅ C thc21
∆T1
Pdiss1
Rth1
∆T2
Cth1
∆T11
∆T22
Cth2
∆T12
VCVS1
VCVS2
c12∆T22
VCCS1
c21∆T11
Rth2
Pdiss2
∆T21
VCCS2
attenuation of heat wave
∆T12
Rthc12
Cthc12
Cthc21
Rthc21
∆T21
delay network
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Distributed electrical network
Finger-partitioning
• Every finger is represented by one transistor model.
• Distinguish three different types of transistor elements:
1. an outer element Tw containing the collector region
2. a center element Tc bounded by base contacts at each side (does not contain collector region)
3. an outer element Tn bounded by a base contact at one side (does not contain collector region)
Tn
Yves Zimmermann, CEDIC
Tc
Tw
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Distributed electrical network
Finger-partitioning
• External collector resistance is partitioned and pulled out of the transistor elements.
• Transistor model parameters are calculated from technology data using the respective
emitter area portion.
rsu
S
C’n
∆rCx
C’c1
∆rCx
S’
B
Tn
C’ck
∆rCx
S’
C’w
TcK
C
S’
S’
Tc1
Csu
rCx1
Tw
E
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Distributed electrical network
Finger-partitioning
• External access to the thermal nodes ∆T enables contacting thermal (coupling) networks
of arbitrary complexity.
∆Tn
Pn
∆Tc1
RTH,n
TnΣ
Yves Zimmermann, CEDIC
Pc1
Tw
TcK
Tc1
Tn
E
RTH,c1
Tc1Σ
∆Tw
∆TcK
PcK
RTH,cK Pw
TcKΣ
RTH,w
TwΣ
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Distributed electrical network
Emitter-partitioning
• The equivalent circuit of one emitter is split into external elements and an internal transistor
Qi, which is represented by a distributed network
rsu
S’
S
CjS
,
C BCx
CdS
ijSC
ijBCx
Csu
iTS
,,
C BCx
B*
CEox
C
C’
B
rBx
rCx
CjEp
ijBEp
Qi
E’
rE
E
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Distributed electrical network
Emitter-partitioning
• The finger (internal transistor Qi) is partitioned and represented by several transistor models.
• Distinguish three different types of transistor elements:
1. a generic element Tg bounded by another element in each direction
bE/k
bE/k
lE/n
Te
Tel
lE/n
Teb
Tg
Tg
lE/2
2. an edge element Te bounding to other elements on 2 sides
3. edge elements Tel and Teb bounding to other
elements on 3 sides
bE/k
lE/n
bE/2
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Distributed electrical network
Emitter-partitioning
• The internal base resistance is partitioned and pulled out of the transistor element model.
• Thermal (coupling) networks can be contacted through access to the thermal nodes ∆T.
r knz
r kny
r 2nz
C’
Tkn
r 2ny
r 1nz
T2n
r 1ny
C’
T1n
E’
E’
r k3z
B*
r k3y
Tk3
r 23y
r k2z
r k2y
C’
r 23z
r 22y
QjCi
QdC
QjEi
QdE
B’
r 22z
Tk2
ijBCi
T23
r 12z
T22
r 12y
C’
iAVL
iT
ijBEi
T12
E’
E’
C’
r k1z
r k1y
Tk1
r 31z
r 31y
r 21z
T31
r 21y
E’
C’
r 11z
T21
r 11y
T11
z
E’
E’
E’
equivalent circuit of a transistor element
(ideal 1-D Transistor model)
E’
y
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Available Model Complexities
electrical
representation
self-heating
(„built-in“)
self-heating
(improved external)
thermal coupling
(inter-device)
thermal coupling
(intra-device)
HICUM/L2
Cell/Device
1 TM per Device/ Cell
X
X
HICUM/L4
Cell
1 TM per Device
X
X
X
HICUM/L4
Finger
1 TM per Finger
X
X
X
X
HICUM /L4
Emitter
1 TM per Finger- subelement
X
X
X
X
(TM = transistor model)
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Conclusion
• Partitioning of emitter fingers enables better simulation of avalanche breakdown.
• Derived distributed models covering self-heating and thermal coupling effects.
• Implemented scaling equations and extraction routines for the respective parameters.
• The approach is based on „fast“ analytic expressions enabling efficient parameter
generation.
• Established automated network generation of different model complexities.
Yves Zimmermann, CEDIC
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4th European HICUM Workshop, Bordeaux, 2004
Generation of distributed electrical and electro-thermal networks with TRADICA
Planned Activities - Outlook
• Verification of distributed electrical and electro-thermal networks.
• Development of scaling equations for substrate coupling.
• Automated generation of distributed models covering substrate coupling.
• Development of scaling equations for backend parasitics.
• Implementation into existing model generation procedures.
• Test and Verification.
Yves Zimmermann, CEDIC
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