Analytical Model for the Current Density in the Electrochemical Synthesis of Porous Silicon Structures with a Lateral Gradient

Layered optical devices with a lateral gradient can be fabricated through electrochemical synthesis of porous silicon (PS) using a position dependent etching current density \(\bm j(\bm r_\|)\). Predicting the local value of \(\bm j(\bm r_\|)\) and the corresponding porosity \(p(\bm r_\|)\) and etch...

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Authors: Ospina-Delacruz, C A, Agarwal, V, Mochán, W L
Format: Article
Language:English
Subjects:
Calibration
Chemical synthesis
Current density
Etching
Mathematical models
Monolayers
Porosity
Porous silicon
Online Access:Get full text
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Summary:Layered optical devices with a lateral gradient can be fabricated through electrochemical synthesis of porous silicon (PS) using a position dependent etching current density \(\bm j(\bm r_\|)\). Predicting the local value of \(\bm j(\bm r_\|)\) and the corresponding porosity \(p(\bm r_\|)\) and etching rate \(v(\bm r_\|)\) is desirable for their systematic design. We develop a simple analytical model for the calculation of \(\bm j(\bm r_\|)\) within a prism shaped cell. Graded single layer PS samples were synthesized and their local calibration curves \(p\) vs \(\bm j\) and \(v\) vs \(\bm j\) were obtained from our model and their reflectance spectra. The agreement found between the calibration curves from different samples shows that from one sample we could obtain full calibration curves which may be used to predict, design, and fabricate more complex non-homogeneous multilayered devices with lateral gradients for manifold applications.
ISSN:2331-8422
DOI:10.48550/arxiv.2101.09189