# Graphene-Based FET Detector forE. coli K12 Real-Time Monitoring and Its Theoretical Analysis

Authors: Jieyi Zhu; Fuzhou Niu; Changan Zhu; Jie Yang; Ning Xi
Journal: Journal of Sensors
 (2016)

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## Abstract

This paper presents a theoretical analysis for a graphene-based FET real-time detector of the target bacteriaE. coli K12. The motivation for this study is to design a sensor device for detection of bacteria in food and water in order to guarantee food safety. Graphene is chosen as our material for sensor design, which has outstanding electrical, physical, and optical performance. In our sensor structure, graphene-based solution gate field effect transistor (FET) is the device model; fabrication and functionalization protocol are presented together in this paper. What is more, a real-time signal display system is the accompanied equipment for our designed biosensor device. In this system, the sensor bias current signal Ids would change obviously when the target bacteria are attached to the sensor surface. And the bias current Ids increases when theE. coli concentration increases. In the latter part, a theoretical interpretation of the sensor signal is to explain the bias current Ids increasing after theE. coli K12 attachment.


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## Body

## 1. Introduction

Over the last few decades, several kinds of nanostructure biosensors have been designed for industrial and household use. The aim of our study is to realize the detection of bacteria in food and water in order to ensure food security and public health safety. So for this purpose we need to design a micro-nanobiosensor to detect bacteria. The design of nanobiosensors includes the materials and structures. For materials, many semiconductor materials are chosen due to good electrical property and excellent applications in electronic devices. For instance, silicone is often used for biosensor design; an example is the high density microelectrode array biosensor in Radke and Alocilja’s paper [1]. For structure, nanostructures include planar, nanowire, nanosphere sensors, even carbon nanotube, and graphene. Graphene is a single layer of carbon atoms which is packed into a hexagonal planar structure. Nowadays, graphene is often chosen as sensing material due to its excellent electrical, physical, and biocompatible properties. Compared to silicon, graphene is a zero-gap semiconductor; it is not easy for electron to scatter in graphene; the carrier mobility of graphene could be as high as 2 × 105 cm2/(V·s) [2], about 140 times larger than that of silicon [3]. Graphene was discovered in 2004, Novoselov et al. describe graphene as having excellent electrical, optical, and mechanical properties [4]. Thus, graphene becomes a suitable material in electronic applications. During the last two years, many novel graphene-based devices came into being for various kinds of detectors. Specifically, graphene-based sensors could be used in detecting bacteria. Now, our project is to design a biosensor to detectEscherichia coli, which is an ordinary bacterium in the issue of food safety. Under this circumstance we develop a graphene-based field effect transistor sensor for detection ofE. coli bacteria. The spread ofE. coli bacteria would cause harm to both environment and human body. The pathogenic strain ofE. coli, likeE. coli O157:H7, can cause bloody diarrhea, hemorrhagic colitis, and hemolytic uremic syndrome. Compared to the pathogenic strainE. coli O157:H7, our target is the nonpathogenic strainE. coli K12, which is currently an indicator for laboratory testing. So far, Huang’s group has presented a graphene-based FET sensor with functionalization for detection ofE. coli K12 [5]; their group detectsE. coli’s concentration andE. coli’s metabolic activities. Moreover, the graphene FET device could also be used to detect glucose concentration [6]. Besides, Chang’s group uses graphene oxide to realize the biosensor for the targetE. coli O157:H7. Thermal reduced monolayer graphene oxide was demonstrated to fabricate a graphene oxide-based FET biosensor [7]. However, there is still a limitation that graphene has been shown to have lower sensitivity due to lack of bandgap [8], as the performance of a FET biosensor depends on the subthreshold swing of the device [9]. Compared to Huang’s sensor model, our FET model uses Si/SiO2 substrate rather than his quartz substrate. Furthermore, this model could also be applicable to some other 2D materials like TiO2 and MoS2, apart from graphene [10]. This model could be extended to two-dimensional transition metal dichalcogenides (TMDC), because when TMDC is changed into a two-dimensional structure from a block structure, its electrical property will be greatly modified due to its bandgap change [11]. Here, in this paper we will report a graphene-based FET detector together with its fabrication protocol (Figure 2) and functionalization protocol, and its model is a solution gate FET sensor. Then we use the protocol to finish a sensor chip with a recording chamber and test the target bacteriaE. coli K12’s presence and concentration by this chip. In our experiments, we fix our sensor chip on the surface of the probe station, connect the electrical circuit by applying bias voltage and gate voltage through the manipulator of the probe station, and measure the FET bias current by the signal process instrument Keithley 2636B with its real-time recording software. From the measurement, we could get signal response whenE. coli K12’s solution is added onto the sensor’s recording chamber. Moreover,E. coli K12’s solution concentration is changing during the real-time measurement; the relationship between bacteria concentration and bias current Ids would be presented and discussed.


