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journal homepage: www.elsevier.com/locate/nanoenergy

Nano Energy (2014) 8, 150–156

http://dx.doi.org/12211-2855/& 2014 E

nCorresponding aEngineering, Georgi0245, United States

E-mail address: z

RAPID COMMUNICATION

Simulation method for optimizing theperformance of an integrated triboelectricnanogenerator energy harvesting system

Simiao Niua, Yu Sheng Zhoua, Sihong Wanga, Ying Liua,Long Lina, Yoshio Bandob, Zhong Lin Wanga,b,n

aSchool of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0245,United StatesbSatellite Research Facility, MANA, International Center for Materials Nanoarchitectonics,National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan

Received 13 May 2014; accepted 29 May 2014Available online 6 June 2014

KEYWORDSMechanical energyharvesting;Triboelectric nano-generators;Equivalent circuits;Simulation method;Integrated systems

0.1016/j.nanoen.2lsevier Ltd. All rig

uthor at: Schoola Institute of Tec.lwang@gatech.ed

AbstractDemonstrating integrated triboelectric nanogenerator energy harvesting systems that containtriboelectric nanogenerators, power management circuits, signal processing circuits, energystorage elements, and/or load circuits are core steps for practical applications of triboelectricnanogenerators. Through the design flow of such systems, theoretical simulation plays a criticalrole. In this manuscript, we provided a new theoretical simulation method for integratedtriboelectric nanogenerator systems through integrating the equivalent circuit model oftriboelectric nanogenerators into SPICE software. This new simulation method was validatedby comparing its results with analytical solutions in some specific triboelectric nanogeneratorsystems. Finally, we employed this new simulator to analyze the performance of an integratedtriboelectric nanogenerator system with a power management circuit. From the study of theinfluence of different circuit parameters, we outline the design strategy for such kind oftriboelectric nanogenerator systems.& 2014 Elsevier Ltd. All rights reserved.

014.05.018hts reserved.

of Materials Science andhnology, Atlanta, GA 30332-

u (Z.L. Wang).

Introduction

Scavenging ambient mechanical energy from the environ-ment has long been considered as a critical research topic[1–5]. Recently, triboelectric nanogenerators (TENGs) based

151TENG integrated system simulation

on contact electrification [6–8] and electrostatic inductionemerge as a promising technology of mechanical energyharvesting, especially for powering portable electronics [9–14]or working as self-powered sensors [15]. Similar to the devel-opment of CMOS integrated circuits and systems, the fully-integrated energy harvesting systems that contain TENGs,power management circuits, signal processing circuits, energystorage elements, and/or load circuits are essential for thepractical applications of the TENGs. Theoretical simulationplays a key role in understanding the working mechanism andanalyzing the output performance of the TENGs, which pavesthe way for future design and optimization of the entiresystem. In this regard, a few efforts have been made to carryout the numerical calculations and analytical studies on theoutput characteristics of the TENG unit with various workingmodes [16–19]. However, all the prior investigations merelyfocus on the behavior of TENG itself, or simply with linearresistive load circuits, while the even more complex analysiswith practical load circuits that contain arbitrary numbers oflinear and non-linear components could hardly be accomplishedby the currently-established simulation approaches. Therefore,a new simulation method of TENGs is highly desired to solve thechallenges in the calculations of practical energy harvestingsystems.

In this manuscript, the first equivalent circuit model ofTENGs was derived to deepen the understanding of their corephysics and assist their simulation process. Then the firstsimulator of an entire TENG system was built by integratingthe TENG equivalent circuit model into circuit design software(commonly called SPICE software). The effectiveness of thissimulator was validated by comparing its results with analyticalsolutions in some specific triboelectric nanogenerator systems.Then to show the potential application of this powerful newmethod, we studied the performance of a TENG with a powermanagement system and outlined the strategy for the design ofsuch system for optimum performance. The new TENG simu-lator demonstrated in this paper is not only a standard tool fortheoretically analyzing the output characteristics of TENGs inany complex systems, but also provides a novel approach foroptimum design of the TENG-based energy harvesting systems.This research will lead to fast development of the TENG'sperformance, and accelerate the process for its practicalapplications and commercialization.

