Nano Res

1

Ionic effect on the transport characteristics of nanowire-based FETs in liquid environment

Daijiro Nozaki1 (), Jens Kunstmann1,2, Felix Zörgiebel1, Sebastian Pregl1, Larysa Baraban1,

Walter M. Weber3, Thomas Mikolajick3, and Gianaurelio Cuniberti1,4,5 Nano Res., Just Accepted Manuscript • DOI: 10.1007/s12274-013-0404-9

http://www.thenanoresearch.com on December 18 2013

© Tsinghua University Press 2013

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DOI 10.1007/s12274-013-0404-9

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Ionic effect on the transport characteristics of

nanowire-based FETs in liquid environment

Daijiro Nozaki*, Jens Kunstmann, Felix

Zörgiebel, Sebastian Pregl, Larysa Baraban,

Walter M. Weber, Thomas Mikolajick, and

Gianaurelio Cuniberti

Technical University of Dresden, Germany

Department of Chemistry, Columbia University

NaMlab gGmbH

Page Numbers. The font is

ArialMT 16 (automatically

inserted by the publisher)

A simulation platform for quantum charge transport through 1D

nanostructures in liquid environments is established and applied to silicon

nanowire field effect transistors. The platform is supposed to be used for the

design and the optimization of nanowire-based chemical or biosensors. The

reduction of the sensitivity of the sensor due to the formation of an electric

double layer could be successfully reproduced.

2

Ionic effect on the transport characteristics of nanowire-based FETs in liquid environment

Daijiro Nozaki1 (), Jens Kunstmann1,2, Felix Zörgiebel1, Sebastian Pregl1, Larysa Baraban1, Walter M. Weber3, Thomas Mikolajick3, and Gianaurelio Cuniberti1,4,5 1 Institute for Materials Science and Max Bergmann Center of Biomaterials, TU Dresden, 01062 Dresden, Germany 2 Department of Chemistry, Columbia University, 3000 Broadeway, New York, NY 10027, USA 3 NaMlab gGmbH, Nöthinger Str. 64, 01187 Dresden 4 Center for Advancing Electronics Dresden (cfAED), TU Dresden, 01062 Dresden, Germany 5 Dresden Center for Computational Materials Science (DCCMS), TU Dresden, 01062 Dresden, Germany

Received: day month year / Revised: day month year / Accepted: day month year (automatically inserted by the publisher) © Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2011

 

ABSTRACT For the development of ultra-sensitive electrical bio/chemical sensors based on nanowire field-effect-transistors

(FET), the influence of the ions in the solution on the electron transport has to be understood. For this purpose

we establish a simulation platform for nanowire FETs in the liquid environment by implementing the modified

Poisson-Boltzmann model into Landauer transport theory. We investigate the changes of the electric potential

and the transport characteristics due to the ions. The reduction of sensitivity of the sensors due to the screening

effect from the electrolyte could be successfully reproduced. We also fabricated silicon nanowire

Schottky-barrier FETs and our model could capture the observed reduction of the current with increasing ionic

concentration. This shows that our simulation platform can be used to interpret ongoing experiments, to design

nanowire FETs, and it also gives insight into controversial issues such as whether ions in the buffer solution

affect the transport characteristics or not.

KEYWORDS

Nanowire FETs, biosensors, silicon nanowires, Poisson-Boltzman theory, Landauer model

1. Introduction

Low-dimensional materials such as carbon

nanotubes [1, 2] and silicon nanowires (SiNWs) [3-6]

are good candidates for use as biological and

chemical sensors. In particular, nanowire-based

field effect transistors (NW-FETs [7-11]) made from

those materials are promising platforms for sensor

applications because of their high sensitivity due to

their high surface-to-volume ratio, their quick

response to target species, and their portable size.

Several applications of NW-FETs such as pH

sensors [9], gas sensors [10, 12], bio-FETs [9, 13]

have been reported.

Although several quantum mechanical theories

[14, 15] have succeeded in describing the transport

characteristics of the NW-FETs, there have been few

theoretical studies on the influence of the aqueous

environment on the charge transport through

NW-FETs [16-19]. Most of the measurements of

current through the NW-FET for sensor

applications take place in solutions including ions.

Nano Res DOI (automatically inserted by the publisher) Research Article

———————————— Address correspondence: daijiro.nozaki@gmail.com, research@nano.tu-dresden.de

3

Thus, for the development of reliable NW-FET

sensors, the influence of the liquid environment on

the transport characteristics of the NW-FETs needs

to be understood. There are two major effects on

charge transport through NW-FETs in aqueous

environments: (1) the effect of surface charge and (2)

effect of the ions in solution.

