Second, the number of devices per wafer is increased. Silicon wafers are ubiquitous in pretty much every electronic device around us. ( Your yield percentage change due to design and die size ) 2. Yield is related to the ratio of defective vs. non-defective, conforming vs. non-conforming or functional vs. non-functional. N G =Gross die per wafer . CS 514 Homework 1 A NEESH K ULKARNI CWID 10427145 Case Study 1 1.1 a) Die Yield is given by the formula, Die Yield = Wafer Yield x 1/ (1 + (Defects per unit area x Die Area)) ^N Let us assume a wafer yield of 100% Die Yield of phoenix chip = (8*10^7) / (7*10^-7 * 12*10^9) X 1/ ( 1+ (200*10^-2 *0.04)^14 = approx. N AV =Average number of die affected per cluster . Even if the first time yields of the individual process steps are high, if the overall process becomes more and more complex, the system rolled throughput yield will continue to erode. • Infant Mortality is measured by life-test, and controlled by burn in. Wafer dicing system for SiC - Duration: 3:39. The required parameters for calculating the gross die per wafer are the die size, the edge exclusion and the wafer size. Index words: Poisson’s formula, yield, defect density, repair rate Abstract This paper describes a model developed to calculate the number of redundant good die per wafer. The gross yield limits for clusters of defects can be calculated by overlaying clustered defects wafer maps with probe wafer maps. It is defect density per cm2 that is the most important factor. and solutions to warpage, because (as will be discussed) Stoney’s formula (relating intrinsic stress and curvature) does not apply for structures warped with compound curvature, and standard wafer warpage measurements are not designed to measure compound curvature. a) Find the yield for both wafers. Here Yline denotes line yield or wafer yield which is the fraction of wafers which survive through the manufacturing line. • Average line yield, the percentage of wafers started that are completed properly, normalized to twenty mask layers. Then, the percent yield would be: Percentage yield of NaCl = 8.50 grams ÷ 9.93 grams × 100%. The gross yield limits for clusters of defects can be calculated by overlaying clustered defects wafer maps with probe wafer maps. The reported defect densities account for all yield losses, including both spot defects and parametric problems. Semiconductor Yield Modeling Using Generalized Linear Models by Dana Cheree Krueger A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Approved March 2011 by the Graduate Supervisory Committee: Douglas C. Montgomery, Chair John Fowler Rong Pan Michele Pfund ARIZONA STATE UNIVERSITY May 2011 . • Defect densities, calculated for major process flows in each fab by using reported die yields and die sizes in the Murphy model of defect density. Quality and material yield are two fundamental drivers of wafer TCO, as shown in the mathematical formula. Use 1 gross die, 2 for net die and 3 for wafer yield. per die Cost per wafer Dies per wafer yield× = -----waferper -----Wafer area Die area ≈ - 1 ()1 Defects+ ()per area Die× area 2 ⁄ 2-----= IMD 1.8-2 In More Depth 1.61 [10] <§§1.4, 1.5> What is the approximate cost of a die in the wafer shown in Figure 1.15 on page 31? A wafer is a thin slice of this semiconductor material, which serves as the substrate for microelectronic devices built in and over the wafer. Wafer manufacturers look for a minimum of 95% quality yield with increasingly tight wafer specifications. Service-based businesses calculate the formula slightly differently: by multiplying the number of customers by the average service price. N G =Gross die per wafer. • Yield is measured at Sort – initial wafer-level testing. threshold voltages or transistor gains) on the yield. Even if the yield decreases with the implementation of smaller features, the total number of functioning devices per wafer may still be a greater number than without the shrink, with larger features . The wafer device yield plays a very important role in cost-effectiveness for Integrated Circuit (IC) manufacturers. This is because there are many variables that affect yield, and this method uses wafer averages and determines the average effect of electrical parameters (e.g. Cost per die = (Cost per wafer / (dies per wafer × yield)) Dies per wafer ≈ Wafer area / Die Area Die Area ≈ Wafer area / Dies per wafer Yield = (1 + (Defects per area × Die area/2))^(-2) or Yield = 1/((1 + (Defects per area × Die area/2))^2) What are response time and throughput and how are they affected by 1) replacing a processor with a faster one or by 2) adding more processors. N AV =Average number of die affected per cluster. where the capital Greek letter pi (Π) tells you to multiply all the first time yields of the system together. A block redundancy scheme is used here, where the entire defective memory subarray is replaced by a redundant element. incremental yield improvements. N D =Total number of die affected by clusters . (all products, modest yield) • Value/Mass of processed wafer $275,000/Kg . L8 3 C. J. Spanos The fraction non-conforming The most inexpensive statistic is the yield of the production line. One important aspect that directly hit the quality is the silicon wafer yield analysis and wafer yield analysis can help the engineers to identify the causes of failures at a very early stage. Effective Area. the number of dies per wafer, and give an explanation of your formula. Some areas of a device are more sensitive to defects than others. Die Yield = Wafer yield * 1 + Defects_per_unit_area * Die_Area Integrated Circuits Costs Die Cost goes roughly with die area 4 { } RHK.S96 9 Real World Examples Chip Metal Line Wafer Defect Area Dies/ Yield Die Cost layers width cost /cm 2 mm 2 wafer 386DX 2 0.90 $900 1.0 43 360 71% $4 486DX2 3 0.80 $1200 1.0 81 181 54% $12 PowerPC 601 4 0.80 $1700 1.3 121 115 28% $53 HP PA 7100 3 0.80 $1300 … In a nutshell, "yields" in the slide mentioned above refer to what percentage of the chips on a given semiconductor wafer actually work. The formula for the yield limit is: Y i = 1-(N C * N AV N * N G) * P k (6) where: P k i = N CD N D. P k i = N C =Number of clustered defects. Let’s assume that you obtained an actual yield of 8.50 grams. As part of this problem, you will want to derive a formula for the die area (note that this will be an approximation). Steep yield ramp means quicker path to high batch yield and hence volume production. The sales revenue formula calculates revenue by multiplying the number of units sold by the average unit price. ii ABSTRACT Yield is a key process … 2.1.2.3. In electronics, a wafer (also called a slice or substrate) is a thin slice of semiconductor, such as a crystalline silicon (c-Si), used for the fabrication of integrated circuits and, in photovoltaics, to manufacture solar cells.The wafer serves as the substrate for microelectronic devices built in and upon the wafer. Production of Silicon Wafers • Silicon starts as beach sand quartzite . This is conceptually similar to intrawafer variation. 3D-Micromac AG Recommended for … Z = Distance between wafer median surface and the point halfway between the upper and lower probe (D/2) To determine the value of Z at any location on the wafer, there are two equations: Z = D/2 – A – T/2 and Z= -D/2 + B + T/2. It is a popular material used to manufacture semiconductors. The die size is the stepping distance on the wafer and not the size of the die after saw. The formula for the yield limit is: ##EQU6## where: ##EQU7## P k i = N C =Number of clustered defects . • Burn in is a stress preceding final test which activates latent reliability defects (LRDs) so that they may be screened out at final test (Class). 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