Current Generation Mechanism in Self-assembled Electret-based Vibrational Energy Generators

been clarified. To clarify the operation mechanism of the SAE-VEG, in this study, the relationship between the surface potential of the SAE and the current generated by electrode vibration in the SAE-VEG is carefully examined. The surface potential is changed over a wide range from negative to positive by controlling the molecular orientation. In addition to establishing a model for the device operation, we demonstrated that the output power of the SAE-VEG can be easily enhanced simply by increasing the thickness of the SAE.


Introduction
Vibrational energy generators (VEGs) have been extensively studied as a next-generation independent power source because they can generate electrical power from vibration, which is widely available in both residual areas and natural environments. (1)(2)(3)(4) In particular, electretbased VEGs (E-VEGs) are interesting since they can be easily miniaturized by using fabrication processes for micro-electro-mechanical systems (MEMS). (5) E-VEGs have a capacitor structure in which the electret and air gap are sandwiched by vibrational and fixed electrodes, as shown in Fig. 1(a). Here, the electret is a dielectric material with quasi-permanent electrical charge or dipolar polarization, (6) and the E-VEGs are automatically charged by the electric field formed by the electret. The surface charges of the electret play an essential role in developing E-VEGs with high output power. Thus, various charging techniques for dielectric materials, such as corona charging, contact electrification, thermal charging, and electron-or ion-beam charging, have been proposed. (6) Furthermore, soft X-ray photoionization and ion implantation have also attracted attention because of their high compatibility with MEMS technology. (7)(8)(9)(10)(11) Among these techniques, corona charging is one of the most widely used charging methods, leading to the formation of the electric field [ Fig. 1(b)]; however, it also involves a factor that limits the productivity of E-VEGs, as is the case with other charging techniques.
To overcome this problem, we proposed the utilization of a self-assembled electret (SAE) for E-VEGs. (12) A notable advantage of SAEs is that they do not require any charging process, and Yamane et al. have recently developed an SAE-based MEMS VEG. (13) The SAE is composed of polar organic molecules used for organic light-emitting diodes (OLEDs) such as tris-(8hydroxyquinolinato)aluminum (Alq 3 ) and 1,3,5-tris(1-phenyl-1H-benzimidazol-2-yl)benzene (TPBi) [Figs. 1(d) and 1(e), respectively], where a molecular dipole spontaneously orders perpendicular to the substrate on average. (14)(15)(16) Thus, in the SAE, both positive and negative polarization charges exist on the film surface and reverse side as shown in Fig. 1(c). The key point is that the electric field is directed from the positive to negative polarization charges and will not be formed outside of the SAE. Therefore, in the SAE-VEG, the apparent driving force inducing charges on the vibrational electrode is unclear. The operation of conventional E-VEG devices has been discussed since Winder and Kaufman proposed the concept of the electrostatic generator (17) and Matthew experimentally demonstrated a practical rotating-type generator. (18) In 1978, Jefimenko and Walker developed an electrostatic current generator having a disk electret and theoretically characterized its operation, (19) and the model and structure were refined by Tada. (20,21) After that, Boland et al. realized a micromachined rotational electret power generator and derived an output power as an intuitively understandable expression, (22) and later, Bartsch et al. extended the model to take parasitic capacitances into account. (23) Although the analytical model of E-VEGs has been gradually improved, the fundamental difference in the generated current (J g ) between the two types of electrets, namely, the unipolar type [ Fig. 1(b)] and dipolar type [ Fig. 1(c)], has not been understood in depth. Recently, Yang et al. have suggested that the electrical field distribution of an E-VEG with a dipolar electret is numerically identical to that of an E-VEG with a unipolar electret. (24) However, the experimental confirmation was not sufficient; they did not evaluate the relationship between the dipolar electret's surface potential (V sp ) and J g in the device. In general, V sp of a dipolar electret should increase linearly with the film thickness if constant polarization charges exist on the top and bottom surfaces of the electret. Thus, to clarify the operation mechanism of the dipolar electret-based VEG, it is essential to precisely control the thickness of the electret and measure J g at each V sp .
An SAE is classified as a dipolar electret and has the characteristic that V sp linearly increases with the film thickness. (14) This is useful for evaluating the V sp dependence of J g , resulting in an understanding of the operation mechanism of not only SAE-VEGs but also conventional dipolar electret-based VEGs. In this study, the relationship between V sp of the SAE and the root-meansquare value of J g (J gr ) in the SAE-VEG was carefully examined by constructing an experimental system that can evaluate them both under the same conditions [ Fig. 1(f)]. V sp was precisely controlled by changing the film thickness. We experimentally demonstrated that J gr in the SAE-VEG linearly increases with V sp of the SAE, and developed a simple model for explaining the J gr ∝ V sp relationship. This result suggests that the output current of an SAE-VEG could be easily enhanced simply by increasing the thickness of the SAE.