First, the surface of the FET devices under

aqueous condition can be charged via protonation

or de-protonation of functional groups at the

surface depending on the pH value of the solution.

This charged surface works as an additional local

gate [9, 20, 21]. This effect is discussed elsewhere.

Second, the ions in solution form an electric

double layer at the solid-liquid interface so that the

sensitivity of NW-sensors to the change of the

external environment by the binding of chemical

compounds is reduced because of the screening

effect [22-25]. The Debye length λD is a widely used

measure for the strength of the electrostatic

screening obtained from the linearized

Poisson-Boltzmann (PB) equation in the limit of low

electric fields (known as Debye-Hückel equation)

[26]:

D 1 kT

2z2e2c, (1)

where ε is the dielectric permittivity, k is the

Boltzmann constant, T is the temperature, “e” is the

elemental charge, c∞ is the bulk concentration of salt

obeying the following relation c∞i = nic∞, c∞i is the

concentration of ion “i” in the bulk, ni is the number

of ions “i” in the electrolyte, and “z” is the valence

number of ion “i”. However, strictly speaking eq. (1)

is only valid if the applied electric field is

sufficiently small [19, 27-30]. Although several

studies applied the nonlinear PB model to charge

transport problems in aqueous solutions to

overcome this restriction [16-19], the PB model

cannot be applied either to systems with high ionic

concentrations [28] or to systems with high applied

electric fields [28]. For a more accurate treatment of

screening effects in the aqueous solutions, more

general approaches such as a modified

Poisson-Boltzmann (MPB) model including the

volume of ions should be used [27-30]. However,

MPB has never been implemented for charge

transport problems through NW-FETs in liquid

condition before. So for the development of robust

NW-FET sensors under aqueous conditions,

creating a model to describe the transport

characteristics of NW-FETs taking into account the

effect of the ions in solution is a demanding

challenge.

For this purpose, in this report, we establish a

simulation platform for the calculation of charge

transport characteristics of NW-FETs in aqueous

solution by implementing a MPB model [27-30] into

Landauer transport theory. We adopted a MPB

equation [27] for the calculation of the electric

potential Ψ(r) and the 3D charge distribution q(r) in

the FET devices. The obtained electric potential Ψ(r)

is then used for the calculation of the transport

characteristics of the NW-FETs with our multi-scale

model. We systematically investigate the influence of

the ionic strength on the electric potential and the

transport characteristics. Using this model, the

reduction of the sensitivity of the sensor due to the

screening effect from the electrolyte on the surface of

silicon nanowires could be reproduced in terms of

the Landauer transport model. Finally we address

the controversial issue of whether ionic

concentration of buffer solution affect the transport

characteristics or not. We have fabricated the

NW-FETs and measured the current under ionic

solutions. We have verified the reduction of current

with the increase of ions using our multi-scale

model.

The workflow for the calculation of electron

transport characteristics is shown in Fig. 1 [31]. The

simulation consists of four steps: (1) modeling of the

device geometry, (2) calculation of the electric

potential Ψ(r) (V), (3) setting up the 1D tunneling

problem, and (4) calculation of the current through

the FET. For steps (1) and (2) we used the TCAD

software COMSOL [32]. After modeling the device

geometry, the three-dimensional (3D) electrostatic

potential Ψ(r) is calculated by solving the MPB

equation with fixed boundary conditions for source,

drain, and gate electrodes for a given ionic

concentration (see Methods section in the electronic

Supplementary Material (ESM) for details). Figure

1(b) shows the cross-sectional potential landscape of

4

a SiNW-FET. Next, the 1D electric potential along the

axis of the SiNW is extracted from the 3D potential in

Fig. 1(b). Then the potential energy barrier U(r) for

the 1D tunneling problem is created from the

extracted 1D potential. The transmission functions

through the left (right) interface TL (TR) are calculated

using the non-equilibrium Green’s function

formalism (see ESM for the details of the

calculations). If the electron transmission through the

channel, TM (E), is given, the effective transmission

function Teff(E) is given from the following relation

[34]:

1Teff (E)

Teff (E) 1TL (E)

TL (E)1TM (E)

TM (E)1TR (E)

TR (E) . (2)

Finally, the current through the NW-FETs is

calculated by integrating the effective transmission

over the energy:

I(V ) Teff (E,V )( fL (E) fR (E))

dE. (3)

In this study we assumed that the current only flows

through the metallic and silicon nanowires, thus

current leakage through the liquid phase or the gate

insulator is not considered.

