Performance Analysis of a Si-NW Biosensor forDetection of Charged Biomolecules

Mohiuddin Munna∗, Md. Obidul Islam†, Md. Kabiruzzaman† and Zahid Hasan Mahmood†∗Department of Electrical and Electronic Engineering,Shahjalal University of Science and Technology†Department of Applied Physics, Electronics and Communication Engineering, University of Dhaka

Corresponding Author Email: iobidul@yahoo.com

Abstract—Biosensors based on Si-NW have already demon-strated for the detection of DNA, proteins, pH levels, etc.Although it is generally accepted that Si-NWs with lower dopingdensity and smaller diameter provides better sensitivity, theinfluence of factors like surrounding environment (air/water)and electrostatic screening due to the ions in the solutionon NW sensor, performance needs to be explained for thesystematic optimization of sensor design. In this theoretical studya simple analytical model, based on reaction-diffusion theoryis developed to predict the trade-off between average responsetime and minimum detectable concentration. Investigating theaverage response time this study shows that, Si-NW sensor givesfaster response than that of nanoscale ISFET sensor. Also thePoissonBoltzmann equation is solved numerically and analyticallybased on the result of the diffusion-capture model to show thatthe electrostatic screening within an ionic environment limits theresponse of a Si-NW biosensor. This study concludes that, theparameters such as the dimension of the Si-NW, the doping levelof the Si-NW, the ions concentration in the solvent, pH of thesolution etc that limit the performance of a Si-NW sensor must beoptimized for high sensitivity biomolecule detection. Numericalsimulation is carried out using biosensorLAB tool , a simulatorfrom Nanohub.org,which is an online based java platform engine.

I. INTRODUCTIONIn recent years, electronic detection of biomolecules in the

solvent is one of the widely studied topics in nanotechnology.Nanostructure based biosystems are gaining importance to theresearchers as these nanometerscale systems can provide fast,low-cost, and high throughput analysis of biological processes.[1] Since the early 1970s, the sensor based on ion-sensitivefield-effect transistor (ISFET) was regarded as a low-costalternative to traditional chemical sensors with potential foron-chip integration [2]. However, several disadvantages, suchas lack of good solid state electrodes, parasitic sensitivity totemperature and light, time dependent instability of sensorparameters, have restrained the development of ISFET asa popular biosensor technology [3]. For fast detection ofbiomolecules at relatively low concentrations the chemicalsensors have adopted fluorescent labeling and parallel opticaldetection techniques, but these fluorescence-based sensorsrequire expensive and time-consuming preprocessing and post-processing for sample preparation and data analysis. In thiscontext, the nanoelectronic sensor systems based on Si-NWcan provide a superior biosensor technology for direct label-free electronic sensing of biomolecules as the diameter of Si-NW is comparable to those of the biological and chemicalspecies being sensed [1]. Because of the enhanced surface

to volume ratio of Si-NWs, their transport behavior may bemodified by changing their surface conditions and since 2Dcylindrical Si-NWs are more sensitive to adsorbed charges(e.g., DNA, protein, etc.) compared to 1D planar ISFET orchemical field-effect transistor, the detecting sensitivity isincreased as compared with traditional thin film biosensortechnology [4]. The major advantage of Si-NW biosensorsis the label free operation, as opposed to the expensive andtime-consuming preprocessing and postprocessing for samplepreparation and data analysis in chemical detection. Otheradvantages include the high sensitivity and the real time andcontinuous operation [1].

Si-NW biosensors have already demonstrated for ultrasen-sitive detection of DNA [3], [5], proteins [6], [7], pH levels[8] etc. But surprisingly it is observed that, the influence offactors like surrounding environment (air/water) and electricpotential damping due to the mobile ions in the solutionon NW sensor performance is generally overlooked in mostsensor design [1]. In this theoretical study, we propose acomprehensive modeling theory and simulation approach toaccount for the ultrasensitive detection of biomolecules withSi-NW biosensor and to unveil that the influence of parameterslike the dimension of the Si-NW (diameter and length), thedoping level of the Si-NW, and surrounding environment (theions concentration in the solvent, pH of the solution etc.) mustbe investigated for the performance optimization of the Si-NWbiosensor.

