Towards Bacteria Counting in DI Water of Several Microliters or Growing Suspension Using Impedance Biochips

We counted bacterial cells of E. coli strain K12 in several-microliter DI water or in several-microliter PBS in the low optical density (OD) range (OD = 0.05–1.08) in contact with the surface of Si-based impedance biochips with ring electrodes by impedance measurements. The multiparameter fit of the impedance data allowed calibration of the impedance data with the concentration cb of the E. coli cells in the range of cb = 0.06 to 1.26 × 109 cells/mL. The results showed that for E. coli in DI water and in PBS, the modelled impedance parameters depend linearly on the concentration of cells in the range of cb = 0.06 to 1.26 × 109 cells/mL, whereas the OD, which was independently measured with a spectrophotometer, was only linearly dependent on the concentration of the E. coli cells in the range of cb = 0.06 to 0.50 × 109 cells/mL.


Introduction
The techniques used to count biological species can be categorized into physical and biological ones. Physical methods will yield a total (living and dead) microorganisms count [1], while biological methods only record living organisms. A routinely used and easy physical way to count bacteria cells is the measurement of optical density (OD) at 600 nm [2]. Since this method measures the turbidity, and thus the scatter of light rather than the absorption, Beer's law and the linear dependence of the OD on the cell number are only applicable in a certain narrow (usually highly diluted, i.e., 0.1 < OD < 1.0) range [3]. Thus, counting of biological species by OD measurements in a large concentration range The amount of viable CFUs in the overnight cultured solution was determined by the PCA technique. Therefore, a solution of OD = 0.1 was diluted to a concentration corresponding 1:10 5 and 1:10 6 in duplicate, respectively. Then, 100 μL of each dilution was plated onto an agar plate and cultivated at 37 °C overnight. Visible colonies were counted the next day. The OD depends linearly on the concentration of E. coli in the OD range from about 0.015 to 0.34, corresponding to 0.22 to 2.3 × 10 8 CFU/mL, respectively. The optical density was determined at a 1:10 dilution in TSB in duplicate to determine the cell count. One microliter of the bacterial suspension was centrifuged at 13,000 xG for 90 s, the bacterial pellet was washed once in Dulbecco's phosphate buffered saline (PBS, Merck Biochrome), and then resuspended in 1 mL PBS. Bacteria were heat-inactivated at 95 °C for at least 30 min. Heat-inactivated E. coli were washed twice in PBS diluted 1:2 in DI water (0.5× PBS) and resuspended in 0.5× PBS to about 12.5 × 10 8 (low concentration) or 63 × 10 8 cells/mL (moderate concentration).

Structural Description
To fabricate the BS (boron-implanted Samples) impedance biochips boron ions (B) were implanted into Si:P, and to fabricate the PS (Phosphorus-implanted Samples) impedance biochips phosphorus (P) ions were implanted into Si:B (Table 1). Figure 2a,b show the structures of the BS and PS impedance biochips, respectively. Approximately 150-nm-thick gold (Au) layers were deposited by DC magnetron sputtering on silicon wafers measuring 525 μm in thickness, while unstructured gold (Au) formed the bottom contact. Au ring electrodes with inner and outer diameters of 5.7 mm and 7.8 mm, respectively, were fabricated using a lift-off process. The amount of viable CFUs in the overnight cultured solution was determined by the PCA technique. Therefore, a solution of OD = 0.1 was diluted to a concentration corresponding 1:10 5 and 1:10 6 in duplicate, respectively. Then, 100 µL of each dilution was plated onto an agar plate and cultivated at 37 • C overnight. Visible colonies were counted the next day. The OD depends linearly on the concentration of E. coli in the OD range from about 0.015 to 0.34, corresponding to 0.22 to 2.3 × 10 8 CFU/mL, respectively. The optical density was determined at a 1:10 dilution in TSB in duplicate to determine the cell count. One microliter of the bacterial suspension was centrifuged at 13,000 xG for 90 s, the bacterial pellet was washed once in Dulbecco's phosphate buffered saline (PBS, Merck Biochrome), and then resuspended in 1 mL PBS. Bacteria were heat-inactivated at 95 • C for at least 30 min. Heat-inactivated E. coli were washed twice in PBS diluted 1:2 in DI water (0.5× PBS) and resuspended in 0.5× PBS to about 12.5 × 10 8 (low concentration) or 63 × 10 8 cells/mL (moderate concentration).

