Quantifying contact status and the air-breakdown model of charge-excitation triboelectric nanogenerators to maximize charge density

Surface charge density is the key factor for developing high performance triboelectric nanogenerators (TENG). The previously invented charge excitation TENG provides a most efficient way to achieve maximum charge output of a TENG device. Herein, criteria to quantitatively evaluate the contact efficiency and air breakdown model on charge excitation TENG are established to enhance and evaluate charge density. The theoretical results are further verified by systematic experiments. A high average charge density up to 2.38 mC m−2 is achieved using the 4 μm PEI film and homemade carbon/silicone gel electrode in ambient atmosphere with 5% relative humidity. This work also reveals the actual charge density (over 4.0 mC m−2) in a TENG electrode based on quantified surface micro-contact efficiency and provides a prospective technical approach to improve the charge density, which could push the output performance of TENG to a new horizon.

). b, The side views of the device #6. c, The photographs of different thickness arch structure which is fabricated by 3D printer. (The "h" means the thickness of the raised part.) Figure 6. The output charge density with different external capacity. a, The output charge density under different external capacitors without voltage stability, the working frequency of the CE-TENG is 3Hz. b, Dynamic charge density output of CE-TENG without using the zener diode (the maximum charge density can achieve 2.55 mC m -2 when the external capacitor is 110nF, the working frequency and the relative humidity are respectively 3Hz and 5%).

Supplementary Tables
Supplementary

Supplementary Note 1. Maximum charge output density limited by air breakdown in excitation TENG
With charge exciting to TENG electrodes and according to Paschen's Law, air breakdown effect would occur between top electrode (TE) and the surface of dielectric primarily when the voltage (Vgap) in between exceeds a critical value during separation process. Therefore, deriving from Vgap and Paschen's Law in atmosphere condition, the maximum charge output density (δmax) on parameters of dielectric layer can be obtained, which would have great significance in enhancing the output of charge excitation TENG (CE-TENG) from the intrinsic material aspect. During the contact-separation process: = (1) Where VTENG is the voltage of TENG, VC is the voltage of external capacitor. When TENG gets fully contacted, the capacitance is: Where S is the effective area of TENG and d is the thickness of dielectric. ε0 and εr represent the vacuum permittivity and relative permittivity for dielectric material respectively.
In the contact state, we assume that the charge in TENG and external capacitor is Q and QC respectively. Thus, the following equation should be satisfied: = (4) When the gap distance x>0, the capacitance of TENG under a random state can be expressed by: Meanwhile, at a random state, we assume the charge in TENG to be Q(x) and the charge in external capacitor would be + ( − ( )). Therefore, the following equation should be satisfied as well: According to Supplementary Equation 2-6, the charge and charge density in CE-TENG can be expressed by: Therefore, the voltage of air gap can be expressed by: According to Paschen's Law, the relationship of the breakdown voltage and the gap distance is: Where P is the pressure of the gas, A and B are the constants determined by the composition and the pressure of the gas. For air at normal atmospheric pressure of 101 kPa, A is 2.87 × 10 5 /( • ), and B is 12.6. In order to avoid air breakdown effect, the Vgap needs to remain smaller than Va-b at any x > 0 states. So the following relationship is needed: Maximum charge density is affected by external capacitor and dielectric thickness, Which is different from that in common TENG.
When C approaches infinity: the voltage of air gap can be expressed by: When C approaches infinity, the maximum charge density in TENG can be expressed by: , →∞ = ( 0 ( + ) (ln( + )) ) Obviously, when C approaches infinity, the maximum charge density of CE-TENG is equal to common TENG.

Supplementary Note 2. The effect of contact status on output with reducing the dielectric thickness
Here, we define the efficiency of contact status as the equation presented: Where Ccontact is the capacitance when device getting compressed, and Cfilm stands for the capacitance of dielectric film with deposited electrodes (Supplementary Figure 7). Considering the existence of air void under compressed state. The following equations can be obtained: Where S is the capacitor electrode area. and 0 is relative permittivity of dielectric and vacuum respectively. h represents the equivalent air gap created by air voids. d is the dielectric thickness. Therefore, the efficiency of contact status can be expressed by:

Supplementary Note 3. Estimating the actual charge density of CE-TENG
In the experiment, although the contact status become better when using soft gel electrode, the capacitance under compressed state still has big loss compared with deposited electrode. In this case, herein, we would like to expect or estimate the charge density that can be achieved while realizing the 100% contact efficiency on TENG devices. From the experimental test, we can obtain the capacitance of dielectric with deposited electrode (Cfilm) and each optimized devices (Ccontact). Thus, the contact efficiency of each devices can be derived: Here, we define the actual contact area for TENG devices as S'. ′ = 0 × ƞ (20) Where S0 is the area of the electrode. Therefore, the actual charge density can be estimated: Where, Q and is the tested output charge and output charge density. In Supplementary Table 3 and Figure 7, we list the estimated actual contact area and actual charge density of 6 devices with contact optimizations.