## 2. Biosensor Structure

In our design, the biosensor structure is a graphene-based field effect transistor (FET) sensor. Then this graphene FET is functionalized to be a specificE. coli K12 sensor. We choose P doped Si/SiO2 substrate to be the sensor bottom; one side of the substrate is Si and the other side is SiO2. The thickness of SiO2 layer is 100 nm. Two electrodes are deposited on the SiO2 side of the substrate as source and drain electrodes by metal deposition. Graphene nanoribbon (1.1 mm × 0.6 mm) is placed across these two electrodes according to a graphene transfer protocol. Besides, silicone rubber is used to coat around the graphene to form a recording chamber. The bias voltage Vds is applied between source and drain electrodes, letting the two manipulator needles touch the source and drain electrodes. Usually, there are two kinds of FET, back-gate FET and solution gate FET. For our real-time measurement we choose solution gate FET. The gate voltage Vg is applied by inserting the third manipulator needle immersed into the solution inside the recording chamber. The source-drain bias and source-gate bias share a common ground, avoiding significant fluctuations in the gate voltage actually applied on graphene. In actual experiments we use wires to connect the source electrode to the probe station for ground connection. The schematic diagram of our biosensor design is shown in Figure 1.Figure 1
The design of solution gate graphene-based field effect transistor. Bias voltageVds is applied between source and drain electrodes; gate voltage Vg is applied to the solution inside the recording chamber.Figure 2
The illustration of fabrication protocol for our microchip. Electrode pattern and graphene pattern are finished in two photolithography processes.


## 3. Fabrication and Functionalization

### 3.1. Fabrication of Microchip

In order to realize the designed microchip, we need to finish device fabrication. The first process is the fabrication of substrate with electrodes. Clean the Si/SiO2 substrate in acetone, alcohol, IPA, and DI water for 10 min in plasma cleaner and spin-coat photoresist on the SiO2 side surface of the substrate. Then prebake the die on hot plate at 110°C for 10 min. After that a photolithography process is done with a designed photomask for the electrodes pattern. Two electrodes (source and drain) are deposited on the Si/SiO2 substrate by two layers of metal deposition, 15 nm Cr and 100 nm Au, by the instrument Q150 TS. After that, photoresist on the substrate is washed away by acetone. The second process is graphene direct transfer process. A layer of PMMA is coated on the copper of graphene/Cu sheet; wait around half an hour for drying off. Put the PMMA/graphene/Cu sheet into FeCl3 aqueous solution at room temperature for Cu layer etching and wait for about 10 hours; the PMMA/graphene layer would detach from PMMA/graphene/Cu sheet. The PMMA/graphene layer is picked up by using a pair of tweezers with a spare substrate. Wash and rinse with DI water three times to remove Fe and Cu ions; three petri dishes with DI water are prepared for this step. At last, put the PMMA/graphene layer on the Si/SiO2 substrate, and use tissue to sip up moisture on the surface of this die. Bake this die with PMMA/graphene layer at 80°C for 5 min first, and then bake it at 150°C for 15 min. After the baking, drip one drop of PMMA onto the surface of each die. Lastly, acetone is used to wash away the PMMA layer. The third process is another photolithography for graphene pattern and graphene transfer to the electrodes. Take one die already with graphene after the second process and design a photomask for graphene pattern. After that, put this die under microscope, choose one appropriate graphene nanoribbon, and mark this one on the platform of probe station. Drip PMMA onto the chosen area, observing it under microscope to make the chosen nanoribbon be covered by PMMA. After 10 minutes, pick out the die by tweezers, and put this die immersed into a Petri dish of DI water. With needle and other tools’ help, the graphene layer is picked up and put onto the substrate with electrodes. Then the graphene layer is adjusted to fit with the substrate, letting the chosen graphene nanoribbon across the two electrodes form an electrical circuit. The adjustment is done by manipulation of probe station.