Structural Description
To fabricate the BS (boron-implanted Samples) impedance biochips boron ions (B) were implanted into Si:P, and to fabricate the PS (Phosphorus-implanted Samples) impedance biochips phosphorus (P) ions were implanted into Si:B (Table 1). Figure 2a,b show the structures of the BS and PS impedance biochips, respectively. Approximately 150-nm-thick gold (Au) layers were deposited by DC magnetron sputtering on silicon wafers measuring 525 µm in thickness, while unstructured gold (Au) formed the bottom contact. Au ring electrodes with inner and outer diameters of 5.7 mm and 7.8 mm, respectively, were fabricated using a lift-off process.  A ring electrode was selected because of the homogenous field distribution between the ring top electrode and unstructured bottom electrode [16]. The detection limit for a small number of cells in a liquid by impedance measurements using the Si biochip strongly depends on the volume of liquid for which the top electrode structure is optimized. The top and bottom electrodes were wire-bonded to the pins of a TO-5 (Transistor Outline with base diameter of 8.9 mm) package (c) and connected to an Agilent 4294A impedance analyzer. A severalmicroliter solvent (i.e., DI water or PBS) and E. coli cells were added into the top ring electrode and the impedance of the biochip was measured.
The presented ring electrode structure was optimized with respect to the inner and outer ring diameters to sense suspension volumes between 10 and 30 μL. Dependent on the concentrations of the implanted dopants, the impedance biochips without liquid filling have a pn junction (boundary between a p-type and n-type semiconductor) capacitance and a capacitance for the Schotty contact formed by the Au ring electrode. The capacitances of the p + n junction in BS and of the n + p junction in PS amount to 4.8 × 10 −9 F and 2.49 × 10 −9 F, respectively. The capacitances of the Schottky contact formed by the Au ring electrodes on BS and PS amount to 3.12 × 10 −7 F and 4.49 × 10 −8 F, respectively. If a smaller suspension volume was detected, the inner and outer diameters of the ring electrodes would have to be reduced. The standard TO-5 package (Figure 2c) was used to assemble the impedance biochip and measurement setup. The top and bottom contacts of the biochips were bonded to the pins of this package and an Agilent 4294A precision impedance analyzer was utilized to record the impedance characteristics of the biochips by sweeping the frequency from 40 Hz to 1 MHz under normal daylight at room temperature. This impedance analyzer works in a range and bottom electrodes were wire-bonded to the pins of a TO-5 (Transistor Outline with base diameter of 8.9 mm) package (c) and connected to an Agilent 4294A impedance analyzer. A several-microliter solvent (i.e., DI water or PBS) and E. coli cells were added into the top ring electrode and the impedance of the biochip was measured.
A ring electrode was selected because of the homogenous field distribution between the ring top electrode and unstructured bottom electrode [16]. The detection limit for a small number of cells in a liquid by impedance measurements using the Si biochip strongly depends on the volume of liquid for which the top electrode structure is optimized.
The presented ring electrode structure was optimized with respect to the inner and outer ring diameters to sense suspension volumes between 10 and 30 µL. Dependent on the concentrations of the implanted dopants, the impedance biochips without liquid filling have a pn junction (boundary between a p-type and n-type semiconductor) capacitance and a capacitance for the Schotty contact formed by the Au ring electrode. The capacitances of the p + n junction in BS and of the n + p junction in PS amount to 4.8 × 10 −9 F and 2.49 × 10 −9 F, respectively. The capacitances of the Schottky contact formed by the Au ring electrodes on BS and PS amount to 3.12 × 10 −7 F and 4.49 × 10 −8 F, respectively. If a smaller suspension volume was detected, the inner and outer diameters of the ring electrodes would have to be reduced. The standard TO-5 package (Figure 2c) was used to assemble the impedance biochip and measurement setup. The top and bottom contacts of the biochips were bonded to the pins of this package and an Agilent 4294A precision impedance analyzer was utilized to record the impedance characteristics of the biochips by sweeping the frequency from 40 Hz to 1 MHz under normal daylight at room temperature. This impedance analyzer works in a range covering 10 −3 to 10 8 Ohm and is suitable for impedance spectroscopy of the investigated Si biochips with impedance changes observed in the range from 10 1 Ohm up to 10 5 Ohm. Before any measurement, the network analyzer was calibrated by performing 3 steps, namely shortcut, open circuit, and 50 Ohm calibration. Typically, one frequency sweep lasts 30 s, i.e., if the impedance data are calibrated with the cell concentration, impedance measurements for cell counting can be performed in less than 1 min. We chose two media liquids and added either DI water solvent and the E. coli or PBS solvent and E. coli into the gold ring top electrode region.