Figure 1 Schematic workflow for the calculation of the I-V characteristics of SiNW-FETs: (a) modeling of the device

geometry with TCAD software, (b) electric potential calculation, (c) set up of 1D electron/hole tunneling problem, and (d)

calculation of I-V characteristics via the Landauer-Büttiker formalism.

2. Result and Discussion

As a first test, we applied our model to a simple 2D

liquid-solid interface at room temperature and

investigated the electric potential profiles as a

function of ionic concentration. The applied bias, the

dielectric constant for water and the effective ion size

was set to 50 mV, 80 and 3 Å, respectively. The

modeled geometry and the electric potential at the

boundaries are shown in Fig. 2(a). The surface plots

of the electric potential with different ionic

concentrations in Figs. 2(b)-(e) show that the electric

potential drops rapidly in the case of high ionic

concentrations. This is because negative counter-ions

from the electrolyte accumulate at the liquid-solid

interface forming an electric double layer that

5

screens out the applied electric potential after short

distances. Figure 2(f) shows the corresponding

charge density distribution near the interface. The

screening lengths for 0.001 M, 0.01 M, and 0.1 M

electrolytes are 13.50 nm, 4.28 nm, and 1.37 nm,

respectively.

Next, in order to investigate the change of the

electric potential profile across a SiNW for different

ionic concentrations, we applied our 2D model to a

SiNW that resides on a SiO2 insulator separating the

SiNW from a gate electrode. The geometry of the

device is shown in Fig. 3(a). The thickness of the

insulator and the liquid phase are set to 100 nm and

300 nm, respectively. The diameter of the SiNW is set

to 20 nm. In COMSOL Multiphysics, the 2D systems

in Figs. 3(a) and 4(a) are extruded for 1 μm in the

third dimension. For simplicity, the SiNW is not

covered with an oxide shell in these 2D simulations.

Figures 3(b) show the calculated electric potential

perpendicular to the liquid-solid interface along the

red line in Fig. 3(a) for an applied voltage of 5 V. One

can see that the applied potential drops almost

completely within the insulator. Similar to Fig. 2, the

potential drops even more rapidly in the case of

higher ionic concentrations. Figure 3(c) and 3(d)

present the negative charge accumulated at the

liquid-solid interface along the red and blue lines in

Fig. 3(a), respectively. In case of higher ionic

concentration, most of the charge of the electric

double layer accumulates within a short distance

from the surface. This trend is also confirmed in the

2D surface plot of the charge density in Fig. 3(e) and

3(f). Apparently, less charge is accumulated for

higher ionic concentrations in Fig. 3(d). However, the

top of the SiNW is already outside of the double

layer and therefore it is less negatively charged than

for lower concentrations. This phenomenon is also

seen in the simple solid-liquid interface (see around

6 nm from the interface in Fig. 2(f)).

For the estimation of the sensitivity of the

NW-FETs, the influence of charged species that are

attached to the NW surface needs to be investigated.

For this purpose, we considered a model charge on

the NW surface, as shown in Fig. 4(a) and analyzed

the change of the electric potential across the NWs

for different charges and different ionic

concentrations (see Fig.4(b)). The model charge is

separated by 2.5 nm from the surface of the NWs and

the considered amount of charge is 1, 2, or 4

elementary charges q. For the case without ions, the

change of electric potential inside of the SiNW is

large, while it gets smaller with increasing ionic

concentrations because of the already mentioned

screening effect. We also analyzed the change of the

electric potential across the NWs for different

separation of the model charge from the surface of

the nanowire and different ionic concentrations. The

result shows that a bigger separation of the model

charge yields smaller change of the electric potential

inside of the SiNW (see Fig. S3 of the ESM for the

details of the calculations). From this analysis it

follows that thin insulators, low ionic concentrations,

and short separations between the attached species

and the NW are desired to have a high sensitivity to

the external charge.

In order to analyze the change of the electric

potential and the transport characteristics for

different ionic concentrations, we applied our model

to SiNW Schottky-barrier FETs [31] including the

liquid environment in 3D. The geometry of the

device is depicted in Fig. 5 (a): the length of the

semiconducting SiNW channel was set to 1000 nm,

the source and drain contacts are metallic NiSi2-NWs

being 100 nm in length, the surface of the NW is

covered with a 3 nm layer of SiO2 (native oxide) and

the diameter of NWs is 20 nm. Figure 5(c)-(f) show

the space charge density for different ionic

concentrations with/without applied source-drain

voltage VD. In all cases the gate field is VG = 5 V. It is

discernible that the negative charge of the electric

double layer accumulates near the surface of the

NWs and that the amount of charge increases with

the ionic concentration and the source-drain voltage.

