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以Arrhenius定律和电化学金属化器件中离子运动的超势理论作为离子运动的基础, 本文建立了修正的Mott-Gurney微分方程组. 虽然Mott-Gurney方程没有解析解, 但采用该方程可求出离子的平均位移. 再通过基于Cell的几何模型, 求出平均位移与导电细丝生长长度的关系. 得到电压与Forming/Set时间方程和导电细丝生长方程. 本文提出了一个提取离子的动力学参数的算法, 采用该算法计算了Ag/ γ-AgI/Pt, Ag/TiO 2/Pt, Ag/GeS 2/W和Cu/SiO 2/Au四种器件的电压-Forming/Set时间特性, 其计算结果与实验数据一致. 计算结果表明Ag +离子在单晶电介质γ-AgI, TiO 2和GeS 2中的跃迁步长是晶胞的某一个晶格常数, 而Ag离子在无定形SiO 2的跃迁步长是O—O键的1.57倍. 导电细丝生长时, Ag +离子在γ-AgI和TiO 2中的导电隧道是间隙隧道, 而在GeS 2和SiO 2中也存在阳离子的导电隧道, 这些导电隧道可以用周期势垒表示. 还计算了这4种器件的离子激活频率、势垒高度、迁移率、扩散系数和导电细丝生长长度与时间特性, 讨论了ECM器件电介质材料选择的标准.
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关键词:
- 阻性存储器/
- Forming/Set时间/
- 导电细丝/
- 跃迁步长和势垒
In this work, a system of modified Mott-Gurney differential equations is based on Arrhenius’ law and the overpotential theory of ionic motion in bipolar electrochemical metallization (ECM) resistive devices. The average displacement of ions is solved by the modified Mott-Gurney equation. Then, the relation between the average displacement and the growth length of the conductive filament is obtained by a geometric model based on cells. The equation of applied voltage versus Forming/Set time and the equation of length of conductive filament growth versus time are deduced by using this relation. In this work, an algorithm for extracting kinetic parameters of ions in a bipolar ECM device is also proposed. By using this algorithm, the characteristics of the applied voltage versus Forming/Set time for Ag/ γ-AgI/Pt, Ag/TiO 2/Pt, Ag/GeS 2/W, and Cu/SiO 2/Au devices are calculated and the calculation results are consistent with experimental data. It is found that in the Forming/Set process, the jump step of silver ion is the lattice constant along the cdirection of a unit cell of the crystal for TiO 2and the lattice constant of the cubic, a, for γ-AgI. These results are explained in the following. In a unit cell of the two crystals there are some tetrahedral and octahedral interstitial sites. The cationic motion path consists of alternating octahedral and tetrahedral sites or some octahedral sites. The cation jumps from tetrahedron to octahedron to tetrahedron, etc. in the γ-AgI with coplanar polyhedron and from octahedron to octahedron in the TiO 2with edge shared octahedron. In GeS 2crystal, it is found that the jump step of silver ions is the lattice constant in the cdirection of a unit cell. Owing to the periodicity of the lattice, the pathways of the ion motion in the three materials can be expressed by a periodic potential barrier each. For the jump situation of the copper ion in amorphous SiO 2, the jump step of copper ions is calculated to be 1.57 times the length of the O—O bond, and the jump pathway can also be explained by a periodic potential barrier. By introducing the cosine potential barrier, the ionic activation frequency, potential barrier height, ionic mobility and diffusion coefficient, and characteristics of the conductive filament growth versus time in several devices are calculated. The criteria of selecting dielectric materials for bipolar ECM devices are discussed by using these data. It is found that the standards for selecting dielectric materials of bipolar ECM devices are the ion activation energy ≤0.5 eV, preferably between 0.1–0.2eV, and the DC conductivity as close to 10 –4Ω –1·cm –1as possible. -
Keywords:
- bipolar resistive memory/
- Forming/Set time/
- conductive filament/
- jump step and potential barrier
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介质 晶胞类型 晶格常数/nm 跃迁步长as/nm 跃迁速率SA/s–1 VT/V σ SA的误差 γ-AgI fcc a= 0.65 0.65 2.0381×10+8 0.2941 0.2769 4.82% TiO2 Rutile a= 0.4594,
c= 0.29560.2956 1.0906×10–6 18.5 0.0082 2.78% GeS2 Monoclinic crystal a= 0.672,
b= 1.6101,
c= 1.14361.1436 4.6912×10+3 0.43 0.45 1.75% SiO2
(amorphous)Tetrahedral a= 0.227 0.357 Cu+: 13.3317,
Cu2+: 7.8867Cu+: 0.0461,
Cu2+: 0.0461Cu+: 0.0191,
Cu2+: 0.0398Cu+: 2.97%
Cu2+: 1.60%
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电介质 离子 as/nm ν/s–1 U0/eV μion/(cm2·V–1·s–1) Dion/(cm2·s–1) σd/(Ω·cm)–1 γ-AgI Ag+ 0.65 6.3193×1011 0.1584 3.3119×10–5 8.6110×10–7 10–5 [13] TiO2 Ag+ 0.2956 3.5913×1012 1.0591 3.6652×10–20 9.9257×10–22 2×10–8*[23],
≈10–5**[23]GeS2 Ag+ 1.1436 5.5495×1011 0.4346 2.3597×10–9 6.1352×10–11 1.25×10–4 [24] SiO2 Cu+ 0.357 2.9321×1012 0.6347 6.5350×10–13 1.6995×10–14 1.76×10–15 [25] SiO2 Cu2+ 0.357 2.9643×1012 0.6487 7.7319×10–13 1.0052×10–14 1.76×10–15 [25] 注:σd是电介质的电导率, TiO2电导率各向异性, *是垂直c轴的电导率, **是平行c轴的电导率. 下载:
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