Equal-capacitance field-moment analysis of electric-field nonuniformity in high-aspect-ratio metal–insulator–metal capacitors

Atomic layer deposition (ALD) provides conformal dielectric coatings for three-dimensional metal–insulator–metal capacitors, yet thickness variations in high-aspect-ratio features can produce localized electric-field enhancement even at the same overall capacitance. Here, we introduce an equal-capacitance field-moment framework that isolates the effect of dielectric-profile shape from the mean inverse thickness. Each nonuniform profile is compared with a uniform dielectric having the same capacitance, and the residual field nonuniformity is quantified by a p-root field-moment factor, R_p, which increasingly weights thin regions through a geometric description of the field distribution. The framework is evaluated computationally using 11 archived measured Al₂O₃ thickness profiles and 101 open ALD transport simulations. Nested leave-one-process-family-out validation shows that normalized penetration depth alone reconstructs R_8 with an RMSE of 1.809, whereas including bottom coverage and transition-front slope reduces the RMSE to 0.279, with improvement in all eight held-out process families. When penetration depth, capacitance factor, and bottom coverage are matched within 5%, the largest R_8 ratio between nonduplicate profiles is 1.015. Relaxing the bottom-coverage tolerance to 10% while retaining the other two matching tolerances at 5% yields a selected maximum ratio of 1.132. Profile-specific planar-gap finite-element calculations preserve all profile rankings and differ from the local-column field moment by at most 0.086%. These results show that conventional conformality descriptors capture most of the electrostatic information contained in the complete thickness profile, with additional information retained in the full-profile field moment. The proposed framework provides a reproducible geometry-based measure for determining when thin-tail variations require full-profile electrostatic analysis.