Characterization and Model Validation ofTriboelectric Nanogenerators using Verilog-A
Ahmed Zaky1, Mohamed Shehata2, Yehea Ismail3, and Hassan Mostafa2,3
1 Nanotechnology Engineering Department, University of Science and Technology at Zewail City, Sheikh Zayed 12588, Egypt.2 Electronics and Communication Engineering Department, Cairo University, Giza 12613, Egypt.
3 Center for Nano-electronics and Devices, American University in Cairo & Zewail City for Science and Technology, Cairo, Egypt
Abstract—Triboelectric nanogenerators (TENGs) are consid-ered a very promising technique for harvesting mechanicalenergy due to its ease of fabrication, relatively cheap materials,large output power and high conversion efficiency comparedto other techniques such as those relying on piezoelectric andelectromagnetic effects. However, no study has yet been reportedto present circuit simulation models for this type of devices. Inthis paper, a Verlilog-A model is established for TENGs as acircuit element to describe the TENGs behavior and explore itsability to be integrated into different applications. These modelsare validated by comparing its results to those obtained in theliterature both analytically and numerically. Simulation resultsshow an excellent agreement with prior work, which was amotivation for further investigation for the performance of thosevarious modes. A unified parameter set is used to the four TENGfundamental modes such that a fair comparison is guaranteedbetween them in terms of both intrinsic characteristics and underdifferent loading conditions.
I. INTRODUCTION
In the past few years, electrical energy harvesting fromthe ambient environment has attracted much of the researchinterests due to the increasing need for energy resources thatsuits the rapid development of power economic electronicdevices in numerous self-powered applications such as theinternet of things (IoT), implantable biomedical devices andwearable electronics. A novel mechanical energy harvestingtechnology, called TENGs, has been introduced showing standout properties which combines both contact-electrification andelectrostatic induction effects. These two phenomena havebeen utilized to invent the first triboelectric nanogenerator(TENG) in 2012 [1].
Since it has been invented, TENGs have been extensivelystudied from different perspectives. For instance, assessmentof environmental life cycle of TENGs has been demonstratedfor different TENG modules [2]. In addition to this, numerousfundamental electronic components and devices have beendemonstrated, and different TENG designs have been devel-oped to suit mobile and wearable applications [3]. Further-more, TENG driven optoelectronic devices [4],[5] and logicgates [6] such as OR, AND, NAND and NOR operations havealso been developed. The performance of the aforementioneddevices and systems has been demonstrated experimentally.Moreover, theoretical analysis and numerical simulations [7]
have been performed to characterize the terminal behavior ofTENGs.
The development of the proposed simulation models ismotivated by the increasing interests in using TENGs to em-power electronic systems with arbitrarily complicated loads.This paper presents a Verilog-A simulation models for fourfundamental TENG types as time varying circuit elements.First, the operation mechanism of each mode is discussed,and its associated mathematical model is briefly overviewed.The accuracy of these simulation models is first verified bycomparing their performance with the results obtained in theliterature both analytically and numerically. Furthermore, theterminal behavior of the developed models is investigated andcompared using a unified parameter set inspired from priorwork on TENG-based devices.
II. FUNDAMENTAL MODES OF TENGS
There are various TENG structures with each one havingits own mode of operation. In this section, four typicalTENG structures are reviewed. The general theory behindthe operation of TENGs relies on both contact electrificationand electrostatic induction. The contact electrification inducesthe static polarized charges on the surface of the tribo-pair materials, while the electrostatic induction is responsiblefor converting the acquired mechanical energy into electricalenergy.
A. Typical Geometrical Structures and Operating modes
Fig. 1 illustrates four typical TENG structures, which con-sist of two different materials in the triboelectric series. Adistance x between the tribo-pairs is varied upon applyinga mechanical force on either of the tribo-pair such thatcontact electrification occurs at x = 0. As a result of contactelectrification, both tribo-materials will have opposite staticcharges on their surfaces. Upon separating the tribo-materials,charges with a magnitude of Q will be transferred from oneelectrode to another such that one electrode will have a +Qcharge and the other will have -Q charge.
Therefore, the potential difference between the two elec-trodes can be represented by a superposition of two differentpotential values. The first is the potential difference due tothe polarized triboelectric charges denoted as Voc(x), and the
Fig. 1. Geometrical structures of the (a): Attached electrode TENG in contactmode (AE-CM), (b): Attached electrode TENG in sliding mode (AE-SM), (c):Single electrode TENG in contact mode (SE-CM) and (d): free standing layerTENG on contact mode (FL-CM).
second is the potential difference originated from the alreadytransferred charges Q between the two electrodes. If it isassumed that no triboelectric charges, the structure can beconsidered as a typical capacitor with the voltage across itgiven by Q/C(x), where C(x) is the capacitance between theelectrodes. Therefore, the total potential difference betweenthe two electrodes is given by:
V = − |Q| /C(x) + Voc(x) (1)
Equation (1), known as (V-Q-x) relation, is the fundamentalgoverning equation of any TENG structure. To fully char-acterize a particular TENG structure operating in a givenmode, both Voc(x) and C(x) need to be known explicitly andsubstituted directly in (1).
