FET pH Sensor Model
Contents
1. 29 1 APK 2 sech By 10910 x ApH 2 _ Ps 7 Po t Cstern Ofer 0 Since X 15 2kT Odl Wo asinh q 041 0 2kT 6 gt p PIX lt 2 2 Cstern B HSPICE toolkit In order to analyze the HSPICE output data HSPICE toolkit available in Matlab is used This can be downloaded from http www cppsim com InstallFiles hspice toolbox tar gz Make sure to add it in the Matlab path You can use the following Matlab command to add this to the default path addpath ocation of hspice toolbox folder C Simulating HSPICE netlist HSPICE code can be run on file filename sp using following command hspice filename sp D Checklist for model analysis 1 Install the HSPICE toolkit to enable data extraction from HSPICE files 2 Download the complete package in folder FETpH Compile the following HSPICE files in case the user needs to change any parameters a Approximate parameter extraction FETpHWH model 1 0 1 HSPICE netlists go match experiment go sp b Transient Analysis FETpHWH model 1 0 1 HSPICE netlisttransientpHtransient sp c Least square fit parameter extraction FETpHW H model 1 0 1 HSPICE netlistsymvs matchYexperiment mvs sp d DGFET pH sensor FETpHWH model 1 0 1 HSPICE netlistdgfet amplification backgate dgfet sp Compilation of these files will generate the FILENAME sw files which will be analyzed using the perform analysis m2. the FET pH sensor model 13 References 1 2 3 4 5 S Rakheja and D Antoniadis Silicon MIT Virtual Source Model 2014 L Bousse N F De Rooij and P Bergveld Operation of Chemically Sensitive Field Effect Sensors As a Function of the EEE Trans Electron Devices vol 30 no 10 pp 1263 1270 1983 E G van Hal J C T Eijkel and P Bergveld A general model to describe the electrostatic potential at electrolyte oxide interfaces Adv Colloid Interface Sci vol 69 no 1 3 pp 31 62 Dec 1996 J Go P Nair and M a Alam Theory of signal and noise in double gated nanoscale electronic pH sensors J Appl Phys vol 112 no 3 p 34516 Aug 2012 E Van Hal J C T Eijkel and P Bergveld novel description of ISFET sensitivity with the buffer capacity and double layer capacitance as key parameters Sensors And Actuators vol 25 pp 201 205 14 Appendix A Derivation of the surface potential across the electrolyte AOH S AOH Ht 1 _ AO0H H AOH 2 AOH AO H 3 _ A0 4 AOH 299 Og Odlo sinh 8 6 qC AOH A07 7 AOH A07 8 By using 2 4 7 and 8 we get AOH aap the 9 S b yt This gives E _ Kp ouis Ka 10 Hs Cet at 550 tanh B 10910 ApH 11
3. to update the output files 2 optimize pHparameters m Input Parameters coeff init Initial guess of the pH parameters in order pKa pKb NOH xdata with column 1 containing pH values and column 2 containing 10 values at which the experiment is performed Output Parameters coeff deltaVt optimized pH parameters 3 surface potential shift m This file determines the change in surface potential relative to the minimum pH and maximum iO value Input Parameters x array containing the pH parameters in order pH pKb and log10 NOH pH 10 array with column 1 containing pH values and column 2 containing corresponding iO values Output Parameters deltapsiO change in surface potential relative to minimum pH and maximum 10 for the input array provided 4 pH robust model 1 0 1 m This is the Matlab implementation of the Verilog A pH sensor model and solves the model equations described in Robust pH sensor model to determine the output parameters Input Parameters pH pKa pKb NOH i0 Cstern sternmod Output Parameters psiO i e V fg geff 5 determine threshold voltage m This Matlab function determines the threshold voltage of the MOSFET type 1 to determine constant current threshold voltage with Icons being the value of the constant current Use type 2 to determine the linear threshold voltage Input Parameters Vgs Ids type Icons Vrange optional Output Parameter Vt Input file format Input file must be p
