sgp model parameter extraction with qucsstudio - a first trial · 5/18 qucsstudio sgp parameter...

dm019.19

SGP Model Parameter Extraction

With QucsStudio - A First Trial...

Didier Céli

19th HICUM Workshop - Letter Session

Munich - May 13/14, 2019

ST Confidential

1/18

QucsStudio SGP Parameter Extraction - dm019.19 ST Confidential

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

2/18


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

3/18


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)

4/18


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)

5/18


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

6/18


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)

7/18


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


8/18


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.


9/18


The function to optimize is set in the goals tab

Then the simulation is launched


10/18


Result after global optimization

Parameter Reference Optimization

IS (A) 1.80 10-17 1.80 10-17

VAR (V) 2.20 2.198


11/18


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)

12/18


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)

13/18


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)

14/18


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)

15/18


• 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

16/18


• 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

17/18


• 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

⋅–

⋅

---------------------------------------------------------------------------------------------------------------------------=

18/18


[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

sgp model parameter extraction with qucsstudio - a first trial · 5/18 qucsstudio sgp parameter...

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