B. Equivalent Circuit Models
As clear from (1), with combining those two terms, thefirst lumped parameter equivalent circuit is found to be aserial connection of ideal voltage source with a capacitor asshown in Fig. 2. In what follows, the capacitance and theopen circuit voltage of each of the four considered TENGtypes are presented such that the (V-Q-x) model in (1) can besolved for each TENG type.
Based on electrodynamics, both Voc(x) and C(x) can bederived for each mode according to its geometry shown inFig.1 and motion scenario. According to [8], the (V-Q-x)relation for each mode is expressed as follows:
1) Attached electrode in contact mode (CM-TENG):
V = − Q
Sε0(d0 + x(t)) +
σx(t)
ε0(2)
2) Attached electrode in sliding mode (SM-TENG):
V = − d0ε0w(l − x(t))
Q+σx(t)d0
ε0(l − x(t))(3)
Fig. 2. Schematic representation of TENG equivalent circuit with an arbitraryload.
3) Single electrode TENG in contact mode (SE-TENG):
In what follows, (2)-(5) are substituted in (1) such thata complete circuit model is constructed using Verilog-A asdescribed in the following section.
III. VERILOG-A MODELING
As mentioned before, a TENG structure can be modeled bya lumped parameter equivalent circuit model as an ideal arbi-trarily time-varying voltage source Voc(x) serially connectedto a capacitor C(x). Considering the simplest case of a pureresistive load, the (V-Q-x) relationship can be expressed asfollows:
Rd
dtQ(x(t)) = V = − 1
C(x(t))×Q(x(t)) + VOC(x(t)) (6)
Where R is the equivalent resistance as seen at the TENGelectrodes. Clearly, the solution of this differential equationin (6) is quite complicated. Especially for more complexloads including active elements (e.g., transistors and diodes),it becomes so tedious to solve these equations analyticallyor using finite element packages such as COMSOL. So, aVerilog-A model is introduced to enable the integration ofTENGs with different applications and circuits using variouscircuit simulation tools (e.g., Cadence Virtuoso).
A. Model Validation
This section is devoted to present numerical results thatvalidate the proposed simulation models of each mode of thefour TENG operating modes considered in Section II. Eachmode is validated by comparing the simulation results withthose obtained in the literature.
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The voltage at the terminals of the AE-CM, AE-SM, FL-CM and SE-CM TENG types are calculated at 100 MΩ, 1 GΩ,1 TΩ and open circuit conditions, respectively, and plotted asshown in Fig. 3. These cases have been investigated in [7],[8]and [9], respectively. As clear from this figure, the resultsproduced by the Verilog-A proposed simulation model showexcellent agreement with those obtained both analyticallyand using COMSOL simulations on the device level. Thisconfirms the validity of the proposed model as a reliable built-in constructed module, which can be used in driving arbitrarilycomplicated loads. The reliability of the obtained results wasa motivation to investigate the performance of those variousmodes from a comprehensive viewpoint.
Fig. 3. Numerical simulation results that validate the TENGs terminal voltageat the (a): AE-CM TENG type loaded with 100 MΩ, (b): AE-SM TENG typeloaded with 1G Ω, (c): FL-CM TENG type loaded with 1 T Ω and (d): SE-CMTENG type with open circuit voltage.
B. Fundamental Modes Comparative Study
In order to hold a fair comparison between the terminalcharacteristics in terms of open circuit voltage, short circuitcurrent and inheritance capacitance of the four modes, aunified parameters set found in Table I is generalized tothem. Those parameters are inspired from a number of priorstudies on TENGs. Throughout all simulations, a linear motionis assumed such that x = vt with a uniform velocity ofv = 1ms−1 is assumed so that the variations of the simulationtime can be directly mapped to numerically equal variationsin the separation distance x.
