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U. Glaeser

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FIGURE 47.4 Point and lithographic defects in IC chip.<br />

This distribution function cannot be used when the chip size increase is not accompanied by corresponding<br />

increase of the wafer size, and the total number of chips on a wafer is small. Then we can apply for<br />

approximation a binomial distribution function given by<br />

© 2002 by CRC Press LLC<br />

(47.17)<br />

where Y c is the value of final chip yield calculated by expression (47.9). Because of the small number of<br />

chips on a wafer, the clustering of defects cannot be recognized and the values of final chip yields Y cl are<br />

very close to each other.<br />

Critical Area Models<br />

n<br />

f ⎛ ---<br />

Y =<br />

⎝ N<br />

⎞ ⎛N⎞ n<br />

Yc<br />

⎠ ⎝n ( 1 – Yc)<br />

⎠<br />

N−n<br />

=<br />

Yield models generally require the estimation of IC critical area associated with each type of catastrophic<br />

defects, i.e., each type of primitive failures. Examples of the defects include point defects (pinholes in<br />

insulator layers, dislocations, etc.) and lithographic defects (spots on IC chip). Some of these defects are<br />

shown in Fig. 47.4.<br />

Critical Area for Point Defects<br />

Two most significant types of primitive failures in ICs related to their layer structure are a vertical short<br />

of two horizontal conducting layers through oxide (caused by a pinhole) and a leakage current increase<br />

(due to defects of silicon crystal lattice in the depletion region of p-n junction). The critical area for both<br />

of them can be defined as an overlap area of layout patterns from different IC conducting layers (silicon,<br />

polysilicon, or metal), i.e., IC mask layers [32]. Consider a domain shown in Fig. 47.5, where two layout<br />

patterns from two different mask layers are overlapping. If (x1, y1) and (x2, y2) denote canonical coordinates<br />

of overlap area, an overlap area Al is given by<br />

Al = ( x2 – x1) ( y2 – y1) (47.18)<br />

In the case of defects in the depletion region of p-n junction, it is needed to calculate a vertical part<br />

of overlap area A v as well. The following expression is used for this calculation:<br />

Aν =<br />

2z x2– x1 [ ( ) + ( y2 – y1) ]<br />

(47.19)<br />

where z is the depth of p-n junction. The total critical area for point defects A p is equal to a sum of the<br />

lateral part A l and the vertical part A v.

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