Variable Capacitor Energy Harvesting Based on Polymer Dielectric and Composite Electrode

FEM Maxwell Simulation of a Capacitor with Composite Electrode

The investigated mechanically flexible elastomer electrode is a composite material which consists of a base polymer and electrically conducting fillers like carbon black, carbon nano-tubes or silver flakes. Hence there will be randomly distributed contacts between the electrically conducting phase and the dielectric and not a homogeneous interface. For the conducting filler particles which not contact the dielectric interface, the electrical field will penetrate through both, the low-k dielectric of the elastomer electrode and the high-k dielectric on the substrate. In addition air may be entrapped at the interface which further reduces the active capacitor area as demonstrated in Figure 2(A). To study the influence of the contact morphology on the specific capacity a 2D electrostatic FEM simulation (AnsysEM Maxwell) was performed were the filler particles are represented by electrically conducting fins as shown in Figure 2(A). An offset y was assumed that represent the case that the filler particles do not contact the interface and are covered with the matrix polymer of the composite electrode. In a first stage the model convergence was tested. At least 12 passes were required to achieve ΔC<1 % for all parameter variants. The results shown in Figure 2(C) indicate that thin layers of dielectric over the conductor phase (fin offset) degrade the capacity greatly; even if there is no fin offset a large distance between the fibers (10 µm) reduces the resulting capacity significantly. Even a very large permittivity of the dielectric can’t compensate the shortcomings of the elastomer electrode. This result is plausible as the set-up can be understood as a serial connection of a high and a low capacitor. In conclusion, the conductive phase should be distributed on the surface of the elastomer as homogeneous as possible with a mean distance below ca. 1 µm.

Figure 2:

(A) Illustration of electrical field distribution, a) elastomer matrix polymer, b) interconnected conducting phase, c) high-k dielectric, d) bottom electrode, e) air entrapment, (B) FEM model, (C) simulated specific capacity as function of fin offset and relative permittivity of the dielectric (dielectric thickness t=20 µm, fin width d=0.1 µm, fin pitch x=10 µm).

Calculation of Losses with the Equivalent Circuit Model

The conductivity of the elastomer electrode may be several orders of magnitude lower than that of metal electrodes. The high-k dielectric have to be deposited with a low cost printing process that may be prone to pin holes and resulting leakage currents. Therefore in order to analyze the efficiency of the capacitive harvester, an equivalent circuit was evaluated which includes parasitic resistances that represent leakage current and conduction losses as illustrated in Figure 3(A). The schematic represents the ideal conditioning circuit implementing a rectangular charge voltage cycle as shown in Figure 3(B) (Galayko and Dudka 2015). The D2 Zener diode was used to establish a constant output voltage V_z. In a real harvesting situation D2 would not be a Zener diode but same as D1 which is conducting during phase 3 in order to charge the output capacitor which takes the place of R_L. We have used the circuit shown in Figure 3(A) to make clear that we evaluate the role of the parasitic elements under idealized conditions of fixed output voltage V_z. The assumed harvesting power is I_CVAR* V_Z during t_f2. C_var represents the ideal variable capacitor. R_s and R_p are the serial and parallel parasitic resistances of the harvester, which represent losses due to the resistivity of the elastomer electrode and the leakage current of the dielectric respectively. C_var, R_s and R_p all together in the dashed line compose the simplified model of the capacitive harvester. The analysis results of the losses will be used to guide the harvester design. In that way, the appropriate dielectric and electrode material will be selected or developed to fulfill the requirements for efficient energy harvesting.

Figure 3:

(A) The equivalent circuit of the investigated energy harvesting system, (B) The voltage and current waveforms of the harvester corresponding to the variation of capacitance, (C) Charge-voltage diagram showing the rectangular Q-V harvesting cycle.

Considering that the C_var can be stimulated with different form of forces, the capacitance of C_var will also vary accordingly in different waveforms. To simplify the analysis, a periodical capacitance variation as shown in Figure 3(C) has been used in this work to calculate the losses in R_s and R_p.