Figure 1 Equivalent circuit model of a triboelectricnanogenerator.

Results and discussion

As a common sense, the equivalent circuit model is one ofthe most important theoretical understandings of an elec-tronic device. Similar to the Ebers–Moll model (EM model)[20] of bipolar transistors that is derived from theirgoverning equation, the equivalent circuit model of TENGscan also be derived from their governing equation (V–Q–xrelationship), as shown below [16,17]

V ¼ � 1CTENG

QþVOC ð1Þ

From Eq. (1), there are two terms at the right side, whichcan be represented by two circuit elements in the equiva-lent circuit model. The first one is a capacitance term,which is originated from the capacitance between the twoelectrodes and can be represented by a capacitor (CTENG).

The other is an open-circuit voltage term, which is origi-nated from the separation of the polarized tribo-chargesand can be represented by an ideal voltage source (VOC). Incombination of these two, the whole equivalent circuitmodel can be represented by a serial connection of an idealvoltage source and a capacitor, as shown in Figure 1.

The above equivalent circuit model is very helpful tounderstand the core physics of TENGs. For example, theoptimum resistance [16] and three-working-region behavior[16] can be easily understood from this equivalent circuitmodel, which is inherently because of the impedance matchbetween CTENG and the load resistance. The inherentcapacitance of TENG will show impedance to the AC voltagesource VOC. Any structural parameters that will increase thisinherent capacitance will lower this impedance and thuslower the matched resistance. Increasing the velocity ofmotion is equivalent of increasing the frequency of the ACvoltage source VOC so the matched resistance will also belowered. Since the impedance of CTENG is independent ofthe tribo-charge density, the matched load resistance is alsonot affected by the tribo-charge density.

This equivalent circuit model extraction is also the firststep of building this new TENG simulator. After the equivalentcircuit model is obtained, the values of the ideal voltagesource and the capacitance in the above equivalent circuitmodel need to be specified to complete this integration tothe SPICE software. From the basic electrodynamics theory,both VOC and CTENG are only functions of the moving distance(x) and structural parameters while independent of motionparameters, such as velocity and acceleration [16–19]. Twomethods are currently developed to specify the VOC–x andCTENG–x relationships. Analytical derivation is a preferredmethod but it only works for certain geometry features suchas parallel plate contact-mode or sliding-mode TENGs. Amore general method which works for all TENGs is numericalcalculation based on finite element method (FEM). In thismethod, the value of VOC and CTENG is first obtained at certainvalues of x. Then, from continuous fraction interpolation, anumerical VOC–x and CTENG–x relationship can be generated inthe entire x region.

Now the TENG can be embedded into the SPICE software asa basic element consisting of a voltage source in serialconnection with a capacitor. To simulate the whole systemin SPICE, several other steps are needed, including insertingother circuit elements, specifying the x(t) relationship thatrepresents the mechanical motion input, as well as initializing

S. Niu et al.152

the storage elements. For example, residue charges of tribo-electric nanogenerators at initial condition (t=0) can berepresented by the initial voltage across the capacitor CTENG.

After the system is set in SPICE, the transit analysis of theTENG system can be performed. To validate the results fromthe SPICE software, we started with some TENG systemsthat can be solved analytically and the comparison of theresults obtained from both methods is shown in Figure 2.

