雙穩態電阻變化元件的模型分析與探討

Model Analysis and Discussion of Bistable Resistance Changing Devices

10.6840/cycu201700664

陳昱霖

憶阻器 ； 非穩態格林函數 ； memristor ； The non-equilibrium Greens function ； NEGF

中原大學電子工程學系學位論文

2017年

碩士

陳至信

繁體中文

本研究論文是針對新型電子元件:憶阻器，以量子力學的薛丁格方程式，進行理論模型的模擬、分析與探討。 憶阻器是一種具有記憶功能的元件，其電阻值不是不變的，而是取決於過去流進多少電流的歷史，故可以記憶先前的電阻值，即便在斷電後，電阻值仍能維持不變。 過程是先以量子力學建構理論模型，探討憶阻器中的傳導電子，對此電子元件中的等效位能障壁，具穿隧特性的量子效應，再透過非穩定格林函數理論，對憶阻器理論模型所相應的薛丁格方程式求解。 解薛丁格方程式是利用量子穿隧效應中，電子所具有的能量與位能障壁的高低及寬度間的關係，設定元件內部的等效位能障壁，模擬類似於真實元件的物理狀態，進而將位能障壁加入非穩定格林函數理論中，運算得到電子的波函數，再計算出穿隧機率與電流。 模擬過程中因元件的位能障壁，會隨過往所加電壓的大小及時間長短而改變，導致元件具變電阻的特性，得到憶阻器類似磁滯曲線的電流電壓特性曲線。

This research focuses on the new electronic devices: memristor. According to the Schrödinger equation of quantum mechanics, we build a theoretical model to analyze and discuss the memristor mechanism. Memristor is a device with memory characteristics. Its resistance is variable, not a constant, which depends on how much current has flowed in what direction through it in the past. So it can remember the last resistance. The resistance value can be maintained even after the power off. Based on quantum mechanics, we construct a theoretical model to explore the conduction electrons of the memristor with quantum effect of tunneling characteristics for the equivalent potential barrier in this device. Then using the theory of non-equilibrium Green's function (NEGF) solves the Schrödinger equation of the memristor theoretical model. To solve Schrödinger equation, according to the relation of the electron energy with the height and the width of potential barrier from quantum tunneling effect, we set an inside equivalent potential barrier of the device to simulate the similar physical status of real device. Further to combine the equivalent potential barrier with the non-equilibrium Green’s function (NEGF) theory, we can get the wave function of the electron. Then the tunneling probability and the current can be calculated. In the simulation process, the potential barrier of device is variable according to the applied voltage magnitude and the applied time -interval. This effect induces device resistance variable. And finally we get a memristor with similar hysteresis curve of the current and voltage.