### 3.2. Functionalization of the Biomolecules

After device fabrication, the graphene-based FET sensor needs to be functionalized. Firstly, a solution of 6 mM 1-pyrenebutanoic acid succinimidyl ester (1-PBSE) in dimethylformamide (DMF) is prepared. Then the device is incubated with this 6 mM 1-PBSE (Sigma-Aldrich, 457078) dimethylformamide (DMF, Sigma-Aldrich, D4551) solution for 2 h at room temperature. Then the sensor chip is thoroughly rinsed in DMF to wash away the excess reagent. Secondly, the antibody incubation of the chip, a 50 ppm anti-E. coli O +E. coli K antibody (Abcam 33604) in DI water solution, is prepared. During this step the sensor device is incubated overnight (about 16–18 hours) in this 50 ppm anti-E. coli O&K FITC antibody (Abcam 33604) solution at 4°C. Thirdly, the microchip is incubated with 0.1 M ethanolamine (pH 9.0) for 1 h. Fourthly, the device is incubated with 0.1% Tween 20. The whole process of functionalization is shown in Figure 3. After all, the silicone rubber (Dow Corning) is coated around the graphene nanoribbon to form a recording chamber.Figure 3
The schematic diagram of functionalization process for our biosensor surface. Our chosen linker is 1-pyrenebutanoic acid succinimidyl ester; the antibody is anti-E. coli O&K antibody (Abcam 33604).


## 3.1. Fabrication of Microchip

In order to realize the designed microchip, we need to finish device fabrication. The first process is the fabrication of substrate with electrodes. Clean the Si/SiO2 substrate in acetone, alcohol, IPA, and DI water for 10 min in plasma cleaner and spin-coat photoresist on the SiO2 side surface of the substrate. Then prebake the die on hot plate at 110°C for 10 min. After that a photolithography process is done with a designed photomask for the electrodes pattern. Two electrodes (source and drain) are deposited on the Si/SiO2 substrate by two layers of metal deposition, 15 nm Cr and 100 nm Au, by the instrument Q150 TS. After that, photoresist on the substrate is washed away by acetone. The second process is graphene direct transfer process. A layer of PMMA is coated on the copper of graphene/Cu sheet; wait around half an hour for drying off. Put the PMMA/graphene/Cu sheet into FeCl3 aqueous solution at room temperature for Cu layer etching and wait for about 10 hours; the PMMA/graphene layer would detach from PMMA/graphene/Cu sheet. The PMMA/graphene layer is picked up by using a pair of tweezers with a spare substrate. Wash and rinse with DI water three times to remove Fe and Cu ions; three petri dishes with DI water are prepared for this step. At last, put the PMMA/graphene layer on the Si/SiO2 substrate, and use tissue to sip up moisture on the surface of this die. Bake this die with PMMA/graphene layer at 80°C for 5 min first, and then bake it at 150°C for 15 min. After the baking, drip one drop of PMMA onto the surface of each die. Lastly, acetone is used to wash away the PMMA layer. The third process is another photolithography for graphene pattern and graphene transfer to the electrodes. Take one die already with graphene after the second process and design a photomask for graphene pattern. After that, put this die under microscope, choose one appropriate graphene nanoribbon, and mark this one on the platform of probe station. Drip PMMA onto the chosen area, observing it under microscope to make the chosen nanoribbon be covered by PMMA. After 10 minutes, pick out the die by tweezers, and put this die immersed into a Petri dish of DI water. With needle and other tools’ help, the graphene layer is picked up and put onto the substrate with electrodes. Then the graphene layer is adjusted to fit with the substrate, letting the chosen graphene nanoribbon across the two electrodes form an electrical circuit. The adjustment is done by manipulation of probe station.


