Contents Introduction 介绍
Recently, the demands on high computing systems have been expanding every year. While conventional 2Dimensional (2D) Interconnects has reached its limitation and is insufficient to satisfy the required system bandwidth, interposer-based 2.5Dimensional (2.5D) Interconnects and 3Dimensional (3D) Interconnects have been highlighted as the key solution to realize the improved system bandwidth. Vertical integration of chips on 2.5D/3D Interconnects has substantially shorter interconnection length and smaller form factor, which allow reduced power consumption and higher bandwidth within a limited area. In 2.5D/3D Interconnects, interposer is needed to route large number of signal traces between chip-to-chip and chip-to-package interconnects. Further, to achieve a higher bandwidth within a limited routing area, the data rate of each pin is increasing and metal-to-metal space between the adjacent channels is decreasing. For example, the data rate of the GDDR5, which is embedded in Ultra High Definition Television (UHDTV), is about to beyond 10 Gbps/pin between GPU-to-GDDR5 [1]–[2]. Also, to achieve wide I/O and higher bandwidth, the number of pin in a memory is increasing tremendously; especially, High-Bandwidth Memory (HBM) has 1024 I/Os for 1TB channel bandwidth. This large number of I/Os between HBM and GPU are routed on a silicon interposer and fine pitch channels are susceptible to unexpected crosstalk effects [3]–[4]. Thus, the distortion of the eye-diagrams from crosstalk effects in the high-speed and wide number of I/O interposer channels on 2.5D/3D Interconnects has become more significant. Fig. 1 describes the distortion of the eye-diagrams from crosstalk effects on interposer channels. As the operating frequency of the electronic devices is increasing, not only the crosstalk effects, but also inter-symbol interference (ISI) and channel loss of the substrate degrade the eye-diagram. If the eye-diagram is too much distorted, it could not be able to recover the original transmitted signal at the receiver. Therefore, signal integrity analysis of the high-speed interposer channel is important in pre-manufacturing process. In this paper, we introduced an efficient eye-diagram and Bit-Error Rate (BER) contour prediction method for shorter simulation time and more convenience with maintaining high-accuracy. Then, the proposed method is applied to analyze the signal integrity of silicon/glass/organic interposer channels on 2.5D/3D interconnects.
近年来，对高计算系统的需求逐年扩大。虽然传统的二维 (2D) 互连已达到其局限性，不足以满足所需的系统带宽，但基于中介层的 2.5 维 (2.5D) 互连和三维 (3D) 互连已被视为实现提高系统带宽的关键解决方案。 2.5D/3D互连芯片的垂直集成具有更短的互连长度和更小的外形尺寸，从而可以在有限的面积内降低功耗并提高带宽。在 2.5D/3D 互连中，需要中介层来在芯片到芯片和芯片到封装互连之间路由大量信号走线。此外，为了在有限的布线区域内实现更高的带宽，每个引脚的数据速率正在增加，并且相邻通道之间的金属到金属的空间正在减小。例如，超高清电视 (UHDTV) 中嵌入的 GDDR5 的数据速率即将超过 GPU 到 GDDR5 之间的 10 Gbps/引脚 [1] – [2] – [4] 。因此，2.5D/3D 互连上的高速和大量 I/O 内插器通道中的串扰效应导致的眼图失真变得更加严重。 Fig. 1 描述了内插器通道上的串扰效应导致的眼图失真。 随着电子设备的工作频率不断增加，不仅串扰效应、符号间干扰（ISI）和基板的通道损耗都会降低眼图的质量。如果眼图失真太大，则无法在接收器处恢复原始传输信号。因此，高速内插器通道的信号完整性分析在预制造过程中非常重要。在本文中，我们引入了一种有效的眼图和误码率（BER）轮廓预测方法，可以缩短仿真时间，更方便，同时保持高精度。然后，应用所提出的方法来分析 2.5D/3D 互连上硅/玻璃/有机中介层通道的信号完整性。
Distrtion of the eye-diagrams from crosstalk effects on silicon/glass/organic interposer with (a) Wide metal space (b) Narrow metal space. Wide I/O has narrow metal space signaling and it has larger crosstalk effects than the wide metal space design.
