Simulation of Electronic Sensing of Biomolecules in Translocation Through a Nanopore in a Semiconductor Membrane - Nanopores: Sensing and Fundamental Biological Interactions - page 168

X X

F 0 ðx i Þv; IðtÞ¼ I i ðx i Þ¼ q i (7.16)

i i

where

x i ¼ x i 0 þ vt (7.17)

and x i 0 is the original position of the charge i for time t ¼ 0.

Here,

dF
dx ;

F 0 ðxÞ¼ (7.18)

where the geometrical factors F are connected to the inner capacitors of the
nanopore by the solid angles

O 2 sustained by the edges of the cylinder, as
shown in Fig. 7.9 . F is associated to the difference between these solid angles:

O 1 and

FðxÞ¼ O i ð x ÞO 2 ð x Þ
4

;

(7.19)

p

and consequently accounts for the magnitude of the electrostatic induction of the
charge on the capacitor plate and varies with its position in the capacitor.
Figure 7.10 illustrates the equivalent circuit of the detection process (the
complete membrane model). One can see each couple current source - inner
capacitor corresponding to each mini-layer connected with the 25-cell resistors
network. In order to produce a clear scheme, we represent the five capacitors related

Fig. 7.10 Equivalent electric
circuit of the overall
nanopore-capacitor: current
sources G i accounting for the
physical modeling of the
DNA strand translocation are
connected to the depletion
capacitors C dep,i . SiO 2 layers
and Sj electrodes are modeled
by a resistor-capacitor
network