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A steady-state mathematical model for an EOS capacitor: the effect of the size exclusion. (English) Zbl 1354.82028

Summary: In this paper we present a suitable mathematical model to describe the behaviour of a hybrid electrolyte-oxide-semiconductor (EOS) device, that could be considered for application to neuro-prothesis and bio-devices. In particular, we discuss the existence and uniqueness of solutions also including the effects of the size exclusion in narrow structures such as ionic channels or nanopores. The result is proved using a fixed point argument on the whole domain.
Our results provide information about the charge distribution and the potential behaviour on the device domain, and can represent a suitable framework for the development of stable numerical tools for innovative nanodevice modelling.

MSC:

82D37 Statistical mechanics of semiconductors
34B15 Nonlinear boundary value problems for ordinary differential equations
58D30 Applications of manifolds of mappings to the sciences
82D80 Statistical mechanics of nanostructures and nanoparticles

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