A complete energy harvesting cycle of the harvesting circuit can be divided into 4 intervals as depicted in Figure 3(C).

Interval 1: The harvester is pressed with a force and the capacitance is rising from C_min to C_max. The voltage drop over the harvester V_Cvar is slightly smaller than the input voltage V_in. There is a current flowing from V_in to charge up the harvester capacitor until V_Cvar reaches V_in. At this moment, the capacitor is charged to the maximum level of charges Q_max.

The declination of the rising slope of the capacitance depends on the rise time t_r and is defined to be,

Interval 2: When the capacitance is keeping being pressed, the V_Cvar equals V_in and there is no current flowing into or out of the harvester.

Interval 3: The harvester capacitance is falling from C_max to C_min. There are two subintervals of time t_f1 and t_f2 during the falling stage. In the time slot of t_f1, although the V_Cvar is increasing, the V_Cvar stays below the threshold voltage V_Z of the zener diode D₂. In this case, D₂ does not conduct yet and there is no charge transfer from C_var to the load resistance R_L. Therefore, the interval of t_f1 corresponds to a charge constrained energy conversion path. As soon as V_Cvar reaches V_Z, D₂ starts to conduct and the V_Cvar is clamped to be V_Z. That means the harvester enters the voltage constrained energy conversion stage in interval t_f2.

The declination of the falling slope is

The time interval of t_f1 can be calculated as following:

The voltage over the harvester and the current through the harvester during the time interval t_f1 and t_f2 has been deduced as below:

Interval 4: The harvester capacitor is completely released and the capacitance maintains at the minimum value C_min. The voltage V_Cvar drops back to V_in.

The power dissipations in R_s and R_p for a complete energy harvesting cycle can therefore be written as:

Based on the analytical analysis above, a design example in Table 1 has been studied and the parameter analysis results regarding to the losses in R_s and R_p have been plotted in Figure 4. Figure 4(A) and (C) show the losses in percentage regarding to the ideally harvested energy. A dashed line is inserted at 20 % as an indicator how parameters have to be adapted to assure that internal losses stay below 20 %. It can be concluded that the losses in R_p are reverse proportional to the stimulating frequency of the harvester and the losses in R_p are independent of the resistance value of R_s. When the stimulating frequency is too low and the R_p is smaller than 10 GΩ, the losses in R_p are so high that the harvester could not harvest any energy at all. That means the leakage current of the harvester is decisive, whether the energy could be harvested at the desired stimulating frequency or not. The losses in R_s only happen at the rising and falling time of the capacitance variation. In the example shown t_r=t_f=1/(2f) and therefore the losses in R_s in Figure 4 have been plotted versus frequency. The losses in R_s are only slightly affected by the R_p value but strongly proportional to the frequency, namely proportional to the rising and falling times. The plots for harvested energy in Figure 4(B) and (D) show that if the losses in R_s and R_p are too high, no energy could be harvested and that’s why the curves have been extended with dashed lines to below zero. Further, Figure 4(D) demonstrates that for the chosen parameters the power output is dominated by the leakage current (Rp) and independent for variant R_s values. This is because for higher losses in R_s the harvester could generate more energy, which is called here ideally harvested energy, but the additional generated energy is consumed inside the harvester through R_s, therefore the out coming practically harvested energy stays the same.

Table 1:

Parameters used for analysis of the losses in the capacitive harvester.

	Case 1		Case2
Input parameters	Rs=50 kΩ	Rp1=1 GΩ	Rp=10 GΩ	Rs1=5 kΩ
		Rp2=10 GΩ		Rs2=50 kΩ
		Rp3=100 GΩ		Rs3=500 kΩ
	Vin=100 V		Vin=100 V
	Vz=200 V		Vz=200 V

Figure 4:

Numerical results of electrical losses and harvested energy for case 1; R_s=50 kΩ; (A) losses in R_p and R_s in per cent of ideally harvested energy; (B) the practically harvested energy for different R_p; for case 2; R_p= 10 GΩ; (C) losses in R_p and R_s in per cent of ideally harvested energy, (D) the practically harvested energy for different R_s.

