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Scintillation and surge current breakdown voltages were measured using constant-current-stress and step-stress-surge-current techniques. Distributions of breakdown voltages were analyzed for 30 different lots of commercial and military-grade capacitors. Results of measurements of temperature dependencies of breakdown voltages were analyzed and the physical nature of surge current and scintillation breakdowns in tantalum capacitors is discussed. The suggested model explains both the scintillation and surge current breakdowns as a result of electron impact ionization and avalanche breakdowns. Charges trapped in the dielectric during a slow voltage increase result in raising of the barrier at the cathode/dielectric interface and enhancing scintillation breakdown voltages compared to surge current breakdown voltages. An anomalous characteristic of the time-dependent breakdown in tantalum capacitors, for which the higher the rate of the voltage increase, the lower the breakdown voltage, is due to the presence of electron traps in anodic Ta2O5 dielectrics. A high concentration of fast electron states is a characteristic feature of anodic Ta2O5 dielectrics and is the major reason for scintillation breakdown voltages being significantly greater than the surge current breakdown voltages.