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In this paper, we carried out an analysis of the breakdown characterization method by the investigation on off-state leakage currents and breakdown curves. For conventional breakdown, seven kinds of breakdown curves are summarized and it is found that only two of them can be shown by the conventional three-terminal breakdown characterization method reasonably. For the other five kinds of breakdown curves, the value of the gate leakage current is larger than that of the drain leakage current for a certain drain-bias range. Besides, the source leakage current cannot represent the buffer leakage current, and the values and signs of them are different. These problems contradict the conventional characterization method, indicating that the conventional method should be modified to characterize the breakdown mechanisms correctly. The similar problems also exist for time-dependent breakdown. The buffer and drain-gate leakage currents were obtained by a simple method and the conventional breakdown characterization method was modified by using these two currents. The problems in the conventional breakdown characterization method are solved by using the modified method. Experiments indicate that the modified breakdown characterization method is crucial to investigate the breakdown mechanisms, especially when source-gate leakage current cannot be neglected compared with the buffer leakage current.