硅/玻璃/有机中介层上串扰效应的眼图分布（a）宽金属空间（b）窄金属空间。宽 I/O 具有窄金属空间信号传输，并且比宽金属空间设计具有更大的串扰效应。
Currently, three materials; silicon/glass/organic, are widely adopted to the packaging techniques. Each material has different advantages and disadvantages. Silicon interposer can be fabricated in fine pitch patterning and has suitable Coefficient of Thermal Expansion (CTE), In contrast, the cost is relatively higher than the other substrates. Glass interposer has closely-matched CTE with low cost. Organic interposer is cost effective, but the I/O density is low and causes CTE mismatches [5]–[8]. The strengths and weaknesses of silicon/glass/organic interposers are introduced in this paper. Also, the paper proposed and simulated the structure of interposer channel. It has 5 metal lines in order of Ground, Signal 1, Signal 2, Signal 3, and Ground which are made of copper. Signal 1 and Signal 3 are the aggressor channels and Signal 2 is the victim channel. Signal 2 will be distorted by the crosstalk effects from Signal 1 and Signal 3. The simulated structures are assumed to have the same design and physical dimensions to analyze only for the material's effects on eye-diagram. The material properties and characteristics of silicon/glass/organic interposer are described in the following section. The permittivity of materials is 11.2, 5.3, and 4.4 for silicon, glass, and organic, respectively. Since they have different electrical properties, the interposer channels show different results. The simulated and estimated results are obtained at data rate of 10 Gbps, which will be applied to the next generation of GDDR series.
目前，三种材料；硅/玻璃/有机材料，被广泛采用的封装技术。每种材料都有不同的优点和缺点。硅中介层可以以细间距图案化制造，并具有合适的热膨胀系数(CTE)，但成本相对高于其他基板。玻璃中介层具有紧密匹配的CTE且成本低。有机中介层具有成本效益，但 I/O 密度较低并导致 CTE 不匹配 [5] – [8] 。本文介绍了硅/玻璃/有机中介层的优点和缺点。此外，本文还提出并模拟了内插器通道的结构。它有 5 根金属线，依次为地、信号 1、信号 2、信号 3、地，材质为铜。信号 1 和信号 3 是攻击者通道，信号 2 是受害者通道。信号 2 将因信号 1 和信号 3 的串扰效应而失真。假设模拟结构具有相同的设计和物理尺寸，以便仅分析材料对眼图的影响。硅/玻璃/有机中介层的材料属性和特性将在以下部分中描述。硅、玻璃和有机材料的介电常数分别为 11.2、5.3 和 4.4。由于它们具有不同的电气特性，因此中介层通道显示出不同的结果。仿真和估算结果是在10 Gbps数据速率下获得的，该结果将应用于下一代GDDR系列。
As a result, the silicon interposer shows the smallest inner eye contour due to the lossy substrate. The eye opening voltages are 0.36 V and 0.34 V from the worst eye-diagram inner contour and BER contour, respectively. The glass interposer shows the largest eye opening voltage, 0.44 V and 0.42V from the obtained worst eye-diagram inner contour and BER contour. However, since the silicon has the lowest crosstalk level, due to diminished crosstalk effects by its lossy substrate. The insertion loss of interposer channel on glass and organic interposer are relatively low, since they have smaller loss tangent and lower permittivity values. Equations for understanding the relation between material properties, frequency, and insertion loss will be explained. Therefore, to obtain higher data rate system, if glass interposer might be fabricated within fine pitch as the silicon's fabrication process, glass interposer will be the most suitable material for the next generation of high bandwidth interposer channel for 2.5D/3D interconnects.
因此，由于有损耗的基板，硅中介层显示出最小的内眼轮廓。最差眼图内部轮廓和 BER 轮廓的眼图张开电压分别为 0.36 V 和 0.34 V。从获得的最差眼图内部轮廓和 BER 轮廓来看，玻璃中介层显示出最大的眼图张开电压，分别为 0.44V 和 0.42V。然而，由于硅具有最低的串扰水平，这是由于其有损耗的基板减少了串扰效应。玻璃和有机中介层上的中介层通道的插入损耗相对较低，因为它们具有较小的损耗角正切和较低的介电常数值。将解释用于理解材料特性、频率和插入损耗之间关系的方程。因此，为了获得更高数据速率的系统，如果玻璃中介层可以像硅的制造工艺那样以细间距制造，那么玻璃中介层将是下一代2.5D/3D互连高带宽中介层通道的最合适材料。
Eye-Diagram Estimation Method for Signal Integrity Analysis of Silicon/Glass/Organic Interposer
用于硅/玻璃/有机中介层信号完整性分析的眼图估计方法
Eye diagram is a graphical index that indicates signal integrity and performance of the high-speed channel. The eye diagram shows the amplitude of the noise voltage and timing jitter within a picture. The eye opening voltage indicates the voltage noise margin from the received data, whereas the timing jitter shows timing variation of the received data. Crosstalk level notices the voltage fluctuation on DC levels with over- and under-shoot area. Thus, in this paper, eye-diagram will be estimated for signal integrity analysis of silicon/glass/organic interposers.