It is instructive to discuss the influence of the losses on the Q-V cycle. The R_p losses result in a constant loss of charges, but as long as D1 is conducting (Phases 1,2) those losses are compensated by additional charge flow from the input source V_in. Therefore, phase 3 starts with Q_max although the overall efficiency was reduced due to loss of charges during the charging process of the capacitor. On the other hand the R_p losses during phase 3 will actually reduce the charges of the Q-V cycle. A charge quantity lower than Q_max is transferred to V_z; the upper right corner of the QV cycle will be reduced to a value Q_max – Q_loss.

R_s losses are not visible in the Q-V cycle as V_in and V_z are constant per definition. At phase 1 the voltage over the variable capacitor is reduced by I*R_s losses but reach V_in when charging is complete. During phase 3 the R_s losses are compensated by a higher voltage on the variable capacitor which is necessary to generate V_z on the output. The R_s losses in phase 3 would only be critical if R_p is relevant as leakage increases with rising voltage or if the break down voltage of the variable capacitor is reached. During phase1 high R_s values may lead to a high time constant and insufficient charging in case of short rise time t_r.

Sample Preparation and Measurement Set-up

The elastomer-electrode was prepared with help of an electrically conductive silicone rubber “ELASTOSIL® LR 3162 A/B” (Wacker Chemie AG), a two-component compound with short curing time. The electrical conductivity is 11 Ωcm and the viscosity is 6,600 Pas according to the data sheet. Doctor blade as well as screen printing was used to deposit the material on copper foil or flexible printed circuit board material. Curing was done for 3 h at 70 °C.

Three types of dielectric were tested: sputtered Al₂O₃ and Ta₂O₅ on silicon substrate, PET films and screen printed composite dielectrics.

1.4 µm thick dielectric BoPET foils (Biaxially-oriented polythelene terephthalate, DuPont Teijin Films, trade name “Mylar”, PET) were laminated onto metal substrates. The dielectric constant and break down voltage is 3.25 and 280 V/µm respectively.

The fabrication process is split into two stages: deposition and fusing with the substrate. Under particle free atmosphere in a flow box the PET-foil is unrolled onto the substrate, cut into optimal dimensions and smoothed with a felt blade to eliminate wrinkles. To melt the foil onto the substrate, it is heated on a hotplate at 260 °C for 10 s.

The screen printing of composite dielectric was done at EURECAT (www.matflexend.eu]) with a novel material developed at IMPERIAL College London (Leese et al. 2016). Strontium doped barium titanate (SBTO) nano fibers were functionalized to improve the wetting between the filler and matrix (epoxy or PVDF).

Dielectric and elastomer electrode foils were mounted in a mechanical cycling station that allowed to adjust the maximum force and cycle frequency. All measured samples had a size of 10 × 10 mm².

The capacity as function of the applied force was measured with help of Agilent 4284A RLC meter. The leakage current was measured at 100 V with Keithley 2450 source meter. A steady state value was achieved after ca. 3 min. For current/charge measurements according to Figure 3(A) the source meter was used as input voltage source (V_in=100 V) and for measurement of the input current. The output current was measured over R_L with help of the oscilloscope 3012(B). In a second configuration the Zener diode D₂ was replaced with a diode identical to D₁ and R_L was replaced by a 3.3 nF capacitor. The transferred charges were calculated based on the increase of the voltage at the output capacitor

Measurements

For initial characterization of the dielectrics metal contacts were sputtered on top of the dielectrics. The obtained capacity per area was in good agreement with the values calculated from thickness and dielectric constant (Table 2). The leakage current at 100 V was in all cases below 1 nA which corresponds to an R_p value of 100 GΩ according to Section “Calculation of Losses with the Equivalent Circuit Model”. Some of the sputtered and screen printed dielectric layers showed higher leakage currents due to defects and were excluded from the experiments. The electrical resistance of the elastomer electrode was measured by pressing it against a metal foil. Values between 3 and 5 kΩcm² at 30 N/cm² were obtained which saturated at a pressure higher than 80 N/cm² at values between 1 and 3 kΩcm². Thus both, R_s and R_p were in the required range for efficient energy harvesting according to the calculations in Section “Calculation of Losses with the Equivalent Circuit Model”.