## 3.2. Functionalization of the Biomolecules

After device fabrication, the graphene-based FET sensor needs to be functionalized. Firstly, a solution of 6 mM 1-pyrenebutanoic acid succinimidyl ester (1-PBSE) in dimethylformamide (DMF) is prepared. Then the device is incubated with this 6 mM 1-PBSE (Sigma-Aldrich, 457078) dimethylformamide (DMF, Sigma-Aldrich, D4551) solution for 2 h at room temperature. Then the sensor chip is thoroughly rinsed in DMF to wash away the excess reagent. Secondly, the antibody incubation of the chip, a 50 ppm anti-E. coli O +E. coli K antibody (Abcam 33604) in DI water solution, is prepared. During this step the sensor device is incubated overnight (about 16–18 hours) in this 50 ppm anti-E. coli O&K FITC antibody (Abcam 33604) solution at 4°C. Thirdly, the microchip is incubated with 0.1 M ethanolamine (pH 9.0) for 1 h. Fourthly, the device is incubated with 0.1% Tween 20. The whole process of functionalization is shown in Figure 3. After all, the silicone rubber (Dow Corning) is coated around the graphene nanoribbon to form a recording chamber.Figure 3
The schematic diagram of functionalization process for our biosensor surface. Our chosen linker is 1-pyrenebutanoic acid succinimidyl ester; the antibody is anti-E. coli O&K antibody (Abcam 33604).


## 4. Experiment and Real-Time Data

### 4.1. Experiment and Real-Time Data

In our experiment, when we finish both fabrication and functionalization, we place the chip on the surface of our probe station. The chip is fixed on the probe station platform by magnetic force. The two manipulator needles contact source and drain electrodes, providing bias voltage from Sourcemeter Keithley 2636B. The third manipulator needle contacts the solution inside the recording chamber, providing gate voltage. The schematic diagram of the sensor structure is shown in Figure1. During our measurement, we add PBS andE. coli solution into the recording chamber of the sensor. Usually, there are two kinds of FET, back-gate FET and solution gate FET. In our experiment we choose solution gate FET for the real-time measurement, and the schematic diagram of solution gate FET is shown in Figure 4.Figure 4
The schematic diagram of graphene-based solution gate FET experimental setup on our probe station. The circle plate stands for the probe station plate; the three blue needles stand for the manipulator needles.The data acquisition system includes the Sourcemeter Keithley 2636B and its real-time signal recording program. After the experimental setup is finished, we turn on the Sourcemeter Keithley 2636B and initialize the real-time signal recording program. Besides, we need to culture the bacteriaE. coli K12 before the real-time measurements.E. coli K12 ER2925 is purchased from Eastwin International Trading Limited, Hong Kong. We culture the bacteria in Luria Bertani (LB) medium overnight at 37°C. The bacteria solution after overnight culture is the next passage. The originalE. coli K12 bacteria solution is passaged to the third generation before the experimental week. Before the measurement, the bacteria are passaged to the fourth generation or the fifth generation. In our real-time measurement, we use the fifth generation of the bacteria. In order to calculate the concentration of the experimentalE. coli solution, we use colony counting method. The fifth-generation bacteria solution is determined to be 2 × 108 CFU/mL. The stock is diluted in PBS solution (pH 7.2) 10 times to produce the desired final concentration ofE. coli K12 for experiments, 2 × 107 CFU/mL. The dilution is conducted in a minicentrifuge tube with 1 mL of PBS and 100 μL of the fifth-generation bacteria solution. At last, we start our real-time bias current recording; firstly 5 μL of PBS is added into the recording chamber, and then add 30 μLE. coli experimental solution 6 times (5 μL each time). In the last three times of addition, we find bias current signal change. Theoretically, the sensor should have signal once we add bacteria solution; however the mixture of solution needs some time, so it is acceptable that there is time delay during the first four times of solution addition. And the change of gate electrode immersion length would lead to some errors in our measurement. During our experiment, we keep gate voltage Vg=0V and bias voltage Vds=0.1V. The real-time figure is shown in Figure 5.Figure 5
The real-time bias currentIds signal curve during our measurement.Summarily, there are six times ofE. coli K12 solution addition along the real-time measurement. Each time the addition amount is 5 μL. During the first three addition times, there are not apparent signal changes and the bias current Ids is around 7 μA. After the fourth addition, the bias current Ids increases from 7 μA to 7.5 μA before the next addition. The fifth addition time is corresponding to 0 s in the real-time figure. After the fifth addition, the bias current Ids increases from 7.5 μA to 9 μA before the sixth addition. The sixth addition time is corresponding to 30 s in the real-time figure. After the sixth addition, the bias current Ids increases from 9 μA to 9.7 μA.


