Flip Chip Technologies 笔记|一

Flip Chip Technologies note 1:

1、The typical wafer diameters are 3in-75mm , 4 in---100mm , 5 in---125mm , 6 in ---150mm , 8 in---200mm.

2、A wafer usually consists of many product unit cell(PUCs),a few test unit cell(TCs),and a few combined mask alignment unit cells(CMAs).

3、The number of possible chips per wafer：      

A means the area of the chip[in square millimeters(mm2)];

Θ means the radio between x and y;

4、some well-known IC yield formulas

<1>Murphy proposed the following yield integral:

where Y=yield probability (or the probability of zero defects)

         A=defect-sensitive area(or susceptible area,designations-sensitive area,and critical area)

         D=defect density,having the units of defects per unit area

       f(D)=defect density distribution function

I think ,Murphy first approximated the Guassian distribution as a function,so it leads to Possion yield model:

 

Next,Murphy approximated the Guassian distribution as a triangular function and obtained:

Finally,Murphy approximated the Guassian distribution as a uniform function,and the yield became:

<2>Seeds assumed the f(D) as an exponential function and obtained:

<3>finally,Stapper assumed f(D) to be a gamma distribution and Okabe et al.assumed f(D) to be an Erlang function(查了很多，有的叫厄兰分布，有的叫爱尔兰分布)，and they arrived at the same form of the negative binomial yield equation:

yield 是指晶圆的成品率，以标准3英寸晶圆为例，75mm直径的晶圆上，肯定要分布很多片的chip，Nc就是算出到底应该有多少片。根据《Flip Chip Technologies》上的图可以看出，随着chip area也就是A的变大，yield随之变小，也就是说有用的chip变少，但chip area 也不可太小，毕竟是受到工艺手段限制的。

Let us consider a half-Gaussian distribution:

substituting fromer equation(我带了半天都没算明白，微积分算白学了) into the half-Gaussian distribution ,and we calculate some parameters,such as a1=0.34802,a2=-0.09588,a3=0.74786.we have : 

and：

有了以上两个式子，我们就可以根据已知的A和D0计算yield probability,这一块D0一直没找到，翻了翻书，我知道D肯定是指defect density，但D0应该是事先给出的，按照书上的plot，D0还是得给出，而且跟chip的大小有关。