The Resistivity Size Effect in Epitaxial Nb(001) and Nb(011) Layers
The Resistivity Size Effect in Epitaxial Nb(001) and Nb(011) Layers
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DOI：
10.1109/ted.2019.2924312
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发表时间：
2019-08
影响因子：
3.1
通讯作者：
E. Milosevic;Sit Kerdsongpanya;Mary E. McGahay;Baiwei Wang;D. Gall
中科院分区：
文献类型：
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作者：
E. Milosevic;Sit Kerdsongpanya;Mary E. McGahay;Baiwei Wang;D. Gall
外延 Nb(011) 和 Nb(001) 层分别溅射沉积到 ${a}$ 平面和 ${r}$ 平面蓝宝石衬底上，并在原位、异位和 77 K 下测量它们的电阻率 $\rho $，作为层厚度 ${d}= 4$ –400 nm 的函数。电阻率随着 ${d}$ 的减小而增加，与层方向无关，并用 Fuchs 和 Sondheimer (FS) 的模型进行描述，提供了室温下体电子平均自由程 $\lambda = {20} \pm {2}$ nm 的值。暴露在空气中会产生 1.5 nm 厚的表面氧化物，并且 $\rho $ 增加高达 74%，这表明表面散射镜面反射率从 Nb-真空界面处的 ${p}_{{{1}}}= {0.9} \pm {0.1}$ 降低到氧化 Nb 表面处的完全漫散射 ( ${p}_{{{1}}}= {0}$ )。或者，这种电阻的增加可归因于表面氧化过程中的粗糙化，同时保留完全漫散射，从而产生 9.0±0.4 nm 的室温 $\lambda $ 下限。体电阻率 $\rho _{o}$ 乘以 $\lambda $ 的乘积与温度无关，并且根据选择粗糙度或镜面反射解释，$\rho _{o}\,\,\lambda = {14}\times {10}^{{-{16}}}$ 或 ${30} \times {10}^{{-{16}}}\,\,\Omega \text{m}^{{{2}}}$ 分别。这些值比之前理论预测的 $\rho _{o}~\lambda $ 大 3.9 和 8.5 倍，表明 Nb 的经典 FS 模型发生了巨大的崩溃，并表明 Nb 中的电阻率尺寸效应比之前的预测要大得多。它们也比 W、Ru 和 Co 更大，使得 Nb 不适用于高电导率窄互连线。
Epitaxial Nb(011) and Nb(001) layers are sputter deposited onto ${a}$ -plane and ${r}$ -plane sapphire substrates, respectively, and their resistivity $\rho $ measured in situ, ex situ, and at 77 K as a function of layer thickness ${d}= 4$ –400 nm. The resistivity increase with decreasing ${d}$ is independent of layer orientation and is described with the model by Fuchs and Sondheimer (FS), providing a value for the bulk electron mean free path $\lambda = {20} \pm {2}$ nm at room temperature. Exposure to air causes a 1.5-nm-thick surface oxide and an increase in $\rho $ by up to 74%, suggesting a decrease in the surface scattering specularity from ${p}_{{{1}}}= {0.9} \pm {0.1}$ at the Nb-vacuum interface to completely diffuse scattering ( ${p}_{{{1}}}= {0}$ ) at the oxidized Nb surface. Alternatively, this increase in resistance can be attributed to roughening during surface oxidation while retaining completely diffuse scattering, yielding a lower bound for the room-temperature $\lambda $ of 9.0±0.4 nm. The product of the bulk resistivity $\rho _{o}$ times $\lambda $ is temperature-independent and, depending on either choosing the roughness or the specularity interpretation, $\rho _{o}\,\,\lambda = {14}\times {10}^{{-{16}}}$ or ${30} \times {10}^{{-{16}}}\,\,\Omega \text{m}^{{{2}}}$ , respectively. These values are 3.9 and 8.5 times larger than $\rho _{o}~\lambda $ from a previous theoretical prediction, indicating a dramatic break down of the classical FS model for Nb and indicating that the resistivity size effect in Nb is considerably larger than predicted earlier. They are also larger than for W, Ru, and Co, making Nb not promising for high-conductivity narrow interconnect lines.