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Competing styles in statistical mechanics have been introduced to investigate physico-chemical systems displaying complex structures, when one faces difficulties to handle the standard formalism in the well-established Boltzmann–Gibbs statistics. After a brief description of the question, we consider the particular case of Renyi statistical approach, which is applied to the study of the "anomalous" (non-Fickian) diffusion that is involved in experiments of cyclic voltammetry in electro-physical chemistry. In these experiments, one is dealing with the fractal-like structure of the thin film morphology present in electrodes in microbatteries. Fractional-power laws are evidenced in the voltammetry measurements and in the analysis of the interphase width obtained using atomic force microscopy. The resulting fractional-powers are related to each other and to the statistical fractal dimension, and can be expressed in terms of the index on which Renyi's statistical approach depends. The important fact that this index, which is restricted to a given interval, provides a measure of the micro-roughness of the electrode surface, and is related to the dynamics involved, the nonequilibrium thermodynamic state of the system, and to the experimental protocol is clarified.

Three different electrode films of highly crystallized LiCoO₂, nano-crystalline LiMn₂O₄ as cathode and amorphous LiNiVO₄ as anode were grown on stainless steel substrates by pulsed laser deposition. Microbatteries were assembled using liquid electrode of LiPF₆. The microbatteries were electrochemically tested by charge/discharge cycling and cyclic voltammetry. Both LiCoO₂/LiPF₆/LiNiVO₄ and LiMn₂O₄/LiPF₆/LiNiVO₄ cells showed smooth charge/discharge curves. Although the cells faced a fast capacity loss in the first 10 cycles, about 20 μA/cm² μm of discharge capacity was attainable after 20 cycles.

Microbatteries are currently the best choice to power microelecronic devices. To maximize both energy density and power density of microbatteries within the areal footprint, the three-dimensional (3D) microbattery architectures have been proposed, comprising a 3D matrix of components (cathode, anode and electrolyte) arranged in either a periodic array or an aperiodic ensemble. As one of the key components, the cathode is vital to the electrochemical performance of microbatteries and the fabrication of 3D cathode is still challenging. This review describes recent advances in the development of 3D self-supported metal oxides as cathodes for lithium-ion microbatteries. Current technologies for the design and morphology control of 3D cathode fabricated using template, laser structuring and 3D printing are outlined along with different efforts to improve the energy and power densities.