It is also notable that in the presence of a non-zero

source-drain voltage the charge accumulates

asymmetrically. Therefore, more charge is at the

drain and less is at the source of the device (Figs. 5(e)

and 5(f)). Thus the sensitivity of the device to

external charges or dipole moments located at the

source is different from that to external charged or

dipole moments located at the drain. Furthermore

the width of the Schottky-barriers is different at the

two contacts.

Figures 5(g) and 5(h) present the 1D electric

potential along the axis of the NW. The potential

drop near the metal-semiconductor interfaces in Fig.

6

5(a) is decreased due to the screening effect of the

electric double layer. It is expected that the electron

current through the NW-FETs is reduced for high

ionic concentrations. Using these 1D electric

potentials, we calculated the drain source-current

through the NW-FETs for different ionic

concentrations. The details of the procedures for the

calculation of the drain current are discussed in Ref.

31 and in the ESM.

Figure 6 presents the dependence of the drain

current through the NW-FET on the ionic

concentration. For the air phase with negative gate

voltages, the hole currents are dominating and the

electron currents can be neglected since the electron

tunneling is blocked by the negatively-gated

conduction band. In the presence of an ionic

solutions, hole currents dominate the transport

behavior as well (see Fig. 6(b)), but the hole current is

slightly reduced with increasing ionic concentration

since the formation of the electric double layer at the

solid-liquid interface of the NW-FETs increases the

width of Schottky barrier for holes (see blue lines in

Fig. 6(b)), while the electron current is enhanced

since the formation of the electric double layer

lowers the height of energy barriers for electronic

thermal emission beyond the conduction band. Note

that the Schottky barrier for electrons ΦSBe is higher

than the one for holes ΦSBh so that the contribution of

the electron current to the drain current is in fact

negligible. This analysis reveals that the current in

Fig. 6 shows a weak dependence on the ionic

concentration, which is in good agreement with

other experimental reports [34-37].

As a final demonstration of our study, we have

fabricated silicon nanowire-based Schottky-barrier

FETs (SiNW-SBFETs), measured the drain current

with different ionic concentrations, and compared

the current with numerical results. We have

extended device configuration from single

SiNW-FETs [38] to a parallel array of SiNW-FETs [39]

that allows to decrease device-to-device variations

and to increase a total current output. The surface of

the device is covered with the layer of Al2O3 to

protect the FET from electrochemical reactions. The

procedure to create the parallel array of the

SiNW-SBFETs and the experimental setup and

measurement are shown in Ref. 39 and in the ESM.

Figure 7(a) presents the ionic concentration

dependence of the measured current through the

device with different ionic concentrations at a fixed

source-drain bias (VSD = 0.25 V) and a negative

gate-field (VG = -1.0 V). We can see that the

SiNW-FETs in liquid show a weak dependence of the

drain current to ionic concentrations and that the

drain current (hole current) is slightly reduced with

the increase of the ionic strength. In order to

demonstrate that this reduction of the hole current is

due to the formation of electric double layers at the

surface of the device as discussed with the band

diagram in Fig. 6(b), we have modeled the

SiNW-SBFETs and calculated the hole current

through the device with different ionic

concentrations. The device geometry and the setting

of parameters are shown in the ESM. Figure 7(b)

shows the numerical result of the ionic dependence

of the current through the SiNW-SBFETs. We can

clearly see that the hole current is reduced with the

increase of the ionic concentrations due to the shift of

the valence band involved with the formation of the

electric double layer at the surface of the device. The

electric potential shown in the inset of Fig. 7(b) also

supports the band diagram suggested in Fig. 6(b).

This is how we could elucidate the weak dependence

of the hole current through the SiNW-SBFETs to the

ionic concentration and the origin of current

reduction using our multi-scale simulation platform.

7

Figure 2 Electric double layer at a 2D liquid-solid interface: (a) The geometry of the interface. Electric potential landscapes for ionic concentrations of (b) 0.001 M, (c) 0.01 M, and (d) 0.1 M. (e) The same potentials plotted along the axis perpendicular to the surface. (f) Accumulated charges as a function of distance from the surface. More charge is accumulated in the case of higher ionic concentrations resulting in a stronger screening effect.

