高速集成电路片内互连的电磁建模和参数提取研究
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摘要
半导体工艺水平的飞速提高使当今集成电路的发展进入深亚微米阶段。随着系统芯片的出现，片内互连技术已成为目前集成电路设计中最具挑战性的领域之一。互连的传输线效应成为限制系统整体性能的“瓶颈”。传统的EDA设计中的基于集总电路概念的参数提取算法已经失去准确性。因此，对互连和封装结构进行电磁建模和参数提取，对于高速集成电路设计具有重要的意义，它是一系列后续工作的基础。
本论文以片内互连的关键长线为研究对象，所涉及的工作即是长线结构的电磁建模和参数提取。在分析互连电特性的同时，侧重方法的研究。研究方法从精度和速度两方面着手，为适合EDA／CAD设计使用，更侧重速度研究。主要研究工作及创新性如下：
1．对片内互连中大量出现的包含不连续性和三维立体特殊性结构的典型代表进行了研究。采用具有高精度数值解的时域有限差分法，对屏蔽共面波导的平面型间隙结构和三维垂直互连结构进行全波数值仿真，首次得到这些结构的电特性分析，并给出不连续性等效电路参数。
2．对集成电路中普遍存在的有耗多导体结构的高速高精度参数提取进行了研究与实现。以双线和三线结构为例，提取了其等效电路参数。在分析中，通过改进，提出并实现了一种非均匀网格的自动划分技术，以简便灵活的方式解决了非均匀网格产生的困难。通过与降维FDTD方法和信号拟合预测技术结合使用，极大地缩减了单纯FDTD法庞大的计算量，提高了仿真效率，在一定程度上有效地解决了多导线分析的困难。
3．针对有耗导体衰减常数难以精确提取的问题，将一种最新改进降维方法应用到有耗多导体系统分析中，并结合非均匀网格划分技术，在得到准确衰减常数的同时有效地减少计算时间。
4．针对数值仿真时间过长，难以实现CAD交互使用的局限性，将人工神经网络引入到电磁建模中。对于屏蔽CPW的间隙不连续性和垂直互连不连续性结构，采用FDTD方法获取训练和检测样本数据，用回传算法训练多层感知器，首次成功地获得了这些结构快速、准确的CAD模型。所得模型具有与电磁仿真同样的精度，而计算时间可忽略不计，成功地解决了纯数值方法的巨大耗时问题，非常适合用于电路设计所需的准确高效的EDA／CAD互连模型的建立。
对以上所有研究内容，均编写了相应的Fortran程序和Matlab程序。在软件实现上开展了初步工作。
With the tremendous improvement of semiconductor technique, today's integrated circuits (1C) technology has entered into deep submicrometer (DSM) region. Now that a single chip is an entire system (the concept of system-on-a-chip, SOC), on-chip interconnect is now one of the most challenging areas of 1C processing. The parasitic effects of interconnect is the bottleneck of the entire circuit system performance. The traditional methods of parasitic parameter extraction in EDA, which based on the concept of lumped component, have lost their accuracy. Electromagnetic modeling and parameter extraction play an important role in 1C design and it is a foundation of the works later.
The subject of dissertation is electromagnetic modeling and parameters extraction of long interconnects in SOC. As analyzing the electronic properties, methods studying are particularly emphasized at the same time. Accuracy and speed are two aspects to be concerned and the later is given more attention for the sake of practical using in EDA/CAD. This dissertation has made the following research:
For the structures comprising discontinuities and three-dimensional specialities, which largely present in SOC, the planar gap and the tridimensional vertical bend of shielded coplanar waveguide (CPW), are analyzed respectively as two typical examples. The finite-difference time-domain (FDTD) method are used for electromagnetic simulation using its highly accuracy. Structure electronic properties are investigated and equivalent circuit parameters are obtained at the first time.
For the lossy multiple conductors configuration, which is essential unit of interconnects, its rapid and accuracy extraction are studied and achieved. Two and three coplanar lines are studied as examples and their equivalent circuit parameters are obtained. An nonuniform mesh partitioning technique is developed by modification. It solves the difficulty of grid producing by an easy and flexible way. Simulation results show that when combine it with the compact FDTD method and the signal curvefit prediction approach, the computation magnitude is tremendously cut down compared to that when only the basic FDTD method is used. So simulation efficiency is greatly enhanced and the analyzing difficulty in dealing with multiple conductors is solved to some extend.
Meanwhile, owing to the fact that there is huge hardness in accurate extracting of attenuation constant, one of the most new modified compact FDTD methods is applied to analyzing lossy multiple conductors to give accurate results. It is combined with the nonuniform mesh partitioning technique to reduce the computing time.
Aiming at the fact that numerical simulations are very time-consuming and are used very limitedly in alternative CAD, Artificial neural network (ANN) is introduced to electromagnetic modeling to solve the problem. For the planar gap and
the tridimensional vertical bend of shielded CPW, FDTD simulations are carried out to produce training and testing samples and error-back propagation algorithm is used to train the multilayer perceptron neural networks (MLPNNs). Rapid and accuracy CAD models of these structures are successfully obtained for the first time. These developed MLPNN models can give the same reliable results as that of the electromagnetic simulations, but their computing time are negligible. Since this approach can efficiently remedy the time-consuming problem of single numerical method, it is very potential in the accurate and efficient interconnect modeling of circuit EDA/CAD.
