【作者】 陈亮；

【导师】 毛军发；

【作者基本信息】 上海交通大学 ， 电子科学与技术， 2020， 博士

【摘要】 随着三维集成电路技术的迅速发展,芯片朝着高密度、多功能、小型化、高性能等方向发展。高速数字信号的频谱已经进入微波波段,引起芯片的电磁兼容问题;不断提高的功耗密度导致芯片严重的热可靠性问题;持续增长的电流密度触发铜导体电迁移失效问题。并且,三个物理场(电磁场/电场、热场和电迁移应力场)之间存在相互作用与耦合效应,是复杂的非线性问题。因此,多物理场耦合分析对集成电路的设计尤为重要。本学位论文主要研究麦克斯韦方程组、热传导方程和电迁移科合隆方程的解析和数值方法。然后,基于数值和解析方法,结合多物理场之间的联系,对集成电路进行多物理场耦合分析。本文的主要研究成果归纳如下:1.基于导体表面粗糙度的梯度模型,推导出线性电导率的解析解与任意电导率的半解析解。根据提出的半解析梯度模型,分析具有同一均方根值的不同分布(均匀、正态和瑞利分布)对传输线导体损耗的影响。证明了导体粗糙度不仅和均方根值有关,也和表面高度分布有关。为描述导体表面粗糙度提供了一个更加合理的模型。2.基于交替方向隐式时域有限差分数值方法,求解嵌入德拜色散模型的麦克斯韦方程组,分析空腔介质谐振器封装天线的屏蔽效能以及空腔内电路的电磁兼容问题。以高斯平面波作为激励,将时域响应做傅里叶变换得到频域电磁场,根据公式得到屏蔽效能,研究屏蔽腔的频域特性。然后,分析高斯脉冲波对屏蔽腔内电路的数字信号影响,研究屏蔽腔的时域特性。为屏蔽腔的设计提供理论依据。3.提出解析方法分析电源供电网络互连线的一维稳态热传导问题。引入半边界Rao-Wilton-Glisson(RWG)基函数,改进的泊松方程方法可以处理三类热边界条件,分析任意二维结构的稳态热传导问题。基于交替方向隐式方法,将空间差分格式等效为热阻,建立热阻网络,分析三维结构的瞬态热传导问题。根据混合物理论,建立硅通孔阵列和微流道阵列的等效电阻计算公式,分析复杂的结构和流体传热问题。为集成电路的热分析提供了高效工具。4.采用分离变量法求解电迁移科合隆方程,分析电源供电网络互连线的电迁移应力分布。其中,分离变量法的关键步骤是特征根的确定,对于多段直线与星形分支线特殊结构,推导其特征根的解析解;针对复杂电源供电网络互连线结构,采用Wittrick-Williams(WW)数值算法计算特征根值。提出快速高斯消去法和弦割法加速传统WW算法,根据矩阵行列式特性,取高斯消去后得到的上三角形矩阵对角线上最后一个元素作为矩阵行列式的值,避免了级联相乘运算与数值溢出。5.基于上述提出的解析方法和数值方法,研究电磁场/电场、热场和电迁移应力的多物理场耦合效应。首先,基于提出的半解析梯度导体粗糙度模型,分析粗糙度对传输线的导体损耗以及平均功率容量的影响,从频域研究电磁-热耦合效应。其次,采用交替方向隐式数值方法研究德拜色散媒质的瞬态电磁-热耦合响应,从时域研究电磁-热耦合机理。然后,采用改进的泊松方程方法分析Gallium Nitride(Ga N)功率器件的热分布,研究电-热耦合引起的自热效应。再用安德森加速方法提高电-热耦合的传统迭代法的收敛速度。最后,基于电迁移-热迁移联合方程,分析电源供电网络互连线的电-热-应力耦合效应。更多还原