眼图是指示高速通道信号完整性和性能的图形指标。眼图显示了图像中噪声电压的幅度和定时抖动。眼图张开电压表示接收数据的电压噪声容限，而时序抖动表示接收数据的时序变化。串扰水平注意到直流电平上的电压波动以及过冲和下冲区域。因此，在本文中，将估计眼图以用于硅/玻璃/有机中介层的信号完整性分析。
Conventionally, PRBS input signals are used to achieve eye diagram. However, we propose that 8 worst case input signals are used to achieve eye opening voltage, timing jitter, and crosstalk levels. 8 worst case input signals for eye diagram estimation is illustrated in Fig. 2(a) ∼ (c). Fig. 2(a) shows the maximized crosstalk effect cases. Fig. 2(b) illustrates that crosstalk effects can be canceled out due to its opposite phase of transitions. Fig. 2(c) describes the 8 worst cases, which build the worst case inner contour and the worst case DC level. The boundary lines of the eye diagrams are consisted of 8 worst output responses. The victim channel is influenced when the aggressor channel transits its voltage stage from VL to VH or VH to VL. However, if the aggressor channel is not in the transition, victim channel will not be affected from the aggressor, that means the output response will be located on the middle of the boundary lines, which is less important to be analyzed. Fig. 2(b) shows its cases. In Fig. 2(c), Case (1) ∼ (4) make inner contour of the eye-diagram, and case (5) ∼ (8) represent for the DC crosstalk level. Finally, 8 worst output cases should be overlapped in a certain Unit-Interval (UI) and timing-shifted to plot the worst eye diagram. After finding 8 boundary lines of the worst eye-diagram, eye opening voltage, timing jitter, and crosstalk level values can be achieved. This method will be applied to analyze and compare the silicon/glass/organic interposer channels.
传统上，PRBS输入信号用于获得眼图。然而，我们建议使用 8 个最坏情况输入信号来实现眼图张开电压、定时抖动和串扰水平。 Fig. 2(a) ∼ (c) 中说明了用于眼图估计的 8 个最坏情况输入信号。 Fig. 2(a) 显示了串扰效应最大化的情况。 Fig. 2(b) 说明串扰效应可以因其相反的转换相位而被抵消。 Fig. 2(c) 描述了8种最坏情况，构建了最坏情况内轮廓和最坏情况直流电平。眼图的边界线由 8 个最差的输出响应组成。当攻击者通道将其电压阶段从 VL 转变为 VH 或从 VH 转变为 VL 时，受害者通道就会受到影响。然而，如果攻击者通道不在转换中，受害者通道将不会受到攻击者的影响，这意味着输出响应将位于边界线的中间，这对于分析来说不太重要。 Fig. 2(b) 显示其案例。在 Fig. 2(c) 中，Case (1) ∼ (4) 表示眼图的内部轮廓，Case (5) ∼ (8) 表示直流串扰电平。最后，8 个最差的输出情况应在一定的单位间隔 (UI) 中重叠并进行时移以绘制最差的眼图。找到最差眼图的 8 条边界线后，即可获得眼图张开电压、时序抖动和串扰电平值。该方法将用于分析和比较硅/玻璃/有机中介层通道。
(a) Output response and crosstalk response on the victim channel at the same phase of aggressor channels. (b) Output response and crosstalk response on the victim channel at the opposite phase of aggressor channels. (c) 8 superposition cases for worst eye-diagram estimation. Each case makes the 8 worst case boundary lines, which builds the worst case inner contour and the worst case of DC level.