1. [1] Chua, Leon. "Memristor-the missing circuit element." IEEE Transactions on circuit theory 18.5 (1971): 507-519.
   連結：
2. [2] Strukov, Dmitri B., et al. "The missing memristor found." nature 453.7191 (2008): 80.
   連結：
3. [3] Yang, Yuchao, et al. "Observation of conducting filament growth in nanoscale resistive memories." Nature communications 3 (2012): 732.
   連結：
4. [4] Lee, Jae Sung, Shinbuhm Lee, and Tae Won Noh. "Resistive switching phenomena: A review of statistical physics approaches." Applied Physics Reviews 2.3 (2015): 031303.
   連結：
5. [5] Waser, Rainer. "Resistive non-volatile memory devices." Microelectronic Engineering 86.7 (2009): 1925-1928.
   連結：
6. [6] Datta, Supriyo. "Nanoscale device modeling: the Green’s function method." Superlattices and microstructures 28.4 (2000): 253-278.
   連結：
7. [9] Yalon, E., et al. "Detection of the insulating gap and conductive filament growth direction in resistive memories." Nanoscale 7.37 (2015): 15434-15441.
   連結：
8. [10] Yoon, Kyung Jean, et al. "Memristive tri-stable resistive switching at ruptured conducting filaments of a Pt/TiO2/Pt cell." Nanotechnology 23.18 (2012): 185202.
   連結：
9. [11] Wang, Changhong, et al. "Investigation and manipulation of different analog behaviors of memristor as electronic synapse for neuromorphic applications." Scientific reports 6 (2016): 22970.
   連結：
10. [12] Yang, J. Joshua, et al. "The mechanism of electroforming of metal oxide memristive switches." Nanotechnology 20.21 (2009): 215201.
    連結：
11. [13] Torrezan, Antonio C., et al. "Sub-nanosecond switching of a tantalum oxide memristor." Nanotechnology 22.48 (2011): 485203.
    連結：
12. [14] Yang, J. Joshua, Dmitri B. Strukov, and Duncan R. Stewart. "Memristive devices for computing." Nature nanotechnology 8.1 (2013): 13-24.
    連結：
13. [15] Lanza, Mario. "A review on resistive switching in high-k dielectrics: a nanoscale point of view using conductive atomic force microscope." Materials 7.3 (2014): 2155-2182.
    連結：
14. [18] S. Kim, S. Choi, and W. Lu, “Comprehensive Physical Model of Dynamic Resistive
    連結：
15. Switching in an Oxide Memristor,” ACS Nano, vol. 8, no. 3, pp. 2369–2376, 2014.
    連結：
16. [19] N. Ge, M.-X. Zhang, L. Zhang, J. J. Yang, Z. Li, and R. S. Williams,
    連結：
17. “Electrode-Material Dependent Switching in TaOx Memristors,” Semiconductor
    連結：
18. [20] Y.-E. Syu, T.-C. Chang, J.-H. Lou, T.-M. Tsai, K.-C. Chang, M.-J. Tsai, Y.-L. Wang,
    連結：
19. M. Liu, and S. M. Sze, “Atomic-level Quantized Reaction of HfOx Memristor,”
    連結：
20. Temperature,” IEEE Electron Device Letters, vol. 34, no. 12, pp. 1506–1508, 2013.
    連結：
21. Resistance Switching in Polycrystalline NiO Films,” Applied Physics Letters, vol.
    連結：
22. [23] N. Ge, M.-X. Zhang, L. Zhang, J. J. Yang, Z. Li, and R. S. Williams,
    連結：
23. “Electrode-Material Dependent Switching in TaOx Memristors,” SemiconductorScience and Technology, vol. 29, no. 10, p. 104 003, 2014.
    連結：
24. [25] Y. V. Pershin, S. La Fontaine, and M. Di Ventra, “Memristive Model of Amoeba Learning,” Phys. Rev. E, vol. 80, no. 2, p. 021 926, 2009.
    連結：
25. [26] M. A. Zidan, H. Omran, C. Smith, A. Syed, A. G. Radwan, and K. N. Salama, “A Family of Memristor-Based Reactance-Less Oscillators,” International Journal of Circuit Theory and Applications, vol. 42, no. 11, pp. 1103–1122, 2014.
    連結：
26. [28] R. Williams, “How We Found The Missing Memristor,” Spectrum, IEEE, vol. 45,no. 12, pp. 28–35, 2008.
    連結：
27. [32] J. Shin, I. Kim, K. P. Biju, M. Jo, J. Park, J. Lee, S. Jung, W. Lee, S. Kim, S. Park,and H. Hwang, “TiO2-Based Metal-Insulator-Metal Selection Device for Bipolar Resistive Random Access Memory Cross-Point Application,” Journal of Applied Physics, vol. 109, no. 3, p. 033 712, 2011.
    連結：
28. [33] Larentis, Stefano, et al. "Resistive switching by voltage-driven ion migration in bipolar RRAM—Part II: Modeling." IEEE Transactions on Electron Devices 59.9 (2012): 2468-2475.
    連結：
29. [7] Datta, Supriyo. Quantum transport: atom to transistor. Cambridge University Press, 2005.
30. [8]Sullivan, Dennis M. Quantum Mechanics for Electrical Engineers. Vol. 23. John Wiley & Sons, 2011.
31. [16] Brunson, Jerilyn. "Hopping conductivity and charge transport in low density polyethylene." (2010). [17] J. C. Yuan Xie and S. Sapatnekar, Eds., Three Dimensional Integrated Circuit Design. Springer US, 2010.
32. Science and Technology, vol. 29, no. 10, p. 104 003, 2014.
33. Applied Physics Letters, vol. 102, no. 17, 172903, 2013.
34. [21] D.-q. Liu, H.-f. Cheng, G. Wang, X. Zhu, and Z.-z. Shao, “Memristive Properties
35. of Transparent (La, Sr)MnO3 Thin Films Deposited on ITO Glass at Room
36. [22] S. Seo, M. J. Lee, D. H. Seo, E. J. Jeoung, D.-S. Suh, Y. S. Joung, I. K. Yoo, I. R.
37. Hwang, S. H. Kim, I. S. Byun, J.-S. Kim, J. S. Choi, and B. H. Park, “Reproducible
38. 85, no. 23, pp. 5655–5657, 2004.
39. [24] Y.-E. Syu, T.-C. Chang, J.-H. Lou, T.-M. Tsai, K.-C. Chang, M.-J. Tsai, Y.-L. Wang,M. Liu, and S. M. Sze, “Atomic-level Quantized Reaction of HfOx Memristor,”Applied Physics Letters, vol. 102, no. 17, 172903, 2013.
40. [27] T. Driscoll, J. Quinn, S. Klein, H. T. Kim, B. J. Kim, Y. V. Pershin, M. Di Ventra,and D. N. Basov, “Memristive Adaptive Filters,” Applied Physics Letters, vol. 97,no. 9, p. 093 502, 2010.
41. [29] H. Kim, M. Sah, C. Yang, and L. Chua，”Memristor-Based Multilevel Memory,”in 12th International Workshop on Cellular Nanoscale Networks and Their Applications (CNNA), 2010, pp. 1–6.
42. [30] B. Abdoli, A. Amirsoleimani, J. Shamsi, Karim, M. Arash, and Ahmadi, “A Novel CMOS-Memristor Based Inverter Circuit Design,” in 22nd Iranian Conference on Electrical Engineering (ICEE), IEEE, 2014, pp. 371–276.
43. [31] Q. Xia, W. Robinett, M. W. Cumbie, N. Banerjee, T. J. Cardinali, J. J. Yang, W.Wu, X. Li, W. M. Tong, D. B. Strukov, G. S. Snider, G. Medeiros-Ribeiro, and R. S. Williams, “Memristor-CMOS Hybrid Integrated Circuits for Reconfigurable Logic,” Nano Letters, vol. 9, no. 10, pp. 3640–3645, 2009.