Discrete Dynamics in Nature and Society

Volume 2015 (2015), Article ID 586842, 6 pages

http://dx.doi.org/10.1155/2015/586842

## Optimal Design of FPGA Switch Matrix with Ion Mobility Based Nonvolatile ReRAM

School of Computer Science and Technology, Zhoukou Normal University, Zhoukou 466001, China

Received 27 December 2014; Accepted 15 February 2015

Academic Editor: Zidong Wang

Copyright © 2015 Peng Hai-yun and Zhou Wen-gang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

There are high demands for research of new device with greater accessing speed and stability to replace the current SRAM storage cell. The resistive random access memory (ReRAM) is a metal oxide which is based on nonvolatile memory device possessing the characteristics of high read/write speed, high storage density, low power, low cost, very small cell, being nonvolatile, and unlimited writing endurance. The device has extreme short erasing time and the stored charge cannot be destroyed after power-off. Therefore, the ReRAM device is a significant storage device for many applications in the next generation. In this paper, we first explored the mechanism of the ReRAM device based on ion mobility model and then applied this device to optimize the design of FPGA switching matrix. The results show that it is beneficial to enhance the FPGA performance to replace traditional SRAM cells with ReRAM cells for the switching matrix.

#### 1. Introduction

As the development of the advanced electronics, a number of fundamental and practical problems start to emerge for traditional devices (such as field effect transistor) due to electrostatic limitations and other inherent constraints in nanometer level fabrication. New devices and architectures are expected to propel the development of semiconductor industry for the next several years. Two-terminal resistive random access memory (ReRAM, also called memristive device or memristor) has attracted increasing attention as a suitable alternative to traditional devices [1–4]. In such a device, a conduction path which has large nonvolatile resistance change is sandwiched between top and bottom electrode. Such device has very simple structure and can be scaled to be less than 10 nm in size. ReRAM device has two basic operations: SET and RESET, which represent low resistance state and high resistance state, respectively. The resistive change can be obtained by applying continuous sweeping pulse. This device has high integration density, random access, and nonvolatile characteristics. Therefore, the advantages of ReRAM give implications to make it a candidate of storage cell for FPGA (field-programmable gate array) switch matrix, which requires both high speed and low threshold voltage.

In this paper, we explore the mechanism of the ReRAM device and put forward a physical model based on ion mobility for this device. The* I-V* characteristics are investigated to describe the device electrical behavior. Furthermore, we propose a novel application of the nonvolatile ReRAM used in the FPGA switch matrix. The results show that the logic function with the ReRAM-based FPGA is quite appropriate.

#### 2. ReRAM Model and Characteristics

Chua first presented the missing circuit element that he called a memristor [5, 6] (memory + resistor) which is deduced from the six possible combinations of the four fundamental circuit variables: , , , and . Five combinations have been well known: resistor (), inductor (), capacitor (), voltage (), and current (). Considering the mathematical symmetry, he claimed that there should be a forth fundamental element called memristor which is defined by the relationship between charge and magnetic flux. Although he predicted the memristor’s existence in the form of the combination of the exist circuits, discovery of a memristor in the form of a physical device has not been discovered before May 2008 [3].

The memristor is actually a nonlinear resistor with memory function, described through relationship between flux and charge according to Chua. Like that a resistor is defined by the voltage and current, capacitance is described by the charge and voltage, and the inductance is defined by the relationship of flux and current. According to the definition, the memristor is expressed by

If (1) is transformed to single value function of charge , then the charge controlled voltage equation can be defined as

We translate charge into the form of integral calculus; then (2) is

We can conclude from (3) that the memristance is decided by the integral calculus of the current from to for the arbitrary time. Therefore, despite the fact that the memristor exhibits the same characteristics as normal resistor for arbitrary time , the resistance depends on the moment when the current flows through the memristor. Therefore, the device can be viewed as both memory and resistor. Once the current or voltage is designated, the memristor is just a linear time-varying resistor, where the form is ohmic characteristics.

In this paper, we present a simplified physical model for memristor (ReRAM) based on the ion mobility model. This model is deduced from a generalized memristive system framework and can explain the dynamic resistive switching phenomena observed in a broad range of devices. Furthermore, by constructing a simple model of the ReRAM, we can apply it for subcircuit simulator.

##### 2.1. The Mechanism of the ReRAM

Most of the ReRAM function models are based on HP dopant metal oxide TiO_{2} structure [3, 7, 8] which presents the on/off conductance ratios of more than 1 × 10^{3}. There is a thin semiconductor film that has two regions, one with a high concentration of dopant that behaves like a low resistance called and the other with a low dopant concentration with higher resistance called . The basic idea is that a dielectric, which is normally insulating, can be made to conduct through a filament or conduction path formed after application of a sufficiently high voltage. The conduction path formation can arise from different mechanisms, including defects metal migration, and so forth. Once the filament is formed, it may be reset (broken, resulting in high resistance) or set (reformed, resulting in lower resistance) by an appropriately applied voltage. Recent data suggest that many current paths, rather than a single filament, are probably involved [9, 10]. Figure 1 shows the initial state, forming, reset, and set process between the TE and BE in the ReRAM cell.