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A parametric delay fault could arise in a through-silicon via (TSV) of a 3-D IC due to a manufacturing defect. Identification of such a fault is essential for fault diagnosis, yield-learning, and/or reliability screening. In this paper, we present an innovative design-for-testability technique called variable output thresholding. We discovered that by dynamically switching the output of a TSV from a normal inverter to a Schmitt-Trigger inverter, the parametric delay fault on the TSV can be characterized and detected. SPICE simulation reveals that this technique remains effective even when there is significant process variation. A scalable test infrastructure indicates that the test time is modest at only 17.2 ms for 1024 TSVs and 648.8 ms for 32768 TSVs when the test clock is running at 10 MHz.