Figure 5 shows the specific capacity (capacity per area) as function of mechanical pressure that was achieved with the elastomer top electrode in contact with all investigated dielectric samples. As demonstrated in Figure 5(C) the values are much lower than the corresponding capacitance with thin film metal electrode. The similarity to the behavior shown in Figure 2(C) is obvious – the higher the theoretical capacity the larger the discrepancy with the capacity obtained with elastomer electrode. Although the bulk conductivity of the elastomer is quite low, the mean distance of the electrical conducting phase at the interface may be too large. Surface roughness of both, dielectric and elastomer electrode plays also an important role. The mean roughness of thin film and PET dielectric was below 1 nm while the thick film dielectric showed a roughness of ca. 30 nm. This results in lower capacity in the low force region on the rough surface as can be seen in Figure 5(B). In another experiment elastomer electrodes were fabricated with a rough surface to reduce the sticking behavior between electrode and dielectric, but these samples showed further reduced maximum capacity (Figure 5(C), open symbols).

Figure 5:

Specific capacity of tested dielectrics in contact with elastomer electrode as function of mechanical pressure; (A): thin film dielectric, (B): thick film and polymer foil dielectric, (C) specific capacity obtained with elastomer electrode at 50 N/cm² as function of the regular capacity with metal electrode.

Precise current measurement turned out to be critical due to the limited time resolution of the equipment and the short current pulses especially during discharge of the variable capacitor. Thus, we did not use the measuring circuit according to Figure 3(A) but have replaced the Zener diode by a diode similar to D1 and measured the voltage increase at the 3.3 nF output capacitor which replaced R_L shown in Figure 3(A).

Figure 6(A) and (B) show the influence of pressing force and cycle time on the harvesting performance of elastomer electrode on PET dielectric. The observed faster voltage increase at shorter cycle time is a result of leakage currents (Figure 6(B)).

Figure 6:

Voltage rise at output capacitor during cycling of the variable capacitor; (A) variation of maximum pressing force (C_max=240 pF, 370 pF for 4.5 and 7.1 N/cm² respectively), (B) variation of cycle time (2 … 5 s in pressed state, 1 … 2 s release, C_max=770 pF), (C) voltage rise of three layer stacked variable capacitor according to Figure 7.

As the specific capacity is limited due to the used elastomer electrode, the foil technology was used to fabricate a stack three capacitor layers (Figure 7) to increase the power density. The voltage rise shown in Figure 6(C) was achieved with the resulting maximum capacity of ca. 1.5 nF. Printed SBTO dielectric was used for the stacked devices.

Figure 7:

Three layer stack harvester demonstrator, A=1 cm², (C_max=1.5 nF, C_min=180 pF); (A) design sketch and packaged device, (B) capacity as function of applied force.

The novel printed composite dielectric results in nearly the same capacitance as the PET foil bus show much better mechanical robustness due to the higher thickness. This is important for a device were the electrode will be pressed thousands to million times against the dielectric. On the other hand point defects were observed in several samples of the printed dielectrics which lead to leakage current and the deposition process must still be improved.

The demonstrator was fabricated based on flexible printed circuit technology and screen printing that will allow later low cost fabricate on. The design (Figure 7(A)) and process for a folded multi-layer harvester including the encapsulation was developed and several samples of harvester devices have been tested. Spacer structures between electrode and dielectric have been introduced to allow quick detachment and low C_min values after pressure release.

Figure 7(B) shows how capacity is changing as function of the applied mechanical force on the tree layer capacitor stack. The remaining capacity at zero force is ca. 200 pF, hence the maximum capacity is ca. 7.5 times higher than the minimum capacity; much more than values achieved with typical variable MEMS capacitors. This results in a large Q-V rectangle of the harvesting cycle (Figure 3(B)). At forces higher than 40 N the capacity increase becomes smaller and reaches saturation at ca. 50 N as can be seen from the rounded shape of the capacity curve.