Logic design with Memristors - Correia, João Vidal (2020)
In 1971, Leon Chua noticed that some relationship between electric charge and magnetic flux was missing and, so, he theoretically proposed a circuit element that established said relationship, to which he called a memristor, because this device is essentially a ”resistor with memory”. Later, in 1976, a generalization to memristive devices was produced, defining a memristive device as a device whose behavior is defined by a state-dependant Ohm’s law controlled by some state variable. This allowed for the creation of synthetic memristors, the first of which was announced in 2008 by Stanley Williams from HP Labs. Memristors have been shown to have some very interesting and unique properties which allow for unprecedented applications. These are very small and fast devices, with sizes in the order of nanometers and switching times in the order of nanoseconds, with the ability to be embedded between two process layers, allowing for highly dense chips, capable of high parallelism. Nowadays, it is known that CMOS down-scaling is becoming increasingly difficult. The characteristics of the memristor, which allow for the creation of logic gates, in addition to its small size, make this device a good substitute for the traditional transistor in logic circuits. Additionally, the materials which compose these devices are compatible with CMOS technology, which points to the prospect of CMOS/Memristor integration. Another appealing feature of the memristor is that it is capable of both data storage and logic processing. This allows for novel computer architectures beyond the traditional von Neumann architecture, combining data storing and processing in a single circuit, removing the need for memory access, thus circumventing the von Neumann bottleneck problem. For this, a study on how memristors may perform logic processing is required. This dissertation’s objective is precisely the study of how Boolean algebra operations may be performed using memristors as the key components in these logic circuits. A review on memristor mathematical models and state-of-the-art logic design techniques using memristors is presented, with some degree of mathematical background, to facilitate posterior simulation. These simulations are performed using a memristor matematical model, the parameters of which were extracted from measurements made on an commercially available device.