Models and methods for power monolithic microwave integrated circuits

Computer aided design of Monolithic Microwave Integrated Circuits (MMICs) depends critically on active device models that are accurate, computationally efficient, and easily extracted from measurements or device simulators. Empirical models of active electron devices, which are based on actual device measurements, do not provide a detailed description of the electron device physics. However they are numerically efficient and quite accurate. These characteristics make them very suitable for MMIC design in the framework of commercially available CAD tools. In the empirical model formulation it is very important to separate linear memory effects (parasitic effects) from the nonlinear effects (intrinsic effects). Thus an empirical active device model is generally described by an extrinsic linear part which accounts for the parasitic passive structures connecting the nonlinear intrinsic electron device to the external world. An important task circuit designers deal with is evaluating the ultimate potential of a device for specific applications. In fact once the technology has been selected, the designer would choose the best device for the particular application and the best device for the different blocks composing the overall MMIC. Thus in order to accurately reproducing the behaviour of different-in-size devices, good scalability properties of the model are necessarily required. Another important aspect of empirical modelling of electron devices is the mathematical (or equivalent circuit) description of the nonlinearities inherently associated with the intrinsic device. Once the model has been defined, the proper measurements for the characterization of the device are performed in order to identify the model. Hence, the correct measurement of the device nonlinear characteristics (in the device characterization phase) and their reconstruction (in the identification or even simulation phase) are two of the more important aspects of empirical modelling. This thesis presents an original contribution to nonlinear electron device empirical modelling treating the issues of model scalability and reconstruction of the device nonlinear characteristics. The scalability of an empirical model strictly depends on the scalability of the linear extrinsic parasitic network, which should possibly maintain the link between technological process parameters and the corresponding device electrical response. Since lumped parasitic networks, together with simple linear scaling rules, cannot provide accurate scalable models, either complicate technology-dependent scaling rules or computationally inefficient distributed models are available in literature. This thesis shows how the above mentioned problems can be avoided through the use of commercially available electromagnetic (EM) simulators. They enable the actual device geometry and material stratification, as well as losses in the dielectrics and electrodes, to be taken into account for any given device structure and size, providing an accurate description of the parasitic effects which occur in the device passive structure. It is shown how the electron device behaviour can be described as an equivalent two-port intrinsic nonlinear block connected to a linear distributed four-port passive parasitic network, which is identified by means of the EM simulation of the device layout, allowing for better frequency extrapolation and scalability properties than conventional empirical models. Concerning the issue of the reconstruction of the nonlinear electron device characteristics, a data approximation algorithm has been developed for the exploitation in the framework of empirical table look-up nonlinear models. Such an approach is based on the strong analogy between timedomain signal reconstruction from a set of samples and the continuous approximation of device nonlinear characteristics on the basis of a finite grid of measurements. According to this criterion, nonlinear empirical device modelling can be carried out by using, in the sampled voltage domain, typical methods of the time-domain sampling theory.

Stochastic models and dynamic measures for the characterization of bistable circuits

During the last few years, a great deal of interest has risen concerning the applications of stochastic methods to several biochemical and biological phenomena. Phenomena like gene expression, cellular memory, bet-hedging strategy in bacterial growth and many others, cannot be described by continuous stochastic models due to their intrinsic discreteness and randomness. In this thesis I have used the Chemical Master Equation (CME) technique to modelize some feedback cycles and analyzing their properties, including experimental data. In the first part of this work, the effect of stochastic stability is discussed on a toy model of the genetic switch that triggers the cellular division, which malfunctioning is known to be one of the hallmarks of cancer. The second system I have worked on is the so-called futile cycle, a closed cycle of two enzymatic reactions that adds and removes a chemical compound, called phosphate group, to a specific substrate. I have thus investigated how adding noise to the enzyme (that is usually in the order of few hundred molecules) modifies the probability of observing a specific number of phosphorylated substrate molecules, and confirmed theoretical predictions with numerical simulations. In the third part the results of the study of a chain of multiple phosphorylation-dephosphorylation cycles will be presented. We will discuss an approximation method for the exact solution in the bidimensional case and the relationship that this method has with the thermodynamic properties of the system, which is an open system far from equilibrium.In the last section the agreement between the theoretical prediction of the total protein quantity in a mouse cells population and the observed quantity will be shown, measured via fluorescence microscopy.