Sub-micrometer Bipolar Transistor Modeling using Neural Networks
This work presents an approach based on Neural Networks
(NN) for constructing models of high speed bipolar transistors, to be used
inside circuit simulators. Since recently physical modeling has been the
prevailing approach to semiconductor modeling for circuit simulation, being
Gummel-Poon the choice for bipolar junction transistors (BJT) at high frequencies.
The knowledge of the underlying physical principles was sufficient for
deriving effective models, where each parameter has a clear physical meaning.
This situation is gradually changing, with the current size of bipolar
junctions made available by the microelectronics manufacturing capabilities.
As long as the ratio of surface to volume increases for the smallest devices,
many boundary effects should be taken into account, leading to complex
multidimensional analysis of the phenomena. Reliable models requires now
a high development cost. Furthermore, precise physical models should now
rely on a number of largely empirical fit parameters. The method here investigated
is based on NN, which can be seen as a fitting techniques, with the advantage
of output functions with unlimited degree of continuity. NN approaches
has gained widespread attention over the past two decades, with a variety
of applications, including dynamic systems identification, control and
simulation. However, the traditional schemes used for dynamic NN, like
tapped-delays feed-forward networks, feedback and self-recurrent networks,
are not immediately usable for models to be embedded in circuit simulators.
Simulators require a representation in terms of continuous-time equations,
since time discretisation will be an internal process of the simulator
itself. In the NN here adopted, nodes can be instances of differential
equations. The whole network has two input nodes, the BJT voltages, and
two output nodes, the BJT currents, and several internal layers populated
with neurons. For the determination of the parameters a combination of
training sets can be used, mixing measured responses of the device in DC
conditions, small-signals in frequency domain, and large signals transient
responses. A combination of global optimization followed by a quasi-Newton
conjugate-gradient method has been used, for computing the internal parameters
of the NN. Once the NN has been trained, the final set of parameters is
used for generating a piece of code in Anacad's HDLA language, implementing
the NN in recall mode. This will be the block modeling the BJT inside the
ELDO circuit simulator.
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