Applied Physics A

, 124:790 | Cite as

A physical–statistical model for the growth process of carbon nanotubes

  • Mengqi Fan
  • Su Wu
  • Chi Xu


In the growth process of carbon nanotube (CNT) arrays, the height and flatness of the array must be controlled. In general, a profile control algorithm can be used to characterize the morphology of the CNT array through considering the parameters of the profile function as control objective. This paper examines the performance of the present model using real data and finds the defect of losing correlation information in the data. To solve this limitation, the semivariogram borrowed from geostatistics is introduced to add a spatial correlation. Furthermore, we drive the growth height formula based on a physical mechanism and then propose a physical–statistical model that contains a spatial correlation. Simulation and validation are provided to verify the performance of the new model.



The work was supported by the National Natural Science Foundation of China under Grant 71072012, and the Tsinghua University Initiative Scientific Research Program. The authors would like to thank Prof. S. Fan, Dr. L. Liu, and Dr. Q. Cai from Tsinghua-Foxconn Nanotechnology Research Center for providing the raw data and expertise on CNTs array production. They also thank to the National Natural Science Foundation of China.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Industrial EngineeringTsinghua UniversityBeijingChina

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