Impedance sensing of a dielectric microparticle: The first objective of our work is to introduce a novel experiment to quantify the sensitivity of electrochemical impedance sensors operated in OECT or microelectrode configuration. To this end we realized the experimental setup shown in Figure 1a and 1b. The setup contains a dielectric microparticle (with diameter of 50 µm) attached to the bottom part of an AFM cantilever to have micrometric control of its position in the 3 spatial directions (Figure 1c). Once the microparticle is finely aligned with the *x-*y coordinates on the center of the sensor surface, we use the *z*-stage of the microscope to control the particle-sample distance *d*. Contact of the microparticle with the sensor surface is determined by the onset of a repulsive force acting on the AFM cantilever. The electric circuit to operate the OECT impedance sensor contains a Ag/AgCl wire that is used as the gate electrode, controlling the electrical potential of the aqueous electrolyte solution (0.1 M PBS). A DC voltage *V**D,DC* is applied between the source (S) and drain (D) electrodes of the OECT to drive the electronic current *I**D,DC* in the PEDOT:PSS channel. The measured transfer and output characteristics of a typical OECT (Figure 1d), demonstrate that the gate voltage effectively modulates the channel current. For impedance sensing we superimpose a small sinusoidal oscillation signal *V**G,AC* (with amplitude 10 mV and angular frequency ω) on the gate bias *V**G*,*DC*. This leads to an AC current in the PEDOT:PSS layer, 31 which is measured by a lock-in amplifier connected to the source contact (*I**S,AC*).

In the microelectrode configuration (Figure 1b) the circuit is simplified, as source and drain electrodes are in short circuit and are jointly connected to the lock-in amplifier. Therefore, no OECT channel current is present, and all the electric current measured during impedance sensing is the gate current *I**G,AC*, flowing from the electrolyte into the PEDOT:PSS layer. All other components are identical to the OECT configuration to permit a direct comparison.

In Figure 1e we show the results of a typical microparticle distance - AC current experiment conducted at 1.17 kHz excitation frequency. The amplitudes of the AC currents in OECT and microelectrode configuration are plotted as a function of time. During the experiment, the microparticle is approached and retracted from the device channel for three consecutive times. For both configurations, the current amplitude follows the motion of the microparticle in a highly reproducible manner over consecutive cycles, highlighting the stability of the characterization method. In Figure 1f, the same data is plotted as a function of the distance between microparticle and sensor surface. Both types of devices produce a reversible, linear response in which the approach leads to a reduction in AC amplitude. Qualitatively, this response is expected, as the microsphere represents a barrier for the ionic current in the electrolyte: when it is close to the sensor surface, the half space through which ions can approach the active layer is reduced, thus increasing the effective impedance of the electrolyte *Z**el*. Consequently, upon approach, the interfacial impedance measured with the sensor increases and the AC current amplitude drops. We note that in first order approximation a similar response is expected when a biological cell adheres to the sensor surface.

The results are crucial for our goal as they permit the quantitative assessment of the sensitivity of the impedance sensor. For the case of a high sensitivity, small changes in the impedance *Z**el* cause large variation in AC current amplitude. Therefore, we define the sensitivity as *s* = ∂*I**AC*/∂*Z**el*. In our experiment, ∂*Z**el* is directly related to the microparticle displacement ∂*Z**el* = *p**∂*d*. The proportionality constant *p* is independent on the sensor configuration (OECT vs microelectrode) and we obtain its numerical value by fitting the microelectrode impedance spectra (see Supp. Inf S2). Accordingly, the sensitivity is given by the slope of the approach curves shown in Figure 1e. We obtain numerical values for this particular case (WxL = 100x100 µm) of *s**OECT* = (0.059±0.002) nA/Ω and *s**µE* = (0.023±0.006) nA/Ω. The values show a greater sensitivity in the OECT device with respect to the microelectrode, due to the contribution of OECT channel current to the AC response.

Quantitative model for PEDOT:PSS-based impedance sensors: We developed an analytical model to express the impedance sensitivity *s* as a function of the sensor operation conditions, material properties and geometry. Objective is a quantitative understanding of the factors that increase sensitivity in OECT configuration with respect to PEDOT:PSS microelectrodes. Many studies decouple charge transport in OECTs in an electronic and an ionic circuit.14 A schematic of this representation is reported in Figure 2a, where the components of the electronic and the ionic circuit are indicated in blue and orange, respectively. Electronic charge carriers (holes) are driven by the drain voltage *V**D,DC* and carry the channel current in an OECT, while ionic charge carriers are driven by the gate voltage *V**G* *= V**G,DC* *+ V**G*,AC and modulate the concentration of holes and, consequently, the electronic conductivity of the transistor channel. The limited conductivity of the electrolyte as well as the presence of dielectric objects close to the sensor surface generate an impedance *Z**el* which causes a potential drop in the electrolyte, and the voltage at the electrolyte/channel interface *V**G** can be considered as the effective gate voltage that acts on the channel and determines the drain current.26 For the impedance sensing we are interested in the AC response of the transistor and we express the AC current flowing in the OECT channel as \({I}_{ch,AC }= {g}_{m,AC}*{V}_{G*,AC}\). Following Bernards model,32 \({g}_{m,AC}\) can be expressed as \({g}_{m,AC}^{lin }= -\frac{W}{L}\mu {c}_{v}t{V}_{D,DC}\) and \({g}_{m,AC}^{sat }= -\frac{W}{L}\mu {c}_{v}t{(V}_{G,DC}-{V}_{t})\)in linear or saturation conditions. In these expressions, *W*, *L* and *t* indicate the width, length and thickness of the sensor channel, *µ**p* the holes mobility, *c**v* the volumetric capacitance of PEDOT:PSS and *V**t* the OECT threshold voltage.

