Calculating Parametric Yield Limits

Laura Peters, Senior Editor -- Semiconductor International, 4/1/1999

Part three in this series of articles on Integrated Yield Management (see www.Semiconductor.Net for complete articles), by Nick Atchison and Ron Ross of Silicon Systems (Santa Cruz, Calif.), describes an accurate, reliable method for calculating parametric yield limits that matches actual yields to within 1%. The method detects design sensitivities and process sensitivities and greatly helps prioritize yield improvement efforts. It is one of several follow-on papers to "A Comprehensive Sequential Yield Analysis Methodology,'' summarized in Semiconductor International, January 1999, p. 38.

Atchison and Ross' method for calculating parametric yield loss takes into account the amount of product affected by a particular variation as well as the frequency distribution of the parameters. Yield limits for a large number of parameters are quickly calculated using a new software program. In cases where two parameters do not independently affect yield, the methodology accounts for their interactivity. It was successfully applied to CMOS and mixed-signal BiCMOS products.

This methodology works well using parametric data and multiprobe results from a significant number of wafers (>=600). As an example, sheet resistance data from a group of wafers processed during a one-month period (Fig. 1) is divided into a small number of groups (three) based on the average value of the parameter. Groups are formed with approximately the same number of wafers in each group. For each group, the parameter average is computed. Next, average probe yield for each group is computed (Fig. 2). If the sample size is large enough and there is no sensitivity of multiprobe yield to the parameter in question, the graph is a horizontal line. In this example, yield appears to degrade for both high and low values of poly sheet resistance. Yield limits are calculated using:

Y_P = F(P)Y(P)dP

Fig. 1. Wafer-average parametric data, grouped to provide approximately the same number of wafers in each group, and equal numbers with high and low yield.

Fig. 2. Average multiprobe yield in each group.

where Y_P is the yield limit associated with parameter P, F(P) is the normalized frequency distribution of parameter P, and Y(P) is the normalized multiprobe yield as a function of parameter P (Fig. 2). F and Y must be normalized prior to evaluating the integral by dividing the height of each bar of the histogram by the total number of wafers in the sample. For Y(P), the maximum yield in Fig. 2 is set to 1.0. In our example, the yield limit was calculated to be 0.954 or a 4.6% yield loss due to variation in poly sheet resistance. Split lot experiments among three poly resistor implant doses showed similar yield degradation at high and low values of sheet resistance, confirming the sensitivity. Because the data was well within its specification of 800 to 1200 ohm/sq, yield loss for wafers with poly sheet resistances within these limits represents a design sensitivity. Design simulations should be run at all process corners, not just worst case conditions, to investigate such sensitivities.

The engineers use a correlation matrix to determine whether yield limit calculations are independent. When significant correlation is found (i.e., R² > 0.5), pairs of parameters are grouped among: R² < 0.5, R² of 0.5-0.9 and R² >0.9. The first group is ignored and yield limits associated with these parameters are included in the final model. With R² >0.9, only one of the yield limits goes into the model and the other is dropped based on prior knowledge of the each parameter's effect on yield. Between 0.5 and 0.9, the parameter with the lower yield limit is used to calculate the yield limit while the other's limit is adjusted by subtracting it from 1.0, multiplying it by R², then adding that value to the higher yield limit.

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