II. DIFFUSION-CAPTURE MODELA. Model Equations

Time dynamics of molecule capture on a sensor surface isessentially a two step process: transport of the target moleculesto the sensor surface and the subsequent conjugation withthe receptor molecules. The response of a nanoscale sensordepends on the analyte concentration as well as dimensionalityof the sensor. Consider an isolated sensor immersed in a staticanalyte solution at time t=0 as shown in Fig. 1. The surfaceof the sensor is functionalized with specific receptors for thetarget molecules. The diffusion of analyte particles towardsa planar device (ISFET) is 1D, and towards a cylindricalnanowire surface is 2D. The Diffusion-Capture (D-C) modelassumes that the molecule transport is diffusion limited and thetarget-receptor conjugation is treated as a first-order chemicalreaction [9] .

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(a) (b)

Fig. 1. Schematic of a sensor immersed in analyte solution.(a)ISFET sensor(b)Nanowire sensor Equilibrium analyte concentration is assumed at a distanceW from the sensor surface[4].

The rate of conjugation between the target and the receptorsis given by

dN

dt= κF (N0 −N)ρs − κRN (1)

where N is the density of conjugated receptors, N 0 isthe density of receptors on the sensor surface, κF and κR arethe capture and dissociation constants (forward and reversereaction coefficients), and ρs is the concentration of analyteparticles at the sensor surface at any given time t [4]. Thefirst term of equation 1 represents the conjugation betweenthe target and the receptors while the second term denotes thedetachment (due to thermal fluctuation, etc.). ρs is determinedby the diffusion of target molecules set by the concentrationgradient at the sensor surface which is given by

dρ

dt= D∇2ρ (2)

where D is the diffusion coefficient of target molecules in thesolution that depends on the fluidic environment and size of thetarget biomolecule. Equations 1and 2 are numerically solvedto get the transient response of biosensors [4].

CD,SS =2πD

log[ (W+a0)a0 ]

(3)

B. Evaluating Transient Response

It can be easily realized that as the forward reaction pro-gresses, the analyte near the sensor surface is depleted as moremolecules diffuse to the sensor surface and are captured by thesurface receptors. Then a new diffusion equivalent capacitance,CD (t) can be defined which is a function of the depletiondistance, (t)=2nDt , where n is dimensionality of the sensor.

For planar ISFET sensor n=1 and CD(t) = D√2Dt

.And for cylindrical Si-NW sensor n=2 and CD(t) =

2πDlog((

√4Dt+a0)/a0))

Then the transient response for a planar ISFET sensor isgiven by,

N(t) = ρ0t

(√2Dt

D+

1

κFN0

)−1(4)

Fig. 2. Schematic of Si-NW biosensor. (a) NW surface is functionalized withreceptors for target biomolecules. (b) Cross-section of the sensor along thedotted line shown in (a). (c) Charge distribution in the sensor system alongthe dotted line shown in (b)[10].

And response for a cylindrical Si-NW sensor is:

N(t) = ρ0t

(a0 log(

√4Dt+a0a0

D+

1

κFN0

)−1(5)

III. POISSON-BOLTZMAN EQUATIONA. Model based on PB Equation

Consider a Si-NW sensor is immersed in an electrolytesolution whose surface is functionalized with specific recep-tor,Fig. 2a. Fig. 2b shows a Cross-section of the sensor alongthe dotted line shown in Fig. 2a. The system can be dividedinto three subregions, as shown in Fig. 2c (1) cylindrical Si-NW of diameter d; (2) insulating native oxide around the NWof thickness tOX ; and (3) electrolyte that contains the targetbiomolecules, and the various ions that provide the necessarybuffer for the stability of targetreceptor binding.