### 4.2. Characterization

After our experiment, we conduct the characterization of our experimental sensor chip by atomic force microscopy (AFM) scanning. The AFM image shows the graphene nanoribbon across the two electrodes. And we scanned the experimental sensor chip afterE. coli attachment in tapping mode. The AFM we recorded is shown in Figure 6.Figure 6
AFM image of the sensor chip after experimental process.


## 4.1. Experiment and Real-Time Data

In our experiment, when we finish both fabrication and functionalization, we place the chip on the surface of our probe station. The chip is fixed on the probe station platform by magnetic force. The two manipulator needles contact source and drain electrodes, providing bias voltage from Sourcemeter Keithley 2636B. The third manipulator needle contacts the solution inside the recording chamber, providing gate voltage. The schematic diagram of the sensor structure is shown in Figure1. During our measurement, we add PBS andE. coli solution into the recording chamber of the sensor. Usually, there are two kinds of FET, back-gate FET and solution gate FET. In our experiment we choose solution gate FET for the real-time measurement, and the schematic diagram of solution gate FET is shown in Figure 4.Figure 4
The schematic diagram of graphene-based solution gate FET experimental setup on our probe station. The circle plate stands for the probe station plate; the three blue needles stand for the manipulator needles.The data acquisition system includes the Sourcemeter Keithley 2636B and its real-time signal recording program. After the experimental setup is finished, we turn on the Sourcemeter Keithley 2636B and initialize the real-time signal recording program. Besides, we need to culture the bacteriaE. coli K12 before the real-time measurements.E. coli K12 ER2925 is purchased from Eastwin International Trading Limited, Hong Kong. We culture the bacteria in Luria Bertani (LB) medium overnight at 37°C. The bacteria solution after overnight culture is the next passage. The originalE. coli K12 bacteria solution is passaged to the third generation before the experimental week. Before the measurement, the bacteria are passaged to the fourth generation or the fifth generation. In our real-time measurement, we use the fifth generation of the bacteria. In order to calculate the concentration of the experimentalE. coli solution, we use colony counting method. The fifth-generation bacteria solution is determined to be 2 × 108 CFU/mL. The stock is diluted in PBS solution (pH 7.2) 10 times to produce the desired final concentration ofE. coli K12 for experiments, 2 × 107 CFU/mL. The dilution is conducted in a minicentrifuge tube with 1 mL of PBS and 100 μL of the fifth-generation bacteria solution. At last, we start our real-time bias current recording; firstly 5 μL of PBS is added into the recording chamber, and then add 30 μLE. coli experimental solution 6 times (5 μL each time). In the last three times of addition, we find bias current signal change. Theoretically, the sensor should have signal once we add bacteria solution; however the mixture of solution needs some time, so it is acceptable that there is time delay during the first four times of solution addition. And the change of gate electrode immersion length would lead to some errors in our measurement. During our experiment, we keep gate voltage Vg=0V and bias voltage Vds=0.1V. The real-time figure is shown in Figure 5.Figure 5
The real-time bias currentIds signal curve during our measurement.Summarily, there are six times ofE. coli K12 solution addition along the real-time measurement. Each time the addition amount is 5 μL. During the first three addition times, there are not apparent signal changes and the bias current Ids is around 7 μA. After the fourth addition, the bias current Ids increases from 7 μA to 7.5 μA before the next addition. The fifth addition time is corresponding to 0 s in the real-time figure. After the fifth addition, the bias current Ids increases from 7.5 μA to 9 μA before the sixth addition. The sixth addition time is corresponding to 30 s in the real-time figure. After the sixth addition, the bias current Ids increases from 9 μA to 9.7 μA.