Modelling
During impedance measurements, a small alternating current (AC) test signal of 50 mV was applied to BS and PS impedance biochips, while the complex resistance, i.e., the impedance, was measured for different test frequencies and plotted in the form of a Nyquist plot. This measurement technique is named impedance spectroscopy (ImS) [17]. The change of the recorded impedance data was correlated with the independently determined cell concentration ( Figure 1). ImS helps to detect biological species in contact with the surface of the impedance biochip, because those biological species change the impedance of impedance biochips in the area inside the ring electrodes. The corresponding electrical equivalent circuit is obtainable based on the electrical properties from the recorded Nyquist plots of the biochips without and with E. coli K12 cells [18]. A Nyquist plot reveals the contribution of different components in the equivalent circuit [19]. As an example, an imperfect semicircle is correlated with constant phase elements (CPE) [20]. In the physical structure of the biochip, the capacitance and resistance are associated with space charge polarization regions and with adsorption of E. coli in the area inside the electrode. Usually, most of the structures with electrodes contain a geometrical capacitance and a bulk resistance in parallel to it [21][22][23]. For the used BS and PS biochips, the bulk capacitance of the p-n junction depletion region and the capacitance of the Schottky contacts between electrodes and semiconductor are modeled with resistor and capacitor pair [20]. To model the equivalent circuit parameters from the electrical equivalent circuit, complex non-linear least square (CNLS) software was used. Based on the Nyquist plot of the biochips. in which there are two imperfect semicircles, the electrical equivalent circuit shown in Figure 3b for the BS biochip and in Figure 4b for the PS biochip were selected [24,25].
Biosensors 2020, 10, x FOR PEER REVIEW 5 of 15 covering 10 −3 to 10 8 Ohm and is suitable for impedance spectroscopy of the investigated Si biochips with impedance changes observed in the range from 10 1 Ohm up to 10 5 Ohm. Before any measurement, the network analyzer was calibrated by performing 3 steps, namely shortcut, open circuit, and 50 Ohm calibration. Typically, one frequency sweep lasts 30 s, i.e., if the impedance data are calibrated with the cell concentration, impedance measurements for cell counting can be performed in less than 1 min. We chose two media liquids and added either DI water solvent and the E. coli or PBS solvent and E. coli into the gold ring top electrode region.