4. used in the pH FET sensor model are listed below Parameter highlighted in bold need to be optimized Table also lists the physical meaning of each parameter Math Verilog A Description Default Unit Symbol Symbol pK pKa logio Ka B AoH H NT on 2 0 where K is the acid dissociation constant for the surface group pK pKb logio Ky A0 Bi T 6 0 where K is the base dissociation constant for the surface group Non NOH Density of the surface groups 5x 1014 cm ig i0 lonic concentration of the buffer solution 0 1 Molar UNES Cstern Stern layer capacitance 0 2 F m z sternmod sternmod 0 for using GC model sternmod 1 1 for using GCS model 2 4 Derived Variables Table below lists the derived variables used in the Verilog A implementation of the model Math Verilog A Formula Description Unit Symbol Symbol DHyzc pzc pK pK 2 pH value at which the surface charge becomes zero ApK deltapK pK pKa Difference between the pK values 00 J 8e v qno The double layer charge density F m at zero surface potential ApH deltapH pH pzc pH relative to pzc e deltapH pH pzc NOH SI 10 Density of surface groups in SI m units No nO X i0 lonic concentration m Wo psiO See Section 3 Potential difference between the V surface and the reference electrode C
5. 2 mA 0 15 0 1 0 05 Fig 3 a Match of change in threshold voltage as a function of pH b c Match of transfer characteristics for 0 6 0 5 0 4 0 3 0 2 different pH values with the pH sensor model 10 5 Circuit Simulation 5 1 Sensitivity enhancement in Double Gated FET pH sensor The sensitivity of a single gated FET pH sensor is limited by Nernst Limit 59 mV dec at room temperature This limit can be overcome by using a double gated FET as reported in literature 4 In DGFET pH sensor one sweeps the metal gate poly silicon gate instead of the fluid gate to obtain the transistor characteristics Ips Vic A fixed bias is applied to the fluid gate Vig and the pH sensitivity is measured in terms of the threshold voltage shift of the metal gate AV m ApH To enable higher sensitivity the metal gate capacitance should be larger than the fluid gate capacitance The maximum sensitivity that can be achieved with metal gate operation is given by S AVrMG _ AVrLG here AVTLG ApH ApH gate operation and a constant metal gate voltage This high sensitivity occurs when both the fluid gate channel and metal gate channel are inverted Fig 4 a and b shows the comparison of Ig Vgs characteristics for 2 different fluid gate voltages Fig 4 c and d show the corresponding change in threshold voltage as a function of pH The device sensitiv
6. FET pH Sensor Model Version 1 0 1 Piyush Dak and Muhammad Ashraful Alam Purdue University West Lafayette IN 47907 Last Updated Sep 11 2014 Table of Contents is Introductionis eae cee te btt ihn docete t e piu i ER Ee d tots 3 2 Terminal Voltages and Parameter List esee nete entera 3 2 1 Definition of Terminal Voltages e eseesseeseseeseesee seen tnnt nennen nennt 3 2 2 J ndamental Material COFnsl ritS seen teretes rte Rhen pa Ee 4 2 3 ParamelerLISL aco lr albos ette pte D RE eee 4 24 Darnved ete eto e htl met tani te eee ees 5 S Made GUAIIONS nr utet etiem dccus 5 3 1 Simplified pH sensor model ute te Ier lten EROR Ent ra e tun Oda rade 6 3 2 Robust pH sensor models rider e nod qud etit y REI otis pera S 6 A Parameter Extraction Procedure ig sorge reete eee 7 4 1 Approximate Extraction Method auetoritate petet 7 4 2 Least Square Fit Extraction method eese tne 8 B Girc it Sada Pte io dS onu a tU dl e 11 5 1 Sensitivity enhancement in Double Gated FET pH 11 5 2 Response of ISFET to stepwise change in 12 D S odas dre cm dates usto db E 13 Men T EE 14 Appendisit C ME 15 A Der
7. alculated by using the following set of equations Here pH is the input parameter other parameters characterize the bulk fluid and the interface between the gate oxide and the fluid The parameters are defined in Sec 2 Vgef Vfg Vo Wo loge 10x v pH PH yz where ft D 1 45 with 8 defined as follows for 2 different models 3 1 1 With Guoy Chapmen Model N q Non Ca X v 3 1 2 With Guoy Chapmen Stern Model N x q Cog X V with Cai x Cstern Cstern and _ApK 6 2 10 2 This model works well only in a limited range of such that ri 2 In order to get more accurate result the robust pH sensor model described next must be used 3 2 Robust pH sensor model 3 2 1 With Guoy Chapmen Model 2qNon tanh loge 10 x ApH Qoi 2 2 cx 1 tanh loge 10 x ApH Wo 2v asinh where c exp log 10 x ar 48e vi qno and ApH pH pH 3 2 2 With Guoy Chapmen Stern Model Wo 2 ve asinh 2 Qon Cstern where tanh Zo loge 10 x ApH 2qNog 2 1 tanh Z9 log 10 x 4 Parameter Extraction Procedure A key challenge of any compact model development is to characterize the parameters of the model see Sec 3 by interpreting the experimental data We suggest two different approaches 4 1 Approximate Extraction Method When the available
