RF-CMOS片上螺旋电感模型及模型库的开发
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摘要
随着硅集成电路技术和无线通讯市场的快速发展,以系统级芯片为趋势的硅基射频集成电路(RFIC)逐渐以低成本、低功耗等优势崛起。电感作为重要的无源器件,在电路中可实现阻抗匹配、可调谐负载、反馈、滤波等功能,在RFIC单元电路如低噪声放大器(LNA)、压控振荡器(VCO)、混频器(Mixer)、滤波器(Filter)、功率放大器(PA)中扮演着举足轻重的角色,其设计和优化已成为整个电路成功设计的关键之一。在标准CMOS工艺中,由于硅衬底是有损耗的,使得硅基片上螺旋电感的品质因数普遍不高。同时,以硅材料为衬底的电路,其工作性能也会因为随工作频率上升而出现的各种损耗(尤其是衬底损耗)而恶化。目前,随着工艺尺寸的减小,射频集成电路的应用频率越来越高,可达到几十甚至几百GHz。在如此高的频率下,电感中的高频寄生效应,如金属的趋肤效应、邻近效应以及衬底的涡流效应等,都会变得非常严重,这也为准确建立电感模型增加了难度。因此,有效地分析并获得硅衬底在片螺旋电感的电路模型及其参数,掌握电感性能随工作频率改变的特性,以用于电感的设计和优化,已成为实现硅衬底射频/毫米波集成电路的一个非常重要的课题。本文主要研究硅衬底在片螺旋电感的分析、仿真和建模。
本文首先介绍片上螺旋电感相关的基础知识,包括电感的结构、性能参数、损耗机制和建模方法等。在电感的损耗机制中,本文着重介绍两大损耗,即金属损耗和衬底损耗。建模方法主要分析了电磁场仿真和等效电路模型,并总结了它们的优缺点和适用范围。
在总结和对比了现有的等效电路模型之后,本文提出了两个新模型,它们分别是单π和双π模型。新的单π模型是一个宽带模型,采用一个横跨在两个端口之间、与直流电感相耦合的R-L-C网络来表征涡流效应,同时在传统的R-C衬底网络中串联一个R-L并联支路来表征衬底损耗。该模型主要提高了单π模型在高频时的精度,拓宽了模型的带宽。新的双π模型改变了趋肤效应和邻近效应的描述方式。模型中用一个由三个R-L串联支路组成的并联网络来描述趋肤效应,邻近效应则用它们相互之间的互感来表示。同时,新的单π模型中的衬底网络也适用于该模型,可以拓展其带宽。
最后,本文利用已见诸于报道的单π和双π模型以及本文提出的双π模型,建立了三个电感scalable模型,即模型库。这三个模型库可分为两种类型:(1)基于已见诸于报道的单π和双π模型的电感模型库,我们采用了经验的方法,先对一批电感进行参数提取和优化,再总结模型中各元件参数值的规律,用与尺寸相关的数学公式来表示等效电路元件值。(2)基于本文提出的双π模型的电感模型库,我们采用了物理的方法,模型中的元件值均用它们的物理公式表示,这些公式与电感的版图尺寸和工艺参数有关。在此基础上,我们再添加一些优化系数来提高拟合精度。
文中两个新模型和三个模型库均采用基于SMIC 0.18μm RF CMOS工艺的平面螺旋电感进行了验证,电感的测试频率从DC到40GHz。从仿真和测试的对比结果来看,新模型和模型库的拟合精度较高,符合电路设计中的应用要求。
With the rapid development of silicon-based integrated circuits technology and wireless communication market, the radio frequency integrated circuits (RFICs) are applied widely for the advantages of low cost and low power. As a critical component of RFIC function cells such as LNA, VCO, Mixer, Filter, and PA, the design and optimization of on-chip spiral inductors are essential in circuits design. In addition, the performance of the devices and circuits on silicon substrate is degrading due to various losses in which the substrate loss is especially significant as frequency increased. Nowadays, advances in nano-scale CMOS technology even have made it feasible to implement W-Band circuits in CMOS. In this case, the parasitic effects such as the skin and proximity effects in the conductor and the eddy current effect in the substrate will become more serious, which increases the difficulty in device modeling. Thus, an accurate equivalent circuit model with robust parameter extraction methodology is indispensable for inductor characterization and circuit simulation for CMOS mixed-signal/RF SoC and millimeter-wave circuit designs. In this thesis, the analysis, Electro-magnetic (EM) simulation and modeling of on-chip spiral inductor are discussed.
