Fast and Accurate Power Distribution Network Modeling of a Silicon Interposer for 2.5-D/3-D ICs With Multiarray TSVs
Fast and Accurate Power Distribution Network Modeling of a Silicon Interposer for 2.5-D/3-D ICs With Multiarray TSVs
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DOI：
10.1109/tcpmt.2019.2895083
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发表时间：
2019-09-01
影响因子：
2.2
通讯作者：
Kim, Joungho
中科院分区：
文献类型：
--
作者：
Cho, Kyungjun;Kim, Youngwoo;Kim, Joungho
在本文中，我们首先提出了电源和接地（P/G）穿孔平面的电源分配网络（PDN）模型，包括基板效应和多阵列硅通孔（TSV）的硅中介层。由于它几乎是不可能的，以模拟一个高金属密度的穿孔PDN结构，我们首先提出了一种建模方法，P/G穿孔平面，以减少模拟时间显着与高精度。为了更快地获得硅中介层的PDN阻抗，我们将穿孔平面转换为具有电介质混合物的固体平面。基于保角映射方法，精确估计了穿孔P/G平面的电容（C）和电导（G）分量。从估计的C和G，固体P/G平面的电介质混合物的物理尺寸和材料特性的确定，分别。由于硅中介层PDN是一种周期性结构，我们对PDN的单元进行了详细的设计和分析。从单位单元分析，一个硅中介层的整个PDN的电特性被成功地估计。提出的固体和穿孔的P/G平面和模拟时间，以获得每个PDN阻抗的PDN阻抗进行了比较和评估，分别。所提出的方法进行了验证，通过一个完整的3-D电磁（EM）仿真的频率范围从0.01到20 GHz。我们还提出了多阵列P/G TSV的模型，可以应用于各种P/G图案的硅中介层。从考虑电流方向的电感矩阵，TSV的自感和互感的准确计算。由于准横向电磁模式通过TSV传播，并且硅中介层的衬底电介质可以被视为均匀电介质，因此可以从电感矩阵计算TSV的电容和电导。提出的多阵列TSV的模型也进行了分析和验证的EM模拟的频率范围从0.01到20 GHz的高精度。
In this paper, we first propose power distribution network (PDN) model of the perforated power and ground (P/G) planes including substrate effects and multiarray through-silicon vias (TSVs) for a silicon interposer. Since it is almost impossible to simulate a high metal density perforated PDN structure, we first suggest a modeling methodology for P/G perforated planes to reduce simulation time significantly with a high accuracy. To obtain the PDN impedance of a silicon interposer faster, we convert the perforated planes to solid planes with a dielectric mixture. The capacitance (C) and conductance (G) component of perforated P/G planes are precisely estimated based on the conformal mapping method. From the estimated C and G, the physical dimension and material properties of the dielectric mixture of solid P/G planes are determined, respectively. Because silicon interposer PDN consists of a periodic structure, we design and analyze the unit cell of a PDN thoroughly. From the unit cell analysis, the electrical characteristic of an entire PDN for a silicon interposer is successfully estimated. The PDN impedance of the proposed solid and perforated P/G planes and simulation time to obtain each PDN impedance are compared and evaluated, respectively. The proposed methodology is validated by a full 3-D electromagnetic (EM) simulation in the frequency range from 0.01 to 20 GHz. We also proposed models of multiarray P/G TSVs that can be applied to the various P/G patterns for a silicon interposer. From the inductance matrix considering current directions, the self- and mutual inductances of TSVs are accurately calculated. Because quasi-transverse electromagnetic mode is propagated through TSVs and the substrate dielectric of a silicon interposer can be regarded as a uniform dielectric, the capacitance and conductance of TSVs can be calculated from the inductance matrix. The proposed model of multiarray TSVs is also analyzed and verified by EM simulations in the frequency range from 0.01 to 20 GHz with a high accuracy.