Materials and Methods
TPBi (sublimed, purity > 99.5%) was purchased from Luminescence Technology Corp. and Alq 3 (device grade) was supplied by Nippon Steel & Sumikin Chemical Co., Ltd. Both were vacuum-deposited with a base pressure of approximately 4 × 10 −4 Pa. The deposition rate was set to 0.2 Å/s. V sp was measured using the Kelvin probe (UHVKP020, KP Technology) in the vacuum chamber, which was directly connected to the evaporation chamber. A current/voltage amplifier (SR570, SRS) and an oscilloscope (TDS2001C, Tektronix) were used to measure J g as shown in Fig. 1(f). In SAE film, V sp disappears on light irradiation during or after film deposition. (16) This occurs because photo-generated electrons and holes compensate for polarization charges. (12) To avoid this depolarization, the film preparation and measurements were performed under dark and vacuum conditions.

Model
Figure 2(a) shows an energy diagram of the SAE-VEG in the case that the vibrational and fixed electrodes are electrically connected. Here, E vac and E f indicate the vacuum and Fermi levels, respectively. Φ fix and Φ vib denote the work functions of the fixed and vibrational electrodes, respectively, and ∆Φ is work function difference (∆Φ = Φ fix − Φ vib ). e and ε 0 are the elementary charge and the permittivity of the vacuum, and l sae and l gap indicate the film thickness of the SAE and the distance between the SAE surface and the vibrational electrode, respectively. V sp is the surface potential of the film with respect to the fixed electrode. V gap is the potential at the surface of the vibrational electrode with respect to the SAE surface (eV gap = ∆Φ − eV sp ). In the case of the potential distribution shown in Fig. 2(a), εV gap is negative because ∆Φ < eV sp . By applying Gauss's law at the surface of the vibrational electrode, the induced charge density (σ 0 ) is given by σ 0 = ε 0 (V gap /l gap ). Thus, we obtain l gap varies with time (t) during electrode vibration, and J g under the short-circuit condition is expressed by the time differential of σ 0 . Assuming that V sp is constant during electrode vibration, J g can be derived as Equation (2) suggests that J g is (inversely) proportional to V sp . Note here that J g of Eq.
(2) can be easily measured using the experimental setup shown in Fig. 1(f).
The total amount of charge of the device (Q 0 ) equals σ 0 S, where S is the active area of the device. Using Eq. (1), we obtain Q 0 = C gap (∆Φ/e − V sp ), where C gap is the capacitance of the air gap (C gap = ε 0 S/l gap ). Therefore an equivalent circuit of the SAE-VEG can be expressed using a simple capacitor circuit, as shown in Fig. 2(b), where R and I g indicate the load resistance and generated current (I g = J g S), respectively. The circuit dynamics during electrode vibration can be obtained using Kirchhoff's law as follows: Because I g = dQ 0 /dt, we obtain Equation (4) can be analytically solved as where t RC denotes the time variation of the time constant in the equivalent circuit. Equations (5) and (6) are helpful for estimating the optimized load resistance and maximum output power under impedance matching.