Modelling
During impedance measurements, a small alternating current (AC) test signal of 50 mV was applied to BS and PS impedance biochips, while the complex resistance, i.e., the impedance, was measured for different test frequencies and plotted in the form of a Nyquist plot. This measurement technique is named impedance spectroscopy (ImS) [17]. The change of the recorded impedance data was correlated with the independently determined cell concentration ( Figure 1). ImS helps to detect biological species in contact with the surface of the impedance biochip, because those biological species change the impedance of impedance biochips in the area inside the ring electrodes. The corresponding electrical equivalent circuit is obtainable based on the electrical properties from the recorded Nyquist plots of the biochips without and with E. coli K12 cells [18]. A Nyquist plot reveals the contribution of different components in the equivalent circuit [19]. As an example, an imperfect semicircle is correlated with constant phase elements (CPE) [20]. In the physical structure of the biochip, the capacitance and resistance are associated with space charge polarization regions and with adsorption of E. coli in the area inside the electrode. Usually, most of the structures with electrodes contain a geometrical capacitance and a bulk resistance in parallel to it [21][22][23]. For the used BS and PS biochips, the bulk capacitance of the p-n junction depletion region and the capacitance of the Schottky contacts between electrodes and semiconductor are modeled with resistor and capacitor pair [20]. To model the equivalent circuit parameters from the electrical equivalent circuit, complex non-linear least square (CNLS) software was used. Based on the Nyquist plot of the biochips. in which there are two imperfect semicircles, the electrical equivalent circuit shown in Figure 3b for the BS biochip and in Figure 4b for the PS biochip were selected [24,25].   (Resistor and Capacitor) pairs. The parallel capacitor (Cp1) and parallel resistor (Rp1) can be transferred from Cdep (depletion capacitor) and Rss (semiconductor resistor) Cb and Rb corresponds to capacitive and resistive parts of biomaterial respectively. Cdep, Rss, Cb and Rb are transferred to the Parallel capacitor Cp2 and Cp3 and parallel resistor Rp2 na Rp3 from Equivalent circuit models of biochips with analyte in a (c) to Maxwell circuit and in a (d) Voigt circuit [14]. Ls and Rs are series inductor and resistor of the interface respectively. and resistor of the interface respectively.. The Rp2-Cp2 and Rp3-CP3 pairs in Figures 3d and 4d correspond to the impedance of the pn junction below the Au ring electrode and below the contact formed by the liquid. Rsch and Csch describe the capacitance of the PS biochip due to the Schottky contact formed by the Au ring electrode (Figure 4c,d). The capacitance of the Schottky contact formed by the Au ring electrode (Figure 3c,d) on the BS biochip can be neglected. The Nyquist plot of the BS biochip without analyte consists of one semicircle. This semicircle can be represented by an associated resistor (R) and capacitor (C) pair, which is shown in Figure 3b. From the other side, the physical structures of the biochips consist of a p + n-junction at the boundary between p+ and n-type silicon. A depletion region is formed at the interface of these two semiconductor types, consisting of Cdep and Rss (Figure 3a,c). Thus, the BS biochip can be described by the introduced model in Figure 3a. This model can be transferred to electrical equivalent circuit shown in the Figure 3b by converting the series structures of Cdep and Rss to the parallel Cp1//Rp1 (Figure 3b), where Cp1 = Cdep·(Q 2 /(1 + Q 2 )), Rp1 = Rss·(1 + Q 2 ) with Q = 1/(ω·Cdep·Rss) [26] [14].
The Nyquist plot for the PS biochip without liquid, however, reveals two non-overlapping semicircles and a resistor-capacitor (RC) pair. These semicircles are due to the n + p-junction and the Schottky contacts that formed at the interfaces between Au top and bottom electrodes and the semiconductor. These metal-semiconductor Schottky contacts can be represented by an extra CPE and resistor pair in the electrical equivalent circuit [27] in Figure 4. The physiochemical model of the PS biochip, which is shown in Figure 4a, can then be transferred into Figure 4b by using series to parallel circuit exchange equations. After the DI water or PBS with E. coli is applied to the ring top electrode of the BS and PS biochips, an additional semicircle appears in the Nyquist plot. This semicircle is directly related to the cell concentration. In the electrical equivalent circuit with inserted liquid and with inserted liquid and E. coli in Figures 3d and 4d, respectively, an additional R3C3 pair is used for modeling. This electrical modeling circuit needs to be equal to the physiochemical model. To transfer these two models, we employed two equivalent circuits that were equal at any  Figure 3b. From the other side, the physical structures of the biochips consist of a p + n-junction at the boundary between p+ and n-type silicon. A depletion region is formed at the interface of these two semiconductor types, consisting of Cdep and Rss (Figure 3a,c). Thus, the BS biochip can be described by the introduced model in Figure 3a. This model can be transferred to electrical equivalent circuit shown in the Figure 3b by converting the series structures of Cdep and Rss to the parallel Cp1//Rp1 (Figure 3b), where Cp1 = Cdep·(Q 2 /(1 + Q 2 )), Rp1 = Rss·(1 + Q 2 ) with Q = 1/(ω·Cdep·Rss) [26] The Nyquist plot for the PS biochip without liquid, however, reveals two non-overlapping semicircles and a resistor-capacitor (RC) pair. These semicircles are due to the n + p-junction and the Schottky contacts that formed at the interfaces between Au top and bottom electrodes and the semiconductor. These metal-semiconductor Schottky contacts can be represented by an extra CPE and resistor pair in the electrical equivalent circuit [27] in Figure 4. The physiochemical model of the PS biochip, which is shown in Figure 4a, can then be transferred into Figure 4b by using series to parallel circuit exchange equations. After the DI water or PBS with E. coli is applied to the ring top electrode of the BS and PS biochips, an additional semicircle appears in the Nyquist plot. This semicircle 7 of 15 is directly related to the cell concentration. In the electrical equivalent circuit with inserted liquid and with inserted liquid and E. coli in Figures 3d and 4d, respectively, an additional R 3 C 3 pair is used for modeling. This electrical modeling circuit needs to be equal to the physiochemical model. To transfer these two models, we employed two equivalent circuits that were equal at any frequencies.
