August_EDFA_Digital

edfas.org ELECTRONIC DEV ICE FA I LURE ANALYSIS | VOLUME 24 NO . 3 6 use the binomial probability function [1] to estimate the expected probability of rejecting an arbitrary sample size of 13 to compare against those values we derived from the MC populations. The simulated MC Disp/K for the S2S population matches the expected binomial probability projections quite well (Fig. 2). However, when comparing results using the W2W MC instead, we find that the addition of w2w leads to noticeable offsets between actual observed Monte Carlo yields relative to binomial probability projections (Fig. 3). Relative to thebinomial probabilityprojections, adding the 50% w2w component to the Monte Carlo reduced the fraction of wafers being flagged at lower disposition thresholds while increasing that fraction at higher thresh- olds. The fundamental problem here is that by adding a w2w component, we no longer have a uniform defectiv- ity rate across each indivi- dual wafer in the population. Figure 4 compares the expect- ed distributions for five wafers across the spectrum of wafer level var iat ion at −3σ w2w , −1.5σ w2w , 0σ w2w , 1.5σ w2w , and 3σ w2w . The top row shows wafers fromMC S2S (100% s2s ) while the bottom row shows them from MC W2W (50% s2s/ 50% w2w ). Since S2S has no w2w variationcomponent, allof its wafers are distributed iden- ticallywitha constant expected nonconformance rate from wafer towafer. UnderW2Wwith w2w , each individual wafer has a slightly tighter distribution (with σ ≈ 0.71 as compared to σ = 1 in top row) but the location of that distribution shifts with wafer mean across columns (from w2w compo- nent at −3σ to +3σ). For wafers with w2w component closer to typical (0σ), the narrower spread within the wafer leads to a lower risk for flagging nonconforming values. As the w2w component pushes away from nominal, the wafers have a greater fraction of their distri- bution within noncompliance regions, offering a greater risk for multiple sites to fail within a sample. For aprocesswithhierarchi- cal s2s and w2w variance com- ponents, the expected fraction of nonconforming sites on a givenwaferwill varydepending Fig. 3 Sample W2W Monte Carlo results do not align with binomial projections. Fig. 4 Individual wafer distributions with w2w variation offsets.