Interface capacitance of nano-patterned electrodes

• Published in: Surface science Vol. 605; no. 1; pp. 240 - 247
• Main Authors: Ibach, Harald, Beltramo, Guillermo, Giesen, Margret
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 2011; Elsevier
• Subjects: Capacitance; Charge; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Condensed matter: structure, mechanical and thermal properties; Cross-disciplinary physics: materials science; rheology; Debye length; Dielectric properties; Electrodes; Electrolytes; Exact sciences and technology; Mathematical analysis; Metal-electrolyte interface; Nano-structured surfaces; Nanostructure; Physics; Stepped; Dielectric properties; Metal-electrolyte interface; Nano-structured surfaces; Capacitance
• ISSN: 0039-6028; 1879-2758
• DOI: 10.1016/j.susc.2010.10.025

By employing numerical solutions of the Poisson–Boltzmann equation we have studied the interface capacitance of flat electrodes with stripes of different potentials of zero charge
ϕ
pzc. The results depend on the ratio of the width of the stripes
l to the dielectric screening length in the electrolyte, the Debye length
d
Debye, as well as on the difference
Δϕ
pzc in relation
k
B
T/e. As expected, the capacitance of a striped surface has its minimum at the mean potential of the surface if
l/
d
Debye
<<
1 and displays two minima if
l/
d
Debye
>>
1. An unexpected result is that for
Δϕ
pzc
≅
0.2V, the transition between the two extreme cases does not occur when
l
≅
d
Debye, but rather when
l
>
10
d
Debye. As a consequence, a single minimum in the capacitance is observed for dilute electrolytes even for 100
nm wide stripes. The capacitance at the minimum is however higher than for homogeneous surfaces. Furthermore, the potential at the minimum deviates significantly from the potential of zero mean charge on the surface if
l
>
3
d
Debye and
Δϕ
pzc is larger than about 4
k
B
T/e. The capacitance of stepped, partially reconstructed Au(11
n) surfaces is discussed as an example. Consequences for Parsons–Zobel-plots of the capacitances of inhomogeneous surfaces are likewise discussed.