8. experimental data is limited the response of the pH sensor is available only for few pH values the best way to extract parameters is to simulate the response of the sensor for different sets of input parameters and compare the results with experimental data A reasonably good match between simulation and experiment identifies the desired parameter set By this method parameters roughly close to their accurate value can be obtained Fig 2 shows the match of the experimental data obtained from Go et al 4 with the compact model 6 10 Fig 2 Match of experimental data with the robust Verilog A pH sensor and BSIM SOI model The model gives consistent results with experimental data The parameters used for the fit are listed in Table below Parameter Value Ref ud W L 16 Calibrated vthO 1 475 Calibrated pKa 6 5 pKb 10 5 NOH 8 x 101 cm 5 4 2 Least Square Fit Extraction method This is more robust and accurate way of extracting the parameters The process of parameter extraction is divided into two parts Step1 Extraction of FET specific parameters In order to determine the FET specific parameters the FET device with metal gate is to be fabricated within the same chip as the pH sensing device The device parameters can be obtained using the extraction procedure provided in the user manual for NEEDs Silicon MIT Virtual Source Model by Rakheja et al 1 For the current work it is ass
9. file 3 Goto the folder containing the perform analysis m file and run it Make sure that the utility file determine threshold voltage m is within Matlab path 16
10. ith gate source and drain terminals It can be any MOS transistor which is supported by the circuit simulator such as long channel MOSFET and a double gated FET etc or more generally an externally defined Verilog A MOSFET model such as MIT Virtual Source Model 1 The gate of the transistor is actuated by which is responsive to the pH of the solution In Fig 1 b the transistor is depicted with 4 terminals source V drain gate and bulk back gate Vy We will define the functional relationship between pH of a solution and the voltage source in Sec 3 but first we need to define the parameters and physical quantities of interest Nodes and corresponding node voltages are as follows Node Description Voltage pHnode logio H V pHnode fg Floating gate voltage V fg geff Effective gate voltage V geff 2 2 Fundamental Material Constants Following fundamental or material constants are used for in the code Math Verilog A Definition Description Value Unit Symbol Symbol Type Nave Navg User defined Avogadro s constant 6 x 107 RP EPSw User defined Relative permittivity of buffer 80 2 solution water q Inbuilt Electronic Charge 1 6 x 10719 C Eo P EPSO Inbuilt Permittivity in vaccum 8 85 x 1071 Vt Svt Inbuilt Thermal voltage at current 0 026 V Function temperature 2 3 Parameter List Parameters
11. ity S increases by almost 5x as the fluid gate voltage changes from 0 8V accumulation inversion to 1 0V depletion inversion mode The sensitivity amplification was tested using BSIM SOI FD model in HSPICE is the pH sensitivity limited by Nernst Limit with fluid 11 Fluid Gate Voltage 0 8V Fluid Gate Voltage Vic 1V 5 Vc V Vc V Fluid Gate Voltage Vic 0 8V Fluid Gate Voltage Vic 1V 7 25 c d 7 2 D 7 15 Cj E gt SE 7 05 E 6 95 4 5 6 7 8 pH Fig 4 Sensitivity enhancement in a double gated n FET pH sensor a b Transfer characteristics with respect to metal gate voltage for two different fluid gate voltages c d Constant current 1 nA threshold voltage as a function of pH for the two cases Sensitivity increase by 5X as is increased from 0 8 V to 1V 5 2 Response of ISFET to stepwise change in pH As an example of the robustness of the model we simulated the response of n channel partially depleted PD SOI MOSFET in response to a stepwise change in pH value Fig 5 a shows the netlist the input pH value as a function of time and output current as a function of time When pH is high pH 8 the proton ion concentration in bulk is small therefore the surface is deprotonated giving a more negative charge on the surface with respect to point of zero charge This leads to lesser channel conductance and hence small current see Fig 5 c When pH decrease
