SPICE macromodel of silicon-on-insulator-field-effect-transistor-based biological sensors

Sensors and Actuators B 161 (2012) 163–170

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SPICE macromodel of silicon-on-insulator-field-effect-transistor-based biological sensors Poornika G. Fernandes a , Harvey J. Stiegler b , Mingyue Zhao a , Kurtis D. Cantley a , Borna Obradovic c , Richard A. Chapman b , Huang-Chun Wen c , Gazi Mahmud b , Eric M. Vogel a,b,d,∗ a

Department of Electrical Engineering, The University of Texas at Dallas, Richardson, TX 75080, United States Department of Material Science and Engineering, The University of Texas at Dallas, Richardson, TX 75080, United States c Texas Instruments Incorporated, Dallas, TX 75243, United States d School of Materials Science and EngineeringGeorgia Institute of Technology b

a r t i c l e

i n f o

Article history: Received 10 May 2011 Received in revised form 18 September 2011 Accepted 3 October 2011 Available online 10 October 2011 Keywords: SPICE Model Biosensor FET Sensor SOI pH Macromodel

a b s t r a c t A user-friendly behavioral macromodel for biological response of FET-based transistors has been developed for use with commercial SPICE versions and will enable circuit level analysis of biosensor chips. The model is based on the physically realistic representation of biological layers using an ion-permeable charged membrane model. Simulations demonstrate good agreement to experimental results. Logarithmic increments in bound membrane charge result in linear threshold voltage shifts. The model accounts for phenomena such as Debye screening of biomolecules resulting in reduced sensor response to increments in salt concentration. Additionally, the presence of site binding charge on oxide surfaces is shown to severely deteriorate sensitivity. © 2011 Elsevier B.V. All rights reserved.

1. Introduction In the 1970s, Bergveld demonstrated the first ion-sensitive field-effect transistor (ISFET) [1] based on a bulk transistor design. Recently, functionalized silicon nanowires have been introduced into sensor architectures to detect a variety of species including proteins [2,3], DNA [4] and even single viruses [5]. While a vast array of experimental work has been performed, the biosensor modeling arena still requires attention. To obtain full circuit level analysis, SPICE models are imperative. Both built-in SPICE models and a SPICE macromodel have been developed for pH sensors by Massobrio [6]; however, a SPICE model for biosensors is lacking. A macromodel is advantageous over a built-in model because of its user-friendliness and versatility in being adaptable to different SPICE versions, as well as to different underlying FET models. A built-in model, on the other hand, becomes specific to a particular version of SPICE and modification requires an extensive understanding of the model and recompilation of the entire code. There have been several modeling efforts for

∗ Corresponding author. Tel.: +1 4043857235; fax: +1 4043949140. E-mail address: [email protected] (E.M. Vogel). 0925-4005/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2011.10.002

FET-based biosensors to date [7–12], but they require simulators and tedious analytical solutions. The ion-permeable membrane model, originally developed by Ohshima in 1985, extended the Donnan potential theory with the Poisson–Boltzmann equation to model the behavior of biological layers in an electrolytic solution [13]. This model is a physically realistic representation of protein or DNA membrane layers where ions in electrolytic solutions can penetrate into the membrane rather than be treated as a sheet of charge. Based on Ohshima’s work, the Landheer group developed an analytical model for a bulk FET-based biosensor [14–17] to obtain numerical solutions to the potentials at the electrolyte-membrane/insulator surface for fixed gate potential values. The macromodel described in this work is based on the membrane model for the protein/DNA layers in the electrolyte and Berkley’s dual-gated BSIM-IMG (Berkeley Short-Channel Insulated – Gate FET model for Independent-Multi-Gates) model for the sensor FET [18]. The formulation of the macromodel is discussed in detail. Simulation results are presented that demonstrate the impact of protein/DNA attachment on the sensor FET. Comparison of modeling results is made to both DNA and protein sensing experimental data. Impact of Debye screening by salt ions and presence of site-binding charge on sensor response is shown.

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as well as the pH and surface potential, 0 . The typical number of sites on a SiO2 surface is 5 × 1014 cm−2 . Some of these sites get bound to the SAM or membrane biomolecules. However, achieving high SAM densities on the SiO2 surface is challenging and typically only 10–50% surface coverage can be expected. Additionally, biomolecules are large and the maximum density on the surface is limited by the size. For instance, a typical DNA molecule has a diameter of 1.5–2 nm. Thus, the maximum packing density is in the 1013 cm−2 range. Therefore, a considerable number of sites remain unbound on the SiO2 surface to form site binding charge.

 0 = qNSil

2

[H+ ] e−2q 2

[H+ ] e−2q

0 /kT

0 /kT



− K+ K− 2

+ K+ [H+ ] e−q

0 /kT

+ K+ K−

The site binding charge is  0 . The potential at the insulator/membrane–electrolyte interface is 0 . The hydrogen ion concentration in the bulk of the solution is H+ and depends on pH. The dissociation constants of the groups participating in the chemical reactions are K+ and K− and depend on the type of surface, in this case SiOH. The Boltzmann constant is k and T is the temperature in Kelvin. The Helmholtz layer consists of the inner and outer Helmholtz planes. The Inner Helmholtz plane (IHP) is formed by the closest layer of non-hydrated salt ions to the insulator surface. The outer Helmholtz plane (OHP) is formed by the closest layer of hydrated salt ions to the insulator surface. The inner and outer Helmholtz plane permittivities are εIHP and εOHP , respectively; dIHP and dOHP are the insulator–nonhydrated ion and the insulator–hydrated ion distances, respectively. The equivalent Helmholtz capacitance is given by the following expression: Fig. 1. (a) Schematic showing cross section through sensor and layers through electrolyte. (b) Solid lines show charges in the top channel of the FET and oxide–electrolyte interface which contains the semiconductor charge  s , site binding charge  0 , the charge throughout a negatively charged membrane  m , and the Gouy/diffuse layer charge  d at physiological pHs with no applied potentials. Dashed lines show the impact of adding more charge to the membrane which takes place after a binding event.