【Abstract】 With the rapid development of 3D ICs technique,the chip achieves higher density,more functionality,smaller size,higher performance,etc.The frequency spectrum of high-speed digital signal reaches a microwave band,which leads to electromagnetic compatibility(EMC)problems.The increasing power density results in serious thermal reliability issues.The high current density can cause electromigration reliability problems of the interconnects.What’s more,there exists interaction and coupling effects between Multiphysics,including electromagnetic/electrical field,thermal field and electromigration stress field,which are complex and nonlinear problems.Therefore,Multiphysics co-simulation is particularly significant for the design of 3D ICs.This dissertation focus on solving the Maxwell’ equations,heat conduction equation and electromigration Korhonen’s equation using numerical and analytical methods.Based on the above methods and connections between Multiphysics,Multiphysics cosimulations of 3D ICs are investigated.The main contributions of the dissertation are shown as follows:1.Based on the gradient model describing conductor surface roughness,an analytical solution for linear conductivity and a semi-analytical solution for arbitrary conductivity are derived to compute magnetic field.By using the proposed semianalytical gradient model(SAGM)model,the impact of surface height distributions with same root-mean-square(RMS)value,such as uniform,normal and Rayleigh distribution,on the coducotor loss of transmission line is studied.It can be seen that conductor surface roughness can not only be described by RMS,but also be charactered by surface height distributions.Therefore,the SAGM model is more reasonable than the gradient model to describe the conductor surface roughness.2.Based on alternating-direction-implicit finite-difference time-domain(ADIFDTD)numerical method,Maxwell’s equations with Debye model are solved to analyze the shielding effectiveness of hollow delectric resonator antenna-in-chip(HDRAi P)and EMC problems of its inside circuits.With the electromagnetic pulse(EMP)plane wave,the time domain of electromagnetic field is transformed into its frequency domain using fourier transform.Based on formula of shielding effectiveness,frequency-domain feature of shielding metallic cavity with aperture is studied.The impact of EMP plane wave on the digital signal of the inside circuits is used to demonstrate the time-domain feature of shielding metallic cavity.Electromagnetic simulation is provided to guide the design of shielding metallic cavity with aperture.3.First,an analytical solution is proposed to perform the 1D steady-state thermal analysis of interconnects of power delivery network(PDN).Then,with the half boundary Rao-Wilton-Glisson(HBRWG)basis function,the improved Poisson equation solver can deal with three types of thermal boundary conditions and solve the2 D steady-state heat conduction equation.After that,based on ADI finite difference method(ADI-FDM),the relationship between the meshes of FDM and thermal resistance is estimated to build thermal resistance network to perform 3D transient thermal simulation.Finally,according to the hybrid material theory,the effective resistances of through-silicon via(TSV)array and microchannels array layers are calculated to perform heat transfer simulation in the complex structure and the fluid.The above proposed methods provide effective tools to perform thermal analysis of 3D ICs.4.Separation of variables method is used to solve Korhonen equation describing the electromigration stress and estimate the hydrostatic stress of interconnects of PDN.The determination of eigenvalues is a key step for the solution of separation of variables method.For straight line and star-like simple structures,analytical solutions are derived to estimate the eigenvalues.For complex PDN interconnects,Wittric-Williams(WW)numerical method is used to calculate the eigenvalues.Then,fast Gaussian elimination and secant method are proposed to accelerate the traditional WW method.Based on the characteristic of determinant of matrix,the last diagonal element of upper triangular matrix obtained by Gaussian ellimination is regarded as the determinant of the matrix,which can reduce the multiply operation and avoid numerical overflow.5.The above proposed numerical and analytical methods are employed to investigate the coupling effects of Multiphysics,including electromagnetic/electrical field,thermal field and electromigration stress field.First,SAGM model is proposed to study the impact of conductor surface roughness on the conductor loss and average power handling capacity of transmission lines and investigate the coupling between electromagnetic and thermal fields in frequency domain.Then,ADI numerical method is used to perform the transient electromagnetic-thermal co-simulation of Debye media and investigate the coupling between electromagnetic and thermal fields in time domain.After that,the improved poission equation solver is employed to perform 2D steadystate thermal simulation of Gallium Nitride(Ga N)power devices and investigate selfheating effects caused by electro-thermal coupling.Anderson acceleration method is used to speed up the convergence speed of coupled electro-thermal iterations.Finally,electromigration-thermomigration(EM-TM)equation is developed to carry out the electro-thermal-stress co-simulation of interconnects of PDN.更多还原