The full charge of the captured bio-molecules is not ef-fective in modulating the conductance of sensors due to theelectrostatic screening of ions present in the electrolyte i.eregion three. To account for screening, one must solve thenon-linear Poisson-Boltzmann equation

−∇2ϕ(r) +κ2

βsinh(βϕ(r)) =

q

εw

N∑i

Ziδ(r − ri) (6)

Where φ is the electrostatic potential, κ1 is the Debye-Huckel screening length and r is the spatial coordinate. κ2 =2q2I0NavoεwKBT

where I0 is the ion concentration in molar unitsand εw is the dielectric constant of electrolyte. The sinh termdenotes the contribution due to a 11electrolyte (e.g., Na+-Cl-), whose ions are assumed to follow Boltzmann distribution(β = q/(kBT )) where q is the electronic charge, kB is theBoltzmann constant and T is the temperature). The right-handside denotes the fixed charge due to the biomolecule, zi andri denoting the partial charge and location of the atoms withinthe biomolecule, respectively(e.g., the phosphate ions in thebackbone of a DNA strand).The detail description of the modelis given in [2], [3].

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B. Estimatting the Sensitivity

The sensitivity S of a Si-NW sensor is defined as the relativechange in conductance

S =|G−G0|G0

=∇GG0

(7)

Sensitivity S in terms of φ0) and other device parametersis given as

S =2εoxϕ0

qa20ND log(1 + tOX

a0)

(8)

Without considering screening of the target molecule φ0)can be expressed as

ϕ0 =σsN(t)(a0 + tOX) log(1 + tOX

a0)

εOX(9)

Finally the sensitivity is found by combining equations 8and 9

S =2σsN(t)(a0 + tOX)

qa20ND(10)

C. Steady State Response with Various Analyte and ElectrolyteConcentration

The full charge of the captured biomolecules is not effectivein modulating the conductance of sensors due to the electro-static screening of ions present in the electrolyte. To accountfor screening, one must solve the nonlinear PoissonBoltzmannequation 6.

From the approximate solution of PoissonBoltzmann equa-tion the sensitivity can be expressed as a function of analyte(target molecule ) concentration ρ0 and electrolyte concentra-tion(ion concentration)I0 , as [10]

S = C1[ln(ρ0)−ln(I0)

2+ C2] (11)

Where

C1 =4εox

βqa20NDlog(1 + tox/a0)(12)

andC2 = ln[σSκFN0

κR

√β

2εW qNavo] (13)

D. Steady State Response for Analyte Solution

The net charge density (charge density due to analytemolecules) on the NW surface can be obtained based on first-order chemical kinetics of bond dissociation for the particulartype of surface functionalization schemes used (-OH, -NH2,etc.)[23].By taking this in consideration the sensitivity S aspH of the electrotyte solution can be expressed as[p-4]

S = C1[C3 +I02− 2.303(pH − pKa)] (14)

Where C3 = 12 ln(

2εwNavoqβN2

F

)

IV. RESULT AND DISCUSSION

The design of a nanoscale biosensor greatly depends on thedimension of the nanostructures, their doping density and alsothe parameters (analyte concentration, ion concentration, pH ofthe solution, etc.) related to the sensor application environmentthat seriously affect the sensor performance. The response of asensor is characterized in terms of its settling time, sensitivityand selectivity. In this study first settling time is calculatedfor both planar ISFET and cylindrical Si-NW sensors andcompared. Then the transient capture of target molecules onthe sensor surface is analyzed without taking into account forthe screening by electrolyte solution, and responses for ISFETsensor and Si-NW sensor are compared. Finally sensitivityof the Si-NW sensor is studied to show how electrostaticscreening affects the sensor performance.

In this study a simulation tool named BioSensorLab [12]is used for the numerical simulation of Diffusion-Captureequations 1 and 2and nonlinear Poisson-Boltzmann equation6. BioSensorLab is a numerical simulator to predict theperformance metrics for various types of label-free, electronicbiosensors. For solving D-C equations the tool assumes thatthe molecule transport is diffusion limited and the target-receptor conjugation as a first order chemical reaction. Toaccount for the electrostatic screening BioSensorLab solvesnonlinear Poisson-Boltzmann equation 1 numerically whichuses NewtonRaphson iteration for convergence.