2. Biosensor macromodel formulation Fig. 1(a) shows a cross sectional diagram of the sensor and membrane/electrolyte. The sensor FET consists of a 30 nm active Si layer with a 145 nm Buried Oxide (BOX) on a SOI wafer where the back gate voltage is applied. Equal voltage is also applied to the electrolyte through a reference electrode. A 3 nm thermal oxide is present between the active Si layer and the electrolyte. The electrolytic portion of the sensor contains the Helmholtz and Gouy layers with the membrane layer modeled between these layers. The membrane is the layer of DNA or proteins attached to the insulator surface. Typically a self-assembled monolayer (SAM) is attached to the insulator and the membrane is attached to the SAM. A SAM layer such as aminopropyltriethoxysilane (APTES), which is most commonly used in biosensors, is only ∼0.5 nm thick compared to the protein/DNA thickness of 5–10 nm and is ignored in this implementation [19]. Fig. 1(b) shows the different charges that would appear on the insulator–electrolyte portion of the sensor. Site-binding charge,  0 , is present on the surface of the oxide. The membrane charge  m , is distributed throughout the membrane. The charge at the interior of the membrane is neutralized by the penetration of mobile ions from the electrolyte. The remaining charge  d comes from the mobile ions in the electrolyte forming the Gouy/diffuse layer. The equation for site binding charge developed by Yates et al. [20] is based on chemical reactions taking place between the pH ions and silanol (SiOH) groups on the silicon dioxide surface. The total charge depends on the number of sites Nsil on the surface

CHelm =

εIHP × εOHP εIHP × dOHP + εOHP × dIHP

The total charge in the membrane and electrolyte is obtained by solving the Poisson–Boltmann (PB) equation. The PB equation in the electrolyte is:



2Zn0 d2 = εm d2 x

 sinh

t

The PB equation inside the membrane is: 2Zn0 d2 = εm d2 x

DP



−1

= sinh

 sinh

t

 vN  m

2Zn0

DP

− sinh

t

 = ln

vNm 2Zn0

,

where

 +

1+

 vN  2



m

2Zn0

The charge density in the membrane is Nm . The valency of the membrane charge is v and the dielectric constant of the membrane is εm . The valency of the salt ions is Z and the salt concentration is n0 . The charge in the membrane Nm enters the equation through the Donnan potential DP through a natural logarithmic dependence. Thus, addition of charge to the membrane does not result in a linear response of the biosensor FET. The above PB equations can be solved for the potentials which can be used to calculate the total charge in the membrane and electrolyte. The model developed in this work uses the following expression for  md based on m which is the potential at the membrane/Helmholtz interface [14,17]: md = −sign(

m

−



DP )

cosh

4qn0 t εm ×

 m

t

− cosh

DP

t

−

m

− t

 DP

1/2 sinh

DP

t

,

t =

kT q

P.G. Fernandes et al. / Sensors and Actuators B 161 (2012) 163–170

This equation is based on the assumption that the membrane is thick enough that charge neutrality is achieved inside the membrane. Therefore, the Donnan potential is reached at the core of the membrane and the electric field at the core is zero. Landheer reports that this is a reasonable assumption because charge neutrality in the membrane is dependent on the screening length inside the membrane. The screening length is shorter than that in the electrolyte because the fixed membrane charge draws in ions, especially when Nm  n0 (salt concentration). Beyond the membrane layer, the Gouy or diffuse layer is formed due to the mobile hydrated ions in the electrolyte. Based on Gauss’s Law, Landheer also reports that the diffuse layer charge will be of equal and opposite magnitude to the membrane charge between the membrane core and membrane/electrolyte interface. In the SPICE model developed in this work, the following relationships are used to obtain two equations relating the site-binding charge  0 , membrane charge  md , and potentials 0 and m . 0

=

m

−

md , CHelm

Fig. 2. Equivalent circuit of dual-gated biosensor. Numbers indicate node values in SPICE macromodel. Top and back gate (TG and BG) are connected together.

the top gate across the thin oxide. Thus, the threshold voltage is low and the sensor is operated at low voltages where back channel inversion can be negligible. Appendix A contains the complete HSPICE macromodel for a DNA sensor with no site-binding charge and 0.001 M salt concentration.

md = −0

4. Simulation results and discussions

By substitution, two relationships are obtained with two unknowns to solve for 0 and m .