12. ivation of the surface potential across the electrolyte 15 B 1 pid tto E E uet p T be EUER QU er Pats 16 C Simulating HSPIGE netlist Ra eere dte n 16 D Checklist for model analysis outer rb qudd Freue 16 1 Introduction The potential of hydrogen pH of a solution is a measure of the concentration of hydronium ions H of a solution and is an important marker for many biological and chemical systems The FET pH sensor model describes operation a field effect transistor FET that can monitor the pH of a solution The model is versatile and can be used for different classes of FET pH sensors In this manual we will discuss the general features of this model and describe how to use the model to characterize the response of the FET based pH sensors and provide a scheme for extracting the parameters from the measurements Finally we will conclude with examples of circuit level simulation using the model To test all the simulations described in the manual the user should run perform analysis m file in Matlab see Appendix B C amp D The circuit simulations have been tested using HSPICE version E 2010 12 SP2 We use different FET models based on the device geometry e g single gate or double gated devices The optimization routine has been tested on Matlab version R2013a 2 Terminal Voltages and Parameter List 2 1 Definiti
13. on of Terminal Voltages pHnode fg Von geff pH dependent f Vpr Po voltage source Transistor Fig 1 a Equivalent circuit representation of electrolyte and surface groups on the oxide functionalized layer The pH acts as a terminal which controls the voltage difference between fg and geff i e Wo Veg b Representation of a pH sensor The pH controlled voltage source and the transistor are treated as separate circuit elements which are connected as shown The FET based pH sensor is modeled as two decoupled circuit elements a pH dependent nonlinear voltage source and a transistor see Fig 1 l pH dependent voltage source The potential across the electrolyte i e the difference between the fluid gate voltage V and effective gate voltage is a function of the pH see Fig 1a Therefore the pH dependence of the sensor can be captured using a pH dependent voltage source yg For circuit simulation pH can be represented as an external voltage source Vp Physically pH is not a voltage source in the same sense battery is but its effect on the transistor l V characteristics can be viewed as a voltage source in the compact model The definition of pH as a voltage source enables transient and small signal analysis with respect to pH in the circuit simulator ll Transistor The second element in Fig 1 b involves a classical MOSFET transistor w
14. rovided in the following format Transfer Characteristics 145 with respect to the fluid gate bias V las A at low Vas las A at high Vas Since the threshold voltage change is independent of the gate bias as the pH changes therefore the third column which contains the Ias V7 characteristics at high Vas can be eliminated Sample experimental synthetic data is provided in folder pH model 1 0 1 experimental data wet measurement b Parameter Optimization Results In order to optimize the pH sensing parameters it is important to have experimental data for a wide range of pH values pH 1 to 13 The optimizer can work with limited range as well albeit with reduced accuracy for the back extracted parameters For the following illustration we use a synthetic experimental dataset for transfer characteristics with respect to fluid gate The difference in threshold voltage give the change in the surface potential relative to a reference pH value This change in surface potential is optimized using optimize pHparameters m as shown in Fig 3 a The optimized parameters are extracted to a file optimized parameters pH txt Once the pH parameters are optimized and FET parameters are known through pre optimization of dry measurement data pH sensor model is complete Fig 3 a shows the match of the pH sensor model with the experimental data a AV V 0 25 0