To derive the overall AC current, it is important to note that in AC transport conditions the source (and drain) current signals are composed of two contributions:

$${I}_{S,AC }= {I}_{ch,AC } + {f}_{OECT}\bullet {I}_{G,AC } \left(1\right)$$

The first (*I**ch,AC*) originates from the channel current, whereas the second (*I**G,AC*) is due to the gate current and regards the capacitive current that has increasing importance at higher frequencies. Its value is given by *I**G,AC* *= V**G,AC**/Z**G* in which *Z**G**=Z**el**+Z**ch* is the overall impedance of the sensor given by the series combination of the electrolyte impedance *Z**el* and the impedance related to the PEDOT:PSS channel capacitance *Z**ch**=1/(iω C**ch**)*. The channel capacitance can further be related to the geometry and the volumetric capacitance of the PEDOT:PSS layer: *C**ch* *= c**v***W*****L*****t*. Possible contributions due to parasitic capacitances are neglected for simplicity. The factor *f**OECT* in eqn. 1 determines how the gate current is distributed between the source and the drain terminal and is typically assumed to be equal to 0.5.33 Several studies demonstrate that the *f**OECT* factor is slightly dependent on *V**D*,*DC* and *V**G,DC* as well as on channel geometry.34 For this reason, *f**OECT* was not assumed as constant in this experiment, but its value was set for each sensor in order to best fit the experimental data with the model.

The figure of merit of the OECT as impedance sensor (the sensitivity *s**OECT* ) indicates its capability to transduce a variation of *Z**el* in a current output. This can be calculated from the model by differentiating eq. (1):

$${s}_{OECT }= \left|\frac{\partial ({I}_{ch,AC}+{f}_{OECT}{I}_{G,AC})}{\partial {Z}_{el}}\right|=|{s}_{ch}+{f}_{OECT}\bullet {s}_{\mu E}| \left(2\right)$$

After inserting the expressions for the two AC current contributions and differentiation we obtain for the channel sensitivity:

$${s}_{ch}=\frac{{g}_{m,AC}}{{Z}_{G}}\left(1-\frac{{Z}_{el}}{{Z}_{G}}\right){V}_{G,AC}$$

3

and the sensitivity of the microelectrode is:

$${s}_{\mu E}= \frac{{V}_{G,AC}}{{Z}_{G}^{2}} \left(4\right)$$

The suitability of this simple approach to model the AC response of an OECT is demonstrated in Figure 2b and c. Figure 2b compares the frequency response of an OECT and of a microelectrode with the model predictions. The PEDOT:PSS channel width and length are *W* = 100 µm and *L* = 100 µm, respectively. The channel capacitance and the electrolyte impedance *Z**el* were extracted for each device geometry by fitting the microelectrode impedance spectrum. The average volumetric capacitance of PEDOT:PSS resulted to be *c**v* = (30.0 ± 1.3) F/cm3, obtaining a result consistent with literature findings.19 The OECT device shows a significantly higher current in the low frequency domain. Here the electronic channel current *I**ch* prevails, and the transistor demonstrates clear amplifying properties. Then, above a cutoff frequency *f**c* = 645 Hz, the transistor response is limited by the slow ionic transport between the channel and the electrolyte.35 At the same time the microelectrode’s response increases with frequency until a current limitation is reached due to the electrolyte impedance. As a consequence, in the high frequency limit both impedance sensor configurations yield the same current response. Importantly, the cutoff frequency that determines the OECT amplification is determined by the channel geometry as demonstrated in Figure 2c. The plot of the current amplitude versus frequency for OECTs with different channel sizes clearly shows that with increasing channel area and length a strong reduction in *f**c* is observed.

Finally, we systematically study the OECTs sensitivity towards electrolyte impedance changes with the microsphere experiment introduced above. Figure 2d shows the measured values for *s**OECT* obtained for three different channel geometries at different AC frequencies. Eq. 2 is in excellent agreement with the frequency dependence of the measured data. In the low-frequency range the sensitivity shows a linear increase with frequency until it reaches a sensitivity maximum *s**OECT**max*. Beyond the maximum, a smaller decrease in sensitivity is observed until it settles to a constant value for high frequencies. It is important to highlight that the position of *s**OECT**max* corresponds to the device cutoff frequency *f**c* (see Supp. Inf. S3 for the full mathematical treatment), and hence is a geometry-dependent parameter.

