# Probing Surface Charge Fluctuations with Solid-State Nanopores

*Entry by Pichet Adstamongkonkul, AP 225, Fall 2011*

*work in progress*

Reference:

**Title**: Probing Surface Charge Fluctuations with Solid-State Nanopores

**Authors**: David P. Hoogerheide, Slaven Garaj, and Jene A. Golovchenko

**Journal**: Physical Review Letters, 2009, Vol. 102, No. 25

## Contents

## Summary

Noise characteristics in nanopores are attributed to the dynamics of both pore and electrolyte, and often times the noise interferes with DNA and protein detections. The analysis in this study suggested that the current noise in solid-state nanopores in the range of 0.1-10 kHz may come from the surface charge fluctuations. The authors also proposed a model of protonization of surface functional groups and tested its validity. The method is quite sensitive; the local surface properties can be examined and single-molecule detection can be optimized.

## Methodology

The nanopores were fabricated to be single, hourglass-shaped channels within silicon nitride film, separating two compartments of KCl electrolyte. The measurement was done via Ag/AgCL electrodes positioned in each compartment.

## Results

The measurements indicated that the noise detected was intrinsic to the nanopore surface. From the Power Spectral Densities (PSDs), in the absence of applied voltage across the membrane, only thermal noise and high-frequency capacitive noise were observed, whereas, in the presence of the applied voltage, the conductance fluctuations, including <math>1/f</math> noise, appeared. In addition, frequency-independent noise between 0.1 kHz and RC filter cutoff at 20 kHz was also detected. It was found that the latter so-called 'white noise' resulted from the conductance fluctuations and was not from the electronics, electrodes, or analysis.

By varying the electrolyte concentration, the noise characteristics changes. The authors mentioned that at high concentrations, the noise varies as <math>c^-3/2</math> and the conductance, determined from the slope of the I-V curve, varies proportionally with c, the electrolyte concentrations. In contrast, at concentrations lower than 100mM KCl, both noise and conductance deviate from the high-concentration behaviors.

## Discussion

The change in behavior of the noise and conductance in the two regimes can be explained by DeBye screening. At high concentrations, the DeBye length <math>\lambda_D</math> ~ <math>1/\sqrt{c}</math> is smaller than the radius of the nanopore and the number of charge carriers that are affected by the fluctuation changes follows the equation:

<math>c \cdot A_{ring}=c \cdot \pi\ \cdot (2 \cdot \lambda_D \cdot R- (\lambda_D)^2)</math> ~ <math>c \cdot \lambda_D</math> ~ <math>\sqrt{c}</math>

The conductance is proportional to the concentration. The current fluctuation, <math>S_I</math>, and the conductance fluctuation, <math>S_G</math>, in an Ohmic system are related by <math>S_I = (S_G/G^2) I^2</math>, where G is the conductance and I is the current. As a result,