電阻式記憶體及電子突觸元件之數值模擬研究

Abstract

在過去，元件尺寸的微縮能夠直接反應在電腦系統效能的提升。然而在傳統的記憶儲存階層架構下，元件的微縮造成固態記憶體和硬碟兩者的存取時間相差愈來愈大，而存取時間的巨大差異使得元件微縮不再能直接提高電腦效能。為了解決存取時間差異的問題，必須在記憶儲存階層中增加儲存記憶體(storage class memory)，來彌補記憶體和硬碟之間的存取時間差異。另一個傳統大型資訊系統的問題是，要作出能與人類智慧匹敵的電腦需要消耗大量的電力。一般人腦的功耗大約是十瓦，而超級電腦的電力消耗高達一百四十萬瓦。因此低功耗且具有容錯特性的電子突觸(electronic synapse)元件與其在類神經計算上的應用是值得關注的。而在儲存記憶體與電子突觸元件發展上，電阻式記憶體(RRAM)都扮演著非常重要的關鍵角色。 對於發展儲存記憶體而言，了解RRAM阻值轉換的機制是必須的。了解阻值轉換的機制才能進一步研究阻值轉換變異、元件熱效應、電流雜訊以及耐久性和保存時間這些特性或現象的根源，進一步幫助改善元件。對於電子突觸元件來說，雖然元件變異對類神經計算系統所造成的影響較小，但研究阻值轉換的機制仍然能提供元件特性解釋以及改善方式，而且建立的物理模型能進一步提供類神經計算系統模擬設計使用。目前已經有不少的電子突觸模型可模擬元件特性，然而大部分提出來的模型仍太過簡化，無法提供時間動態的物理解釋以及元件改善的建議。 本篇論文建立了兩個RRAM的數值模擬模型，一個是TiN/HfO2/Pt燈絲型(filamentary)電阻式記憶體模型，另一個是Ta/TaOx/TiO2/Ti非燈絲型電阻式記憶體模型。燈絲型電阻式記憶體模型是根據滲透理論(percolation theory)所建立的。這個模型考慮了缺陷輔助穿隧電流、氧缺(oxygen vacancy)的生成與消滅、氧離子的移動以及焦耳熱效應。這個模型以SET和RESET過程中缺陷的分佈成功地解釋阻值轉換的現象。也成功地模擬出I-V特性和SET切換電壓的韋伯分佈(Weibull distribution)。 Ta/TaOx/TiO2/Ti非燈絲型電阻式記憶體模型是根據均值能障調變機制所建立的模型。這個模型考慮了被TaOx限制的WKB(Wentzel-Kramers-Brillouin)穿隧電流、帕松方程式(Poisson equation)以及計算氧離子移動的連續方程式。這個模型以SET和RESET過程中氧缺和氧離子的分佈成功地解釋阻值轉換和自我整流的現象。也成功模擬出RESET造成的多階阻態轉換以及調變不同材料厚度的影響。此外，這個模型也成功模擬了電子突觸的特性，像是突觸連結的增強(potentiation)和抑制(depression)、STDP(spike-timing-dependent plasticity)以及PPF(paired-pulse facilitation)，和實驗結果相較皆有很好的一致性。

In order to continue improving performance of large-scale information systems, it is essential to revolutionize the present memory and storage hierarchy where a large access time gap exists between DRAM and hard disks. Storage class memory (SCM) is proposed to fill the access time gap and significantly improve the system performance. Another critical issue of large-scale information systems is the power consumption. To achieve human-level intelligence, the required power consumption is as high as 1.4 MW by using the most advanced supercomputer, while the power consumption of human brain is merely 10 W. Aiming for energy-efficient, fault-tolerant and high-performance information systems, electronic synaptic devices for neuromorphic computing now attract significant attention. Among many emerging devices for storage class memory and electronic synapse, it is widely believed that RRAM is an extremely competitive candidate. For SCM, a comprehensive understanding of RRAM switching mechanism is the foundation of studying resistive-switching variation, thermal effect, current noise, retention/endurance degradation, and device optimization. For electronic synaptic devices, although there have been a few models proposed to explain the device behavior, most of them are oversimplified and cannot be applied for dynamic response, device optimization strategy, and simulation of large-scale neuromorphic computing systems. In this thesis, two numerical models are constructed for RRAM physical simulation. One is TiN/HfO2/Pt filamentary RRAM, and the other is Ta/TaOx/TiO2/Ti non-filamentary RRAM. The filamentary RRAM model is constructed based on the percolation theory. The model considers trap-assisted-tunneling current, oxygen ion migration, generation/recombination of oxygen vacancies, and Joule heating. The transient defect patterns of forming, SET, and RESET are investigated to explain the resistive switching. The I-V characteristics and Weibull distribution of SET voltage are also simulated. Furthermore, the Ta/TaOx/TiO2/Ti non-filamentary RRAM model is constructed based on homogeneous barrier modulation mechanism. The model considers WKB tunneling current limited by the TaOx barrier, Poisson equation, and continuity equation of ion migration. The transient oxygen ion and vacancy profiles during SET and RESET are investigated to explain the resistive switching and self-rectifying I-V curves. The multi-level RESET and film-thickness dependence are also successfully simulated. Furthermore, the Ta/TaOx/TiO2/Ti non-filamentary RRAM model is applied to simulate various electronic synaptic characteristics, including potentiation, depression, spike-timing-dependent plasticity, and paired-pulse facilitation, and show excellent agreements with the experiment data.