Closed-form internal impedance model and characterization of mixed carbon nanotube bundles for three-dimensional integrated circuits  

作　　者：卢启军 朱樟明 杨银堂 丁瑞雪 李跃进 

机构地区：[1]School of Microelectronics, Xidian University

出　　处：《Chinese Physics B》2018年第1期520-525,共6页中国物理B（英文版）

基　　金：Project supported by the National Science and Technology Major Project of China(Grant No.2015ZX03001004);the National Natural Science Foundation of China(Grant Nos.61604113,61625403,61334003,61376039,61574104,and 61474088)

摘　　要：Based on the complex effective conductivity method, a closed-form expression for the internal impedance of mixed carbon nanotube （CNT） bundles, in which the number of CNTs for a given diameter follows a Gaussian distribution, is proposed in this paper. It can appropriately capture the skin effect as well as the temperature effect of mixed CNT bundles. The results of the closed-form expression and the numerical calculation are compared with various mean diameters, standard deviations, and temperatures. It is shown that the proposed model has very high accuracy in the whole frequency range considered, with maximum errors of 1% and 2.3% for the resistance and the internal inductance, respectively. Moreover, by using the proposed model, the high-frequency electrical characteristics of mixed CNT bundles are deeply analyzed to provide helpful design guidelines for their application in future high-performance three-dimensional integrated circuits.Based on the complex effective conductivity method, a closed-form expression for the internal impedance of mixed carbon nanotube （CNT） bundles, in which the number of CNTs for a given diameter follows a Gaussian distribution, is proposed in this paper. It can appropriately capture the skin effect as well as the temperature effect of mixed CNT bundles. The results of the closed-form expression and the numerical calculation are compared with various mean diameters, standard deviations, and temperatures. It is shown that the proposed model has very high accuracy in the whole frequency range considered, with maximum errors of 1% and 2.3% for the resistance and the internal inductance, respectively. Moreover, by using the proposed model, the high-frequency electrical characteristics of mixed CNT bundles are deeply analyzed to provide helpful design guidelines for their application in future high-performance three-dimensional integrated circuits.

关 键 词：mixed carbon nanotube （CNT） bundle internal impedance closed-form expression complex ef-fective conductivity method 

分 类 号：O4[理学—物理]