A. Anatysis of Transient Response and Settling time

Fig. 3. Response time for Si-NW (red) and ISFET (green) sensor as functionof analyte concentration (analytical simulation).

Fig. 3 presents the numerical results (response time versusanalyte concentration) for both Si-NW and ISFET sensors.The results are obtained by numerically solving the equations 1and2 using the simulation tool BioSensorLab.Fig. 3 allows oneto predict the trade-off between settling time and the minimumdetectable concentration for planar (1D) and cylindrical (2D)nanosensors for a typical DNA detection problem. For areasonable incubation time (300 sec), a 2D cylindrical Si-NW sensor can detect down to about 300 fM concentrationswhereas a 1D planar sensor based on ISFET can detect onlyto nanomolar levels.Thus there exist fundamental limits inthe concentration of biomolecules which can be detected by

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any sensor under reasonable settling time. And the detectionlimit of a typical 2D nanowire sensor (for the same responsetime) is three to four orders of magnitude higher compared toplanar 1D sensor. Then with proper design and technologydevelopment, Si-NW -based cylindrical sensors should beable to achieve ultrafast detection ( 300 sec) at femtomolarconcentration.

Fig. 4. Transient response for cylindrical Si-NW sensor (density of capturedtarget molecules vs time)

Fig. 4 shows the transient response of cylindrical Si-NWbiosensor. It shows sensor response at two different analyteconcentrations ,100 fM and 1 nM indicated by blue and redline respectively. As can be seen sensor response improvesas time goes and become saturated after a certain time. Thissaturation is due to the balance of forward and backwardreaction. It is seen that the number of captured analytemolecules increases with analyte concentration as expected.

(a) Numerical Simulation (b) Analytical Simulation

Fig. 5. Comparison of sensor response between ISFET and Si-NW sensor at100 fM analyte concentration

Fig. 5b allows us to make a comparison for biomoleculeconjugation between planar 1D and cylindrical 2D nanowiresensors. It is seen that the conjugation of target biomoleculesfor Si-NW sensor reach equilibrium fast than that of ISFETsensor.Which is in consistent with the theoretical predictionof Nair et al [4]. Hence the 2D Si-NW sensor gives fasterresponse. Also it can be seen that at first sensor responsevaries linearly with time both for ISFET and Si-NW sensorbut after a short time response for ISFET sensor does notobey the linearity. At the beginning the sensors capture theanalyte particles available very close to the surface , so theresponse for both ISFET and Si-NW sensor varies linearly

Fig. 6. Sensitivity of NW sensor as function of radius.

with time. Once the region near the surface is depleted ofDNA strands, the diffusion-limited transport of DNA throughwater molecules dictates sensor response which is proportionalto t1/2 for a 1D planar sensor and t1 for cylindrical sensor asseen from equations 4 and 5.

B. Analysis Sensitivity

The most attractive feature of nanoscale biosensor is thatits performance improves as the diameter of the nanowire aswell as doping density decreases. Fig. 6 shows the sensitivityof Si-NW sensor increases as radius of the NW decreases forvarying doping density. Similar conclusion is also suggestedby Nair et.al[1]Sensitivity for three different doping levels(Nd = 1017cm−3, 1018cm−3 and 1019cm−3) is investigated.Nanowire length is kept constant (2m) and air is assumed asthe surrounding medium of the nanowire.Fig. 6 clearly showsthat sensitivity increases with smaller diameter and reduceddoping density, which is consistent with equation10.

