Cu-CNT异质同轴硅通孔的电学特性优化与设计指导

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本文是一篇发表在《2017年7月IEEE Transactions on Nanotechnology》第16卷第4期的研究论文，标题为“Cu-CNT异质同轴硅通孔（HCTSVs）的电学建模与分析”。作者通过对3维集成电路（3-D ICs）中的铜-单壁碳纳米管（Cu-SWCNT）和铜-多壁碳纳米管（Cu-MWCNT）异质同轴穿硅通孔（HCTSVs）进行深入研究，提出了一个等效电路模型。研究的核心内容是利用复有效导电性方法来比较铜制单壁和多壁碳纳米管HCTSV的电阻和电感特性，以及它们与传统的铜同轴穿硅通孔（Cu-CTSVs）的性能对比。研究表明，Cu-SWCNT HCTSV由于其更高的金属成分，其传输性能优于Cu-CTSVs。特别是Cu-MWCNT HCTSVs在高频下的表现更佳，显示出明显的改进。论文重点探讨了Cu-MWCNT HCTSVs的传输特性，这对于未来高速3-D ICs的设计具有重要的指导意义。通过这些模型和分析，设计者可以更好地理解如何优化碳纳米管增强的Cu-HCTSV结构，以满足高速、低损耗的需求，从而推动3-D IC技术的发展。文章的关键索引术语包括3-D ICs、铜基材料、碳纳米管、异质同轴结构、穿硅通孔、等效电路模型、插入损耗和高频性能。这项工作不仅提供了对新型HCTSV设计的重要理论依据，还为高性能电子器件的集成和优化提供了实用的设计策略。通过深入理解这些纳米材料在三维集成中的作用，可以预见未来的电子设备将更加紧凑、高效，有助于缩小芯片尺寸并提升整体性能。

IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 16, NO. 4, JULY 2017 695

Electrical Modeling and Analysis of Cu-CNT

Heterogeneous Coaxial Through-Silicon Vias

Qijun Lu, Zhangming Zhu, Yintang Yang, Ruixue Ding, and Yuejin Li

Abstract—An equivalent-circuit model of Cu-carbon nanotube

heterogeneous coaxial through-silicon vias (HCTSVs) in 3-D inte-

grated circuits (3-D ICs) is proposed in this paper. Based on the

complex effective conductivity method, the resistances and induc-

tances of Cu-single walled carbon nanotube (SWCNT) HCTSVs

and Cu-multi walled carbon nanotube (MWCNT) HCTSVs are

compared with that of Cu coaxial through-silicon vias (CTSVs).

Furthermore, using the proposed model, the magnitudes of their

insertion losses are compared. It is shown that the transmission

performance of Cu-SWCNT HCTSVs with higher metallic frac-

tion and Cu-MWCNT HCTSVs is better than that of Cu CTSVs,

and the improvement of Cu-MWCNT HCTSVs is more obvious at

high frequencies. Finally, the transmission characteristics of Cu-

MWCNT HCTSVs are analyzed deeply to provide helpful design

guidelines for them in future high-speed 3-D ICs.

Index Terms—3-D integrated circuits (3-D ICs), carbon nan-

otube (CNT), equivalent-circuit model, heterogeneous coaxial

through-silicon vias (HCTSVs), transmission characteristics.

I. INTRODUCTION

INCE the scaling limits of physics, technology, and econ-

omy encountered in planar integrated circuits become in-

creasingly prominent, and to meet the continuous demand

for miniaturized, high performance, and high-speed microelec-

tronic systems, three-dimensional integrated circuits (3-D ICs)

have attracted great interest of researchers [ 1]–[3]. Through sil-

icon vias (TSVs), which are high aspect ratio vertical intercon-

nects providing connectivity between active layers, constitute a

key component of 3-D ICs [4]–[6]. They have the potential ben-

eﬁts of improving the electrical performance including speed,

bandwidth, and functionality, and reducing power consumption

by shortening the interconnection path in 3-D ICs [7], [8].

