倒装芯片塑料球栅阵列封装器件在外应力下的失效机理

倒装芯片塑料球栅阵列(FC-PBGA)封装形式独特而被广泛应用, 分析研究其在实际应用过程中, 在高温、电、水汽等多种综合环境应力条件作用下的失效机理对提高其应用可靠性有重要意义. 本文对0.13 μm 6层铜布线工艺的FC-PBGA FPGA器件, 通过暴露器件在以高温回流焊过程中的热-机械应力为主的综合外应力作用下的失效模式, 分析与失效模式相对应的失效机理. 研究结果表明, FC-PBGA器件组装时的内外温差及高温回流焊安装过程中所产生的热-机械应力是导致失效的根本原因, 在该应力作用下, 芯片上的焊球会发生再熔融、桥接相邻焊球致器件短路失效; 芯片与基板之间的填充料会发生裂缝分层、倒装芯片焊球开裂/脱落致器件开路失效; 芯片内部的铜/低k互连结构的完整性受损伤而影响FC-PBGA器件的使用寿命.     

Beam Parameters for End Diffraction of TE0 Mode of Planar Waveguide

The relation between diffractive beam parameters and normalized frequency is analyzed that leads to two improved Tormulas for two kinds of mode-field halT-widths and several formulas for divergence angle as well as beam propagation factor. The numerical calculation indicates that the maximal relative error is less than 0.5% within a reasonable parameter range.     

矩形光波导E_(00)~y模衍射特性分析

基于Marcatili近似理论,给出了一种矩形光波导Ey00模模场的近似表达,根据平面波角谱理论,推导出了矩形光波导Ey00模衍射场的空间频谱表达式,探讨了其x轴方向上的空间频谱分布特性,分析了矩形光波导Ey00模在x,y轴方向上的光传输因子M2,并采用方形桶桶中功率对矩形波导Ey00模空间频率半宽度进行数值分析,得到了由方形桶桶中功率定义的矩形光波导Ey00模空间频率半宽度随归一化频率变化的关系曲线。     

高斯光束经环形光栅的衍射特性分析

基于傅里叶-贝塞尔变换计算高斯光束垂直入射环形光栅时的衍射远场分布,分析了其衍射远场光强分布的一般规律,并与平面波入射时的情况进行了比较.计算结果表明：当光栅半径为1.5倍高斯光束束腰半径时, 随着光栅环数的增加,中央亮斑半值全宽先减小后增大、中央亮斑所包含的功率占总功率的比值减小、中央主极大光强值减小,三者的变化趋势与平面波入射时的趋势一致;中央亮斑半径、次极大光强值变化趋势与平面波入射时的变化趋势不同.当环数小于5时,高斯光束经过环形光栅的衍射场光强变化无规律;当环数大于10后两种情况下衍射场光强变化都不明显;当环数趋于无穷时中央亮斑半径、中央亮斑半值全宽、次极大光强值趋于圆孔衍射(环数等于1)时的值,中央亮斑所包含的功率占总功率的比值约等于圆孔衍射时的1/2,中央主极大光强值约等于圆孔衍射时的1/4.     

高斯光束经环形光栅的衍射特性分析

基于傅里叶-贝塞尔变换计算高斯光束垂直入射环形光栅时的衍射远场分布,分析了其衍射远场光强分布的一般规律,并与平面波入射时的情况进行了比较.计算结果表明:当光栅半径为1.5倍高斯光束束腰半径时,随着光栅环数的增加,中央亮斑半值全宽先减小后增大、中央亮斑所包含的功率占总功率的比值减小、中央主极大光强值减小,三者的变化趋势与平面波入射时的趋势一致;中央亮斑半径、次极大光强值变化趋势与平面波入射时的变化趋势不同.当环数小于5时,高斯光束经过环形光栅的衍射场光强变化无规律;当环数大于10后两种情况下衍射场光强变化都不明显;当环数趋于无穷时中央亮斑半径、中央亮斑半值全宽、次极大光强值趋于圆孔衍射(环数等于1)时的值,中央亮斑所包含的功率占总功率的比值约等于圆孔衍射时的1/2,中央主极大光强值约等于圆孔衍射时的1/4.     

Diffractive beam parameters of LP01 mode of fiber

The diffractive beam parameters of LP01 mode of fiber are analyzed in detail. Based on solving linear equations, two formulas for two kinds of mode-field radii as functions of normalized frequency are presented, and relations between angular radius of far-field divergence, beam propagation factor, and normalized frequency are given. Numerical calculation indicates that the maximal relative error is smaller than 1% within a reasonable parameter range.     

非局部—非对称拟连续统理论

本文基于原子点阵模型,应用广义函数论,建立了非局部一非对称拟连续统理论.并讨论了非对称应力的物理—力学模型,即微观—宏观相结合的模型理论.     

A Physical theory of asymmetric plasticity

Experiments have shown the strong rotation in plastic deformation, which is caused by the disclination, specific arrangement of dislocation and inhomogeneity of the gliding motion of the defects in the microscopic scale. Based on the microscopic mechanism of the rotational plastic deformation, the conservation equation satisfied by the defects motion (dislocation and disclination) has been developed in this paper. Then the diffusion motion of the defects are reduced based on the asymmetric theory of continuum mechanics. By utilizing the maximization procedure for the micro plastic work and a scale-invariance argument, various models of Cosserat-type plasticity are obtained in this manner.     

Analysis on Far-Field of Slab Waveguide and Its Gaussian Approximation

This paper researches end diffraction of slab waveguide and then matching efficiency between the far-field and its Gaussian approximate field is analyzed leads to a new definition of divergence half-angle. Finally, why the far-field can be approximated by a Gaussian function is presented according to characteristic of beam propagation factor.     

Mode-field half widths of Gaussian approximation for fundamental mode of two kinds of optical waveguides

This paper analyzes the characteristic of matching effciency between the fundamental mode of two kinds of optical waveguides and its Gaussian approximate field.Then, it presents a new method where the mode-field half-width of Gaussian approximation for the fundamental mode should be defined according to the maximal matching effciency method. The relationship between the mode-field half-width of the Gaussian approximate field obtained from the maximal matching effciency and normalized frequency is studied; furthermore, two formulas of mode-field half-widths as a function of normalized frequency are proposed.