(a) 与攻击者通道相同相位的受害者通道上的输出响应和串扰响应。 (b) 与攻击者通道相反相位的受害者通道上的输出响应和串扰响应。 (c) 最差眼图估计的 8 种叠加情况。每种情况都制作8条最坏情况边界线，从而构建最坏情况内部轮廓和最坏情况直流电平。
Simulation Setup and Comparison of Silicon/Glass/Organic Interposer Interconnects
硅/玻璃/有机中介层互连的仿真设置和比较
A. Simulation Setups for Eye-Diagram Estimation of Silicon/Glass/Organic Interposer Interconnects
A. 硅/玻璃/有机中介层互连的眼图估计的仿真设置
Fig. 3 describes the simplified circuit model for the eye diagram estimation of three different interposer substrates.
Fig. 3 描述了用于三种不同中介层基板的眼图估计的简化电路模型。
Simplified circuit model to estimate eye-diagrams on silicon/glass/organic interposer interconnects
用于估计硅/玻璃/有机中介层互连上的眼图的简化电路模型
Three signal lines, which should be routed in narrow space to achieve higher system bandwidth, but can degrade each other by crosstalk effects, will be designed and simulated. The input signals
将设计并模拟三条信号线，这三条信号线应在狭窄的空间内布线以实现更高的系统带宽，但会因串扰效应而相互降低性能。输入信号
B. Simulated Structure and Material Properties of Silicon, Glass, Organic Interposers
B. 硅、玻璃、有机中介层的模拟结构和材料特性
Fig. 4 shows the structure of the simulated various interposer channel. To compare the difference of the material only, we assumed to share the same design and dimensions for three different interposers, however, the material properties of substrates and dielectrics are applied differently. Even though organic and glass interposer do not satisfy the fine pitch patterning of silicon, we expected the fabrication process of organic and glass interposer will be possible as silicon in the future. Three signal lines are routed in narrow space, so that can be degraded by crosstalk effects each other. 5 metal lines are routed respectively in (GND/SIG1/SIG2/SIG3/GND), which are made of copper. Signal 1 and Signal 3 are the aggressor channels and Signal 2 is the victim channel. Signal 2 will be distorted by the crosstalk effects from Signal 1 and Signal 3.
Fig. 4 显示了模拟的各种内插器通道的结构。仅为了比较材料的差异，我们假设三种不同的中介层具有相同的设计和尺寸，但是，基板和电介质的材料特性应用不同。尽管有机和玻璃中介层不能满足硅的精细间距图案化，但我们预计有机和玻璃中介层的制造工艺在未来将可能像硅一样。 3条信号线走线在狭窄的空间内，因此会因相互串扰而降低性能。 （GND/SIG1/SIG2/SIG3/GND）分别走5条金属线，材质为铜。信号 1 和信号 3 是攻击者通道，信号 2 是受害者通道。信号 2 将因信号 1 和信号 3 的串扰效应而失真。
Cross-sectional view of the 3 channels system on silicon/glass/organic interposer with material properties. Physical dimensions are assumed to be same to compare the channel performance of each interposer.
硅/玻璃/有机中介层上 3 通道系统的横截面图以及材料特性。假设物理尺寸相同，以比较每个内插器的通道性能。
表 I. 硅/玻璃/有机中介层通道的材料特性
表二.硅/玻璃/有机中介层特性比较
The material properties of silicon/glass/organic interposer are described in Table I. In addition, the characteristics of silicon/glass/organic interposer are summarized in Table II. Permittivity of materials are 11.2, 5.3, 4.4 for silicon/glass/organic, respectively. Due to their different material properties, the interposer channels will have different results in eye-diagram.