The Maxwell circuit in Figures 3c and 4c can be transferred into the Voigt circuit, as illustrated in Figures 3d and 4d. In brief, the impedance change, which is dependent on the bacterial concentration, was modeled with 4 parameters, Rp2, Cp2, Rp3, and CP3. In a future work we will develop another model approach to fit the Cb and Rb of the liquid and of the liquid with the biomaterial directly in the Maxwell circuit. The parameters Rp2, Cp2, Rp3, and Cp3 depend on Cdep, Rss, Cb, and Rb. Therefore, a multiparameter is needed to quantify the concentrations of E. coli cells by using the BS and PS biochips ( Table 1).
The electrical equivalent circuit model of the BS impedance biochip with no medium and no bacteria consists of a CPE in parallel with a resistor (Figure 3b), while the electrical equivalent circuit for BS biochips BS with medium and with E. coli cells consists of two pairs of CPEs and resistors (Figure 3b). The PS biochip without analyte is modeled using two pairs of CPEs in parallel with resistors (Figure 4b), while for the PS biochips with medium and with E. coli cells the circuit consists of three pairs of CPEs and resistors (Figure 4c). The equivalent circuit parameters Rs and Ls contribute to the lead impedances. Note that the equivalent circuit model shown in Figure 3b for the BS biochip and Figure 4c for the PS biochip were applied to model impedance changes of the BS and PS biochips after adding 1, 2, 3, 4, and 5 µL of medium with bacteria at low (0.06 to 0.25 × 10 9 cells/mL) and moderate concentrations (0.29 to 1.26 × 10 9 cells/mL).

Results and Discussion
E. coli cells were kept in DI water-0.5× PBS at cell concentrations of c b = 0.06 to 0.25 × 10 9 cells/mL (low concentration range, Figure 5b,d,j,l), and at cell concentrations of c b = 0.29 to 1.26 × 10 9 cells/mL (moderate concentration range, Figure 5f,h,n,p). The impedance changes of PS and BS biochips were studied under the same experimental conditions without any analyte in the area inside the top of the ring electrode, shown as black thick curves in Figure 5 (no filling). We used four BS impedance biochips and PS four impedance biochips (indicated by blue boxes for results with DI water and red boxes for 0.5× PBS in Figure 5). Impedance data in the same box were obtained by performing reference measurements without E. coli cells and measurements with E. coli cells on the same impedance biochip. First, we added 20 µL liquid without E. coli cells, plus 1, 2, 3, 4, and 5 µL liquid without E. coli cells on a given impedance biochip. After letting 25 µL of the liquid evaporate, the impedance of the impedance biochip without filling was remeasured and 20 µL liquid without E. coli was added and remeasured. Then, we added 1, 2, 3, 4, and 5 µL liquid with E. coli cells and measured the impedance. Note that the impedance of the biochips after evaporation of the liquid with E. coli cells is not the same as the impedance of the biochips after evaporation of the liquid without E. coli cells. The impedance values of biochips after adding 20 µL DI water without E. coli cells are shown in Figure 5a,b,e,f,i,j,m,n; and after adding 20 µL 0.5× PBS without E. coli cells are shown in Figure 5c,d,g,h,k,l,o,p. The impedance values of biochips after adding 1-5 µL DI water without E. coli cells are shown in Figure 5a,e,j,m; and after adding 1-5 µL 0.5× PBS without E. coli cells are shown in Figure 5c,g,k,o. Every filling step and corresponding impedance measurement lasted 1 min. Impedance values after adding 1-5 µL 0.5× PBS with E. coli cells to 20 µL DI water are shown in Figure 5b,f,j,n; and with 20 µL 0.5× PBS are shown in Figure 5d,h,l,p. Because