4.1. pH response with biosensor model

m

0

=

=

0

+

md ( m ) , CHelm

m

+

0 ( 0 ) CHelm

The above equations are solved in the sub-circuit block of the HSPICE macromodel to determine the change in effective top gate voltage due to biomolecule attachment that will be applied to the FET. Since this is not a built-in model, the semiconductor charge is ignored in the above charge balance equation. At the voltages used in this work the average inversion charge densities are in the 3 × 1012 cm−2 range. This is lower than the singly-charged ionized site-binding charge density of 6.4 × 1013 cm−2 at the physiological pH of 8. Further comparison using a fully charge balanced numerical simulation for the sensor structure used in this work [21] shows that a pH change from 7 to 8 results in a 58% change in site-binding charge but only a 7.5% change in inversion charge. For the biological layers the charge densities are even higher, ranging from 1018 to 1021 cm3 resulting in higher  md compared to  s . Based on similar assumptions, Massobrio implemented a HSPICE behavioral macromodel for a pH sensor. Massobrio showed good agreement in pH sensitivity (mV/pH) between simulation results obtained with the built-in model, BIOSPICE, which accounts for semiconductor charge and the macromodel [6].

165

The biosensor model can be used to simulate pH sensors by setting Nm = 0. The sensitivity obtained in this work is in good agreement with the pH ISFET macromodel reported by Massobrio [6]. In our fabricated device measurements, no bias is applied to the electrolyte, but the voltage is measured using a gold electrode in contact with the solution [21,22]. Very strong capacitive coupling causes a linear relationship between this electrolyte voltage and the applied gate voltage. The least squares linear fit to the measured electrolyte voltage as a function of the gate voltage is individually determined for each pH value. Then as the gate voltage is swept to produce an I-V curve in the SPICE model, the voltage applied to the top gate (TG) terminal (node 1 in Fig. 2) is VTG = 0.332 VBG + 0.94. Using this approach, an excellent fit of the model to measured data is obtained, as shown in Fig. 3. The relevant model parameters used to obtain this result are as follows: PhiG1 (top gate workfunction) is 5.4 eV, PhiG2 (bottom gate workfunction) is 5.1 eV, U0 (low field mobility) is 14 × 10−3 m2 /V s, MUE (mobility reduction factor) is 0.5 cm/MV, THETAMU (mobility reduction exponent) is 1.7 and Nsil is 5 × 1014 cm−2 .

3. HSPICE macromodel definition Fig. 2 shows the HSPICE equivalent circuit. The top electrolyte gate (TG) and bottom gate (BG) voltages are tied together. The change in calculated potential 0 is the change in effective top gate voltage as a result of attachment of charged biomolecules. This value depends on 5 parameters – the number of site-binding sites Nsil ; the pH of the solution; the salt concentration n0 ; the charge density in the membrane Nm ; and the valency v of the membrane charge. This effective gate voltage, at node 2, acts as the top gate voltage of a dual-gated FET modeled using the BSIM-IMG model [18]. The BSIM-IMG FET is representative of a dual-gated SOI-based sensor. The BSIM-IMG model uses the back-gate voltage to tune the threshold voltage of the devices and therefore does not handle inversion charge on the back channel. For our sensor structure, this model suffices because the sensor is primarily controlled from

Fig. 3. pH response obtained using Biosensor SPICE model by setting membrane charge = 0. The model is fitted to pH sensing data obtained for dual-gated sensor with coupling of back-gate voltage to electrically floating solutions on top side of sensor. Very good agreement is demonstrated between the model and experimental results [21,22].

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that seen with logarithmic increases in bound charge densities of protein. The above simulations show that the voltage sensitivity is diminished when there is charge already on the surface compared to beginning with an uncharged surface and adding protein. DNA detection is performed by immobilizing a strand of DNA and capturing or hybridizing a complementary DNA strand [27]. The charge densities used in the above simulations are also representative of negatively charged DNA molecules. Typically, DNA molecules can be modeled as cylinders with diameters of 1.5-2 nm with lengths of ∼10 nm. Each base pair which makes up the DNA molecules is about 0.34 nm long with one net negative charge. In this case, the surface will already be charged. Thus, the maximum signal from hybridization is obtained when all the immobilized strands are saturated, i.e. the surface charge is doubled. The signal obtained for DNA detection would therefore be less than that seen with a biotin–streptavidin system, for instance. Simulation results from this work were also compared to experimental data for DNA sensing. Uslu [27] showed hybridization of 20 bp DNA on SiO2 with APTES. Although the authors state that signal amplitudes for immobilization are typically higher than hybridization, the relative voltage shifts measured for immobilization (attachment of DNA to APTES functionalized surface) and hybridization (binding of complementary DNA to immobilized DNA) were 4 mV and 5 mV, respectively [27]. Surface density of probes was determined to be 2 × 1011 cm−2 by radioactive labeling and phosphor imaging techniques. Our results show shifts of 10.5 mV and 9 mV for immobilization and hybridization respectively, assuming no site binding charge. The presence of site binding charge reduces the sensitivity significantly; assuming 50% APTES coverage, the signal is 0.61 mV and 0.56 mV, respectively. Uslu’s experimental values [27] fall within this range. However, to obtain an accurate fit, the APTES coverage will need to be known. Uslu does not report this value. Fig. 4. (a) Logarithmic increments to membrane charge density results in linear shift of threshold voltage on the sensor (b) Linear increments in membrane concentration result in non-linear response while doubling of surface concentration results in equal magnitudes of voltage shifts.