Firstly, the fundamentals of on-chip spiral inductors such as layout structures, performance parameters, loss mechanisms and modeling methods are discussed. The losses of metal and substrate which are two types of major loss mechanisms are discussed in detail. Subsequently, the major modeling methods of on-chip spiral inductor are presented including EM simulation, segmental equivalent circuit model and compact lumped-element model.
Two new equivalent-circuit models are proposed in this paper, which are single-πand double-πmodels. The new single-πmodel has better wideband prediction capability than traditional single-πorΤ-models. The eddy current in substrate is represented by an R-L-C network coupled with DC inductance. A new substrate network, consisting of R/L/C, is proposed to model the broadband loss mechanisms in the silicon substrate. In the new double-πmodel, the skin and proximity effects are represented by a parallel network, consisting of several R-L series branches and mutual inductors. As the skin and proximity effects are frequency-dependent, the number of branches varies with the frequency of interest, and more branches are needed with increasing frequency. The substrate network in the new single-πmodel is also proved to be suitable for this double-πmodel.
Lastly, three inductor model libraries are developed based on the proposed double-πmodel and two reported models. These model libraries can be categorized into two types: (1) The empirical scalable models based on the reported single-πand double-πmodels. Performing the parameter-extraction procedure on a series of inductors, then the values of equivalent-circuit elements are expressed by a set of functions related to the geometry parameters of inductors. (2) The physical scalable model based on the new double-πmodel. The scalable expressions are determined by physical meanings, geometry parameters and process parameters.
A series of inductors with different geometries are fabricated in standard SMIC 0.18-μm 1P6M RF CMOS process to verify the new equivalent-circuit models and inductor libraries. Excellent agreements have been obtained between the modeled and measured data up to 40 GHz.
本文首先介绍片上螺旋电感相关的基础知识,包括电感的结构、性能参数、损耗机制和建模方法等。在电感的损耗机制中,本文着重介绍两大损耗,即金属损耗和衬底损耗。建模方法主要分析了电磁场仿真和等效电路模型,并总结了它们的优缺点和适用范围。
在总结和对比了现有的等效电路模型之后,本文提出了两个新模型,它们分别是单π和双π模型。新的单π模型是一个宽带模型,采用一个横跨在两个端口之间、与直流电感相耦合的R-L-C网络来表征涡流效应,同时在传统的R-C衬底网络中串联一个R-L并联支路来表征衬底损耗。该模型主要提高了单π模型在高频时的精度,拓宽了模型的带宽。新的双π模型改变了趋肤效应和邻近效应的描述方式。模型中用一个由三个R-L串联支路组成的并联网络来描述趋肤效应,邻近效应则用它们相互之间的互感来表示。同时,新的单π模型中的衬底网络也适用于该模型,可以拓展其带宽。
最后,本文利用已见诸于报道的单π和双π模型以及本文提出的双π模型,建立了三个电感scalable模型,即模型库。这三个模型库可分为两种类型:(1)基于已见诸于报道的单π和双π模型的电感模型库,我们采用了经验的方法,先对一批电感进行参数提取和优化,再总结模型中各元件参数值的规律,用与尺寸相关的数学公式来表示等效电路元件值。(2)基于本文提出的双π模型的电感模型库,我们采用了物理的方法,模型中的元件值均用它们的物理公式表示,这些公式与电感的版图尺寸和工艺参数有关。在此基础上,我们再添加一些优化系数来提高拟合精度。
文中两个新模型和三个模型库均采用基于SMIC 0.18μm RF CMOS工艺的平面螺旋电感进行了验证,电感的测试频率从DC到40GHz。从仿真和测试的对比结果来看,新模型和模型库的拟合精度较高,符合电路设计中的应用要求。
With the rapid development of silicon-based integrated circuits technology and wireless communication market, the radio frequency integrated circuits (RFICs) are applied widely for the advantages of low cost and low power. As a critical component of RFIC function cells such as LNA, VCO, Mixer, Filter, and PA, the design and optimization of on-chip spiral inductors are essential in circuits design. In addition, the performance of the devices and circuits on silicon substrate is degrading due to various losses in which the substrate loss is especially significant as frequency