## 4.2. Characterization

After our experiment, we conduct the characterization of our experimental sensor chip by atomic force microscopy (AFM) scanning. The AFM image shows the graphene nanoribbon across the two electrodes. And we scanned the experimental sensor chip afterE. coli attachment in tapping mode. The AFM we recorded is shown in Figure 6.Figure 6
AFM image of the sensor chip after experimental process.


## 5. Theoretical Analysis

After we acquired the bias currentIds, we started to analyze and explain the experimental results by our theoretical derivation and simulation. Consider that our sensor model is a planar FET sensor, and the sensor surface is functionalized with specific receptors, which is the linker-antibody for the targetE. coli K12 bacteria molecules. So the conjugation calculation is based on the Langmuir adsorption equation. And firstly the adsorption model is regarded as an ideal model without doping effect. If we set the initial addition time as t=0s, the conjugation rate between the target bacteriaE. coli K12 molecules and the receptors is given by the following equation [12]:(1)dNdt=kFN0-Nρ0-kRN.In this equation, N is the density of conjugated receptors, N0 is the receptors’ density when t=0s, kF and kR are adsorption constant and desorption constant between target molecules and the linker-antibody receptors, and ρ0 is the concentration of the analyte target. The conjugation number increases from the start time t=0; at one time the conjugation number becomes steady until the next addition. The Langmuir parameters are acquired from the adsorption isotherm experiment. The equation of conjugation numbers is given by a group of equations as follows [13]:(2)Nt=ρ0t2DtD+1kFN0-1,NTt→∞=kFN0ρ0kFρ0+kR=kTN0ρ0kTρ0+1.In this group of equations, N(t) is the conjugation numbers before equilibrium and NT(t→∞) is the conjugation numbers after equilibrium. The equilibrium condition stands for the fact that that the conjugation numbers become saturate. D is the diffusion coefficient. The normalized Langmuir parameter kT is calculated as kT=kF/kR, and ρ0 is the concentration of the analyte target. For the two signal steps, the first one is corresponding to the fifth addition; after the fifth addition the target concentration is 1.67 × 107 CFU/mL. The second one is corresponding to the sixth addition; after the sixth addition the target concentration is 1.7 × 107 CFU/mL. According to theI-V curve equation, the carrier density is calculated as n=IdsL/(WVdsqμeff). Vds=0.1V, e=1.6  × 1019 C, μeff=1200 cm2/V·s,  W/L=60/110. Thus, the carrier density figure along the real-time signal measurement is shown in Figure 7.Figure 7
The graphene channel’s carrier density along the real-time sensor signal measurement.In the carrier density real-time Figure7, we could find the corresponding relationship between bacteria concentration and carrier density. After calculating from the full real-time data, we could find that the carrier density before bacteria attachment is 6.68 × 1011/cm2. Then the relationship between bacteria concentration and carrier density is listed in Table 1.Table 1
The relationship between bacteria concentration and carrier density.
E. coli K12 concentration (CFU/mL)
0
1.6 × 107
1.6 × 107
1.7 × 107
Carrier density (/cm2)
6.68 × 1011
7.1 × 1011
8.5 × 1011
9.26 × 1011The two groups of simulation parameters are below. The Langmuir parameter iskT=kF/kR= 5.88 × 106/mol [14], the target molecule size is 2 μm, the oxidation thickness is 100 μm, and the diffusion coefficient D is 7.6 × 106. The target concentration for the fifth addition is 1.67 × 107 CFU/mL, and the target concentration for the sixth addition is 1.7 × 107 CFU/mL. From the MATLAB calculation of (2), a simulation curve is acquired based on the target-receptor adsorption model. The simulation curve is shown in Figure 8.Figure 8
