Abstract
The target of an analytical MOSFET model is the consistent and physically correct description of the transistor, within the frame of a modern CMOS technology. But, on the other hand, a model has much more to offer to the designer than a black box that answers the wondering of how a certain element of a circuit works, and how the circuit’s behaviour may be optimized. At this thesis the modelling of the MOSFET is studied. Its product is the implementation of an analytical MOSFET model, compatible with a plethora of simulators of electrical circuits, able to cover all the phenomena that appear in modern submicron CMOS technologies. A quantitative and qualitative verification of the behaviour of the model is presented, in comparison with modern technologies of minimum channel length down to 70nm, and also against tests based on the physics theory that describes the behaviour of the transistor. The modelling procedure that is analyzed here, is based on the charge sheet theory. According to ...
The target of an analytical MOSFET model is the consistent and physically correct description of the transistor, within the frame of a modern CMOS technology. But, on the other hand, a model has much more to offer to the designer than a black box that answers the wondering of how a certain element of a circuit works, and how the circuit’s behaviour may be optimized. At this thesis the modelling of the MOSFET is studied. Its product is the implementation of an analytical MOSFET model, compatible with a plethora of simulators of electrical circuits, able to cover all the phenomena that appear in modern submicron CMOS technologies. A quantitative and qualitative verification of the behaviour of the model is presented, in comparison with modern technologies of minimum channel length down to 70nm, and also against tests based on the physics theory that describes the behaviour of the transistor. The modelling procedure that is analyzed here, is based on the charge sheet theory. According to this theory, the inversion charges at the two nodes at the ends of the channel are calculated, and the calculation of the various electrical quantities of the transistor is based on the integration along the channel. The equations of the analytical model demand a series of approximations, which do not affect the overall accuracy of the model but at unimportant degree, justifying, this way, fully their usage. The most basic approximation is the assumption of a linear relation between the inversion charge and the surface potential. The result of the usage of the physical theory for the extraction of the model, and not empirical relations, is that a unified set of equations is used at the bottom line, for the correct description of the behaviour of the transistor, under any bias conditions, and under any level of inversion. This adherence to the physical theory allows, also, the minimization of the model parameters that are demanded to be calculated for the fitting of the behaviour of the model upon a certain technology. At this thesis, the physical theory, that covers the behaviour of the model, is carefully presented, as it is adopted for describing modern submicron technologies. All the new phenomena that appear today, and did not in older similar technologies are being addressed. Typical examples are the quantum effects that are more intense as the insulator gets thinner, as well as the gate current that cannot be further neglected. On the other hand, all the customary phenomena that appear in CMOS technologies are also described. The description covers all sides of the behaviour of the transistor, and comparisons are made with static measurements, as well as transconductances and Y-parameters, with frequency up to decades of GHz. In parallel with the presentation of the model, and according to each phenomenon that is studied each time, a comparison of the simulations results against relative measurements is displayed, verifying this way in action the correct behaviour of the model. A model, though, can also operate as a designer’s tool in other ways. On the one side, it is important the understanding of the behaviour of the model through a simplified analysis of the structure. Such knowledge, in favor of which a model can contribute, allows the designer to apprehend better the capabilities of the device. On the other side, the modelling approach that is presented here may be used within the frame of a first order approach to design a circuit, assuming simplified models and performing hand calculations. A consistent modelling formulation for all these perspectives, primes the designer with an important tool for his/hers work. Furthermore, it can be noted that an analytical model may have an auxiliary role at the procedure of the evolution of the technologies. Through the physical connection between the parameters of the model and the procedure of manufacturing of the integrated devices, an estimation is able to be performed, of the value of evolution of a technology towards a specific direction, based on results of circuit level. These results may be supplementary to results from numerical simulator software of structures in device level, whose complexity does not allow them to be extended to circuit level. The model, in order to be a usable tool within a simulator of electric circuits, has to be coded according to the specifications of the software. For this purpose the Verilog-A language has been chosen. Important advantages of this behavioural language is that, on the one side, it is compatible with the whole of the simulators, and, on the other side, it is specially designed to cover the needs of the description of the behaviour of analogue components. On the other hand, its drawbacks, that are related with the non optimal writing of the model for fast simulations, can be solved with the usage of synthesizers of C-code, after the Verilog-A code, and its compilation into a dynamic library. A complete model owes to offer, also, a fast and handy methodology that allows the fitting of the model upon a certain technology, having as a quantitative and final criterion the measurements on a range of devices of this specific technology. Within this thesis, the principles according to which the parameters of this model are extracted for a specific technology are discussed. The physical foundation of the model, allows the minimization of the used parameters, thus eases their extraction, as well as limits their linear dependence, easing again their extraction. Finally, a model that describes a physical structure owes to be consistent with the laws of physics that characterize all technologies, and not a specific implementation of these structures. These tests are characterized as qualitative verification tests of the model and attest its correct behaviour. The MOS transistor is a basic component of the modern integrated circuits. Today’s technologies are able for channel lengths as small as some decades of nanometers. On the other hand, there is a new generation of structures, more complicated than the classical MOSFET, of multigate devices that intend to pick up the dominance of MOSFET, when the needs in frequency and channel length will not allow to the last to operate normally, due to intense short channel effects. The evolution of the models, in order to keep on tracking the behaviour of the next generation MOSFET, as well as, their contestant successors, the multigate devices, states a challenge.
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