sgp model parameter extraction with qucsstudio - a first trial · 5/18 qucsstudio sgp parameter...
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SGP Model Parameter Extraction
With QucsStudio - A First Trial...
Didier Céli
19th HICUM Workshop - Letter Session
Munich - May 13/14, 2019
ST Confidential
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To demonstrate the possibilities and the limits of free SPICE simulators for model para-
meter extraction
Using a simple test case as example
• Extraction of the saturation current IS and of the reverse Early voltage VAR of the SGP model
With QucsStudio [1]
Why to choose QucsStudio?
• Right now it is the most flexible and robust free SPICE simulator
• Possibility to compile Verilog-A code on the fly (“turn-key” approach)
• Good convergence
QUCS 0.0.19 QucsStudio 2.47
HICUM/L2 v2.4.0
Purpose and comments
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2 different approaches are possible
The first one is to use the engine of QucsStudio (qucssim.exe) in extraction tools deve-
loped in various possible languages (C++, Fortran, Python, Matlab, Octave...)
• Works very well
• Time is needed to develop the code
• Not shown in this presentation
The second approach is to use all the features of QucsStudio directly via the GUI
• Slider for tuning parameters
• Equation and optimization boxes
• Faster (but limited) approach and easy to implement for testing a new extraction method
How to use QucsStudio for model parameter extraction
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Objectives
• Independently of the model used, we want reliable model parameters
• Reliable meaning both physical and accurate model parameters
• Do not forget that a physics-based model with inaccurate model parameters can be worse than a less accurate
compact model but with physical model parameters
Constraints
• All models have their own limitations
• Measurements are more or less accurate
• Therefore, how to determine model parameters both accurate and physics-based taking into account the limits of
the compact models and the inaccuracy of measurements?
Key solution
• Developing direct extraction procedures using e.g. linear regression (no need for initial guess), gives the solution
without any iteration loop, and then avoids correlation between model parameters...
Advantages
• Easy parameter extraction, the only difficulty being to find the adequate transformations for linearizing the
equations of the compact models, an important job of modeling engineers.
• Allows to validate both the compact models and the measurements. If the theory predict that a given characteris-
tic must be linear and if the measurements are also linear, that validates both the measured data and the model
equations. If it was not the case, that allows to alert the modeling engineer: either it is a model limitation or the
measurements are not accurate enough (limitation of the equipments, wrong test structures or measurement
setup), or both.
SPICE parameter extraction strategy: basic principle (1/2)
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Comments
• This principle is used with success since several years for bipolar parameter
extractions
The parameter extraction is performed in several steps
• With possible loop between the steps
At each extraction step
• a given set of model parameters is determined
• from electrical characteristics (DC, AC, noise, temperature, ...) that are most sensi-
tive to the set of model parameters to be extracted.
Each step is divided in 2 parts
• The first part consists of a direct extraction of the model parameters.
• The second part uses non-linear least-squares algorithm for the determination of the
parameters with initial guess coming from the first part.
Step 1
Step 2
Step i
Step n
Begin
End
SPICE parameter extraction strategy: basic principle (2/2)
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Model equation (SGP model)
• At low VBE and VBC = 0 V, the collector current of the SGP model can be written
(1)
• IS is the saturation current of the transistor, VAR is the reverse Early voltage which models the base width modu-
lation with VBE, and finally VT = k.T/q is the thermal voltage.
• For Si devices, the non-ideality factor NF must be set to 1 as described in Appendix A
Extraction principle
• From (1) we can define the normalized collector current ICN as
(2)
• This characteristic is a linear function of VBE. The intercept
allows to calculate IS, and after the slope to determine VAR
(3)
IC IS 1VBE
VAR
----------–
e
VBE
NF
V⋅T
-------------------
1–
⋅ ⋅≈
VBE
ICN
IS
IS
VAR
----------–
ICN
IC
e
VBE
VT
-----------
1–
-------------------- IS
1VBE
VAR
----------–
⋅= =
IS
intercept=
VAR
intercept
slope-------------------------–=
IS, VAR parameter extraction principle
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With the present version of QucsStudio, as it is
not possible to use imported data in equation, to
validate the extraction procedure, a transistor T1
is used to generate the synthetic data (simulated
measurement).
The right transistor T2 is used to make the com-
parison between the extracted parameters _IS,
_VAR and the reference parameters of T1 Is, Var.
As in QucsStudio linear regression are not imple-
mented, the formulations, allowing to compute
the slope, the intercept and the correlation coeffi-
cient of a straight line, have been defined in an
equation box using Appendix B.
Another equation box allows to calculate IS and
VAR from (3)
IS, VAR parameter extraction with QucsStudio (1/5)
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The normalized collector current (2) is computed as
and then the x and y vectors are set for the linear regression
Result after the direct extraction of IS and VAR
Parameter Reference Direct extraction
IS (A) 1.80 10-17 1.80 10-17
VAR (V) 2.20 2.198
Comments
• Very good results in comparison with the reference
values
• These values are then used as initial guess for the
optimization
IS, VAR parameter extraction with QucsStudio (2/5)
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After direct extraction of IS and VAR, these data are used as
initial values for the optimization sequence
• They must be filled by hand in the variables tab of the optimization box
(QucsStudio limitation)
Optimization methods in QucsStudio [1]
• An important option in the optimization component is the method that tries to
find the best parameter set. There are three types of algorithms available in
QucsStudio (based on ASCO [2]).
• The method grid search goes along the whole user-defined variable domain
and stores the best position. Therefore, it only works for problems with few,
tight-limited variable spaces. Usually this isn't the best choice.