Figure 3 Electric double layer at a 2D liquid-solid interface of a SiNW on a SiO2 insulator: (a) device geometry, (b) profiles of the electric potential along the red line in panel (a), and (c)-(d) the space charge density as a function of distance from the gate electrode along (c) the red line and (d) the blue line in panel (a) at different ionic concentrations. The gate voltage is 5 V in (b)-(f). 2D surface plots of the space charge density for two ionic concentrations are shown in (e) and (f). The applied potential almost completely drops in the insulator and it drops even more rapidly in the case of high ionic concentrations. Although the accumulated charge looks small for 10 mM in panel (d), this is due to the fact that charge accumulates only in close proximity of the SiO2 water interface.

8

Figure 4 Sensitivity of a SiNW sensor device to a model charge as a function of charge and ionic concentration in a 2D model. Electric potential profiles of SiNWs on insulators with a single model charge calculated in a 2D model: (a) the device geometry is the same as Fig. 3(a), except for a model charge that is placed at a distance of 2.5 nm above the surface of the SiNW. (b) Electric potential along the red line in (a) for different charges and ionic concentrations. The gate voltage is VG = 5 V and q is the elementary charge. The influence of the model charge on the electric potential is reduced for higher electronic concentrations. The results indicate that thin insulators, low ionic concentrations, and short separations between the attached species and the NW are desired to have a high sensitivity of the sensor device.

Figure 5 The electric double layer in a 3D SiNW-FET device. Charge densities and potential profiles: (a) the device geometry, (b) FEM mesh used for the calculations, (c)-(f) cross-sectional plots of the space charge density of NW-FET for different source-drain voltages and ionic concentrations, (g)-(h) 1D electric potential along NW axis for different ionic concentrations with/without source-drain voltages VD. In all calculations, the gate field is VG = 5 V. The surface of the SiNW is covered with a native SiO2 layer of 3nm SiO2 (not visible in (a)). Note that the color scales in (c)-(f) are not the same. In the presence of a

9

non-zero source-drain voltage, the charge of the double layer accumulates asymmetrically. A cross-sectional view of the device geometry including the oxide shell covering the SiNW is shown in Electronic Supplementary Material (See Fig. S4).

Figure 6 The ionic concentration dependence of the drain current through the NW-FET device shown in Fig. 5(a) with positive gate fields. (b) The corresponding energy band diagram for the NW-FET explains why hole currents are enhanced and electron currents are reduced with increasing ionic concentration. The Schottky-barrier height for electrons is larger than that for holes (ΦSB

h = 0.44 eV, ΦSBe= 0.68 eV), In all calculations, the gate voltage and the voltages at source and drain are

fixed to VS = 0 V, and VD = 0.5 V, respectively.

Figure 7 Ionic concentration dependence of the drain current through the parallel array of the SiNW-SBFETs under negative gate field in (a) experiment and (b) theory. Panel (a) is 2D histogram of measured drain current with different ionic concentration. In the both results, the hole currents are slightly reduced with increasing ionic concentration. The Schottky-barrier for holes is set to (ΦSB

h = 0.15 eV). In all calculations, the voltages at source and drain are fixed to VS = 0 V, and VD = 0.25 V, respectively. The gate voltage in both calculations and experiment is VG = -1.0 V. In numerical calculations, we assumed that there are 1000 NW-FETs between electrodes. Corresponding electric potentials along the silicon channel are shown in inset.

3. Conclusion

In summary, in order to investigate the influence of

ions in liquid environments on the transport

characteristics of NW-FETs for sensor applications,

we have implemented a modified

10

Poisson-Boltzmann model into the

previously-developed multi-scale model. The model

correctly describes the formation of the electric

double layer at the solid-liquid interface. It can

explain and quantify the experimentally well-known

reduction of the sensitivity of the device to surface

charges in the case of high ionic concentrations, and

the weak dependence of the drain current on the

ionic concentration of the buffer solutions. As a

demonstration, we have fabricated NW-FETs,

measured the current in the ionic solutions, and

compared the measured current with our model

showing a good agreement.

We have established a simulation platform for

NW-based FET devices in liquid environments. It can

be used for the interpretation and elucidation of

experimental observations, as guidelines for the

planning of future experiments, as well as for the

optimal design of nanowire-based sensors.

Acknowledgements We thank Kannan Balasubramanian for inspiring

discussions. This work is funded by the European

Union (ERDF) and the Free State of Saxony via the

ESF project 080942409 InnovaSens, and by the World

Class University program funded by the Ministry of

Education, Science and Technology through the

National Research Foundation of Korea (R31-10100).

We also gratefully acknowledge support from the

German Excellence Initiative via the Cluster of

Excellence EXC 1056 “Center for Advancing

Electronics Dresden" (cfAED).

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