4.2. Response of biosensor to membrane charge Fig. 4(a) shows the response of the sensor to increases in negative membrane charge density. Site binding charge is assumed to be zero by setting Nsil = 0. The salt concentration has been set to a low value (0.001 M) to prevent screening of the biomolecules. Due to the logarithmic dependence of the membrane charge density Nm on the membrane charge  md , the threshold voltage shift is linear with logarithmic increments of Nm . This simulation is representative of a biotin–streptavidin detection system for instance. Biotin is neutral [23] and the streptavidin has 4 negative charges [24]. Based on the size of streptavidin (5 nm in diameter) [25], the maximum number of attachments on the surface corresponds to a surface areal density of ∼1013 cm−2 . With 4 negative charges distributed over a ∼5 nm height, the surface is saturated when Nm reaches a value of ∼1021 cm3 . Thus, in the linear region of FET operation logarithmic increases in protein concentration cause linear increases in current. Linear response to logarithmic increases in Streptavidin concentration has been observed experimentally [3,26]. Linear increments to membrane charge densities show a nonlinear sensor response as shown in Fig. 4(b). Thus, once binding of charged protein such as Streptavidin has already taken place, any further linear increases in membrane charge density will yield diminishing responses. Fig. 4(b) (filled circles) also shows that to obtain comparable Vt shifts, the membrane charge density needs to be progressively doubled. The shift overall is also smaller than

4.2.1. Impact of site-binding charge on sensitivity Site binding charge plays a role in the sensitivity of the sensor and needs to be considered in sensor design. This is because the charge is very close to the surface and can overwhelm the effect due the charge that is distributed throughout the membrane [14]. Two components affect the amount of site binding charge – the number of binding sites Nsil and the pH of the solution through the H+ term. This is shown in the relationship for site binding charge as discussed in Section 2. Fig. 5(a) shows the impact of varying the number of binding sites on the sensitivity of the sensor. The maximum number of sites Nsil on a SiO2 surface is typically 5 × 1014 cm−2 . For this case, the voltage shift due to attachment of protein/DNA is drastically reduced from that of a charge free surface (Nsil = 0). Simulations also shows the impact of reducing the number of sites to 1% (Nsil = 5 × 1012 cm−2 ) of the available sites on a SiO2 surface. The sensitivity is restored to ∼99% that observed for a charge-free surface. This result emphasizes the importance of attaching dense SAMs on the SiO2 surface, thus reducing Nsil . Alternatively, the biomolecular charge could be increased to get better sensitivity. One experimental technique demonstrated to achieve this is attachment of dNTPs (deoxynucleotide triphosphates) to telomerase, a cancer marker. Attachment of the dNTPs resulted in an increase in the net charge and correspondingly the signal [28]. However, factors such as steric hindrance and its impact on saturation time are trade-offs that need to be considered in designing sensors [20]. The other considerations for site-binding charge are the pH of the solution and the point of zero charge (pzc) of the insulator used in the sensor. Simulation results (not shown) show that the loss of sensitivity due to addition of membrane charge can be restored

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167

near physiological pHs. An Al2 O3 surface would be just such a candidate with its pzc near pH 8. However, simulations results (not shown) still revealed poor biosensor response [15]. This behavior can be attributed to the low intrinsic buffer capacity of Al2 O3 and higher number of sites compared to SiO2 [29]. The intrinsic buffer capacity is the rate of change of site-binding charge to small changes in pH and is dependent on the number of sites as well as the difference between pK values (log of the dissociation constants) for the surface reactions. Around the pzc (pH 2), SiO2 has the least amount of site binding charge, compared to Al2 O3 or Ta2 O5 . From a practical stand-point, even though Al2 O3 has a pzc near physiological pHs, the high site-binding charge reduces sensitivity. The significance of this simulation result lies in highlighting that the amount of the site-binding charge is the concern. Even if the total number of sites cannot be controlled very precisely using SAMs, one way to increase sensitivity is to reduce the amount of site-binding charge. 4.2.2. Impact of salt concentration and screening The SPICE macromodel accounts for the screening effects due to salt ions. The Debye length D in an electrolyte containing two monovalent mobile ions species is dependent on the ion concentration n0 , the dielectric constant ε, the permittivity of space ε0 , Boltzmann’s constant k, the electronic charge q, and the temperature T (in Kelvin) through the following relationship:

 D =

Fig. 5. (a) Shows the reduction in threshold voltage shifts from the case with no binding sites to that with the maximum number of sites. If the number of sites is reduced to a 1% of the maximum value (5 × 1012 cm−2 ), the sensitivity is greatly increased. (b) As salt concentration is increased, membrane charge is screened resulting in a reduction in sensor response to addition of membrane charge. Salt concentration is increased from 0.001 M (1 mM) to 0.01 M (10 mM) to 0.1 M (100 mM). (c) Shows the impact on sensitivity of voltage shift of the sensor as a function of salt concentration and site binding charge.

by reducing the pH to 2 (pzc of SiO2 surface is near pH ∼2). However, the impact of acidic pHs on the stability of proteins/DNA and the resulting change in net charge of the biomolecules would also have to be assessed. For instance, the point of neutral charge or isoelectric point (pI) for Streptavidin lies in the pH 4–5 range. Thus, the protein will be positively charged around pH 2 compared to pH 8. The alternative is to use insulators and layers that have pzc’s