of the different results for the impedance characteristics of the biochips with different media (e.g., Figure 5a,c), one can deduce that both biochips can be used to distinguish between these different media, namely DI water and 0.5× PBS, which is not possible with an optical microscope. Additionally, and more importantly, the impedance biochips can also be used to count adsorbed cells. Adsorbed cells cause a significant change in the impedance of the biochips. The impedance characteristics of the biochips with DI water or 0.5× PBS and the corresponding impedance characteristics of the biochips with E. coli ( Figure 5) confirm the significant sensitivity of the biochips to adsorbed E. coli cells in the area inside the ring electrode. Remarkably, an additional significant semicircle forms in the impedance plot of the biochips with added E. coli. This additional semicircle is pointed out by an arrow in Figure 5b, d, f, h, j, l, n, p. We modeled the experimental impedance data and analyzed the modeled equivalent circuit parameters dependent on the filling of the area inside the ring electrode. The equivalent circuits for the biochips with DI water/0.5× PBS and for the BS biochip with dispensed E. coli in DI water/0.5× PBS are shown in Figure 3a,b, respectively. the biochips with DI water/0.5× PBS and for the BS biochip with dispensed E. coli in DI water/0.5× PBS are shown in Figure 3a,b, respectively.
Without solvent and bacteria, the equivalent circuit consists of two imperfect capacitors or CPEs (Cp1, Cp2), two parallel resistors (Rp1, Rp2), a contact resistor (Rs), and a contact inductor (Ls). The modeled impedance circuit parameters are listed in Appendix A Tables A1-A12. The equivalent circuits of the impedance spectra of the biochips with and without E. coli cells are different due to the additional appearance of the semicircles, which are indicated by arrows in Figure 5.
Accordingly, based on the experimental impedance characteristics of the biochips after adding analyte, the composition and cell numbers of the E. coli added to the biochips can be determined by modeling the parameters of the equivalent circuit shown in Figure 3b for the BS biochip, which consists of two imperfect capacitors (Cp1, Cp2); and those shown in Figure 4b for the PS biochip, which consists of three imperfect capacitors (Cp1, Cp2, Cp3) and three resistors (Rp1, Rp2, Rp3), a contact resistor (Rs), and a contact inductor (Ls).

Figure 5. Experimental (symbols) and modeled (solid lines) Nyquist plots of the (a-h) BS and (i-p) PS
biochips with no filling (black symbols and lines) and with 20 μL DI water/PBS (red symbols and lines), and with additional DI water/0.5× PBS with and without E. coli in steps of 1 μL: 1 μL (Navy), 2 μL (blue), 3 μL (violet), 4 μL (green), and 5 μL (orange). Here, 1 μL of E. coli and 5 μL of E. coli respectively correspond to bacterial cell concentrations of 0.06 × 10 9 /mL in 21 μL medium and 0.25 × 10 9 /mL in 25 μL medium for low concentrations; and of 0.29 × 10 9 /mL in 21 μL medium and to 1.26 × 10 9 /mL in 25 μL medium for moderate concentrations. The significant additional semicircles in the Nyquist plots, which are caused by the E. coli, are indicated by arrows. In the plots, blue boxes represent the results with DI water and red boxes represent the results 0.5× PBS. W represents DI water, P is short for 0.5× PBS, K stands for E. coli K12, and the numbers represent the volumes in microliters; the total volumes of the liquids on the top electrode are mentioned in the legend in microliters. The standard deviation error bars for 3 repeated measurements are also added to the measurement points.

