Simulation of Electronic Sensing of Biomolecules in Translocation Through a Nanopore in a Semiconductor Membrane - Nanopores: Sensing and Fundamental Biological Interactions - page 159

conditions at the top and the bottom bias gate regions ( f top-gate ¼f bottom-gate ¼ 0).

Neumann boundary conditions were applied for other regions.
The self-consistent three-dimensional Poisson Solver is set up as following:
upon entering the initial guess charge distribution, i.e., DNA charge plus electrolyte
ionic charge, the numerical solution starts from solving the Poisson equation to
obtain the potential distribution. The local potential is then substituted into the
materials constructive equations to obtain a corresponding local charge concentra-
tion (ionic concentration in the buffer solution region, electrons in other regions).
The charge concentration is then inserted back into the Poisson equation and the
new potential distribution is calculated. The procedure is repeated for every input
charge distribution until convergence is obtained. For the potential, the conver-
gence tolerance was 1

mV . Due to the DNA strand translocation through the
nanopore, the DNA charge distribution is position-dependent.
In order to calculate the voltage induced on the Si electrodes due to a charge
translocation we average the potential over the circular perimeter of the pore at the
intersection of the SiO 2 and Si layers. Thus, we record the potential at the nearest
possible distance between the electrode and the DNA. In this way we obtain two
potential values, one for the upper ( cis ) electrode and one for the lower ( trans )
electrode. We subtract the corresponding values of the potential for the empty
nanopore (pore without translocating charge) to obtain the potential difference
induced on the electrodes by the translocating charge.

7.4 Results and Discussion for the 3D Self-Consistent
Modeling of the Capacitor Response

We first characterized the modeled device, as well as study the translocation of the
negative test charge and two linear sequences of charges, the results were published
previously in [ 19 ]. We further follow these tests with simulation of the electrical
response of the layered membrane to a ssDNA translocating through the pore.
We can estimate the number of ions in the volume of the nanopore as N pore ¼
CV pore , where C¼ 1 M is the average electrolyte solution concentration in the

nanopore as a cylinder of height h ¼

2 nm with radius R pore ¼ (2.5/2) nm. Thus,

N pore ¼ 7.53. This value compares very well with the average number of potassium

and chlorine ions in the pore during the course of molecular dynamics simulation,
where there are 5-10 potassium and chlorine ions on average present in the
pore [ 17 ].
The charge on the surface of the pore was calculated as [N surface x 2 ˚ ][ hx
2pR pore ] e -

3.14 e - , which is comparable to the value inferred from the measured
electrolytic conductivity [ 14 ]. This number is consistent with the number of ions in
the pore, so that there is an overall neutrality of the region. For comparison, a DNA
carries an excessive charge of 1 e - per base and several bases may be trapped
between the electrodes at any particular time during a DNA translocation.