εε0 kT 2q2 n0

Debye screening reduces the effective charge seen by the sensor. The membrane model accounts for this effect. Screening results in a smaller shift in interface potential 0 between the insulator and membrane-electrolyte as the salt concentration is increased. Reduction in sensitivity due to Debye screening has also been demonstrated in experimental biotin–streptavidin FET-based sensing results [3,30]. Fig. 5(b) shows the impact of screening for a surface that is already charged. The sensor response, in this case, is also reduced by screening. The sensitivity is reduced from 41.4 mV to 35.4 mV as the salt concentration is increased from 1 mM to 10 mM. For a ∼10 nm long DNA chain, the Debye screening length is 7.3 nm in 1 mM buffer solutions, while it is 2.3 nm in 10 mM solutions. The reduction is drastic at 100 mM because the Debye length is only 0.7 nm. The result is a threshold voltage shift of only 8.2 mV. If site-binding charge were present, the shift would be reduced even further. Experimental results of biosensing and pH sensing are demonstrated as real-time Vt, Id or gm shifts as solutions are flowed over the sensor surface. Fig. 5(c) demonstrates the impact of salt concentration and site binding charge on sensor response discussed above in terms of voltage shifts. The SPICE model voltage shift results are compared to protein binding experimental data with varying salt concentrations with very good agreement. Hideshima [19] reported experimental results using APTES-functionalized biotinylated FET-based sensor. The sample was exposed to a 40 nM solution of avidin which is positively charged in solution. Experimental Vg shifts were obtained for different salt concentrations. Hideshima also developed a methodology for calculating the charge numbers on the molecules which depend on the ionic strength of the electrolyte and charged groups in the protein (obtained from the Protein Data Bank). The charge numbers obtained were +24.6, +11.3 and +1.4 for avidin in 0.001 M, 0.01 M and 0.1 M salt concentrations, respectively. Using fluorescence techniques, Hideshima determined that the surface coverage of avidin was 5.77 × 1011 cm−2 . The charge numbers divided by the length of the avidin molecules (∼5 nm) and surface

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Table 1 Comparison between experimental data for biotin-avidin binding reported by Hideshima and biosensor SPICE model developed in this work. Protein concentration, Nm (cm−2 )

Salt concentration (M)

Vg (Hideshima) (mV)



1.6 × 1018 1.3 × 1019 2.8 × 1019

0.1 M 0.01 M 0.001 M

0.930233 31.6279 111.86

0.4 24.4 99.7

coverage density give the volume density. Corrections were made to the experimental Vg shift due to differences in salt concentration. Table 1 shows the corrected experimental values of Vg shift. Experimental results trend well with the  0 calculated in our model with <12 mV differences between model and experiment at the highest protein concentration. Percentage error between model and experiment increase at lower protein concentrations, where noise margins and detection limits of experimental results would strongly impact measurements as well. Experimental surface densities determined using samples for physical characterization may not correspond exactly to the FET sensing area and can impact modeled values obtained. Additionally, exact values of experimental salt concentrations need to be known. Further, the model is based on the assumption that the membrane charge is uniformly distributed throughout the protein/DNA layer and tethering the molecule to one end does not impact the calculated membrane charge.

5. Conclusions A physically realistic SPICE model was developed and shows both pH and biosensor response for a dual-gated sensor. The model demonstrates similar trends to experimental data for protein and DNA sensors. Simulated results show that logarithmic increments in bound membrane charge result in linear threshold voltage shifts. The model accounts for phenomena such as Debye screening of biomolecules. Screening effects reduce the response of a sensor. Additionally, the presence of site binding charge on a SiO2 surface severely deteriorates sensitivity. Site binding charge can be reduced by attaching dense layers of SAMs to the SiO2 surface. Alternatively, using buffer solutions with pH near the point of zero charge (pzc) of the insulator surface can also reduce site binding charge. Tradeoffs between impact on sensitivity due to the site binding charge density and adverse effect of using non-physiological pH on protein can motivate the investigation of materials and surfaces with lower charging properties for use in sensors. Additionally, circuit simulations will aid the realization of fully integrated electronic sensor chips for use in biomedical applications as well as help optimize device design.

Acknowledgement This work was partly supported by SRC-GRC TxACE.

Appendix A.

**************************************************************************************** ******** Parameter list General constants: q = electronic charge [C] k = Boltzmann’s constant [J/K] T = Absolute temperature [K] NAv = Avogadro’s constant [1/mole] ISFET geometrical parameters:

b

(This work) (mV)