Figure 5. Experimental (symbols) and modeled (solid lines) Nyquist plots of the (a-h) BS and (i-p) PS
biochips with no filling (black symbols and lines) and with 20 µL DI water/PBS (red symbols and lines), and with additional DI water/0.5× PBS with and without E. coli in steps of 1 µL: 1 µL (Navy), 2 µL (blue), 3 µL (violet), 4 µL (green), and 5 µL (orange). Here, 1 µL of E. coli and 5 µL of E. coli respectively correspond to bacterial cell concentrations of 0.06 × 10 9 /mL in 21 µL medium and 0.25 × 10 9 /mL in 25 µL medium for low concentrations; and of 0.29 × 10 9 /mL in 21 µL medium and to 1.26 × 10 9 /mL in 25 µL medium for moderate concentrations. The significant additional semicircles in the Nyquist plots, which are caused by the E. coli, are indicated by arrows. In the plots, blue boxes represent the results with DI water and red boxes represent the results 0.5× PBS. W represents DI water, P is short for 0.5× PBS, K stands for E. coli K12, and the numbers represent the volumes in microliters; the total volumes of the liquids on the top electrode are mentioned in the legend in microliters. The standard deviation error bars for 3 repeated measurements are also added to the measurement points.
Without solvent and bacteria, the equivalent circuit consists of two imperfect capacitors or CPEs (Cp1, Cp2), two parallel resistors (Rp1, Rp2), a contact resistor (Rs), and a contact inductor (Ls). The modeled impedance circuit parameters are listed in Appendix A Tables A1-A12. The equivalent circuits of the impedance spectra of the biochips with and without E. coli cells are different due to the additional appearance of the semicircles, which are indicated by arrows in Figure 5.
Accordingly, based on the experimental impedance characteristics of the biochips after adding analyte, the composition and cell numbers of the E. coli added to the biochips can be determined by modeling the parameters of the equivalent circuit shown in Figure 3b for the BS biochip, which consists of two imperfect capacitors (Cp1, Cp2); and those shown in Figure 4b for the PS biochip, which consists of three imperfect capacitors (Cp1, Cp2, Cp3) and three resistors (Rp1, Rp2, Rp3), a contact resistor (Rs), and a contact inductor (Ls).
The corresponding ImS modeling results of the biochips based on Tables A1-A8 are shown in Figure 6.The E. coli cell concentration was determined by measuring the OD of a diluted stock solution and calculating the corresponding number of cells using the calibration data from Figure 1. Observed impedance changes can be related to concentrations of E. coli cells for low concentrations (0.06 × 10 9 to 0.25 × 10 9 /mL) and moderate concentrations (0.29 to 1.26 × 10 9 /mL). The modeled equivalent circuit elements Rp2, Rp3, Cp2, and Cp3 depend linearly on the concentration of E. coli cells. There is a linear relationship with the nominal number of bacterial cells extracted for the biochips with low concentrations (0.06 × 10 9 /mL to 0.25 × 10 9 /mL) and with moderate concentrations (0.29 × 10 9 /mL to1.26 × 10 9 /mL). The modeling parameters Rp1 and Cp1 represent the Schottky contact at the electrode-semiconductor interface. If the size of the contact area is denoted as A, by adding the E. coli suspension to the top electrode region of the biochips, the effective area of the top contact is increased based on the equation Rp2 = ρ(d/A), where d denotes the thickness of the Schottky barrier and the resistance is reversely related to area A. Thus, there is a reduction in resistance Rp2 by adding the bacterial suspension. If we consider Cp2 = ε(A/d), with ε as the permittivity of the semiconductor, the relationship between Cp2 and A results in an increasing Cp2 with the increasing number of E. coli in the suspension. The corresponding ImS modeling results of the biochips based on Tables A1-A8 are shown in Figure 6.The E. coli cell concentration was determined by measuring the OD of a diluted stock solution and calculating the corresponding number of cells using the calibration data from Figure 1. Observed impedance changes can be related to concentrations of E. coli cells for low concentrations (0.06 × 10 9 to 0.25 × 10 9 /mL) and moderate concentrations (0.29 to 1.26 × 10 9 /mL). The modeled equivalent circuit elements Rp2, Rp3, Cp2, and Cp3 depend linearly on the concentration of E. coli cells. There is a linear relationship with the nominal number of bacterial cells extracted for the biochips with low concentrations (0.06 × 10 9 /mL to 0.25 × 10 9 /mL) and with