Simulation figure for the two responses due to our fifth addition and the sixth addition ofE. coli K12 solution.The above carrier density calculation is based on an ideal condition without doping. In fact, carrier density depends on multiple factors such as doping level. The graphene we used in our experiment is the copper-based CVD graphene. Even under the circumstance ofVg=0, the copper-based CVD graphene is usually already P doped. And the doping level could be tuned by gate voltage via field effect. We could find difference between experimental curve and calculation curve. In this case, we could use the difference of gate voltage and Dirac voltage to reflect the doping level caused by applied gate voltage. According to the reference considering the effects of doping level [15], the equation of carrier density calculation would be modified as shown in (3); Cg and V0 stand for gate capacitance and Dirac voltage, respectively. Consider(3)n=n02+CoxVg-VDe2.Next we will analyze the electrical property of our material graphene. Graphene is made out of carbon atoms arranged in hexagonal structure. Intrinsic graphene is a zero-gap semiconductor [16]; in order to calculate the energy bands of graphene, we could deduce that from tight-binding model. After a series of calculation of vectors and Hamiltonian, the energy bands equation is as follows [17]:(4)E±k=±3+fk-t′fk,(5)fk=2cos⁡3kya+4cos⁡32kyacos⁡32kxa.In these two equations,t(≈2.8eV) is the nearest-neighbor hopping energy (hopping between different sublattices) and f(k) is wave function in the graphene plane. kx and ky are horizontal vector and vertical vector and a is the distance between two neighbor carbon atoms, a≈1.42A. Combining (4) and (5) together, we could get the energy band equation as follows [18]:(6)E±k=±2.83+2cos⁡3kya+4cos⁡32kyacos⁡32kxa.From this equation, we could draw out the graphene’s energy band by MATLAB. After inputting a MATLAB calculation program, we could draw out a three-dimensional energy band structure, as shown in Figure 9.Figure 9
The simulation figure of graphene energy band structure. The upper curve stands for the conduction band and the lower curve stands for the valence band.For intrinsic graphene, the conduction band and the valence band contact at one point, which is called Dirac point, and Fermi energy band is across the Dirac point. When it is for P doping graphene or N doping graphene, graphene’s Fermi surface would shift down or move up. In our experiment, the target bacteriaE. coli K12 carry negative charge on their molecule; whenE. coli K12 molecules are adsorbed onto the functionalized surface of graphene, they will induce positive charge in the graphene channel, causing more holes and leading holes to become majority carriers. Thus, ourE. coli K12 real-time experiment is a P doping example. However, it is difficult to precisely measure the doping level caused byE. coli attachment, as the graphene is already P doped beforeE. coli attachment. The difference between intrinsic graphene and P doping graphene is shown in Figure 10.Figure 10
The comparison between intrinsic graphene energy band and P doped graphene energy band. The left figure stands for the intrinsic graphene energy band and the right figure stands for the P doped graphene energy band.In our real-time measurement, we use the bias currentIds as the electrical signal. For graphene FET sensors, usually there are two important curves:I-V curves and transfer curves.I-V curves present the relationship between bias current Ids and bias voltage VD when gate voltage Vg=0V. Transfer curves present the relationship between bias current Ids and gate voltage Vg with a fixed bias voltage VD. In our real-time measurement, we always set the gate voltage Vg=0V. The current-voltage relationship is deduced from the Landauer formula [19], which can define the conductance equation of the monolayer graphene model. In the Landauer formula, e is the electron charge, h is Planck’s constant, and f(E) is the probability of the Fermi level with electrons, which is known as the Fermi-Dirac distribution function. Consider(7)G=2e2h∫0+∞METE-dfEdEdE.Then in Meric’s GFET electrical model, he deduced the current-voltage equation from the basic Landauer formula, considering the drift velocity vdrift and carrier density n. Consider(8)Id=WL∫0Lenxvdriftxdx.In Meric’s paper, the author raises a compact model for graphene FET [20]. Besides, Parrish’s paper also provides reference for a compact model of graphene FET [21]. Combining these references together, we could