15. s to a smaller value pH 3 the surface of the oxide becomes positively charged and hence results in a higher drain current For the transient simulation BSIM SOI PD model was used 12 a o 40 b c 35 pH t MO KR ON o 5 30 4 u _5 25 20 4 6 8 0 2 4 6 8 Time s Time s Fig 5 a Circuit diagram b Input pH as a function of time c Output drain current as function of time 6 Summary The manual describes the generalized FET based pH sensor model The implementation of the model in Verilog A as well as the parameter extraction procedures are discussed When the available experimental data are limited then the parameters can be obtained by directly comparing the simulation data for different sets of parameters with the experimental data However to obtain precise value of model parameters it is recommended to obtain characteristics for both dry measurement without fluid gate but same transistor and wet measurement with different pH and iO values and do a least square minimization to obtain the best model fit parameters The model also illustrates the sensitivity amplification in DGFET pH sensor Future work involves inclusion of CV analysis for pH sensing model inclusion of finite ion size effects in the model and inclusion of DNA sensing model Please contact Piyush Dak piyushjdak gqmail com regarding any questions comments about
16. u Cdl J 86 v qno 2v Double layer capacitance at zero F m surface potential delta 2x10 2 p beta See Section 3 Buffer capacity of the surface a alpha 1 8 w ew X y Permittivity of buffer solution F m water 3 Model Equations As stated earlier the electrolyte combined with the interface charges is equivalently modeled as a pH dependent voltage source Two different versions of model are introduced First a simplified pH sensor model 2 which relates the surface potential of the MOSFET as a linear function of the change in pH above its point of zero charge pzc The second model is more accurate and relates the surface potential as an implicit function of pH of the buffer solution see Appendix A for derivation Further each of these models have two different options namely to use the Guoy Chapman GC model or Guoy Chapman Stern GCS model 3 for computation of the surface potential In GC theory the ions are considered as point charges that can approach arbitrary close to the surface This may causes unrealistic high concentrations of ions near interface for high surface potentials The GCS model corrects this by introducing a dielectric layer between interface and diffuse layer to limits the point of nearest approach of ions The equations describing each of these models are as follows 3 1 Simplified pH sensor model The effective gate potential for the transistor is c
17. umed that these device parameters have already been obtained Step2 Extraction of pH specific parameters Three pH specific parameters need to be optimized i e pKa pK and Noy These parameters depend on the type of the oxide or the functionalized metal layer used to do pH sensing For a known oxide functionalized surface these parameters are more or less constant and can be obtained from literature However for accurately representing the device characteristics it is good to optimize these parameters The lower and upper bounds of the parameters and their initial guesses are mentioned in the Table below Parameter Lower Bound Upper Bound Initial Guess pKa 15 15 1 pKb 15 15 4 NOH 2e14 8e14 3e14 a Description of the parameter extraction routine The following files are required to extract the pH specific parameters 1 run optimizer m This file runs the optimizer for extraction of pH dependent parameters It takes a set of Ias characteristics for different pH and ionic concentration values and runs the determine threshold voltage m file to extract threshold voltage for different curves The change in surface potential Aug AV This change along with the pH and iO values are fed into the optimize pHparameters m file to obtain the optimized parameters Once the optimized parameters are obtained these are manually updated into Verilog A file experiment mvs sp Then HSPICE simulation is run
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