This paper is devoted to the study of the local existence, uniqueness, regularity, and continuous dependence of solutions to a logistic equation with memory in the Bessel potential spaces.

Microstructral and charge-trap properties of single Hf-silicate dielectric films are presented versus annealing treatment. The as-grown films were found to be homogeneous and amorphous. It is shown that annealing treatment results in the formation of alternated Hf-rich and Si-rich layers. The mechanism responsible for this phenomenon is found to be surface directed spinodal decomposition. The increase of annealing temperature up to 1000-1100°C resulted in the crystallization of Hf-rich phase. The stability of its tetragonal phase caused an enhancement of film permittivity was observed. The evolution of charge trapping properties of the films results in the memory effect which nature was discussed.

Diodes were formed by intermediating a thin film of PEDOT:PSS between aluminum and heavily doped silicon. Both p-type and n-type Si substrates were used. Hysteresis loops were observed in their current-voltage (I-V) characteristics. A ‘state’ can be written by applying a voltage pulse to aluminum electrode. The state of the device can be read out from the current under a small probe voltage (0.3-0.6 V, to Al electrode). Appling +4.0 V induces a ‘low’ conductance state while applying -4.0 V switches the device back to the ‘high’ conductance state. The current difference between two states is up to 3 orders of magnitude. The space charge storage in the polymer is believed to be responsible for the memory effect. Upon positive voltage bias the charges are injected into the place near the Al/PEDOT:PSS interface. The charges are stored there and will resist subsequent charge injection, resulting in the ‘low’ conduction state. The redox reactions further reduce the conductance of the device. Negative bias can remove the stored charges and reverse the redox reactions, thus recover the device back to ‘high’ conduction state.