acquire a group of equations for bothI-V curves and transfer curves. Consider(9)Ids=eWLμeffn0Vds(10)Ids=W/2Leμeff-CoxVg-VD/e+n02+CoxVg-VD/e2Vds1+μeffVds/Lνsat.AfterE. coli attachment, we would consider the induced charge caused by the attachedE. coli molecules. In this case, the current equation would be modified in (11)Ids′=eWLμeffn0+VIVT·c·ρ0kTρ0kT+1·QEVds+ΔId.In these equations, (9) and (11) describe graphene FETI-V curve characteristic when gate voltage Vg=0V beforeE. coli attachment and afterE. coli attachment and (10) describes graphene FET transfer curve characteristic with a fixed bias voltage. For these parameters, W and L are the graphene channel width and length, μeff is the effective carrier mobility in graphene channel, n0 is the initial carrier density without gate voltage, Vg is gate voltage, VD is threshold voltage at Dirac point, Vds is bias voltage, Cox is the oxidation layer gate capacitance, νsat is saturation velocity, VI and VT are the injection volume and total volume, respectively, c is theE. coli concentration, QE is the charge quantity eachE. coli molecule carries, and ΔId is current change caused byE. coli doping.According to the transfer curves equation, the simulated transfer curves are finished to compare intrinsic graphene and P doping graphene transfer characteristics. The P doping transfer curve is a schematic curve, not in very precise calculation. Thus, in the simulation (Figure11), we could see that in P doping circumstance, the transfer curve right shifts. The bias current Ids value at Vg=0 increases after P doping. So it can explain why, afterE. coli attachment, the real-time bias current signal increases. For parameters e=1.6×1019 C, the graphene width and length are W=0.6 mm and L=1.1 mm, carrier mobility is μeff = 1200 cm2/V·s, the intrinsic carrier density is n0 = 6.68 × 1011/cm2, the oxidation gate capacitance is Cox = 400 nF [22], and the saturation velocity νsat is νsat = 5.5 × 106 cm/s according to one reference paper [23]. The data fitting ofI-V curves corresponding to threeE. coli K12 concentrations are in Figure 12.Figure 11
The qualitative transfer curves of intrinsic graphene FET and P doped graphene FET.Figure 12
Data fitting ofI-V curves corresponding to threeE. coli K12 concentrations.Above all, we compare three data fittingI-V curves according to the real-time measurement. In our data fitting curves (Figure 12), the blue curve is corresponding to the 0 s in the real-time figure (Figure 5), which is after the fourth addition, and theE. coli K12 concentration is 1.6 × 107 CFU/mL. The purple curve is corresponding to the 25 s in the real-time figure (Figure 5), which is after the fifth addition, and theE. coli K12 concentration is 1.67 × 107 CFU/mL. The deep blue curve is corresponding to the 40 s in the real-time figure (Figure 5), which is after the sixth addition, and theE. coli K12 concentration is 1.7 × 107 CFU/mL.


## 6. Conclusion

In summary, we have developed a graphene FET detector for the targetE. coli K12 and recorded real-time bias current Ids signal measurement; then a theoretical study is conducted to explain the signal. In our analysis, we explained that after theE. coli K12 molecules with negative charge attach on the sensor surface, the bacteria will induce holes increasing in the graphene channel. Thus, the bias current of graphene FET increases due to the carrier numbers increasing. A calculation based on target-receptor model is conducted to be compared with the experimental result. Finally, a simulation based onI-V curve equation and data fitting is done to present the relationship of the bias current Ids and theE. coli K12 concentration. The real-time measurement result indicates that our sensor chip could have a proportional relationship between bias current Ids signal response and different bacteria concentrations. Thus, our sensor chip has application value for detecting the presence and concentration ofE. coli K12. Moreover, in future, this biosensor may be modified for detecting the pathogenic strainE. coli O157:H7, becoming more useful in ensuring food or environmental safety.



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*Source: 4641398-2016-05-18.xml*