Fortran and Matlab programs are written for all the above approaches. Some primary work are done in soft realization.
本论文以片内互连的关键长线为研究对象，所涉及的工作即是长线结构的电磁建模和参数提取。在分析互连电特性的同时，侧重方法的研究。研究方法从精度和速度两方面着手，为适合EDA／CAD设计使用，更侧重速度研究。主要研究工作及创新性如下：
1．对片内互连中大量出现的包含不连续性和三维立体特殊性结构的典型代表进行了研究。采用具有高精度数值解的时域有限差分法，对屏蔽共面波导的平面型间隙结构和三维垂直互连结构进行全波数值仿真，首次得到这些结构的电特性分析，并给出不连续性等效电路参数。
2．对集成电路中普遍存在的有耗多导体结构的高速高精度参数提取进行了研究与实现。以双线和三线结构为例，提取了其等效电路参数。在分析中，通过改进，提出并实现了一种非均匀网格的自动划分技术，以简便灵活的方式解决了非均匀网格产生的困难。通过与降维FDTD方法和信号拟合预测技术结合使用，极大地缩减了单纯FDTD法庞大的计算量，提高了仿真效率，在一定程度上有效地解决了多导线分析的困难。
3．针对有耗导体衰减常数难以精确提取的问题，将一种最新改进降维方法应用到有耗多导体系统分析中，并结合非均匀网格划分技术，在得到准确衰减常数的同时有效地减少计算时间。
4．针对数值仿真时间过长，难以实现CAD交互使用的局限性，将人工神经网络引入到电磁建模中。对于屏蔽CPW的间隙不连续性和垂直互连不连续性结构，采用FDTD方法获取训练和检测样本数据，用回传算法训练多层感知器，首次成功地获得了这些结构快速、准确的CAD模型。所得模型具有与电磁仿真同样的精度，而计算时间可忽略不计，成功地解决了纯数值方法的巨大耗时问题，非常适合用于电路设计所需的准确高效的EDA／CAD互连模型的建立。
对以上所有研究内容，均编写了相应的Fortran程序和Matlab程序。在软件实现上开展了初步工作。
With the tremendous improvement of semiconductor technique, today's integrated circuits (1C) technology has entered into deep submicrometer (DSM) region. Now that a single chip is an entire system (the concept of system-on-a-chip, SOC), on-chip interconnect is now one of the most challenging areas of 1C processing. The parasitic effects of interconnect is the bottleneck of the entire circuit system performance. The traditional methods of parasitic parameter extraction in EDA, which based on the concept of lumped component, have lost their accuracy. Electromagnetic modeling and parameter extraction play an important role in 1C design and it is a foundation of the works later.
The subject of dissertation is electromagnetic modeling and parameters extraction of long interconnects in SOC. As analyzing the electronic properties, methods studying are particularly emphasized at the same time. Accuracy and speed are two aspects to be concerned and the later is given more attention for the sake of practical using in EDA/CAD. This dissertation has made the following research:
For the structures comprising discontinuities and three-dimensional specialities, which largely present in SOC, the planar gap and the tridimensional vertical bend of shielded coplanar waveguide (CPW), are analyzed respectively as two typical examples. The finite-difference time-domain (FDTD) method are used for electromagnetic simulation using its highly accuracy. Structure electronic properties are investigated and equivalent circuit parameters are obtained at the first time.
For the lossy multiple conductors configuration, which is essential unit of interconnects, its rapid and accuracy extraction are studied and achieved. Two and three coplanar lines are studied as examples and their equivalent circuit parameters are obtained. An nonuniform mesh partitioning technique is developed by modification. It solves the difficulty of grid producing by an easy and flexible way. Simulation results show that when combine it with the compact FDTD method and the signal curvefit prediction approach, the computation magnitude is tremendously cut down compared to that when only the basic FDTD method is used. So simulation efficiency is greatly enhanced and the analyzing difficulty in dealing with multiple conductors is solved to some extend.
Meanwhile, owing to the fact that there is huge hardness in accurate extracting of attenuation constant, one of the most new modified compact FDTD methods is applied to analyzing lossy multiple conductors to give accurate results. It is combined with the nonuniform mesh partitioning technique to reduce the computing time.
Aiming at the fact that numerical simulations are very time-consuming and are used very limitedly in alternative CAD, Artificial neural network (ANN) is introduced to electromagnetic modeling to solve the problem. For the planar gap and
the tridimensional vertical bend of shielded CPW, FDTD simulations are carried out to produce training and testing samples and error-back propagation algorithm is used to train the multilayer perceptron neural networks (MLPNNs). Rapid and accuracy CAD models of these structures are successfully obtained for the first time. These developed MLPNN models can give the same reliable results as that of the electromagnetic simulations, but their computing time are negligible. Since this approach can efficiently remedy the time-consuming problem of single numerical method, it is very potential in the accurate and efficient interconnect modeling of circuit EDA/CAD.
Fortran and Matlab programs are written for all the above approaches. Some primary work are done in soft realization.
引文
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