(a) Numerical Simulation (b) Analytical Simulation

Fig. 7. Sensitivity versus analyte concentration for constant ion concentration(10-3 M)

Fig. 7a shows that sensitivity improves as target moleculedensity increases. The ratio of the reaction coefficients, kF /kRis taken as 3x108. Water is considered as the surroundingmedium. For all cases the receptor density on the sensorsurface is taken 1012(cm−2). The ion concentration is taken10−3M . The graph shown in Fig. 7a clearly shows that dueto the electrostatic screening of ions in the solvent minimumdetectable concentration cannot be achieved in the femto molarrange , rather in nanomolar range. This result is obtainedfrom BioSensorLab that numerically solves the equations 6

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and 8simultaneously. The analytical result presented in Fig.7b shows the logarithmic dependency of sensitivity on analyteconcentration which validate our numerical result.From theresult shown in Fig. 7a one can easily predict the range ofanalyte concentration over which log dependency is observed.The ratio of maximum to minimum analyte concentration overwhich log dependency is observed is about 103.

Fig. 8 shows the logarithmic dependency of sensitivity onanalyte concentration for two different kF /kR ratios: 3x108

(red line) and 3x106 (green line). It is seen that kF /kR ratiomust be high enough to detect low analyte concentration. Bycomparing the two curves one may easily predict that themaximum analyte concentration for which log dependency isobserved is approximately equal to the inverse of thekF /kRratio.

Fig. 8. Sensitivity versus analyte concentration for two different kF /kRratios (numerical simulation).

Fig. 9 shows nanowire surface potential changes linearlywith pH of the solution. This study is based on the first orderchemical kinetics of bond dissociation for the functionalizationgroups of OH and NH2. For OH and NH2 groups, pKa valuesare taken 3.9 and 7.2 respectively. Ion concentration is keptconstant (10−5M). The density of surface functionalizationgroups is considered 1014(cm−2). As can be seen surfacepotential decreases as pH of the solution increases. This isobvious because high pH of the solution means the high con-centration of OH ion in the solution and high ion concentrationlower the surface potential by decreasing the charge effectivein conductance modulation. The slope of the line gives the rateof change of surface potential with pH ( 45mV/pH).Whereas maximum rate of change of surface potential with pH is60mV/pH mentioned in literatures [10], [11].

V. CONCLUSION

This study investigates the minimum detectable concen-tration for nanoscale biosensors and shows that nanoscalebiosensors can detect up to a certain limit. By comparing theresponses of Si-NW and ISFET biosensors this study showsSi-NW sensor gives faster response than nanoscale ISFETsensor. This study also shows that due to the electrostaticscreening of ions in the solvent desired sensitivity cannot beachieved. Also for better sensitivity detection of biomolecules,

Fig. 9. Nanowire surface potential versus pH of electrolyte solution (analyticalsimulation).

one must concern about the pH of the solution.Finally thisstudy concludes that, to design highly sensitive biosensor usingSi-NW one must systematically optimize sensor response asa function of sensor geometry (diameter and length of theNW), the doping level of the Si-NW, fluidic conditions (ionsconcentration in the solvent and pH of the aqueous solution).

ACKNOWLEDGMENT

The authors would like to thank Pradeep RamachandranNair for the simulator softwares. They would also like to thankNetwork for Computational Nanotechnology (NCN) for thejava engine used to run the simulator.

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[1] P. R. Nair and M. A. Alam,Design Considerations of Silicon NanowireBiosensors,IEEE Transactions on Electron Devices, Vol. 54, NO.12,2007

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[3] P. Bergveld, Thirty years of IsfetologyWhat happened in the past 30years and what may happen in the next 30 years, Sens. Actuators B,Chem., vol. 88, no. 1, pp. 120, Jan. 2003.

[4] P. R. Nair and M. A. Alam,”Performance limits of nanobiosensors”Applied Physics Letters 88, 233120 ,2006

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[9] H. C. Berg., Random Walks in Biology Princeton University Press,Princeton, NJ, 1993.

[10] P. R. Nair and M. A. Alam,Screening-Limited Response of NanoBiosen-sors, Nanoletters, vol.20, No.10,2008

[11] M. N. Masood, S. Chen, E. T. Carlen, and A. van den Berg, All-(111)Surface Silicon Nanowires: Selective Functionalization for BiosensingApplications American Chemical Society, Vol. 16, NO. 12, 34223428,Nov. 2010.

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