Surface potential and generated current measurements
To investigate the relationship between V sp and J g [Eq.
(2)], l sae dependences were measured in Alq 3 -and TPBi-based SAEs. Figure 3(a) shows the contact potential difference (V cpd ) as a function of l sae in Alq 3 , and the inset shows an enlarged view of the thin-film region (l sae ≤ 20 nm). Here, V cpd equals V sp − ΔΦ/e: V sp with respect to the fixed electrode can be obtained by subtracting V cpd at l sae > 0 nm from V cpd at l sae = 0 nm (−ΔΦ/e = −281.5 mV). The right vertical axis denotes V sp obtained in this manner. In the case of l sae ≥ 20 nm, V sp linearly increased with increasing l sae and reached 1.8 V at 200 nm without using a charging process. This giant surface potential (GSP) originates from the spontaneous orientation of the permanent dipole of Alq 3 , as discussed in depth in Ref. 14. Moreover, the constant electric field suggests that positive and negative polarization charges exist on the film surface and reverse sides, respectively. The surface charge density (σ s ) was estimated to be 0.3 mC/m 2 using a relative permittivity of 3.2 (15) and a slope of 10.8 mV/nm [see the solid line in Fig. 3(a)]. In a previous report, σ s of Alq 3 was estimated to be 1.1 mC/m 2 , (15) which is comparable to that of a polymer-based electret after corona charging (25) and approximately 3.7 times larger than that estimated in this study. This difference originates from the difference in the fabrication process, especially the deposition rate, which will be reported elsewhere. (26) It is important to note that, at l sae ≤ 20 nm, V sp linearly decreases with a slope of 13.7 mV/nm [see the solid line in the inset of Fig. 3(a)]. This result indicates that the polarity of the surface  Fig. 3(a) shows an enlarged view of the thin-film region (0 nm ≤ lsae ≤ 20 nm). charge is negative in this thickness range, implying the opposite orientation of Alq 3 , in complete contrast from previous reports. (14)(15)(16) We also found that the polarity is related to the amount of deposition during the KP measurements. Clarification of the polarity change will enable understanding of the mechanism of spontaneous orientation; however, this is beyond the scope of this article and will be discussed in a separate paper. The notable points for clarifying the relationship between V sp and J g are that (i) at l sae ≤ 20 nm, V sp is negative and decreases linearly with increasing l sae and (ii) V sp is positive and increases linearly at l sae ≥ 20 nm.
In addition to the Alq 3 -based samples, V sp and J g are enhanced with increasing l sae in the TPBi-based sample as shown in Figs. 4(a) and 4(b), respectively. This result clearly suggests that J g can be controlled by changing l sae in SAE-based VEGs at l sae ≥ 20 nm. V sp of TPBi at l sae < 20 nm is, on the contrary, almost constant around 0.1 V [inset in Fig. 4(a)]. It may be that V sp depends on the deposition conditions, similarly to V sp of Alq 3 [ Fig. 3(a)], although the possibility of some effect of the substrate on V sp cannot be ignored at this stage.

Relationship between surface potential and generated current
As shown in Figs. 3(c) and 4(b), J g increases with l sae except in the thin-film region, suggesting that J g depends on V sp . To examine the relationship, J gr in the Alq 3 -VEG is estimated from Fig. 3(c) and compared with V sp . Figure 5(a) shows the V sp dependence of J gr , indicating that J gr is almost proportional to V sp of Alq 3 . Furthermore, this linear relationship was also observed in a TPBi-based VEG as shown in Fig. 5(b). These results indicate that Eq. (2) is valid and that the J gr ∝ V sp relationship is maintained. In other words, J g of the SAE-VEG can be easily enhanced simply by increasing the film thickness. This guideline is simple but essential to realize an SAE-based VEG with high output power.
Finally, a close look at Figs. 3(b) and 3(c) reveals that the polarity of J g changes: at l sae ≥ 100 nm, J g becomes negative and positive when the electrode moves away from and approaches the Alq 3 surface, respectively. On the other hand, J g at l sae = 20 nm shows positive and negative values as the electrode leaves and approaches, respectively. This change can be explained by the polarity change of the ∆Φ/ε − V sp term in Eq. (2), which changes from positive to negative when V sp is larger than ∆Φ/ε. This result also supports the conclusion that Eq. (2) is valid for the SAE-VEG. Thus, we conclude that, in the SAE-VEG, charges on the vibrational electrode are induced by V sp of the SAE in accordance with Eq. (1).

Conclusions
To clarify the current generation mechanism in an SAE-VEG during electrode vibration, the relationship between V sp of the SAE and J gr in the SAE-VEG was precisely examined by developing a measurement system that can evaluate both of them under the same conditions. J gr in the SAE-VEG increased proportionally to V sp of the SAE according to the proposed model, suggesting that the electric field of the SAE induces the charges on the vibrational electrode. These results demonstrate that the output current of SAE-VEGs is easily enhanced by increasing the film thickness of the SAE.
To understand the device physics of SAE-VEGs in more detail, it is important to study whether the waveform of J g [Eq.
(2)] corresponds to the experimental results of Figs. 3(b), 3(c), and 4(b). Then, the equivalent circuit in Fig. 2(b) and Eqs. (5) and (6) can be used to estimate the maximum output power and optimized resistance of the device. Related research is ongoing. We believe that a high-output-power and easy-to-fabricate E-VEG can be realized by constructing an appropriate device structure for the SAE.
calculations. This research was supported by the Japan Science and Technology Agency (JST), PRESTO (Grant Number JPMJPR17R6), and KAKENHI (Grants Nos. 20H02810 and 21K05208).