Sub-micrometer Bipolar Transistor Modeling Using Neural Networks Alessio Plebe 1 , A. Marcello Anile 1 , and Salvatore Rinaudo 2 1 University of Catania Department of Mathematics and Informatics V.le Andrea Doria, 8 I-95125 Catania, Italy 2 ST Microelectronics Str. Primosole, 50 I-95121 Catania, Italy Abstract. An approach based on Artificial Neural Networks (ANN) for construct- ing models of high speed bipolar transistors is described. This method is proposed as an alternative for physical modeling for circuit simulation, when high frequency and small device size make classical models very complex or even unreliable. In the ANN here adopted, neurons are represented in terms of continuous-time dif- ferential equations, allowing the immediate application inside conventional circuit simulators. The most difficult task in this approach is the network training from the measurements on the real device, and the usual learning rules for ANN’s easily lead to poor approximation or unacceptable slowness. A generative method has been developed, where a subset of the network parameters is trained inside an aux- iliary static network, using measurements at fixed DC bias. The complete network is trained on the full set of measurements using this subset as a starting point. The learning rule is a combination of global optimization followed by a quasi-Newton conjugate-gradient iterative process. 1 Introduction Until recently physical modeling has been the prevailing approach to semi- conductor modeling for circuit simulation, Gummel-Poon being the choice for Bipolar Junction Transistors (BJT) at high frequencies [1]. The knowledge of the underlying physical principles was sufficient for deriving effective mod- els, where each parameter has a clear physical meaning. The effort required to derive the parameters was still acceptable, since it was basically reduced to a number of one-dimensional phenomena analyses, and neglecting several complex side-effects was not causing a significant loss in accuracy. This situation is gradually changing, with the current size of BJT 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 require now a high development cost. Furthermore, precise physical models should now rely on a number of largely empirical fit parameters. An adopted alternative is the use of so called Table Models [9] [11], where interpolation techniques are used to fit behavior of BJT in every possible working condition, from a set of measured data. One of the drawbacks of