The present study is an effort to develop a simple analytical model without any adjustable parameter for observing the collective effect of size, dimension and shape on electrical susceptibility and dielectric constant of nanomaterials. The size dependence of electrical susceptibility and dielectric constant has been observed for some pure as well as binary semiconductor nanomaterials, in three different dimensions (i.e., nanoparticles, nanowires and nanofilms). It has been observed that the electrical susceptibility and dielectric constant both show reduction with the decrement in size, due to the increased surface-to-volume ratio and lower coordination number. The present study reveals that the difference between the values of electrical susceptibility of nanoparticles and nanowires (5–50%) is less in comparison with nanofilms (10–90%). This difference diminishes on moving toward the higher size range. The decrement in the value of dielectric constant with size is found, maximum for nanoparticles (10–80%) followed by nanowires (10–70%) and minimum in nanofilms (5–60%). The outcomes for the size-dependent dielectric constant have been compared with the available experimental and other theoretical data and found consistency in calculated results with experimental data. The model has been extended to investigate the cross-sectional shape effect along with size on the electrical susceptibility and dielectric constant of nanowires due to large applications by incorporating shape factor. Four different cross-sectional shapes: spherical, square, rectangular and hexagonal nanowires, have been taken for the present study. The calculated results of dielectric constant have been compared with the available experimental data, and close agreement was found. It has been observed that the electrical susceptibility and dielectric constant have the highest value for spherical cross-sectional-shaped nanowires and the lowest for rectangular cross-sectional-shaped nanowires. Deviation graphs show that the values of electrical susceptibility and dielectric constant for rectangular, square and hexagonal cross-sectional-shaped nanowires deviate from spherical nanowires as 2–14%, 2–4% and 1–2%, respectively. The present study confirms the importance of shape effect along with size and dimension for electrical properties of semiconductor nanomaterials.

中文翻译：

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尺寸、尺寸和形状对半导体纳米材料电学行为影响的理论模型

本研究致力于开发一个没有任何可调参数的简单分析模型，用于观察尺寸、尺寸和形状对纳米材料的电敏感性和介电常数的集体影响。对于一些纯半导体纳米材料和二元半导体纳米材料，在三个不同的维度（即，纳米颗粒、纳米线和纳米膜）观察到电敏感性和介电常数的尺寸依赖性。已经观察到，由于表面积与体积比的增加和配位数的降低，电敏感性和介电常数都随着尺寸的减小而减小。本研究表明，与纳米膜（10-90%）相比，纳米颗粒和纳米线的电敏感性值（5-50%）之间的差异较小。这种差异随着向更高尺寸范围移动而减小。发现介电常数值随尺寸减小，纳米颗粒最大（10-80%），其次是纳米线（10-70%），纳米薄膜最小（5-60%）。尺寸相关介电常数的结果已与可用的实验和其他理论数据进行了比较，并发现计算结果与实验数据的一致性。通过结合形状因子，该模型已经扩展到研究横截面形状效应以及纳米线的电敏感性和介电常数的尺寸效应，因为纳米线的应用广泛。本研究采用了四种不同的横截面形状：球形、方形、矩形和六边形纳米线。将介电常数的计算结果与现有的实验数据进行了比较，发现非常吻合。已经观察到电导率和介电常数对于球形横截面形状的纳米线具有最高值，对于矩形横截面形状的纳米线具有最低值。偏差图显示，矩形、正方形和六边形横截面形状的纳米线的电导率和介电常数值与球形纳米线的偏差分别为 2-14%、2-4% 和 1-2%。本研究证实了形状效应以及尺寸和尺寸对半导体纳米材料的电性能的重要性。已经观察到电导率和介电常数对于球形横截面形状的纳米线具有最高值，对于矩形横截面形状的纳米线具有最低值。偏差图显示，矩形、正方形和六边形横截面形状的纳米线的电导率和介电常数值与球形纳米线的偏差分别为 2-14%、2-4% 和 1-2%。本研究证实了形状效应以及尺寸和尺寸对半导体纳米材料的电性能的重要性。已经观察到电导率和介电常数对于球形横截面形状的纳米线具有最高值，对于矩形横截面形状的纳米线具有最低值。偏差图显示，矩形、正方形和六边形横截面形状的纳米线的电导率和介电常数值与球形纳米线的偏差分别为 2-14%、2-4% 和 1-2%。本研究证实了形状效应以及尺寸和尺寸对半导体纳米材料的电性能的重要性。方形和六边形横截面形状的纳米线与球形纳米线的偏差分别为 2-14%、2-4% 和 1-2%。本研究证实了形状效应以及尺寸和尺寸对半导体纳米材料的电性能的重要性。方形和六边形横截面形状的纳米线与球形纳米线的偏差分别为 2-14%、2-4% 和 1-2%。本研究证实了形状效应以及尺寸和尺寸对半导体纳米材料的电性能的重要性。