dihp = distance between the Inner Helmholtz Plane (IHP) and the ISFET surface [m] dohp = distance between the Outer Helmholtz Plane (IHP) and the ISFET surface [m] ISFET electrochemical parameters: Ka = positive dissociation constant [mole/l] Kb = negative dissociation constant [mole/l] Kn = dissociation constant for amine sites [mole/l] Nsil = silanol (or oxide) surface site density [#/m2] Nnit = amine surface site density [#/m2] Cbulk = electrolyte concentration [1/moles] epsihp = relative permittivity of the Inner Helmholtz layer epsohp = relative permittivity of the Outer Helmholtz layer epsw = relative permittivity of the bulk electrolyte solution Reference-electrode electrochemical parameters: Eabs = absolute potential of the standard hydrogen electrode [V] Erel = potential of the ref. electrode (Ag/AgCl) relative to the hydrogen electrode [V] Phim = work function of the metal back contact / electronic charge [V] Philj = liquid-junction potential difference between the ref. solution and the electrolyte [V] Chieo = surface dipole potential [V] Membrane parameters: Nm = volume density of membrane charge (#/m3 ) v = valence of charge on macromolecules(+ve or -ve #) Z = valence of mobile cations and anions *************************************************************************************** ****** *Biosensor SPICE file .hdl “bsimimg.va” .include “modelcard.nmos t” .temp 27 .OPTION LIST ingold = 0 post probe +ingold = 1 post = 2 .PARAM + k = 1.38e-23 T = 300 eps0 = 8.85e-12 + Ka = 15.8 Kb = 63.1e-9 + Nsil = 5e14 + Cbulk = 0.001 + Nm = 1e25 +v=- 1 +Z=1 * Beginning of the sub-circuit definition *= = = = = = = = = = = = = = = = = = = = = = = = = = = = = SUBCKT ISFET 6 1 3 4 101 * drain | ref.el | source | bulk | pH input + q = 1.6e-19 NAv = ‘6.023e23*1e3’ + epsw = 78.5 epsihp = 32 epsohp = 32 epsm = 78.5 + dihp = 0.1n dohp = 0.3n + Eabs = 4.7 Phim = 4.7 Erel = 0.200 Chieo = 3e-3 Philj = 1e-3 + ET = ‘q/(k*T)’ + sq = ‘sqrt(8*eps0*epsw*k*T)’ + Cb = ‘NAv*Cbulk’ + KK = ‘Ka*Kb’ + Ch = ‘((eps0*epsihp*epsohp)/(epsohp*dihp + epsihp*dohp))’ Eref 1 10 VOL = ‘Eabs - Phim - Erel + Chieo + Philj’ EP1 46 0 VOL = ‘log(KK) + 4.6*V(101)’ RP1 46 0 1G EP2 23 0 VOL = ‘log(Ka) + 2.3*V(101)’ RP2 23 0 1G ˆ EDP 25 0 VOL = ‘(1/(Z*ET))*log((v*Nm/(2*Z*Cb)) + sqrt(1 + (v*Nm/(2*Z*Cb))2))’ RDP 25 0 1G EUM 15 0 VOL = ‘V(2,10) + (1/Ch)*(sqrt(4*eps0*epsm*k*T*Cb)*(-sgn(V(15,0)V(25)))*sqrt(((cosh(ET*V(15,0)))-(cosh(ET*V(25)))-(((ET*V(15,0))ET*V(25))*sinh(ET*V(25))))))’ RUM 15 0 1K EPH 2 10 VOL = ‘V(15,0) + (q/Ch)*(Nsil*((exp(-2*V(2,10)*ET) exp(V(46)))/(exp(-2*V(2,10)*ET) + exp(V(23))*exp(1*V(2,10)*ET) + exp(V(46)))))’ RpH 101 0 1K

P.G. Fernandes et al. / Sensors and Actuators B 161 (2012) 163–170 * Transistors with top and bottom gate swept together X1 6 2 3 4 nmos1 t

**************************************************************** .ENDS Biosensor *= = = = = = = = = = = = = = = = = = = = = * Beginning of the example circuit XIS 100 1 0 1 200 ISFET Vbias 1 0 DC 1 VpH 200 0 DC 8 Vd 110 0 DC 0.05 Vid 110 100 DC 0

.OP debug .DC Vbias -0.5 0.5 0.1 .PRINT DC I(Vid) V(1,XIS.2) V(XIS.2) V(XIS.23) V(XiS.46) V(XiS.15) I(XIS.X1.fg) .PROBE DC I(Vid) V(1,XIS.2) V(XIS.2) V(XIS.23) V(XiS.46) V(XiS.15) I(XIS.X1.fg) .OPTION post = 1 runlvl = 0 .END

