Improvements in electronic chip manufacturing techniques have seen the number of components per electronic chip double on average every two years for the past thirty years. This has meant that the computing power of chips has grown enormously, and has been principally responsible for the huge improvements we have been enjoying in consumer items such as computers, game boxes, mobile phones and TVs, and also services such as internet and telephone. However the doubling of components, which depends on each component continuously shrinking, is in danger of stopping in the near future. This is because they are becoming so small that their sizes are approaching the size of individual molecules, when material behaves very differently to the way they behave on a large scale.The solution to try and keep shrinking components and maintaining the growth in computing power that we have come to expect, is to develop new kinds of components that exploit the way materials behave on very small scales. In fact researchers have already built and demonstrated many new and exciting kinds of devices, but equally important are ways of reliably predicting how these devices will behave, before they are actually built. This is the only way that electronics designers can use these components in their different designs, and in the past they have always had access to these kinds of predictive models.The problem with the new and very small devices is that their behaviour is governed by a complicated theory called quantum mechanics, which cannot be solved exactly except for very simple atomic structures. Hence approximate theories have been developed, but even these are too time consuming to solve for the millions upon millions of interconnected components which form modern chips. In fact electronic designers need models that have very well defined characteristics, and which tell them exactly what parameters they can change to make the device behave in different ways. This kind of model is called a black-box model, where some parameters are available to be adjusted, and the output for a given input is presented accordingly, and the internal calculations are hidden. These models may calculate the output in many ways. One of the most important kind is one where the output can be calculated by using a common set of elements known as circuit elements, which allows designers to use powerful computer-assisted tools for solving large numbers of connected components. This project proposes to develop such circuit theoretic models for some devices identified as being among the most important in the future, by a collection of the foremost experts in the world.Now these models have to be developed in two phases. In the first phase, it is necessary to use the approximate theories mentioned earlier, to develop a method to calculate output voltages and currents in very small structures. This method can then be used to investigate how the targeted devices behave for different inputs, for different device sizes and structures in the second phase. This helps to answer questions such as how the outputs differ for the same input to the same kind of device, when one device is twice the length of the other. When such a tool is available, reliable methods which have been developed over the years can be used to build circuit theoretic models as described earlier.The final part of the project is concerned with analysing the models developed in phase 2. What designers really want to know is how suitable a device is going to be as a building block to build a particular kind of electronic circuit and also how powerful a system built from such devices will be. Analysing the behaviour predicted by the models will give answers to questions such as whether the output can be related to the input by a constant, what margin of error is allowed, and how much power it will consume. It can also tell us ultimately what computing power is available from a large collection of devices.