moderate concentrations (0.29 × 10 9 /mL to1.26 × 10 9 /mL). The modeling parameters Rp1 and Cp1 represent the Schottky contact at the electrode-semiconductor interface. If the size of the contact area is denoted as A, by adding the E. coli suspension to the top electrode region of the biochips, the effective area of the top contact is increased based on the equation Rp2 = ρ(d/A), where d denotes the thickness of the Schottky barrier and the resistance is reversely related to area A. Thus, there is a reduction in resistance Rp2 by adding the bacterial suspension. If we consider Cp2 = ε(A/d), with ε as the permittivity of the semiconductor, the relationship between Cp2 and A results in an increasing Cp2 with the increasing number of E. coli in the suspension. Figure 6. Modeled equivalent circuit parameters (dots) and linear fitting curves (red lines) for (a,c,e,g) Rp1 and Cp1 and for (b,d,f,h) Rp3 and CP3 for the BS biochip, dependent on the number of cells in 10 7 /mL in DI water or PBS. Modeled equivalent circuit parameters (dots) and linear fitting curves (red lines) for (i,k,m,o) Rp1 and Cp1 and for (j,l,n,p) Rp3 and CP3 for the PS biochip, dependent on the cell number in units of 10 7 /mL with the DI water and PBS media. The quality of the linear fitting was measured by the R-square or coefficient of determination (COD), as shown in the brackets for each data set. (This value is between 0 and 1; if the value is close to 1, the relationship between a data point and a line will be regarded as very strong.).

Conclusions
We counted E. coli cells with concentrations from cb = 0.06 × 10 9 /mL to cb = 1.26 × 10 9 /mL in DI water and in PBS by analyzing the impedance of two different Si-based impedance biochips whose surfaces were in contact with the E. coli cells. Such impedance biochips are useful for disturbancefree monitoring of the cultivation of E. coli cells, providing significant time efficiency and high accuracy for a promising large range of cell concentrations. The significant changes between the impedance spectra before and after addition of the E. coli suspension into the top electrode region of the impedance biochips were evaluated. Developing a two-phase electrode structure helped to determine a proper equivalent circuit for the biochips with added bacteria. The modeling parameters Figure 6. Modeled equivalent circuit parameters (dots) and linear fitting curves (red lines) for (a,c,e,g) Rp1 and Cp1 and for (b,d,f,h) Rp3 and CP3 for the BS biochip, dependent on the number of cells in 10 7 /mL in DI water or PBS. Modeled equivalent circuit parameters (dots) and linear fitting curves (red lines) for (i,k,m,o) Rp1 and Cp1 and for (j,l,n,p) Rp3 and CP3 for the PS biochip, dependent on the cell number in units of 10 7 /mL with the DI water and PBS media. The quality of the linear fitting was measured by the R-square or coefficient of determination (COD), as shown in the brackets for each data set. (This value is between 0 and 1; if the value is close to 1, the relationship between a data point and a line will be regarded as very strong.).

Conclusions
We counted E. coli cells with concentrations from c b = 0.06 × 10 9 /mL to c b = 1.26 × 10 9 /mL in DI water and in PBS by analyzing the impedance of two different Si-based impedance biochips whose surfaces were in contact with the E. coli cells. Such impedance biochips are useful for disturbance-free monitoring of the cultivation of E. coli cells, providing significant time efficiency and high accuracy for a promising large range of cell concentrations. The significant changes between the impedance spectra before and after addition of the E. coli suspension into the top electrode region of the impedance biochips were evaluated. Developing a two-phase electrode structure helped to determine a proper equivalent circuit for the biochips with added bacteria. The modeling parameters Rp2, Cp2, Rp3, and Cp3 show the linear relationship with the E. coli cell number. Such linearly-dependent parameters were used to quantify the E. coli concentration. In comparison with impedance data, the dynamic range of OD data with respect to the cell concentration is smaller. OD data are only linear in the range of 0.06-0.5 × 10 9 cells/mL. In the future, detection of the dead and living biomaterials will be studied for different cell sizes and concentrations, and the further applications in microbiology, food industry, and medicine will be evaluated.

Conflicts of Interest:
The authors declare no conflict of interest.