• The methods that follow the descent of the function value are steepest
descent and Nelder-Mead. They only find the optimum if there are no local
minima, or if the starting point is close enough to the global minimum.
Nelder-Mead is the most robust method, but steepest descent is often
faster.
• Difficult problems with several local minima can only be solved with heuristic
algorithms like differential evolution (DE). They need many simulation runs,
but are astonishingly successful. DEGL/SAW proved to be most suitable,
even though DE/current-to-pbest/1/bin is usually very good, too. For very
hard problems DE/best-of-rand/2/bin and DE/rand/1/bin are also worth a try.
The size of the population should be about ten times the number of used
variables.
IS, VAR parameter extraction with QucsStudio (3/5)
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The function to optimize is set in the goals tab
Then the simulation is launched
IS, VAR parameter extraction with QucsStudio (4/5)
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Result after global optimization
Parameter Reference Optimization
IS (A) 1.80 10-17 1.80 10-17
VAR (V) 2.20 2.198
IS, VAR parameter extraction with QucsStudio (6/6)
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It is possible to import ASCII data in various file formats but after these data cannot be
used in the equation boxes for the optimization
• In recent optimization examples (April 2019) the
measurements are entered by hand [1].
No native linear regression and multiple
variables linear regression in the simula-
tions tab
• Key point to have good initial valuesfor the optimization
• Main of the SGP parameters can beextracted only using linear regres-sion
What is missing for model parameter extraction? (1/2)
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The slider is a very interested feature in the new QucsStudio
version for tuning parameters
• To add in the simulations tab a box for the slider, that will allow to keep in the schematic
the data of the slider, like with the optimizer
• Add the possibility to tune the variables in linear or log scale
Possibility to select the data to be fitted by draw-
ing a box on the screen, or by given the boundar-
ies in a dialog box (Xmin, Xmax)
What is missing for model parameter extraction? (2/2)
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This simple example allows to demonstrate that, through some limitations, it is possible to
build in few minutes (once we know how to do) a QucsStudio schematic for SPICE model
parameter extractions.
Summary and future works (1/2)
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Extend this first example to other SGP parameters
Parameters Signification Extraction procedure
BF, ISE, NE Low base current linear regression
VAF Forward Early voltage linear regression
IKF Forward knee current linear regression
RB, RBM Base resistance linear regression
RE Emitter resistance linear regression
RC Collector resistance Optimization
TF Low current transit time linear regression
XTF, VTF, ITF High current transit time Optimization
EG, XTI, XTB Thermal parameters linear regression
CJE, VJE, MJE BE depletion capacitance linear regression
CJC, VJC, MJC BC depletion capacitance linear regression
CJS, VJS, MJS CS depletion capacitance linear regression
Summary and future works (2/2)
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• In the SGP model, 2 parameters NF and NR were introduced in order to take into account the non-ideality of the
slope of the collector current in forward and reverse mode.
• These additional model parameters are useless and must be never used for Si BJT and SiGe HBT devices.
• In fact, as demonstrated below, the non-ideality of the collector current is already taken into the model via the term
q1 (Early effects) of the normalized majority charge in the neutral base.
• A low current densities and for VBE greater than several 4. VT, at VBC = 0 V, the collector current is expressed as
• Assuming VAR > VBE, we can write
with
> 1
IC
IS
q1
----- e
VBE
VT
-----------
⋅ I=
S
1VBE
VAR
----------–
e
VBE
VT
-----------
⋅ ⋅≈
IC IS
e
VBE
VAR
-----------–
e
VBE
VT
-----------
IS
e
VBE
VT
----------- 1VT
VAR
-----------– ⋅
⋅ IS
e
VBE
1VT
VAR
-----------+ VT⋅--------------------------------------
⋅ IS
e
VBE
NF
V⋅T
-------------------
⋅=≈=⋅ ⋅≈
NF
1VT
VAR
----------+=
Appendix A: About non-ideality factors NF and NR
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• Linear regression is a method for calculating the equation of the best straight line that passes through a set of points.
• The best meaning the straight line that passes as closely as possible to as many points as possible.
• The best straight line equation is y = a.x + b, where the slope a and the intercept b are given by
a
n xi yi⋅
i 1=
n
⋅ xi
i 1=
n
yi
i 1=
n
⋅–
n xi2
i 1=
n
⋅ xi
i 1=
n
2
–
-------------------------------------------------------------------=
b
yi
i 1=
n
xi2
i 1=
n
⋅ xi
i 1=
n
xi yi⋅
i 1=
n
⋅–
n xi2
i 1=
n
⋅ xi
i 1=
n
2
–
------------------------------------------------------------------------------=
Appendix B: Linear regression formula
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• The correlation coefficient r is given by
• It is a number which give you an idea if how closely the straight line fits the data. r is between +1 and -1. Values of
close to +1 or -1 indicate a good fit. Value of r close to 0 indicate a poor fit. The sign of r is linked to the sign of the
slope. Therefore, sometime r² is used instead r to represent how well the line fits the data.
r
xi yi⋅
i 1=
n
1
n--- xi
i 1=
n
yi
i 1=
n
⋅ ⋅–
xi2
i 1=
n
1
n--- xi
i 1=
n
2
⋅–
yi2
i 1=
n
1
n--- yi
i 1=
n
2
⋅–
⋅
---------------------------------------------------------------------------------------------------------------------------=
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[1] QucsStudio, “A Free and Powerful Circuit Simulators”, http://dd6um.darc.de/QucsStudio/about.html.
[2] ASCO, ‘A SPICE Circuit Optimizer’, http://asco.sourceforge.net/index.html.
References