In Figure 2e we compare the sensitivity of a microelectrode and an OECT with the same dimensions (WxL = 200x50 µm). The transistor amplification, which is significant at low frequencies, has a relevant impact on the sensitivity. However, at high frequencies the response of both devices is limited by the electrolyte resistance and no significant differences are present. Such an observation is reflected by a frequency dependent OECT gain, which can be directly calculated with our model from eq. 2 and 4:

$${gain }_{OECT}= 20\bullet {{log}}_{10}\left(\frac{{s}_{OECT}}{{s}_{microel}}\right) \left(5\right)$$

The OECT gain is highest in the low-frequency regime, but is still significant in the 0.1-10 kHz range, where the impedance of the cell layers is typically measured.36 This justifies the use of a transistor structure for high precision bioelectronic impedance sensing experiments.5 Figure 2f demonstrates that the OECT gain is a geometry-dependent parameter. The smallest device (WxL = 50x50 µm) shows the highest gain, while a rectangular channel geometry is preferable for OECTs with the same area, since the gain is proportional to W/L ratio.

Single cell impedance sensor experiment: We demonstrated the value of the mathematical model here proposed for the optimization of a PEDOT:PSS-based single cell impedance sensor by monitoring single cell adhesion and detachment in an in-vitro experiment, simultaneously measuring the impedance changes with both an OECT and a microelectrode. According to the model prediction and the AFM experiment, we patterned the device channels with a 200x50 µm rectangular geometry, which provides the best performances in terms of sensitivity. The T98G cell line cultured in Minimum Essential Medium was diluted to have a final density of 1 x 103 cells/cm3 and poured on the surface of the impedance sensors (see the Methods section for full details). After seeding, the cells reached the underlying substrate by gravity. We microfabricated a linear array of 10 PEDOT:PSS channels (see Supp. Inf. S4) to largely increase the probability of a single cell settling onto a sensor. An optical image of the final experimental configuration is reported in Figure 3a, showing a single T98G cell positioned at the center of the PEDOT:PSS channel. The encapsulation of the metallic electrodes with negative photoresist insulates the device from all the remaining cells which are not lying in the PEDOT:PSS active layer. We acquired the current spectra of both the OECT and the microelectrode at consecutive time intervals to make a real-time detection of the cell adhesion process. To stress the full consistency of the measurements acquired with the OECT and the microelectrode, we plot in Figure 3b the current amplitudes measured at 625 Hz as a function of time. The sensing frequency was selected in correspondence to the OECT cutoff (measured at time *t*=0), where the model indicates the maximum sensitivity. The signals acquired at the beginning of the experiment are stable around a maximum value. Afterwards, at time *t*=20 min the current start to decrease, indicating the beginning of the cell adhesion process. This produces a rapidly varying response until *t*=60 min, when the decrease becomes slower, and the current stabilizes around a minimum value. At *t*=200 min, we used a cell dissociation agent (trypsin) to completely remove the cell from the sample surface, and devices recovered their original current amplitude.

We report in Figure 3c the full current spectra acquired before and after the treatment with trypsin *(t*=180 min and *t*=240 min, respectively). The cell adhesion produced a large shift of the OECT low-pass cutoff towards smaller frequency. In parallel, the current spectrum of a control device placed in the same reservoir, but with no cell seeded on the PEDOT:PSS layer, remained unaltered (see Supp. Inf. S5). After trypsinization, the initial cutoff frequency is fully recovered. These combined observations clearly demonstrate that the cutoff shift is only caused by the single cell adhesion on the PEDOT:PSS layer. The same considerations can be extended to the PEDOT:PSS microelectrode. Here, the cell adhesion process is revealed by a decrease in the gate current amplitude, which reaches its minimum at *t*=180 min, coherently with the OECT measurements. After the cell detachment (*t=*240 min), the current increases to its original values.

To provide a direct comparison between the sensing performances, we averaged the current amplitudes acquired when the cell is detached *(t*<30 min and *t*=240 min) and attached (120*<t*<180 min*)*, and we subtracted the resulting values to calculate the experimental sensitivity for both devices. Repeating this analysis in the whole frequency spectrum, we obtained the curves reported in Figure 3d, that reflect and assess the results of the quantitative AFM experiments (Fig. 2e). The transistor amplification has a significative impact on the device sensitivity in the frequency range between 102 and 104 Hz, with a peak at 625 Hz, corresponding to the OECT cutoff. On the other hand, when the modulation frequency is high, the OECT transconductance becomes negligible, and the transistor structure does not offer substantial advantages with respect to a microelectrode. The OECT gain (Figure 3e) was calculated by applying Eq. 5 and reaches a value of (20.2±0.9) dB at the highest sensitivity point (625 Hz).