References [1] P. Bergveld, Thirty years of ISFETOLOGY - what happened in the past 30 years and what may happen in the next 30 years, Sensors and Actuators B-Chemical 88 (2003) 1–20. [2] Y. Cui, Q.Q. Wei, H.K. Park, C.M. Lieber, Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species, Science 293 (2001) 1289–1292. [3] E. Stern, J.F. Klemic, D.A. Routenberg, P.N. Wyrembak, D.B. Turner-Evans, A.D. Hamilton, D.A. LaVan, T.M. Fahmy, M.A. Reed, Label-free immunodetection with CMOS-compatible semiconducting nanowires, Nature 445 (2007) 519–522. [4] Z.Y. Li, X.M. Li, T.I. Kamins, Y. Chen, R.S. Williams, Sequence-specific DNA sensing based on silicon nanowires, Nanosensing: Materials and Devices 5593 (2004) 215–221. [5] F. Patolsky, G.F. Zheng, O. Hayden, M. Lakadamyali, X.W. Zhuang, C.M. Lieber, Electrical detection of single viruses, Proceedings of the National Academy of Sciences of the United States of America 101 (2004) 14017–14022. [6] S. Martinoia, G. Massobrio, A behavioral macromodel of the ISFET in SPICE, Sensors and Actuators B-Chemical 62 (Mar 2000) 182–189. [7] S. Birner, C. Uhl, M. Bayer, P. Vogl, Theoretical model for the detection of charged proteins with a silicon-on-insulator sensor, Physics-Based Mathematical Models for Low-Dimensional Semiconductor Nanostructures: Analysis and Computation 107 (2008). [8] C. Heitzinger, N.J. Mauser, C. Ringhofer, Multiscale modeling of planar and nanowire field-effect biosensors, Siam Journal on Applied Mathematics 70 (2010) 1634–1654. [9] C.W. Mundt, H.T. Nagle, Applications of SPICE for modeling miniaturized biomedical sensor systems, IEEE Transactions on Biomedical Engineering 47 (2000) 149–154. [10] S. Uno, M. Iio, H. Ozawa, K. Nakazato, Full three-dimensional simulation of ion-sensitive field-effect transistor flatband voltage shifts due to DNA immobilization and hybridization, Japanese Journal of Applied Physics 49 (2010). [11] B.K. Wunderlich, P.A. Neff, A.R. Bausch, Mechanism and sensitivity of the intrinsic charge detection of biomolecular interactions by field effect devices, Applied Physics Letters 91 (2007). [12] P.R. Nair, M.A. Alam, Screening-limited response of nanobiosensors, Nano Letters 8 (2008) 1281–1285. [13] H. Ohshima, S. Ohki, Donnan potential and surface-potential of a charged membrane, Biophysical Journal 47 (1985) 673–678. [14] D. Landheer, G. Aers, W.R. McKinnon, M.J. Deen, J.C. Ranuarez, Model for the field effect from layers of biological macromolecules on the gates of metaloxide-semiconductor transistors, Journal of Applied Physics 98 (2005). [15] D. Landheer, W.R. McKinnon, G. Aers, W. Jiang, M.J. Deen, M.W. Shinwari, Calculation of the response of field-effect transistors to charged biological molecules, IEEE Sensors Journal 7 (2007) 1233–1242. [16] D. Landheer, W.R. McKinnon, W.H. Jiang, G. Aers, Effect of screening on the sensitivity of field-effect devices used to detect oligonucleotides, Applied Physics Letters 92 (2008) 253901. [17] W.R. McKinnon, D. Landheer, G. Aers, Sensitivity of field-effect biosensors to charge, pH, and ion concentration in a membrane model, Journal of Applied Physics 104 (2008) 124701. [18] M.V. Dunga, C.H. Lin, D.D. Lu, W. Xiong, C.R. Cleavelin, P. Patruno, J.R. Hwang, F.L. Yang, A.M. Niknejad, C. Hu, BSIM-MG: a versatile multi-gate FET model for mixed-signal design, 2007 Symposium on VLSI Technology, Digest of Technical Papers (2007) 60–61. [19] S. Hideshima, H. Einati, T. Nakamura, S. Kuroiwa, Y. Shacham-Diamand, T. Osaka, Theoretical optimization method of buffer ionic concentration for protein detection using field effect transistors, Journal of the Electrochemical Society 157 (2010) J410–J414.

169

[20] D.E. Yates, S. Levine, T.W. Healy, Site-binding model of electrical double-layer at oxide–water interface, Journal of the Chemical Society-Faraday Transactions I 70 (1974) 1807–1818. [21] R.A. Chapman, P.G. Fernandes, O. Seitz, H.J. Stiegler, H.-C. Wen, Y.J. Chabal, E.M. Vogel, Comparison of methods to bias fully-depleted SOI-based MOSFET nanoribbon pH sensors, IEEE Transactions on Electron Devices 58 (2011) 1752. [22] P.G. Fernandes, O. Seitz, R.A. Chapman, H.J. Stiegler, H.C. Wen, Y.J. Chabal, E.M. Vogel, Effect of mobile ions on ultrathin silicon-on-insulator-based sensors, Applied Physics Letters 97 (Jul 2010) 034103. [23] E. Stern, Label-free sensing with semiconducting nanowires, in Electrical Engineering. vol. PhD New Haven: Yale University, 2007, p. 214. [24] T. Windbacher, V. Sverdlov, S. Selberherr, Biotin–streptavidin sensitive BioFETs and their properties, in: J.F.A. Fred, H. Gamboa (Eds.), Biomedical Engineering Systems and Technologies, vol. 52, Springer-Verlag, Berlin, Heidelberg, 2010, pp. 85–95. [25] E.V. Piletska, S.A. Piletsky, Size matters: influence of the size of nanoparticles on their interactions with ligands immobilized on the solid surface, Langmuir 26 (2010) 3783–3785. [26] N. Elfstrom, A.E. Karlstrom, J. Linnrost, Silicon nanoribbons for electrical detection of biomolecules, Nano Letters 8 (2008) 945–949. [27] F. Uslu, S. Ingebrandt, D. Mayer, S. Bocker-Meffert, M. Odenthal, A. Offenhausser, Labelfree fully electronic nucleic acid detection system based on a field-effect transistor device, Biosensors & Bioelectronics 19 (2004) 1723–1731. [28] G. Zheng, F. Patolsky, Y. Cui, W.U. Wang, C.M. Lieber, Multiplexed electrical detection of cancer markers with nanowire sensor arrays, Nature Biotechnology 23 (2005) 1294–1301. [29] R.E.G. Vanhal, J.C.T. Eijkel, P. Bergveld, A novel description of Isfet sensitivity with the buffer capacity and double-layer capacitance as key parameters, Sensors and Actuators B-Chemical 24 (1995) 201–205. [30] E. Stern, R. Wagner, F.J. Sigworth, R. Breaker, T.M. Fahmy, M.A. Reed, Importance of the debye screening length on nanowire field effect transistor sensors, Nano Letters 7 (2007) 3405–3409.