Coaxial through-silicon vias (CTSVs), which use an outer

shell both as the return path of the inner signal wire and as the

shielding layer, can effectively reduce signal loss and coupling

noise, and their characteristic impedance is easy to be controlled.

Manuscript received August 27, 2016; revised January 19, 2017 and March 27,

2017; accepted May 21, 2017. Date of publication May 26, 2017; date of current

version July 7, 2017. This work was supported in part by the National Basic Re-

search Program of China (973 Program) under Grant 2014 CB339900 and in part

by the National Natural Science Foundation of China under Grant 61604113,

Grant 61625403, Grant 61334003, Grant 61376039, Grant 61574104, and Grant

61474088. (Corresponding author: Zhangming Zhu.)

The authors are with the School of Microelectronics, Xidian Univer-

sity, Xi’an 710071, China (e-mail: luqijun2000@126.com; zmyh@263.net;

yangyt@xidian.edu.cn; rxding@mail.xidian.edu.cn; yjli@mail.xidian.edu.cn).

Color versions of one or more of the ﬁgures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TNANO.2017.2708509

Therefore, the fabrication of Cu CTSVs was implemented

[9], [10], and their frequency- and temperature-dependent

equivalent-circuit model [11] and wideband impedance model

were proposed [12]. Furthermore, the latency, power, insertion

loss, and crosstalk of Cu CTSVs were evaluated and compared

with that of Cu signal-ground TSV pairs, respectively, showing

that Cu CTSVs have better electrical performance [13]. On the

other hand, due to their extremely desirable properties of high

mechanical and thermal stability, high thermal and electrical

conductivity, and large current carrying capacity, carbon

nanotube (CNT) bundles have been identiﬁed as a promising

candidate for next generation high-speed interconnect systems

even if at present the fabricating cost is much higher [14]–[16].

Recently, CNT bundle TSV arrays were fabricated successfully

using various methods [17]–[21], and the equivalent-circuit

model of single walled carbon nanotube (SWCNT) bundle

signal-ground TSV pairs was established [22]. Then, the

stacking of silicon chips with CNT TSVs was experimentally

demonstrated [23]. Furthermore, the equivalent-circuit model

[24] and the electrothermal cosimulation [25] of carbon

heterogeneous interconnects consisting of horizontal multilayer

graphene transmission lines and vertical CNT TSVs were also

reported. In addition, the CNT-Cu composite can also be used as

the conducting material of TSVs, and the mechanical integrity

[26] and the thermo-mechanical stresses and reliability analysis

[27] of Cu-CNT hybrid TSVs were investigated deeply.

The objectives of this paper are t o propose an equivalent-

circuit model of Cu-CNT heterogeneous coaxial through-silicon

vias (HCTSVs), which use CNT bundle and Cu as their inner

signal wire and shielding layer conducting materials, respec-

tively, and study their transmission characteristics. Its organi-

zation is as follows. In Section II, an equivalent-circuit model

of Cu-CNT HCTSVs is proposed and simpliﬁed. Using the

proposed model, the resistances, inductances, and transmission

performance of Cu-CNT HCTSVs are compared with that of

Cu CTSVs, respectively, in Section III. Furthermore, a deep

analysis of transmission characteristics of Cu-multi walled car-

bon nanotube (MWCNT) HCTSVs is carried out in Section IV.

Finally, some conclusions are drawn in Section V.

II. E

QUIVALENT-CIRCUIT MODEL OF CU-CNT HCTSVS

The 3-D and cross-sectional views of a Cu-CNT HCTSV

conﬁguration are shown in Fig. 1, where H and r

(i =

1 − 6) are the height and the radii, respectively. In this pa-

per, the equivalent-circuit model of Cu-CNT HCTSVs is de-

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Cu-CNT异质同轴硅通孔的电学特性优化与设计指导

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