Study Of Memristor From The Theoretical Definition And Percolation Model

Nowadays, the research community has shown great research interests in memristor related fundamental theory, underlying conductive mechanism, physical fabrication and numerous plausible applications. Among them, significant achievements have been attained in electronics, computer science, materials and bio-inspired technologies. It should be highlighted that memristor has been highly considered to be one of the promising candidate for implementation of next generation non-volatile memory, which thus could advance Moore?s Law beyond the present silicon roadmap horizons. Moreover, memristive devices naturally combine the logic, storage and computing function together, which will definitely promotes the development of new instant-on computer architecture, and finally significantly affect our life style in information society. This thesis encompasses two key contributions, namely mathematical expression of memristor and percolation model.Initially, this thesis proposed a novel formulation to express an approximation of ideal memristor mathematically. The new expression can be used to model physical device with the memristive phenomena, and show the better capability of fitting v-i curve than ideal memristor, which decipher the mathematical differences between the ideal memristor and the memristor in physical reality. Furthermore, those differences could help to guide the fabrication of memristor. The memristor, memory resistor, is a two-terminal device characterized by a constitutive relation between two basic circuit variables flux j and charge q. The v–i loci(Lissajous figure) of the ideal memristor is always a pinched hysteresis loop, containing some basic characteristics which are consider to be the fingerprints of ideal memristor. Until now, a number of crossbar type memristor prototypes have been implemented. And some traditional electronic devices, like discharge tubes, are also treated as memristors. However, the loci of those practical memristors cannot meet basic characteristics required by the ideal memristor. Chua then proposed a more general concept memristive system, also called the generalized memristor to extend the circuit limitation of the ideal memristor definition. But it still has some drawbacks to express practical memristor, and the main flaw lies in the continuity restriction of memristance and changing rate, which as a result could limit the development of math model. Based on the generalized memristor, this thesis proposed a novel formulation of memristance in practical device, which further extends the mathematical expression of ideal memristor. This formulation has no bounded requirement and removes the continuity restriction of changing rate and memristance. Besides, a new concept, nonlinear current/voltage controlled generalized memristive system, is introduced here. Three memristive devices are sampled pedagogically to demonstrate that the proposed formulation can accommodate those discontinuity or not “well-defined” situations which cannot be modeled by the ideal memristor and the generalized memristor. The proposed mathematical expression can not only help us to build more accurate conductive analysis model, but also decipher the mathematical differences between the ideal memristor and the memristor in physical reality, which provides theoretical support to guide the fabrication of memristive device.Secondly, this thesis analyzes the impact of pristine state, including the initial percolation percentage and the initial percolation distribution, on the conductive filaments formation within memristor active cores, which could finally affect the unipolar resistive switching. These rules will contribute to the implementation of practical memristive devices with filamentary mechanism being dominant. To improve the computational efficiency, the original percolation network model is simplified. The dynamic procedure simulation of forming conductive channel during the forming operation verifies the efficient of the simplified model. Based on this model, we firstly investigate the influence of distinct initial percolation defects density on the formation of conductive percolation channel, with results demonstrating the resistance fluctuation. Additionally, we explore the relation between defects density and switching potential and found devices with larger percolating defects density required relatively lower average switching potentials. Then, the influence of distinct initial percolation distribution influence the formation of conductive channel is also studied. Simulation results show the fluctuation of low resistance during the forming operation is close to Gaussian distribution, which is consistent with the actual memristor. Moreover, the mean and variance of resistance fluctuation are related to the pristine state information, which include the doped concentration and the doped place distribution in the practical memristor. After further analysis, the underlying causation is due to the different structure of conductive channel inside the memristor. Devices with distinct initial filaments distribution could possess quite dissimilar structure of conductive channel, which can be mainly classified to three types of tree-like structure. And the structure of conductive channel determines the overall resistance information of memristor. These features contribute to deciphering the unknown conductive mechanisms and need to be confirmed by using TEM to attain insight evidence, and then guide the fabrication of memristive device toward the customized memristor with the requirement of forming voltage and stability.