Redundancy Yield Model for SRAMS

This paper describes a model developed to calculate the number of redundant good die per wafer. A block redundancy scheme is used here, where the entire defective memory subarray is replaced by a redundant element. A formula is derived to calculate the amount of improvement expected after redundancy. This improvement is given in terms of the ratio of the overall good die per wafer to the original good die per wafer after considering some key factors. These factors are memory area, available redundant elements, defect density and defect types with respect to the total reject die and defect distribution on the memory area. The model uses Poisson’s equation to define the yield, then the appropriate boundary conditions that account for those factors are applied. In the case of a new product, knowing the die size, memory design, and total die per wafer, the model can be used to predict the redundancy yield for this product at different initial yield values. Optimizing the memory design by varying the number of memory blocks and/or redundant elements to enhance redundancy is also discussed. The model was applied to three products from two different process generations and showed good agreement with the measured data. Introduction Due to the continuing increase in the size of memory arrays, reaching a high yield from the same wafer is more challenging than ever. Redundancy is a way to improve the wafer yield and to reduce the test cost per good die by fixing potentially repairable defects. In order to forecast the volume of a certain product when redundancy is applied, it is important to estimate, as accurately as possible, the number of die gained after redundancy. Redundancy is the process of replacing defective circuitry with spare elements. In SRAMs, rows and/or columns can be replaced, as well as an entire subarray. In a previous study[1], a redundant yield estimation methodology was developed. It is applicable to row, column or block redundancy schemes. It distinguishes between repairable and non-repairable faults within a memory block. In order to apply this method, new CAD tools are required. This method is useful if row or column redundancy is used. This paper will focus only on the yield estimation for block redundancy, as block redundancy was preferred over row and column redundancy for the SRAM architecture. It is usually easier to replace the entire subarray. This might seem like overkill; however, replacing the entire subarray allows for the replacement of defective peripheral circuits in addition to just the memory array elements. It also allows for the replacement of multiple bad bits, or other combinations of failing bits, rows and columns. A yield multiplier M is defined as the ratio of the total good die after redundancy to the original good die per wafer, or M = total redundant good/original good (1) so that the redundant yield , Yred , is given as Yred = M x Y (2) where Y is the initial yield. Forecasting of the redundancy yields is based on how accurately the factor M is calculated. A formula for M was obtained by using the correlated defect model. According to this model, an expression for the yield of die containing a number of defects, I, is given by yI={(n+I+1)! x (DA) }/{(I! n )x(1+D A/n)} x f (3) where yI = yield of a die with I defects Intel Technology Journal Q4’97 2 D = average defect density ( #/cm ) A = die area (cm ) n= correlation factor between defects f = fraction of the die area that contains the defects The yield of die with zero defects can be obtained by setting I = 0 and f = 1 as Y = 1 / { 1 + (A D / n) } (4) With n = 4 and using equation (4) to substitute for the defect density, equation (3) becomes yI= Y x ((I+3)(I+2)(I+1) /6) x f I x ( 1-Y ) I (5) Introducing g as the fraction of repairable defects, g varies depending on the number of repaired defects. An expression for M was obtained by summing yI over the ratio of correctable defects and substituting in (2) M = 1 + ΣI = 1 ((I+3)(I+2)(I+1) /6) x( g f ( 1-Y )) I (6) M was calculated by entering arbitrary values of g and f in equation (6). However, there was no evidence to support the values of the repairable defect density represented by g used to calculate M. Another formula was used to estimate the yield multiplier M . The yield is derived from Poisson’s equation [2]