edfas.org 21 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 26 NO. 3 is achieved by consistently gathering and analyzing more empirical and simulation data. As more information becomes available, the thresholds can be adjusted to better reflect the realities of x-ray imaging, leading to improved inspection outcomes. DFI scorer and formulation of the metric. The next step after determining the thresholds for PDFI is to calculate the CMx-ray score of the test design. The DFI scorer needs to be given two inputs: the DFI parameter thresholds and the specifications of the DFI parameters of the test sample. The end result is a quantified measure of how compatible the test design will be to inspection using x-ray imaging once it is fabricated. CMx-ray is calculated based on the extent of compliance of the DFI parameters with their respective maximum thresholds set by the DFI evaluator. As mentioned earlier, PDFI is the set of all the DFI parameters to be considered for a given package architecture. For example, PDFI = [Pb, Sbr, Srr, Pi, Srt, Pt] in Table 2. Each element in the set represents a DFI parameter threshold value. Because factors such as feature geometry, g, material composition, m, and imaging resolution, r, directly impact these thresholds, PDFI can be expressed as a function of these physical factors. The relation can be generalized by the following expression: (Eq 1) Let T1, T2, T3,....Tn be the set of DFI parameter values of a test IC package that is to be evaluated for x-ray compatibility. The extent of observability or compliance of the nth DFI parameter is expressed as a compatibility score of that DFI parameter, referred to as Cn. Therefore, compatibility score of nth DFI parameter (P n) is expressed as: (Eq 2) This equation expresses the distribution of the compatibility score of each DFI parameter as an inverse tangent function (as shown in Fig. 10), with -1 and 1 as lower and higher bounds, respectively. The closer Cn is to the higher bound the more compatible is the DFI parameter value of a test design, and vice versa. CMx-ray is defined as the weighted average sum of the compatibility scores of all the elements in PDFI, or in other words, all the DFI parameters. (Eq 3) (Eq 4) In Eq 3, Wk is the weight of the kth DFI parameter. The values of the relative weights must satisfy the constraints in Eq 4. The way CMx-ray is defined suggests that it will always have a value in the range 0 to 1. The closer the CMx-ray value lies to 1 for a test design, the more compatible it will be to x-ray imaging, and less susceptible it will be to noise interference and presence of unresolvable features. VALIDATION OF THE METRIC In order to substantiate the efficacy of the proposed CMx-ray metric, a comprehensive validation process was undertaken. This involved applying the metric to a real-world test case: a highperformance GPU from Nvidia utilizing CoWoS technology.[20] This technology is notable for its intricate stacking of multiple memory and computer dies, presenting an ideal challenge for our metric’s capabilities. Table 2 A list of possible DFI parameters for a CoWoS package Notation DFI parameter Pb Bump pitch Sbr Bump-RDL spacing Srr RDL-RDL spacing Pi Interconnect spacing Srt RDL-TSV spacing Pt TSV pitch Fig. 10 Plot of the compatibility score of a DFI parameter as a function of test value to threshold value ratio.
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