Theory of the Impedance of Electron Diffusion and Recombination in a Thin Layer

Abstract

This paper analyzes the small signal ac impedance of electron diffusion and recombination in a spatially restricted situation with application in systems such as porous TiO 2 nanostructured photoelectrodes and intrinsically conducting polymers. It is shown that the diffusion-recombination model with the main types of boundary conditions assumes a finite set of possible behaviors in the frequency domain, which are classified according to relevant physical parameters. There are four possible cases: (i) the impedance of finite diffusion with reflecting boundary, (ii) the impedance of finite diffusion with absorbing boundary, (iii) the impedance of diffusion-reaction in semiinfinite space or Gerischer impedance, and (iv) the impedance that combines Warburg response at high frequency and a reaction arc at low frequency. The generality of the approach is discussed in terms of the spatial distribution of the electrochemical potential or quasi-Fermi level and also in terms of the transmission line representation. An extension is considered to the diffusion in lithium intercalation electrodes coupled to a homogeneous solid-state reaction. The connection is established with other frameworks for the description of transport and reaction in electrochemical systems.

Diffusion–Recombination Impedance Model for Solar Cells with Disorder and Nonlinear Recombination

“…[24] In the electrical case, the model is defined in a 1D system with a local voltagef and currentî and local impedances c and z [Eqs. (43) and (44)]: [1] @f @x ¼ ÀcðxÞî ð43Þ…”

Physical electrochemistry of nanostructured devices

“…73 Recently, many studies have determined the properties of DSC using EIS. 40,64,66,[74][75][76][77][78] This technique has the advantage of identifying different types of operational elements, consisting either in electronic or ionic processes, in photoelectrochemical devices.…”

Three-Channel Transmission Line Impedance Model for Mesoscopic Oxide Electrodes Functionalized with a Conductive Coating

“…[1][2][3][4] Eventually, the transverse branch of the TL contains a recombination or reaction resistance that describes the loss of the diffusing species. 1,4 For two oppositely charged species, the classical solution with local electroneutrality gives a threechannel transmission line where the central channel contains a chain of capacitors that describes the local polarization. 5 This last model is used for ionic transport of a dissociated salt in a membrane 5 and also for the transport of electronic species in semiconductors [6][7][8] and electronically conducting polymers.…”

“…Usually, in these systems, the electronic communication between the large internal surface covered with optically active molecules and the external contact occurs by electron transport through the assembly of sintered semiconductor nanoparticles. Impedance spectroscopy has proved to be a very useful technique for the characterization of properties of dye solar cells 1,[19][20][21][22] and electrochromic windows. 23 Recently, a new approach has been taken [24][25][26][27][28] toward electric and electrooptic devices formed by molecular functionalized mesoscopic oxides, such as photovoltaic cells, sensors, and Figure 1.…”

“…Scheme of the two-channel transmission line model for a porous electrode in electrolyte solution. 1 is the specific conductivity in the solid phase, 2 is the specific conductivity in the liquid electrolyte, and is the specific polarization/charge-transfer element at the solid/ liquid interface. switchable molecular electronics, etc., in which the molecular layer adsorbed in the surface serves, instead or in addition to the optical functions commented above, as an electron or hole transport relay.…”