Simulation of Electronic Sensing of Biomolecules in Translocation Through a Nanopore in a Semiconductor Membrane - Nanopores: Sensing and Fundamental Biological Interactions - page 166

layers to decrease the parasitic capacitance resulting from the electrolyte double
layer at the inner interface between the solution and the semiconductor layers.
As the upper and lower electrodes are identical, we only describe the modeling of
the upper layer as detailed below.

7.5.1 Modeling of the n-Doped Silicon Electrodes

The combination of the electrolyte double layer [ 32 - 34 ] and the depletion zone in
the semiconductor layer at the inner interface of the nanopore behaves as a
cylindrical capacitor. In this work, the depletion thickness W is assumed to be
constant and equal to 1 nm as estimated from multi-scale simulation for a N D ¼ 2.

10 20 cm 3 Si doping in the Si layer and a surface potential

0.16 V [ 19 ]. As the
double layer capacitor connected in series with the depletion capacitor presents a
quite large value, its effect is negligible with respect to the lower capacitance of the
depletion layer. In order to account for the 30 slanted angle, the n-doped Si part is
divided into five mini-layers, each defining a cylindrical capacitor characterized by
a radius r i (see Fig. 7.9 ). The wall slope inside each mini-layer is assumed to be
negligible. The depletion capacitance in each mini-layer is computed as:

Ф S

2 phr i

W :

C dep;i ¼ e 0 e Si (7.12)

The silicon electrode is modeled by a network of resistors which is obtained by
dividing each mini-layer into five elementary cells so that the whole electrode is
comprised of 25 electric cells. One elementary cell is therefore a ring characterized
by its height h , its external radius r i , ext , and its internal radius r i , int . It is made of
two radial resistors, R r /2, and two so called “thickness” resistors, R th / 2, all
interconnected as shown on Fig. 7.9 . The corresponding resistances are given by:

R r ¼ r Si
2

ln r i;ext

r i;int ;

(7.13)

ph

r Si h
pðr i;ext r i;int Þ ;

R th ¼ (7.14)

where p Si is the resistivity of the doped silicon layer.

Fig. 7.9 Schematic of the
solid angles defined by a point
charge and sustained by the
edge surfaces of the
cylindrical capacitor C dep