hw4solutions

hw4solutions - Solutions to HW 4 IEOR 130 Prof Leachman 1...

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Solutions to HW 4 IEOR 130 Prof. Leachman 1. Computing die yield DY according to Poisson, Murphy and Seeds yield models. Given a die area A and a defect density D per unit area, the models are as follows: Poisson Model: DY = exp { -AD } Murphy Model: DY = [ ( 1 - exp {-AD} ) / AD ] **2 Seeds Model: DY = 1 / ( 1 + AD ) A D AD Poisson DY Murphy DY Seeds DY 0.1 0.5 0.05 0.9512 0.9514 0.9524 0.2 0.5 0.1 0.9048 0.9056 0.9091 0.5 0.5 0.25 0.7788 0.7829 0.8000 0.5 1 0.5 0.6065 0.6193 0.6667 1 0.5 0.5 0.6065 0.6193 0.6667 1 0.75 0.75 0.4724 0.4949 0.5714 1 1 1 0.3679 0.3996 0.5000 1 1.5 1.5 0.2231 0.2682 0.4000 2 1.5 3 0.0498 0.1003 0.2500 2. Computing defect densities according to Poisson and Murphy models. A DY Poisson D Murphy D 0.25 0.92 0.3335 0.3360 0.5 0.85 0.3250 0.3296 0.5 0.92 0.1668 0.1680 1 0.65 0.4308 0.4474 1 0.85 0.1625 0.1648 3. (a) Fatal defects from current sputtering machine: (.12 particles per sq cm)(2 passes)(.25 are fatal) = .06 per sq cm Fatal defects from new sputtering machine: (.05 particles per sq cm)(2 passes)(.25 are fatal) = .025 per sq cm Thus the new machines would decrease defect density by .035 per sq cm. (b) Current DY = 0.80, A = 0.50 sq cm. Assuming Poisson yield model, the total fatal defect density at present is

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