In a comprehensive analytical study of dielectric breakdown (BD) of ultra-thin MgO in 28 nm embedded MRAM (eMRAM) test chips, it was observed that breakdown in MgO is polarity dependent, and that device lifetime is reduced for bipolar (AC) stress. Furthermore, it was found that the breakdown trend substantially deviates from the Poisson area scaling law; this deviation can be attributed to self-heating in larger area devices. Further investigation of BD also reveals that self-heating effects are predominantly observed at lower frequencies; percolation paths exhibit fast transient (thermal runaway) temperatures; and that BD statistics are poorly represented by the standard Weibull model.