Device modelling

1. TYPES OF DEVICE
MODELS(Part 2)
DONE BY:
SUDHARSHA.G(17D094)

2. ABOUT PART-1
In the previous lecture we learnt about the
 classification of device models based on the rate of time variation of the
voltage or current
 classification based on frequency of applied current or voltage signal.
 low frequency and high frequency models
 rigorous and phenomenol logic model based on derivation
 analytic and numerical solution techniques

3. Further classification:
In this lecture we shall learn about further classification of device
models namely
 Classification based on the attributes of the mathematical
functions.
 Classification based on the parameters and constant
 applications

4. Classification based on attributes of
function:(applies to analytical models)
 Analytical function:
a function expressible as taylor’s series.
 Analytical models can be formulated in terms of analytical functions.
 Some types of analytical functions possible for analytical models
1.Algebraic and Non –Algebraic(Transcendental)
2.Implicit or explicit

5. Forms of algebraic functions:

6.  Algebraic functions and a class of non algebraic functions forms a closed form
type of functions.
 Closed form functions are analytic functions excluding infinite series,
continued fraction, Bessel and Gamma funtions
 Another way of identifying closed form functions is consisting of finite number
of elementary functions combined using + - * /.
 The elementary functions are some types of constants, exponentials,
logarithmic functions ,trigonometric functions , inverse trigonometric
functions ,hyperbolic signs and so on.

7.  Another way of classification of analytical functions is IMPLICIT and
EXPLICIT functions
 Closed form can be of from both implicit and explicit type
 EXPLICIT FUNCTION is of the form i=f(v1,v2,……).In this form the
dependent variable is isolated on one side of the expression.
 IMPLICIT FUNCTION is of the form f(i,v1,v2,…)=0.Here the dependent and
the independent variable is on the same side of the expression.

8. EXAMPLES OF ANALYTICAL MODELS:

9. Classification based on attributes of the
parameters and constants:
They are classified as follows:
1.Empirical model
2.Semi-empirical model/Semi-physical model
3.Physical model

10. DEFINITIONS:
 EMPIRICAL MODEL:
If all the parameters in the model have no physical meaning, then the
model is said to be a empirical model.
 PHYSICAL MODEL:
If all the parameters in the model have physical meaning, then the model
is a physical model.
 SEMI-EMPIRICAL MODEL:
Most of the models belong to this category because it is difficult to
model all physical effects in a equation which is efficient.

11. TERMS ASSOCIATED WITH MODELS:
 1.Predictive or Scalable model:
A model which correctly predicts the effects of parameter variations on
the characteristics.
For example, In a MOSFET a scalable model is one which is predictive with
respect to W,L.
 2.Process aware model:
A model in which all process parameters appear explicitly in model
equation.
For example ,Doping(Detailed doping information rather than the no of
dopants)

12. Classification based on application:
Classified into
1.Device Simulation Models
2.Circuit Simulation Models
 Majority of the device models users do circuit simulation.
 In order that the model will be suitable for circuit simulation , it should satisfy
several constraints such as computational efficiency , continuity and so on…

13. CIRCUIT SIMULATION MODELS:
Table-look up model:
A table of current or small signal parameter values for a large number
of combinations of bias voltages . It is the most fast model but has no physical
basis.
SOME OF THE MODELS WITH PHYSICAL BASIS:
1.Black-box model:
Examples of these models are h-,y-,z-,s- parameter models, curve fit
equations
2.Behavioral model:
A simple model which captures the device behaviour but is not necessarily
physical.

14. SUB-CIRCUIT & MACRO MODEL:
A complex device structure modelled as an interconnection of simpler
devices.
example : Power MOSFET, thyristor etc…
COMPACT MODEL:
This is the most suitable model for circuit simulation, which satisfies
GCAPS criteria . This is the most important model in circuit simulation.

15. FEATURES OF COMPACT MODELS:
 These are of great interest of the large number of IC designers.
 These illustrate the various conflicting GCAPS requirements and challenges in
modelling.

17. Final classification based on application:
 Digital model of a mosfet
Goal is prediction of inverter switching speed, for which, accurate
prediction of drive current and parasitic capacitance sufficient.
Here the model equations are regional for sub-threshold , linear , saturation
, depletion , accumulation.
They contain more number of simple equations.
 Analog model of a mosfet
Both DC and small signal characteristics(transconductance due to body
effect) should be predicted accurately.
Here the model equation is a single equation which smoothly connects all
regions.
They contain a single complex equation.

18. WHAT IS DRIVE CURRENT???
 In a Id-Vd characteristic of a MOSFET , the current corresponding to
VDS=VDD which is the maximum current in the device is called as a drive
current.

19. Difference between digital and analog
model

20. Inverse Modeling:
 Extraction of device structured
from measured data.
 Eg : Extraction of 2-D doping
profile in a MOSFET from
measured C-V data.

21. Inverse Modeling Flowchart: