﻿ 三维TSV集成电路电磁敏感性分析方法<sup>*</sup>
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Electromagnetic susceptibility analysis method for 3D TSV ICs
QIN Haichao, YAN Zhaowen, SU Donglin, ZHANG Wei
School of Electronic and Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2016-11-03; Accepted: 2016-12-16; Published online: 2017-02-07 11:17
Foundation item: National Natural Science Foundation of China (61271044, 61427803)
Corresponding author. YAN Zhaowen, E-mail:yanzhaowen@buaa.edu.cn
Abstract: This paper focuses on the circuit modeling method of through silicon via (TSV) and power distribution network (PDN) in 3D integrated circuits (3D ICs). Combined with the PDN on printed circuit board (PCB) and the chip PDN model, an electromagnetic susceptibility (EMS) modeling and collaborative analysis method for 3D ICs on PCB was proposed. Firstly, a ground-signal (GS) TSV pair and two TSV pairs of ground-signal1-signal2-ground (GSSG) were established in, and these circuit models were compared with the numerical simulation results, which validated the accuracy of the circuit modeling method of TSV. Then, the modeling method of PDN of PCB, PCB through via hole, IC's package parameters in an IC were discussed. Finally, an EMS cascade connection analysis model from PCB to 3D ICs was developed and used to analyze the electromagnetic susceptibility characteristics of 3D ICs to power interference, which can guide the susceptibility analysis of 3D ICs.
Key words: through silicon via (TSV)     circuit model of TSV     power distribution network (PDN)     electromagnetic susceptibility (EMS)     printed circuit board (PCB)

1 GS结构TSV的电路模型

 图 1 GS结构TSV对的立体图 Fig. 1 Space diagram of GS-structure TSV pair
 图 2 一个GS结构TSV对的电路模型 Fig. 2 Circuit model of single GS-structure TSV pair

 μm 参数 数值 h 100 rTSV 10 tOX 0.6 pTSV 40 t 1 t1 1 注：tOX—SiO2厚度；t1—铜平面厚度；t—SiO2平面厚度。

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L(x, h)为TSV的自感和互感计算公式。在计算自感时，x为其半径；在计算互感时，x为2个TSV之间的距离。

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CTSVGSi为TSV铜柱和半导体硅之间的容性效应电导引起的损耗。COX为顶层和底层TSV铜导体之间的容性耦合效应。

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 图 3 HFSS和ADS中S11和S21的结果对比 Fig. 3 Comparison of S11 and S21 resultsbetween HFSS and ADS
2 带有BUMP的GSSG结构TSV的电路模型

 dBUMP—凸点直径；dTSV—TSV直径；hBUMP—凸点高度。 图 4 GSSG结构的TSV示意图 Fig. 4 Schematic diagram of GSSG-structure TSV

 μm 参数 数值 hTSV 100 rTSV 10 tOX 0.6 pTSV 40 rBUMP 15 hBUMP 5 t 1 注：rBUMP—凸点半径; hTSV—TSV高度。

 参数 数值 σSi/(S·m-1) 10 σTSV/(107 S·m-1) 5.8 σBUMP/(107 S·m-1) 5.8 εr, Si 11.9 εr, OX 4 εr, BCB 2.65 μr, TSV 1 μr, BUMP 1 注：σBUMP—凸点电导率；εr, Si—硅相对介电常数；εr, BCB —BCB相对介电常数；μr, TSV、μr, BUMP —TSV、凸点相对磁导率。

 图 5 GSSG结构TSV的电路模型 Fig. 5 Circuit model of GSSG-structure TSV

 图 6 ADS中建立的GSSG结构TSV的等效电路图 Fig. 6 Equivalent circuit diagram of GSSG-structure TSV in ADS
 图 7 HFSS和ADS中S参数仿真结果对比 Fig. 7 Comparison of S parameter simulation results between HFSS and ADS
3 PCB到三维集成电路的电源分布网格模型 3.1 PCB电源/地平面建模

 图 8 完整电源/地矩形平面 Fig. 8 Intact power/ground plane

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3.2 过孔的分段式建模

 图 9 单个过孔结构的分解示意图 Fig. 9 Schematic diagram of single via hole structure divided into small parts
 图 10 单平面对中单个过孔的等效电路 Fig. 10 Equivalent circuit of single via in single plane

 图 11 三维集成电路与PCB板连接结构 Fig. 11 Connecting structure between 3D ICs and PCB

 图 12 HFSS中建立的电源过孔模型 Fig. 12 Power via hole models established in HFSS
 图 13 在电源过孔中心电源/地平面间设置集总端口 Fig. 13 Lumped port added between power and ground plane in center of power via hole
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PCB过孔本身存在着寄生电容，定义PCB过孔在铺地层上的阻焊区直径为d2，PCB过孔焊盘的直径为d1，PCB板的厚度为hPCB，则PCB过孔的寄生电容数值(单位为pF)近似于：

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 图 14 电源过孔电路模型 Fig. 14 Circuit model of power via hole
3.3 BGA封装参数提取

 图 15 BGA 64封装视图 Fig. 15 View of a BGA 64 package
 图 16 选取pin1~pin4作为GPPG引脚 Fig. 16 pin1 to pin4 chosen as GPPG pins

 电阻/Ω 电容与互容/pF 自感与互感/nH R11=0.143 C11=0.209 L11=3.732 R22=0.142 C22=0.221 L22=3.697 R33=0.134 C33=0.218 L33=3.408 R44=0.122 C44=0.210 L44=3.092 C12=0.073 L21=1.621 C23=0.071 L13=1.062 C24=0.002 L14=0.521 C34=0.060 L23=1.492 C13=0.002 L24=0.619 L34=0.749

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 图 17 pin1~pin4引脚的封装模型 Fig. 17 Package circuit model of pin1 to pin4
3.4 IC-PDN建模

1) 在HFSS建立IC-PDN模型，电源/地平面尺寸为1 mm×2 mm，铜厚为1 μm，介质为硅，介电常数为11.9，介质厚度为10 μm。在电源/地平面的中心添加集总端口仿真电源地平面S参数和阻抗参数。

 图 19 IC-PDN平面Z参数 Fig. 19 Z parameter of IC-PDN plane

3) 在ADS中建立串联LC模型，对阻抗参数拟合得到LC的值，如图 20所示。此时的电感为7.302 7 pH，电容为21.007 9 pF。

 图 20 LC串联电路模型 Fig. 20 Series circuit model with LC
3.5 三维集成电路敏感性预测模型

 图 21 敏感性协同仿真模型 Fig. 21 EMS collaborative simulation model

 图 22 敏感性协同仿真结果 Fig. 22 EMS collaborative simulation results

4 结论

1) 提出了单对GS结构TSV、多对GSSG结构TSV的准确电路模型。

2) 提出了PCB板PDN、三维集成电路PDN的建模方法。

3) 结合PCB和IC级PDN模型，提出一种三维集成电路电磁敏感性的建模分析方法。

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#### 文章信息

QIN Haichao, YAN Zhaowen, SU Donglin, ZHANG Wei

Electromagnetic susceptibility analysis method for 3D TSV ICs

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(12): 2406-2415
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0847