increased. Nowadays, advances in nano-scale CMOS technology even have made it feasible to implement W-Band circuits in CMOS. In this case, the parasitic effects such as the skin and proximity effects in the conductor and the eddy current effect in the substrate will become more serious, which increases the difficulty in device modeling. Thus, an accurate equivalent circuit model with robust parameter extraction methodology is indispensable for inductor characterization and circuit simulation for CMOS mixed-signal/RF SoC and millimeter-wave circuit designs. In this thesis, the analysis, Electro-magnetic (EM) simulation and modeling of on-chip spiral inductor are discussed.
Firstly, the fundamentals of on-chip spiral inductors such as layout structures, performance parameters, loss mechanisms and modeling methods are discussed. The losses of metal and substrate which are two types of major loss mechanisms are discussed in detail. Subsequently, the major modeling methods of on-chip spiral inductor are presented including EM simulation, segmental equivalent circuit model and compact lumped-element model.
Two new equivalent-circuit models are proposed in this paper, which are single-πand double-πmodels. The new single-πmodel has better wideband prediction capability than traditional single-πorΤ-models. The eddy current in substrate is represented by an R-L-C network coupled with DC inductance. A new substrate network, consisting of R/L/C, is proposed to model the broadband loss mechanisms in the silicon substrate. In the new double-πmodel, the skin and proximity effects are represented by a parallel network, consisting of several R-L series branches and mutual inductors. As the skin and proximity effects are frequency-dependent, the number of branches varies with the frequency of interest, and more branches are needed with increasing frequency. The substrate network in the new single-πmodel is also proved to be suitable for this double-πmodel.
Lastly, three inductor model libraries are developed based on the proposed double-πmodel and two reported models. These model libraries can be categorized into two types: (1) The empirical scalable models based on the reported single-πand double-πmodels. Performing the parameter-extraction procedure on a series of inductors, then the values of equivalent-circuit elements are expressed by a set of functions related to the geometry parameters of inductors. (2) The physical scalable model based on the new double-πmodel. The scalable expressions are determined by physical meanings, geometry parameters and process parameters.
A series of inductors with different geometries are fabricated in standard SMIC 0.18-μm 1P6M RF CMOS process to verify the new equivalent-circuit models and inductor libraries. Excellent agreements have been obtained between the modeled and measured data up to 40 GHz.
引文
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[2] Cheng Y. Anoverview of Device Behavior and Modeling of CMOS Technology for RFIC Design[J]. Electron Devices for Microwave and Optoelectronic Applications, 2003: 109-114.
[3] Iwai H. CMOS Technology Future[J]. Device , Circuits and Systems, 2004: 179-182.
[4] Haran B S. 22nm Technology Compatible Fully Functional 0.1μm2 6T-SRAM Cell[J]. IEDM, 2008: 1-4.
[5] A.M.Niknejad, C.Doan, S.Emami, M.Dunga, X,Xi, J.He, R. Broderson, and C.Hu. Next Genera- tion CMOS Compact Models for RF and Microwave Applications[J]. RFIC Symposium, 2005, 1:141-144.
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