硅/玻璃/有机中介层的材料特性在 Table I 中描述。另外， Table II 中总结了硅/玻璃/有机中介层的特性。硅/玻璃/有机材料的介电常数分别为11.2、5.3、4.4。由于其材料特性不同，内插器通道在眼图中会有不同的结果。
Comparison and Analysis of Eye-Diagram of Silicon/Glass/Organic Interposer Interconnects for 2.5D/3D Interconnects
2.5D/3D 互连的硅/玻璃/有机中介层互连的眼图比较和分析
A. Eye-Diagram of Silicon/Glass/Organic Interposer Interconnects
A. 硅/玻璃/有机中介层互连的眼图
Eye diagram estimation results of silicon/glass/organic interposer interconnects at the data rate of 10 Gbps are figured in Fig. 5. All of eye diagrams are obtained by using the proposed method, and analyzed to compare the three different interposer substrates. The crosstalk effects are captured at the DC levels of VL & VH and voltage transition time as ripples. These ripples can be out of the permitted region of over- and under-shoot area. For example, HBM specification allows 0.35 V of over- and under-shoot area [4]. The ripples on switching regions are made by output responses of case (1) ∼ (4) and crosstalk effect near VL and VH is made from the case (5) ∼ (8). By overlapping the case (1) ∼ (4), eye opening voltage and timing jitter can be achieved. Likewise, crosstalk level on DC is achieved from case (5) ∼ (8). Timing jitter is increased and eye diagram is more distorted because of the crosstalk effects. Therefore, the bandwidth might be limited by the distortion factors such as ISI, loss, and crosstalk effect, which are mentioned previously. From the Fig. 5, The estimated silicon interposer eye diagram shows the lowest crosstalk effect among all three substrates. Since the crosstalk effects from the aggressor channel is so small that it can be diminished by the lossy characteristic of the silicon. Moreover, eye opening voltage is relatively low due to its lossy characteristic. Silicon interposer interconnect has the smallest worst eye diagram. In contrast, since glass and organic substrate are not lossy as the silicon, these interconnects include higher crosstalk effects on their eye diagrams than the eye diagram of silicon interposer. However, glass and organic substrates have larger eye opening voltages than silicon. In short, three interposers have different frequency-dependent channel's characteristics, and they show different eye-diagram shapes.
10 Gbps 数据速率下硅/玻璃/有机中介层互连的眼图估计结果如图 Fig. 5 所示。所有眼图都是通过使用所提出的方法获得的，并进行分析以比较三种不同的中介层基板。串扰效应在 VL 和 VH 的直流电平以及电压转换时间处以纹波形式捕获。这些纹波可能超出了上冲和下冲区域的允许范围。例如，HBM 规范允许 0.35V 的过冲和下冲区域 [4] 。开关区域的纹波是由情况 (1) ∼ (4) 的输出响应造成的，并且在 V L 和 V H 附近产生串扰效应由(5)～(8)的情况可知。通过重叠 (1) ∼ (4) 的情况，可以实现眼图张开电压和定时抖动。同样，DC 上的串扰水平由情况 (5) ∼ (8) 获得。由于串扰效应，定时抖动增加，眼图更加扭曲。因此，带宽可能会受到前面提到的 ISI、损耗和串扰效应等失真因素的限制。从 Fig. 5 来看，估计的硅中介层眼图显示所有三种基板中串扰效应最低。由于干扰通道的串扰影响非常小，因此可以通过硅的有损特性来减弱。此外，由于其有损特性，眼图张开电压相对较低。硅中介层互连具有最小的最差眼图。相反，由于玻璃和有机基板不像硅那样有损耗，因此这些互连对其眼图的串扰影响比硅中介层的眼图更高。 然而，玻璃和有机基板具有比硅更大的眼图张开电压。简而言之，三个中介层具有不同的频率相关通道特性，并且它们呈现不同的眼图形状。
Estimated eye-diagram estimation of (a) Silicon (b) Glass (c) Organic interposer interconnects
(a) 硅 (b) 玻璃 (c) 有机中介层互连的估计眼图估计
In addition to the crosstalk effect, many other distortion factors such as channel loss and ISI also have become more significant at high frequency. Fig. 5 shows silicon interposer's 0.36 V of eye opening voltage, and organic has 0.42 V of eye opening voltage. Glass interposer has the highest eye opening voltage among them with 0.44 V. The reason is that the insertion loss depends on the loss tangent and relative permittivity. The relation between material properties, frequency, and insertion loss are explained in Eq. (1). Since the glass and organic interposer has lower permittivity and smaller loss tangent, insertion loss results of glass and organic show lower values than the silicon interposer's result.
