Improving Yield Prediction Accuracy

Laura Peters, Senior Editor -- Semiconductor International, 8/1/2000

As shown in the previous installment of this series, probe yields can be readily estimated for new technologies if the current and next-generation technologies are similar, and if the relative defect densities and defect size distributions are known.

The CAA graph is used to calculate defect limited yield at each critical mask layer.  (Source: Texas Instruments)

Having shown the cost-effectiveness of implementing such a similar, next-generation technology, Ron Ross of Texas Instruments presents a more detailed wafer probe yield forecast resulting from the use of in-line inspection data for each of the critical layers in a new technology.

In cases where detailed defect density data are available from in-line inspection tools and the product layout is complete, critical area analysis (CAA) provides a more accurate yield prediction (see "Enhancing Yield Using Critical Area Analysis", for CAA details). Given the actual defect density and size distribution for each critical layer, a defect density constant, k, can be calculated using:

Once k is known, CAA results and the defect size distribution function for each layer can be used to calculate the defect limited yield for each layer. Failure probabilities based on defect size for a real product produced at Texas Instruments' Santa Cruz, Calif., facility (Figure) can be multiplied by the die area to calculate defect limited yield according to:

where li is the average number of fatal defects per die, Y_di is the yield limit for defects at critical layer i, A is the die area and pi(x) is the probability of failure (from CAA graph) for layer i as a function of defect size (x). The lower limit is set at zero as the probability of failure is zero until defect size reaches the minimum feature size for layer i. Evaluating the integral numerically, one can determine yield loss at each layer; these are then multiplied together to give the total random defect loss. For example, assuming a die area of 0.4 cm², k of 1.2 and defect size distribution function of 1/x³, combined with CAA data from the figure and defect size increments of 2 µm, the average number of defects per die (Table) and the probability of metal-1 shorts are calculated using:

Therefore, yield loss due to metal-1 shorts is 0.33%. Where greater accuracy is required, a computer program that interfaces with the critical area program should be used. •