The first example is a parallel plate sliding-mode tribo-electric nanogenerator loaded with a resistor. The para-meters utilized in this calculation are listed in Table 1. Thetop plate of this triboelectric nanogenerator is under aconstant velocity condition with the maximum movingdistance within the range of the bottom plate and themotion process is shown below.

x¼ vt tr xmax

v

� �ð2Þ

Figure 2 Verification of the built simulator. (a) Equations of contacTENG system loaded by a resistor (b–e) Comparisons of outputs frcomparison under 1 MΩ load and Q0=0 conditions for the sliding-mQ0=0 conditions for the sliding-mode TENG. (d) Current output commode TENG. (e) Voltage output comparison under 100 MΩ load and

Table 1 Parameters of the TENGs utilized to validate the new

Sliding-mode

Dielectric 1 εr1=4, d1=12Dielectric 2 Metal, d2=0 mEffective dielectric thickness d0=d1/εr1+dWidth of dielectrics w 0.05 mLength of dielectrics l 0.08 mTribo-charge surface density σ 100 mCm�2

Maximum separation distance xmax 0.05 mVelocity v 1 ms�1

From our previous analysis, the governing equation of thiswhole system combining the TENG and the resistor can begiven as [17]:

RdQdt

¼ V ¼ � 1CTENG

QþVOC ¼ � d0

wε0ðl�xÞQþ σd0xε0ðl�xÞ ð3Þ

With the boundary condition of Q (t=0)=Q0 (the initialcharges on the plates of triboelectric nanogenerators areQ0), the output voltage and current of the resistor can beobtained analytically by solving the above differentialequation, as shown below [17]:

I¼ σwvd0

Rwε0v�d0

ll�vt

expd0

Rwε0vln

l�vtl

� �� ��1

�

�Q 0expd0

Rwε0vln

l�vtl

� �� �d0

Rwε0ðl�vtÞ tr xmax

v

� �

ð4Þ

t and sliding-mode TENGs and equivalent circuits for the wholeom the simulator and analytical equation. (b) Current outputode TENG. (c) Voltage output comparison under 1 GΩ load andparison under 100 kΩ load and Q0=0 conditions for the contact-Q0=10 nC conditions for the contact-mode TENG.

simulator.

TENG Contact-mode TENG

5 mm εr1=3.4, d1=125 mmm Metal, d2=0 mm

2/εr2=31.25 mm d0=d1/εr1+d2/εr2=36.76 mm0.05 m0.1 m8 mCm�2

0.002 m0.1 ms�1

� �� �� 153TENG integrated system simulation

V ¼ σwvRd0

Rwε0v�d0

ll�vt

expd0

Rwε0vln

l�vtl

�1

�Q 0expd0

Rwε0vln

l�vtl

� �� �d0

wε0ðl�vtÞ tr xmax

v

� �

ð5Þ

Real-time outputs from the simulator for some specificvalues for R and Q0 are plotted in Figure 2b and c, withcomparison of the analytical results obtained from Eqs.(4) and (5). From these figures, we can observe that bothmethods show exactly the same solution for any loadresistances and initial condition.

The second and a more complicated example is a parallelplate contact-mode triboelectric nanogenerator loadedwith a resistor. The parameters used in this calculationare listed in Table 1. To be more accurate to the realexperimental conditions, the top plate of this triboelectricnanogenerator is set to move in a simple harmonic mode asdescribed below.

x¼ xmax

2� xmax

2cos

πvxmax

t� �

ð6Þ

From our previous analysis, the governing equation of thiswhole system combining the triboelectric nanogeneratorsand the resistor can be given as [16]:

RdQdt

¼ V ¼ � 1CTENG

QþVOC ¼ � d0þxε0wl

Qþ σxε0

ð7Þ

With the boundary condition of Q (t=0)=Q0, the analyticalresults of output voltage and current can be given as [16]:

