Impact of surface charge density modulation on ion transport in heterogeneous nanochannels

Abstract

The PNP nanotransistor, consisting of emitter, base, and collector regions, exhibits distinct behavior based on surface charge densities and various electrolyte concentrations. In this study, we investigated the impact of surface charge density on ion transport behavior within PNP nanotransistors at different electrolyte concentrations and applied voltages. We employed a finite-element method to obtain steady-state solutions for the Poisson-Nernst-Planck and Navier-Stokes equations. The ions form a depletion region, influencing the ionic current, and we analyze the influence of surface charge density on the depth of this depletion region. Our findings demonstrate that an increase in surface charge density results in a deeper depletion zone, leading to a reduction in ionic current. However, at very low electrolyte concentrations, an optimal surface charge density causes the ion current to reach its lowest value, subsequently increasing with further increments in surface charge density. As such, at $V_{\mathrm{app}}=+1\text{V}$ and $C_0=1\text{mM}$ , the ionic current increases by 25% when the surface charge density rises from 5 to 20 $\text{mC}.{\text{m}}^{-2}$ , whereas at $C_0=10\text{mM}$ , the ionic current decreases by 65% with the same increase in surface charge density. This study provides valuable insights into the behavior of PNP nanotransistors and their potential applications in nanoelectronic devices.

Keywords: Bipolar smart nanochannel; Depletion zone; Electroosmotic flow; PNP nanotransistor; Surface charge density.

Figure 1

(a) Illustration of a PNP nanotransistor with internal surface charge only; (b) Schematic of a cylindrical-shaped nanochannel along with applied boundary conditions for simulation. (Note: The red and yellow dashed lines represent cut lines at r = 0 and r = 5 nm respectively).

Figure 2

The dependence of the total ionic current magnitude along the nanochannel on the number of mesh elements is illustrated for $\mathrm{\sigma }=1\text{mC}.{\text{m}}^{-2}$. Additionally, it is noted that the inset highlights the mesh independence test for $=20\text{mC}.{\text{m}}^{-2}$.

Figure 3

Axial distribution of concentration of for (${\text{a}}_1,{\text{b}}_1,{\text{c}}_1,{\text{d}}_1$) cations, (${\text{a}}_1,{\text{c}}_1$) at cut line $\text{r}=0$, (${{\text{b}}_1,\text{d}}_1$) at cut line $\text{r}=5\text{nm}$; (${\text{a}}_2,{\text{b}}_2,{\text{c}}_2,{\text{d}}_2$) anions, (${\text{a}}_2,{\text{c}}_2$) at cut line $\text{r}=0$, (${{\text{b}}_2,\text{d}}_2$) at cut line $\text{r}=5\text{nm}$; and (${\text{a}}_3,{\text{b}}_3,{\text{c}}_3,{\text{d}}_3$) total ions (${\text{C}}_{\text{T}}\left(\text{mM}\right)$), (${\text{a}}_3,{\text{c}}_3$) at cut line $\text{r}=0$, (${{\text{b}}_3,\text{d}}_3$) at cut line $\text{r}=5\text{nm}$ at different surface charge densities (${\mathrm{\sigma }}_1=1\text{mC}.{\text{m}}^{-2}$ black line, ${\mathrm{\sigma }}_2=5\text{mC}.{\text{m}}^{-2}$ red line and ${\mathrm{\sigma }}_3=20\text{mC}.{\text{m}}^{-2}$ green line) at ${\text{V}}_{\text{app}}=\pm 1\text{V}$. (It should be mentioned that, in all panels, the bulk concentration is 5 mM).

Figure 4

Axial distribution of total concentration of ions (${\text{C}}_{\text{T}}$) for (a) ${\text{V}}_{\text{app}}=+1\text{V}$ and (b) ${\text{V}}_{\text{app}}=-1\text{V}$ at different surface charge densities (${\mathrm{\sigma }}_1=1\text{mC}.{\text{m}}^{-2}$,${\mathrm{\sigma }}_2=5\text{mC}.{\text{m}}^{-2}$ and ${\mathrm{\sigma }}_3=20\text{mC}.{\text{m}}^{-2}$).

Figure 5

The axial velocity distribution for various surface charge densities (${\mathrm{\sigma }}_1=1\text{mC}.{\text{m}}^{-2}$ black line,${\mathrm{\sigma }}_2=5\text{mC}.{\text{m}}^{-2}$ red line and ${\mathrm{\sigma }}_3=20\text{mC}.{\text{m}}^{-2}$ green line) for (${\text{a}}_1,{\text{b}}_1$) at cut line $\text{r}=0$ and (${\text{a}}_2,{\text{b}}_2$) at cut line $\text{r}=5\text{nm}$ at ${\text{V}}_{\text{app}}=\pm 1\text{V}$. (It should be mentioned that, in all panels, the bulk concentration is 5 mM).

Figure 6

The axial electrical potential distribution versus surface charge densities $({\mathrm{\sigma }}_1=1\text{mC}.{\text{m}}^{-2}$ black line,${\mathrm{\sigma }}_2=5\text{mC}.{\text{m}}^{-2}$ red line and ${\mathrm{\sigma }}_3=20\text{mC}.{\text{m}}^{-2}$ green line) on for (${\text{a}}_1,{\text{b}}_1$) at cut line $\text{r}=0$ and (${\text{a}}_2,{\text{b}}_2$) at cut line $\text{r}=5\text{nm}$ at ${\text{V}}_{\text{app}}=\pm 1\text{V}$. (It should be mentioned that, in all panels, the bulk concentration is $5\text{mM}$).

Figure 7

I–V curves for various surface charge densities $({\mathrm{\sigma }}_1=1\text{mC}.{\text{m}}^{-2}$ black line,${\mathrm{\sigma }}_2=5\text{mC}.{\text{m}}^{-2}$ red line and ${\mathrm{\sigma }}_3=20\text{mC}.{\text{m}}^{-2}$ green line) in PNP cylindrical nanochannels for )a) cations, (b) anions and (c) total ions. (It should be mentioned that, in all panels, the bulk concentration is 5 mM).

Figure 8

$\text{I}-\mathrm{\sigma }$ curves for various bulk concentrations $({\text{C}}_0=1\text{mM},10\text{mM and}100\text{mM}$) in PNP cylindrical nanochannels for )a,c) cations and anions, (b,d) total ions, at ${\text{V}}_{\text{app}}=+1\text{V}$ (a,b) and ${\text{V}}_{\text{app}}=-1\text{V}$ (c,d). (It is important to note that in panels (a,b), the solid line, the dashed line, and the dashed-dotted line represent ${\text{C}}_0=1\text{mM},10\text{mM and}100\text{mM}$, respectively).