The resistivities of metal nanocrystalline materials exhibit significant size effect due to the additional scattering sites provided by grain boundaries compared to bulk materials. In this work, the authors investigate the electron ballistic transport in nanocrystalline materials under an applied electric field using the transfer-matrix approach. The theoretical results show that the resistivity increases remarkably due to the quantum effect for the grain size lower than the characteristic parameters such as the electron mean free path, and the predications are in excellent agreement with experimental data. The resistivity is also dependent on the external electric field when the grain size is at several nanometer scale.
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