A model for electrochemical oscillations at the Si∣electrolyte contact

Grzanna, J.; Jungblut, H.; Lewerenz, H. J.

doi:10.1016/s0022-0728(00)00142-x

Cited by 58 publications

(60 citation statements)

References 16 publications

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“…The presence of pores in such oxides was postulated already early ("local pitting" (16)). It has been proven experimentally (17) and represented a fundamental prerequisite for the development of a theoretical model (21,22). The present study addresses the formation of such an oxide as mask for the process steps resulting in the nanoemitter solar cell.…”

Section: Introductionmentioning

confidence: 94%

“…Alternatively, the formation of large scale nanostructured areas by properly designed self organized processes was also referred in (13). A suited candidate for such a process might be the formation of anodic oxides on silicon during current oscillations which were extensively investigated by different groups (16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26). The presence of pores in such oxides was postulated already early ("local pitting" (16)).…”

Section: Introductionmentioning

confidence: 99%

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Electrochemically Induced Self-organized Nanostructures on Silicon for Realization of a Novel Nanoemitter Solar Cell Concept

et al. 2007

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Oscillatory behaviour of silicon electrodes in fluoride containing solution results in formation of nanoporous oxides. Metal electrodeposition into these pores results in local Schottky junction formation. Metal nanoemitters are contacted with a transparent conductive oxide and aluminum contact fingers for preparation of the first device (Al/ZnO/Pt-SiO2/Si/GaIn/Ag). Present solar-to-electrical conversion efficiencies are small and various improvement possibilities are outlined.

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Electrochemically Induced Self-organized Nanostructures on Silicon for Realization of a Novel Nanoemitter Solar Cell Concept

et al. 2007

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“…The trajectory is determined ( figure 3 left) using the microscopic nanopore model [5,9] at which in dependence on the starting time s the evolution of a nanopore as the mean of the evolution of real nanopores during one cycle is regarded. For simplicity, we set…”

Section: Brownian Motion Of a Virtual Particlementioning

confidence: 99%

“…In photo-electrochemistry and electrochemistry, oscillatory behaviour has been extensively studied on Si photo-electrodes [2]. Various models for the oscillation phenomena were discussed based on self-oscillating domains [3], the so-called current bursts [4], and oxide-induced interfacial stress [5] where the latter model explains sustained current oscillations with the existence of two types of oxides with different nanopore densities. The observation of nano-dimensioned pores, fluctuating with the phase of the oscillating (photo) current of Si electrodes immersed in dilute ammonium fluoride solutions motivated the further development [6][7][8] of the original stress model, also to spatial resolution, by applying cellular automates [7].…”

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confidence: 99%

Oscillations at the Si/electrolyte contact: Relation to Quantum Mechanics

Grzanna

Lewerenz

2015

J. Phys.: Conf. Ser.

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Abstract. The basic process at the surface of the Si electrode is characterized by a cyclic oxidation of a thin silicon layer and the subsequent removal of the oxide by etching. Here, the oxide thickness evolves not uniformly due to cracks and nanopores. The mathematical model used to describe the phenomenon is based on a sequence of time dependent (oxide thickness) oscillator density functions that describes the passing of the (infinitesimal) oscillators through their minimum at each cycle. Two consecutive oscillator density functions are connected by a second order linear integral equation representing a Markov process. The kernel of the integral equation is a normalized Greens Function and represents the probability distribution for the periods of the oscillators during a cycle. Both, the oscillator density function and the twodimensional probability density for the periods of the oscillators, define a random walk. A relation between the oscillator density functions and solutions of the Fokker-Planck equation can be constructed. This allows a connection of the oscillations, originally considered only for the description of a photo-electrochemical observation, to the Schrödinger equation. In addition, if the trajectory of a virtual particle, located at the silicon oxide electrode surface, is considered during one oscillatory cycle, then it can be shown that the displacement of the particle measured at the electrode surface performs a Brownian motion. IntroductionOscillation phenomena of silicon electrodes in electrochemical systems have been known for a long time [1]. In photo-electrochemistry and electrochemistry, oscillatory behaviour has been extensively studied on Si photo-electrodes [2]. Various models for the oscillation phenomena were discussed based on self-oscillating domains [3], the so-called current bursts [4], and oxide-induced interfacial stress [5] where the latter model explains sustained current oscillations with the existence of two types of oxides with different nanopore densities. The observation of nano-dimensioned pores, fluctuating with the phase of the oscillating (photo) current of Si electrodes immersed in dilute ammonium fluoride solutions motivated the further development [6][7][8] of the original stress model, also to spatial resolution, by applying cellular automates [7]. If the model is presented by a special phase space analysis based on the holographic principle [9][10], then an analogy between the spectral energy densities of the black body radiation and that obtained from the model for current oscillations can be shown [10]. We first describe (section 2) the mathematics of the model and the relation to the FokkerPlanck and Schrödinger equation. The Brownian motion of a virtual particle, which position is defined by an infinitesimal point located at the silicon surface, is discussed in section 3.

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“…It is attributed to dielectric nature of oxide. In the last time, the idea of self-oscillating SiO 2 domains appears and was investigated theoretically [16,17] and they calculated the relationship between thickness oscillators and the resulting current oscillations. ____________________ * Corresponding author: e-mail: jjakubow@sol.put.poznan.pl…”

Section: Introductionmentioning

confidence: 99%

Study of surface morphology of electrochemically etched n‐Si (111) electrodes at different anodic potentials

Jakubowicz

2003

Cryst. Res. Technol.

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Changes of n-Si (111) silicon surface morphology after anodisation at different voltage conditions in dilute NH 4 F solutions were studied by AFM technique. The electrochemical etching was done with respect to current-voltage (I-V) characteristics. The Si surface was investigated at increasing and constant voltage conditions. The porous silicon was formed at potentials slightly anodic from the rest potential (from -0.6 V to 0.02 V). On the other hand silicon oxide formation and electropolishing occurs at higher anodic potentials. The sustained current oscillations take place in the Si electrode, at 6 V potential in dilute NH 4 F solution. The nature of oscillations was attributed to cyclic silicon oxide formation and its dissolution. The surface undergoes from smooth (before oscillation peak) to rough (little before top of the peak) during oscillation peak, and finally transforms to smooth at the bottom of the peak. It was confirmed by the roughness parameter.

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A model for electrochemical oscillations at the Si∣electrolyte contact

Cited by 58 publications

References 16 publications

Electrochemically Induced Self-organized Nanostructures on Silicon for Realization of a Novel Nanoemitter Solar Cell Concept

Electrochemically Induced Self-organized Nanostructures on Silicon for Realization of a Novel Nanoemitter Solar Cell Concept

Oscillations at the Si/electrolyte contact: Relation to Quantum Mechanics

Study of surface morphology of electrochemically etched n‐Si (111) electrodes at different anodic potentials

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