\begin{equation*}
\mathrm{G}_{\text{leakage}} = \frac{1}{\mathrm{R}_{\text{leakage}}}=\omega\tan(\delta)\mathrm{C}. \tag{1}
\end{equation*}除了串扰效应之外，许多其他失真因素（例如通道损耗和 ISI）在高频下也变得更加重要。 Fig. 5 表示硅中介层的眼图张开电压为0.36V，有机中介层的眼图张开电压为0.42V。其中玻璃中介层的开眼电压最高，为 0.44 V。原因是插入损耗取决于损耗角正切和相对介电常数。材料特性、频率和插入损耗之间的关系如公式 1 所示。 (1) 。由于玻璃和有机中介层具有较低的介电常数和较小的损耗角正切，因此玻璃和有机中介层的插入损耗结果显示出比硅中介层的结果更低的值。
\begin{equation*}
\mathrm{G}_{\text{leakage}} = \frac{1}{\mathrm{R}_{\text{leakage}}}=\omega\tan(\delta)\mathrm{C}. \tag{1}
\end{equation*}B. Bit Error Rate (BER) Contour of Silicon/Glass/Organic Interposer Interconnects
B. 硅/玻璃/有机中介层互连的误码率 (BER) 轮廓
Eye opening voltage, timing jitter and crosstalk values can be obtained from the worst eye-diagram with 8 boundary lines of the eye-diagram. The Worst eye-diagram expresses Deterministic Jitter (DJ) of the channel. The worst inner contour of the eye-diagram indicates eye opening voltage and timing jitter, and the worst DC level shows the amplitude of crosstalk level. Unfortunately, the worst eye-diagram is impossible to consider Random Jitter (RJ) effect of the channel. However, Bit Error Rate (BER) contour includes not only DJ, but also RJ Probability Density Function (PDF). Thus, BER contour has more detailed channel characteristics than the worst eye-diagram. However, BER contour spends more simulation time than the worst eye-diagram because of more complex calculation. From this aspect, the worst eye-diagram has advantage on time, and the BER contour has advantage on more detailed information of the channel. Therefore, to analyze the eye-diagram in short time with high accuracy, these two kinds of eye-diagrams should be achieved efficiently. The amount of eye-diagram degradation due to the channel effects is graphically shown from the worst eye-diagram. In the case of the BER contour, it shows RJ effect on a diagram. The RJ source can be thermal noise, shot noise, or random modulation. RJ is unbounded and unpredictable. In this paper, RJ is defined to be as a normal distribution, which is explained in (2). To obtain total jitter PDF of the channel, convolution between DJ and RJ PDF is needed. Equations of BER ‘0’ and BER ‘1’ are shown in (3) and (4).
\begin{gather*}
f(x)= \frac{1}{\sqrt{2\pi}\sigma}e^{-(x-m)^{2}/2\sigma^{2}}. \tag{2}\\
BER0 (x)= \int\limits_{x}^{\infty} PDFdx. \tag{3}\\
BER1 (x)= \int\limits_{-\infty}^{x} PDFdx\tag{4}
\end{gather*}眼图张开电压、时序抖动和串扰值可以从具有8条眼图边界线的最差眼图中获得。最差眼图表示通道的确定性抖动 (DJ)。眼图的最差内部轮廓表示眼图张开电压和定时抖动，最差直流电平表示串扰电平的幅度。不幸的是，最差的眼图无法考虑通道的随机抖动 (RJ) 效应。然而，误码率 (BER) 等值线不仅包括 DJ，还包括 RJ 概率密度函数 (PDF)。因此，BER 轮廓比最差的眼图具有更详细的信道特征。然而，由于计算更复杂，BER 轮廓比最差眼图花费更多的模拟时间。从这方面来看，最差眼图在时间上具有优势，而BER轮廓在更详细的信道信息上具有优势。因此，为了在短时间内高精度地分析眼图，需要高效地获得这两种眼图。由通道效应导致的眼图退化量以最差眼图的图形方式显示。就 BER 等值线而言，它在图表上显示了 RJ 效应。 RJ 源可以是热噪声、散粒噪声或随机调制。 RJ 是无界且不可预测的。本文中，RJ 被定义为正态分布，解释见 (2) 。为了获得通道的总抖动PDF，需要DJ和RJ PDF之间的卷积。 BER‘0’和BER‘1’的方程如 (3) and (4) 所示。
\begin{gather*}
f(x)= \frac{1}{\sqrt{2\pi}\sigma}e^{-(x-m)^{2}/2\sigma^{2}}. \tag{2}\\
BER0 (x)= \int\limits_{x}^{\infty} PDFdx. \tag{3}\\
BER1 (x)= \int\limits_{-\infty}^{x} PDFdx\tag{4}
\end{gather*}
Estimated BER contours of (a) Silicon (b) Glass (c) Organic interposer interconnects
(a) 硅 (b) 玻璃 (c) 有机中介层互连的估计 BER 轮廓
Fig. 6 shows the BER contour of silicon/glass/organic interposer interconnects. Silicon shows 0.34 V eye opening voltage, and organic has 0.39 V. However, glass interposer shows the highest eye opening of 0.42 V. From the aspect of eye width, silicon has 93ps, organic has 94ps, and glass has 95ps. As the demand on higher data rate, glass interposer will be the most suitable material for the next generation of interposer, which has high-speed and wide number of I/O interconnects, with enough voltage and timing margin.
