Simulation of Electronic Sensing of Biomolecules in Translocation Through a Nanopore in a Semiconductor Membrane - Nanopores: Sensing and Fundamental Biological Interactions - page 158

We also include in our model a thin (2 ˚ ) layer of negative charge at the surface
of the semiconductor structure with the density of N surface ¼ 10 21 cm -3 , resulting

from the etching process [ 14 ]. While the density of this surface charge is not known
presicely, the amplitude of the calculated voltage signal due to DNA translocation
varies by 5% if the magnitude of the charge present on the surface of the nanopore is
reduced to N surface ¼ 10 10 cm -3 . The surface charge density value is selected to

accommodate the experimental data [ 14 ]. In our treatment we do not consider the
tunneling current between the electrodes through the DNA.

7.3.2.3 Self-Consistent Scheme

The system under investigation consists of several material regions which are the
Si and SiO 2 layers, and the buffer solution containing the DNA. The charge in
different regions of the device originates from different sources. In the Si layers the
charge comes from the doping ions, electrons and holes. The charge density in
the solid-state regions is given by:

;

Þ¼qN d ð ÞN a ð r solidstate ð r r r Þþpð r Þnð r Þ (7.9)

where N d is the donor density, assumed to be fully ionized, and N a ð r Þ is the

acceptor density which is zero in our model.
In the buffer solution, contributions to the charge include the K + and Cl - ions,
along with the charge distribution on the DNA strand,

r DNA (r). The charge density

of the solution is then

½K þ ð Þ½Cl ð r solution ð r Þ¼q f r r Þ g þ r DNA ð r Þ: (7.10)

Each material is characterized by its relative permittivity, i.e., e Si ¼ 11 : 7 ;

e SiO 2 ¼ 9. For the buffer solution we chose the dielectric constant to be that

of water, i.e.

3 :

e solution ¼ 78. We also assume the same value inside the nanopore

( 78), although due to the size of the pore, the dielectric constant may exhibit

significant local variation [ 29 ]: the relative permittivity inside the pore may vary
from 78 to 1 depending on whether or not the water is completely excluded from the
pore during the DNA translocation. The exclusion of water may have a dramatic
effect on the signal and therefore we are motivated to study translocations in narrow
(~1 nm) diameter pores.
Poisson's equation

e pore ¼

rðeð r Þrfð r ÞÞ ¼ rð r Þ (7.11)

is solved self-consistently by a multigrid method [ 30 ] on the whole volume of
simulated structure with the following boundary conditions: Dirichlet boundary