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edfas.org 7 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 22 NO. 4 (resistance map) is proportional to a map of potential across the device if a potential were applied (and if that potential would not significantly alter device resistance). Figure 3 shows a 3D topographic representation of this EBIC-derived potential map, which displays the fractional change inpotential if the leftelectrode inFigs. 2 and3were grounded and an arbitrary voltage were applied to the right electrode. As in the electronic-hydraulic analogy, the height is analogous to potential. This map vividly shows the irregular potential distribution thatwouldbeproduced under bias: the landscape appears as flat “plains” on the leftwith sharp “cliffs” leading to the terraced “highlands” on the right. Treating the EBIC as amap of potential, a correspond- ing map of the electric field can be calculated by taking the negative gradient at each pixel, i.e., the vector result of the difference between nearest neighbors in x and y. It should be noted that, while illustrative, these resistance, potential, and electric field calculations are not entirely rigorous and are subject to some approximations and caveats, as discussed by Hubbard et al. [8] The right image in Fig. 2 is an electric field map generated from the Fig. 2 EBIC image, with arrows indicating field direc- tion and intensity of the green contrast indicating field strength. The few highly resistive grain boundaries (the cliffs in Fig. 3) are also where the electric field would be concentrated under a bias. These grain boundaries would thereforebe themost susceptible to field-drivenprocesses like oxygen vacancy migration, which is expected to be a dominant failure mechanism for Ni/BaTiO 3 MLCCs. [10] The capacitor from which this device was extracted was not stressed, and had not failed, prior to preparation of the FIB sample. But, without applying any bias, the EBIC indicates where, in this field of view, failure would be most likely to occur under bias. In contrast, the standard STEM imaging provides no information about the electronic properties of these components aside from the location and grain structure of the metallic and dielectric regions. CONCLUSION Transmission electron microscopes are ubiquitous in academic research, microelectronic characterization, and semiconductor manufacturing. In each of these com- munities there is an unmet need for precise determina- tion of electronic structure at nanometer length scales. A TEM-based solution to this problem is particularly appealing, as it would allow for such characterization to fit within existing workflows. The results presented here demonstrate that STEM EBIC, and in particular the newly uncoveredmode SEEBIC, provides electronic contrast that is complementary to, but inaccessiblewith, standardSTEM imaging. In this particular example, STEM EBIC was used to map the distribution of resistivity, potential, and elec- tric field in a cross section extracted from an off-the-shelf component. Possible failure points in this volume were identified, without electrically stressing, within 10 nm. While these results are encouraging, the difficulty of sample preparation is one of the main hurdles to STEM Fig. 3 3D topographic renderingof the EBICdata inFig. 2. As in thehydraulic-electronic analogy, height is analogous topotential. Here the left Ni electrode (blue) is grounded and an arbitrary voltage is applied to the right Ni electrode (white). Figure adapted from Hubbard, et al. [8]