TABLE IUNIFIED PARAMETERS UTILIZED IN THE COMPARATIVE STUDY BETWEEN
Thickness of the metal electrodes dm 1 µm 1 µm 1 µm 1 µm
Surface area S 0.01m2 0.01m2 0.01m2 0.01m2
Surface charge density σ 8 µC 8 µC 8 µC 8 µCMaximum separation distance xmax 0.02 m 0.09 m 0.02 m 0.02 m
Air gap distance g - - 0.001 m 0.01 m
Average velocity v 1ms−1 1ms−1 1ms−1 1ms−1
C. Simulation Results And Discussion
The impact of the gap distance x on the open circuit voltage,the short circuit current and the inherent TENG capacitanceis depicted in Fig. 4 (a), (b) and (c) respectively. Clearly, theopen circuit voltage shown in Fig. 4 (a) indicates a monotonicincrease while increasing the gap distance between the tribo-pair up to 1 cm for the four TENG types. The sensitivity ofthe output voltage to the variation in the gap distance is clearlyvery high for the AE-CM, FL-CM and SE-CM TENG types,especially for gap distances below 0.01 mm. For the AE-SMTENG, the open circuit voltage becomes more sensitive forgap distances higher than about 1 mm between the tribo-pairswith an open circuit voltage less than 4 V, (i.e., less than halfthat is achieved by the other three configurations beyond theirrespective dead regions).
Fig. 4 (b) indicates that the short circuit currents of theAE-CM and the SE-CM TENGs are relatively stable with thevariations in the gap distance up to about 1 µm and 1 mmfor the AE-CM and the SE-CM TENGs respectively. Beyondthese distances, the short circuit current of both TENG typesdecreases with further increase in the gap distance. For theAE-SM, the short circuit current is monotonically increasingwith increasing gap distance between the tribo-pair, while forthe FL-CM, the short circuit current is almost constant andseems insensitive to the variations in the gap distance up tothe maximum value considered.
Fig. 4 (c) illustrates the inheritance capacitive behavior forthe four TENG types. The capacitance of the AE-SM, FL-CMand the SE-CM TENGs is almost insensitive to the variationsin the gap distance. This observation enables constructingtime-invariant circuit models for these TENG types. Thesemodels can be easily simulated and theoretically analyzedusing the conventional theories and techniques of the lineartime invariant systems such as the Laplace transform, theFourier transform...etc. Essentially, the capacitance of the AE-CM TENG is constant with the variations in the gap distanceonly in the sub-micrometer range regime. At gap distancesbeyond about 1 µm, the capacitance decreases with increasingthe distance between the tribo-pair.
Fig. 5 (a)-(d) depicts the electrical power that can beextracted from the electrodynamics of the four TENG types,each loaded with different values of load resistance R. Itis observed that the AE-CM and the SE-CM TENG typesshow very similar behavior in the variations of their respectiveoutput powers with the shift distance between the tribo-pair. Interestingly, AE-SM and FL-CM TENGs also showvery similar behavior. The common behavior between AE-CM and SE-CM TENG types is that for each resistancevalue, there exist optimal distances at which the output powerattains a global maximum. Increasing the gap distance beyondthe value which leads to this maximum leads directly to aloss of the TENG output power. Moreover, this peak poweralways increases with increasing the load resistance of AE-CM TENG. For SE-CM TENG, increasing the load resistanceleads to a corresponding decrease in the optimal peak output
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Fig. 4. Characterization of the terminal behavior of the AE-CM TENG type, the AE-SM TENG type, the FL-CM TENG type and the SE-CM TENG typein terms of the (a): open circuit voltage, (b): short circuit current and (c): the inherent capacitance.
Fig. 5. The evolution of the output power with the shift distance for differentvalues of the load resistance R at the terminals of the (a): AE-CM TENG type,(b): AE-SM TENG type, (c): FL-CM TENG type and (d): SE-CM TENG type.
power. For AE-SM and FL-CM TENGs, the output electricalpower is monotonically increasing with increasing the shiftdistance between their tribo-pairs. This is true only if bothTENG types are loaded by more than 100 kΩ. The sensitivityof the output power of the AE-SM TENG to the variationsin the gap distance becomes apparent only beyond about 0.5mm, while for FL-CM, there is almost no observable powerbelow 0.5 µm. For both TENG types, the monotonic increasein the output electrical power levels off for a load resistanceof 100 kΩ.
IV. CONCLUSION
This paper presents, to the best of the authors’ knowl-edge, the first circuit simulation model for triboelectric nano-generators using Verilog-A. Four different TENG types areconsidered, and their terminal behavior is simulated andverified. The developed models enable the designers of self-
powered electronic systems having arbitrary input impedanceto investigate and optimize the performance of their designedsystems and assess the capabilities and limitations of thesesystems. Moreover, the developed TENG simulation modelscan be generalized and applied to different TENG typeshaving different structures and modes of operation other thoseconsidered in this paper.
ACKNOWLEDGMENT
The authors would like to thank the supporting and fundingagencies. This work was supported in part by Cairo University,in part by Zewail City of Science and Technology, in part byAUC, in part by the STDF, in part by Intel, in part by MentorGraphics, in part by ITIDA, in part by SRC, in part by ASRT,in part by NTRA and in part by MCIT.
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