The dynamics of reading and writing the partial polarization state in ferroelectric (FE) capacitors have been explored for use in nonvolatile analog memory for application in training neural networks. New pulse measurement protocols that minimize spurious interface charging effects have been developed to more precisely measure polarization, polarization reversal, and current-voltage characteristics. Analytic methods to interpret these measurements have also been developed.A strictly symmetric pulse protocol, where the integral of the measurement waveform over a measurement cycle is zero, was developed to measure dynamic effects in FE capacitors. In this way, the effects of biasing were balanced equally to minimize charging of the interfaces. Unsaturated polarization reversal was observed in TiN/HZO/TiN capacitors with asymmetric measurements; the unsaturation was substantially eliminated using the strictly symmetric protocol.Using the strictly symmetric measurement protocol, partial polarization in metal-FE-metal capacitors was shown to be stable up to 250 ms. A surprising dependence of partial polarization on the delay between reset and write pulses, and the reset conditions, was discovered, with the partial polarization changing by 50% of the FE remanent polarization. This delay-before-write dependence was qualitatively attributed to the dynamics of subcritical nuclei that exist up to 1 s in HZO, and whose size is estimated to be less than 4x4x4 HZO unit cells.A strictly symmetric pulsed protocol was designed for current-voltage-time (I-V-t) measurements on Pd/HZO/p+ Si capacitors. The I-V-t measurements showed the capacitor current direction to be opposite to the applied bias polarity for voltages lower in magnitude than certain characteristic zero crossing voltages. The current magnitudes increased when the applied bias magnitudes were decreased further. A quantitative analysis showed these observations to be consistent with the assumption that the HZO electric field controls the capacitor current direction, and that a flat band condition exists in HZO at the zero crossing voltages.A spectroscopic photoresponse measurement system was constructed, capable of measuring electrical responses to photons ranging in energy from 0.6 - 7 eV, to measure polarization dependent band offsets of metal-FE-semiconductor capacitors by internal photoemission (IPE). The bandgap of HZO was extracted as 6.2 +/- 0.2 eV from Pd/HZO IPE transitions.