Biographies Poornika G. Fernandes received her B.S. in computer engineering in 2004 from Wichita State University. She worked at LSI Logic as a Product Test intern and contractor from 2002 to 2006. She obtained an M.S. in 2008 and PhD in 2011 in electrical engineering from the University of Texas at Dallas. She is currently working in the Analog Technology Development Group at Texas Instruments. Harvey J. Stiegler received the B.S.E.E. degree from Texas Tech University, Lubbock, TX, in 1973 and the M.S. and PhD degrees, both from Rice University, Houston, TX, in 1985 and 1989, respectively. After graduation from Texas Tech, he served in the U.S. Air Force until joining Texas Instruments (TI) Incorporated in 1979. At TI he was primarily involved in the development of nonvolatile memory products and dynamic RAM’S as well as analog and mixed signal products as a Design Engineer and Design Manager. He was elected TI Senior Member, Technical Staff, in 1993. In 2009 he joined the University of Texas at Dallas as a Research Scientist in Materials Science and Engineering. He is a member of the American Physical Society and the American Association for the Advancement of Science. Mingyue Zhao received the B.S.E.E. degree from Shandong Jiaotong University, Shandong, China in 2009. Since Spring 2010, he has been pursuing the Master’s degree in electrical engineering at the University of Texas at Dallas. His current research interests include biosensor circuit modeling and ASIC design. Kurtis D. Cantley received the B.S.E.E. degree from Washington State University in 2005 and during that time worked in the National Security Internship Program at Pacific Northwest National Laboratory. He obtained the M.S.E.E. degree in 2007 from Purdue University, where his research involved simulation of III–V materials in nanoscale transistors. Since 2007, he has been working toward the PhD degree in electrical engineering at the University of Texas at Dallas with funding from the National Defense Science and Engineering Graduate Fellowship. His main research area involves nanoscale devices and materials for artificial neural circuits. Borna Obradovic received a B.Sc. in Physics, M.S. Electrical Engineering and a PhD in Electrical Engineering from the University of Texas at Austin, in 1994, 1996, and 1999, respectively. He joined the Intel TCAD department in 1999, where he worked on novel devices simulators, CMOS and SiGe HBT transistor design and optimization, modeling of stress impact on mobility, non-planar multi-gate MOSFET architectures, as well as electron transport in devices such as silicon nanowires and carbon nanotubes and nanoribbons. Borna joined Texas Instruments in 2006, as a TCAD engineer supporting 45 nm CMOS development. In 2007, Borna joined the Analog Technology Development SPICE Modeling Lab. His primary responsibility is the development of “non-standard” SPICE and TCAD models, such as those for various non-volatile memories, dynamic reliability simulations of PowerFETs, ESD simulation, MEMS devices, and magnetic devices. He has over 40 published journal and conference papers, a book chapter, as well as 18 accepted or pending patents. Richard A. Chapman earned his BA’54, MA’55, and PhD’57 all in physics from Rice University in Houston, TX. After two years with General Electric Corporation, he joined Texas Instruments in Dallas, TX in 1959 and retired in 1998 as a TI Senior Fellow specializing in scaling of CMOS transistors. During 1999–2007 he was a

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consultant to Texas Instruments. Since 2008, he has been a Research Scientist with The University of Texas at Dallas. In 1987 he was co-recipient of the IEEE Jack Morton Award for his earlier work on HgCdTe Charge Transfer IR Sensor Arrays. Dr. Chapman is a Fellow of the American Physical Society. He was General Chairman of the 1996 IEEE Symposium on VLSI Technology after having been Program Chairman, Secretary, and Local Arrangements Chairman. Huang-Chun Wen received the BS degree from the Electrical Engineering Department at the National Chiao Tung University (NCTU), Taiwan in 2000. She later completed the MS degree in Electrical Engineering from NCTU in 2002. In 2006, she received her PhD degree in Electrical and Computer Engineering Department from the University of Texas at Austin. In 2004, she joined SEMATECH and engaged in the research of high-k/metal gate electrodes for the 32–45 nm CMOS technology, and continued as a post doctoral fellow working on non-volatile flash memory in 2007. Since May 2007, she has been working in the Analog Technology Development group at Texas Instruments. She is author or co-author of more than 60 refereed publications in journals and conference proceedings, including 3 invited talks. Gazi Mahmud received his BS in Mechanical Engineering in 2005 from Bangladesh University of Engineering and Technology. He obtained his MS in Mechanical Engineering in 2009 from Wichita State University. Currently, he is working on his

doctoral degree in Materials Science and Engineering at the University of Texas at Dallas. His research focus are biosensor fabrication, characterization and functionalization. Eric M. Vogel received a BS in Electrical Engineering from Penn State University in 1994 and a PhD degree in 1998 in electrical engineering from North Carolina State University. He then joined the National Institute of Standards and Technology becoming leader of the CMOS and Novel Devices Group in 2001 and Founding Director of the NIST Nanofab in 2003. Dr. Vogel joined the University of Texas at Dallas (UTD) in August of 2006 where he was an Associate Professor of Materials Science and Engineering and Electrical Engineering and Associate Director of the Texas Analog Center of Excellence and lead UTD’s portion of the Southwest Academy for Nanoelectronics. Currently, Dr. Vogel is a Professor of Material Science and Engineering at Georgia Tech. Dr. Vogel’s research interests relate to devices and materials for future electronics including advanced MOS devices and materials and nanoelectronic devices. He has published over 100 archival publications, written 4 book chapters, given over 50 invited talks and tutorials, and over 70 contributed presentations. He has been involved in several conferences including the general chair of the 2005 IEEE Semiconductor Interface Specialists Conference, high-k (dielectric) program chair of the 2008 (2001) IEEE International Reliability Physics Symposium and co-organizer of the 2000 MRS Workshop on High-k Gate Dielectrics. He is a member of APS and MRS.