Fig. 6 显示了硅/玻璃/有机中介层互连的 BER 轮廓。硅的眼图张开电压为0.34V，有机为0.39V。然而，玻璃中介层的眼图张开最高为0.42V。从眼图宽度来看，硅为93ps，有机为94ps，玻璃为95ps。由于对更高数据速率的需求，玻璃中介层将是下一代中介层最合适的材料，它具有高速和广泛的I/O互连，具有足够的电压和时序余量。
Conclusion 结论
In this paper, silicon, glass, organic interposers for 2.5D/3D interconnects are investigated for signal integrity analysis. Worst eye-diagram and BER contours for highspeed silicon/glass/organic interposer interconnects are estimated, analyzed and compared. To analyze the crosstalk effects from the three different substrates, physical structure and dimensions are assumed to be same as the silicon's fabrication process. To shorten the simulation time with high accuracy, an efficient method to find 8 boundary lines of the eye-diagram was introduced in Chapter II. This method requires only the set of 8 worst input cases for finding the boundary lines of the entire eye-diagram. Simulation time can be reduced than by using PRBS inputs. Thus, the method is verified to be widely applied to estimate eye-diagram of various interconnects, such as multiple channels system in single-ended or differential signaling system.
在本文中，研究了用于 2.5D/3D 互连的硅、玻璃、有机中介层，以进行信号完整性分析。估计、分析和比较高速硅/玻璃/有机中介层互连的最差眼图和 BER 轮廓。为了分析三种不同基板的串扰效应，假设物理结构和尺寸与硅的制造工艺相同。为了缩短仿真时间并保持高精度，第二章介绍了一种寻找眼图8条边界线的有效方法。该方法仅需要 8 个最差输入情况的集合来查找整个眼图的边界线。与使用 PRBS 输入相比，可以减少仿真时间。因此，该方法被证明可以广泛应用于估计各种互连的眼图，例如单端或差分信号系统中的多通道系统。
With the proposed method, worst eye-diagram and BER contours of silicon/glass/organic interposer interconnects at 10 Gbps are estimated and compared. Consequently, silicon interposer shows the smallest eye opening voltage due to its lossy characteristic of the substrate. However, high portion of the crosstalk effects are diminished from the eye diagram by its lossy characteristic. On the other hand, glass and organic interposers contain more crosstalk effects on the eye-diagram. Lower relative permittivity and smaller loss tangent of the glass and organic interposer lead to lower insertion loss than silicon. In this case, the low attenuation characteristic cannot remove the crosstalk effects on eye-diagram. Especially, glass interposer shows slightly wider eye opening voltage and smaller crosstalk level than the organic interposer. Thus, if the glass interposer can be fabricated within fine pitch as the silicon in the future, glass interposer will be the most suitable interposer substrate to achieve better electrical performance on high-speed and wide I/O interposer interconnects for 2.5D/3D IC.
利用所提出的方法，可以估计并比较 10 Gbps 时硅/玻璃/有机中介层互连的最差眼图和 BER 轮廓。因此，硅中介层由于其基板的损耗特性而显示出最小的眼图张开电压。然而，大部分串扰效应因其有损特性而从眼图中减弱。另一方面，玻璃和有机中介层对眼图的串扰影响更大。玻璃和有机中介层较低的相对介电常数和较小的损耗角正切导致插入损耗低于硅。在这种情况下，低衰减特性无法消除眼图上的串扰影响。特别是，玻璃中介层比有机中介层表现出稍宽的开眼电压和更小的串扰水平。因此，如果未来玻璃中介层能够像硅一样以细间距制造，那么玻璃中介层将是最合适的中介层基板，以在2.5D/3D IC的高速和宽I/O中介层互连上实现更好的电气性能。