ELECTRICAL-RESISTIVITY MODEL FOR POLYCRYSTALLINE FILMS - CASE OF ARBITRARY REFLECTION AT EXTERNAL SURFACES
ELECTRICAL-RESISTIVITY MODEL FOR POLYCRYSTALLINE FILMS - CASE OF ARBITRARY REFLECTION AT EXTERNAL SURFACES
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DOI：
10.1103/physrevb.1.1382
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发表时间：
1970-01-01
期刊：
影响因子：
--
通讯作者：
SHATZKES, M
中科院分区：
文献类型：
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作者：
MAYADAS, AF;SHATZKES, M
在本文中，从一个模型计算了金属薄膜的总电阻率，其中三种类型的电子散射机制同时起作用：各向同性背景散射（由于声子和点缺陷的联合作用），由平面电位分布（晶界）引起的散射，以及由外表面引起的散射。本征电阻率或体电阻率是通过求解同时考虑晶界和背景散射的玻尔兹曼方程得到的。总电阻率是通过强加边界条件，由于外部表面（如在富克斯理论）在这个玻尔兹曼方程。用计算的固有电阻率解释已发表的块状材料的晶界散射数据，用计算的总电阻率解释薄膜材料的晶界反射系数，结果表明：(1)Al的晶界反射系数≈0.15，而Cu的晶界反射系数略高；（ii）观察到的薄膜电阻率的厚度依赖性是由于晶界散射和Fuchs尺寸效应；（三）单晶薄膜比多晶薄膜具有更低的电阻率这一普遍现象可能是由于晶界效应，而不是由于表面散射性质的差异。
In this paper, the total resistivity of a thin metal film is calculated from a model in which three types of electron scattering mechanisms are simultaneously operative: an isotropic background scattering (due to the combined effects of phonons and point defects), scattering due to a distribution of planar potentials (grain boundaries), and scattering due to the external surfaces. The intrinsic or bulk resistivity is obtained by solving a Boltzmann equation in which both grain-boundary and background scattering are accounted for. The total resistivity is obtained by imposing boundary conditions due to the external surfaces (as in the Fuchs theory) on this Boltzmann equation. Interpretation of published data on grain-boundary scattering in bulk materials in terms of the calculated intrinsic resistivity, and of thin-film data in terms of the calculated total resistivity suggests that (i) the grain-boundary reflection coefficient in Al is≈ 0.15, while it is somewhat higher in Cu;(ii) the observed thickness dependence of the resistivity in thin films is due to grain-boundary scattering as well as to the Fuchs size effect; and (iii) the common observation that single-crystal films possess lower resistivities than polycrystalline films may be accounted for by grain-boundary effects rather than by differences in the nature of surface scattering.