**4. Discussion**

Due to the appearance of non-overlapping semicircular curves in the Nyquist plots which have been shown in Figures 4 and 5, it can be directly estimated that the associated resistor (R) and capacitor (C) can be used for describing the physical structures of the biochips [20]. Based on this initial estimation and the experimental impedance data (Figure 8), the transferring of the equivalent circuits, based on the physical mechanism of the biochips (Figure 9a,c) to the ones based on the assumed associated resistor-capacitor RC pairs (Figure 9b,d), can be validated.

**Figure 8.** Impedance magnitude measured at test frequencies of 40 Hz, 400 Hz, and 4000 Hz on biochips (**a**) BS5 (Table S1) and (**b**) PS5 (Table S2) that depend on the number of bacteria. The experiments are carried out under normal illumination.

**Figure 9.** Equivalent circuit models of biochips without analyte bacteria (**a**) based on the physical structure of biochip and (**b**) based on the associated RC pairs. The parallel capacitor C2 and resistor R2 are transferred from Cdep and Rss. Equivalent circuit models of biochip with analyte (**c**) in Maxwell fashion and in (**d**) Voigt fashion. The Voigt fashion can be transferred into Maxwell fashion by using Equations (1)–(3).

For the proposed p-n junction-based Si biochip, the Schottky contacts are formed at the interfaces both between Au top electrode/semiconductor and between Pt bottom electrode/semiconductor. These two metal/semiconductor Schottky contacts can be represented by one pair of CPE and resistor in the electrical equivalent circuit [21]. As demonstrated in Figure 9a, the p-n junction in the biochip PS5 or BS5 can be described by depletion region capacitor Cdep and semiconductor resistor Rss, which can be further converted to the parallel C2 // R2 pair fashion (Figure 9b), where C2 = Cdep·(Q2⁄ (1+Q2)), R2 = Rss·(1+Q2) with the definition of Q = <sup>1</sup>/(<sup>ω</sup>·Cdep·Rss) [22]. Thus, the impedance spectra from solo biochips PS5 and BS5 as depicted in thick black curves in Figures 4 and 5 can be modeled by using equivalent circuits in Figure 9b.

After applying the analytes (DI water or bacteria), a two-phase electrode contact [23] can be developed by using the proposed biochips, where one phase is resulted from the electrodes of biochips and the other phase is related to the added analytes [24]. The Maxwell circuit in Figure 9c can be transferred into Voigt circuit as illustrated in Figure 9d by utilizing the following equations [25]:

$$\mathbf{C}\_{2,3} = 2\mathbf{C}\_{\mathbf{b}} \left( 1 \mp \frac{\frac{\mathbf{R} \mathbf{s} \mathbf{s}}{\mathbf{R} \mathbf{b}} - \frac{\mathbf{C} \mathbf{b}}{\mathbf{C} \mathbf{d} \mathbf{p} + 1}}{k^{1/2}} \right)^{-1} \,, \tag{1}$$

$$R\_{2,3} = \frac{Rb}{2} \left( 1 \pm \frac{\frac{Cb}{Cdep} - \frac{Rss}{Rb+1}}{k^{1/2}} \right) \tag{2}$$

$$\mathbf{k} = \left(\frac{\mathbf{C}b}{\mathbf{C}dcp} + \frac{\mathbf{R}s\mathbf{s}}{\mathbf{R}b} + 1\right)^2 - \frac{4\mathbf{C}b.\mathbf{R}s\mathbf{s}}{\mathbf{C}dcp.\mathbf{R}b}.\tag{3}$$

The validity of equivalent circuit for biochips after applying bacteria can be described by experimental impedance data as shown in Figure 8. Here, the impedance magnitude of the biochips PS5 and BS5 after adding additional 1–5 μL bacteria has been depended on cell concentration. The overall impedance magnitude at di fferent frequencies is decreasing with increasing bacteria concentration, which indicates the validity of parallel connection of RC pairs for the equivalent circuit of biochips with added bacteria. It means that the RC pair which is corresponding to the added bacteria should be in parallel with the p-n junction-based RC pair as shown in Figure 9d. Thus, it can be concluded that the additional semicircles after adding the bacteria as demonstrated in Figures 4b and 5b are caused by the liquid phase in the two-phase electrode structure.

Based on the development of two-phase electrode contact, the final equivalent circuit for the biochips with analytes can be achieved as shown in Figure 3b, where three RC pairs applied. The two-phase electrode structure o ffers the opportunity for detecting the adhesion of bacteria by analyzing the impedance changes recorded in the Nyquist plot with higher accuracy and e fficiency.