I tð Þ ¼ � σd0

Rε0þ 2d0þxmax�xmax cos ððπv=xmaxÞtÞ

2Rwlε0

�exp�� 1

Rwlε0d0tþ

xmax

2t� xmax

2

2πvsin

πvxmax

t� �� ��

� σwl�Q 0þσd0

Rε0

Z t

0exp

1Rwlε0

�d0zþ

xmax

2z

��

� xmax2

2πvsin

πvxmax

z� ���

dz

ð8Þ

V tð Þ ¼ � σd0

ε0þ 2d0þxmax�xmax cos ððπv=xmaxÞtÞ

2wlε0

�exp�� 1

Rwlε0

�d0tþ

xmax

2t� xmax

2

2πvsin

�πvxmax

t���

��σwl�Q 0þ

σd0

Rε0

Z t

0exp

�1

Rwlε0

�d0zþ

xmax

2z

� xmax2

2πvsin

�πvxmax

z���

dz

ð9Þ

These equations are very complex, from which obtainingnumerical outputs can only be achieved through compli-cated numerical calculation methods. As a comparison, anumerical output solution can be easily obtained from thesimulator we built above, which is plotted in Figure 2d and etogether with the analytical results from Eqs. (8) and (9).Similar to the above comparison, the simulator providesalmost the same results with the analytical solution.

Above we provided two simple examples to show thevalidity of this newly-built simulator. In these cases, thisintegrated simulator can provide the correct results with a

much easier-to-use interface. However, the application ofthis simulator is much more beyond these two simpleexamples. In real applications, first, the load circuits areusually a combination of linear and nonlinear elements,including resistors, diodes (rectifiers), transistors, capaci-tors, inductors (transformers), and so forth. Besides, thereal mechanical motion could be quite irregular. Moreover,the triboelectric nanogenerator itself is not so ideal andcannot be analytically represented. In such circumstances,utilizing the analytical method to solve non-linear differ-ential equation sets is nearly an impossible task (Seesupporting information for a practically unsolvable exampleof the analytical method). Therefore, utilizing this newsimulator is the only way to handle these practical problemsand below we will provide an example that utilizing thissimulator to design an on-chip power management systemfor triboelectric nanogenerators.

Because of the inherent capacitive characteristics [17],TENGs can only provide unstable AC voltage/current out-puts, which is undesirable for most portable electronicapplications. Therefore, a power management circuit isvery necessary to convert these AC outputs from TENGs toDC outputs. Figure 3b shows a typical TENG power manage-ment circuit [21], including a diode bridge rectifier (D1 toD4, parameters shown in Table S1) and a filter capacitor(CL). The resistive load is now represented by a load resistorRL, which is in parallel connected with the filter capacitor.As an example, the TENG in this system is a parallel-platecontact-mode TENG with the parameter given in Table 1.Same as above, the top plate of this TENG is also under thesame cosine motion. With the initial condition of Q (t=0)=Q0=0 and no charges on the filter capacitor, the output ofthe whole circuit can be simulated by the simulator.

The output voltage curves under CL=10 μF and RL=10 kΩ,100 kΩ are shown in Figure 3c and d, respectively. Since thereare no initial charges on the filter capacitor CL, both ofthese two circumstances has a transition state, during whichthe capacitor is under charging. After several seconds, thetransition state ends while the output goes to a periodicsteady state, which has the same period as the mechanicalmotion. This periodic voltage signal is the steady state outputsignal, which has a DC component (VDC) and a ripplecomponent (vripple). The DC component of the output isdependent on the load resistance. For example, underRL=100 kΩ condition, the DC component of the output is0.185 V, much larger than 0.0187 V, the DC component whenRL=10 kΩ. Besides the DC component, there is also anundesirable ripple component in the output, which affectsthe stability of the output as a DC power source. The stabilityof the output under RL=100 kΩ condition is much better thanthat under RL=10 kΩ condition. Quantitatively, this stabilityis shown by the ripple factor (fr), defined as the ratiobetween the effective value of vripple and VDC. fr underRL=100 kΩ condition is 0.86%, which is much smaller thanthat under RL=10 kΩ condition (8.61%).

To systematically understand the influence of the filtercapacitance and the load resistance on the output perfor-mance, the output under several filter capacitances andload resistances is calculated and the corresponding DCvoltage, average power, and ripple factor are plotted inFigure 4a–c. As shown in Figure 4a, VDC quickly increaseswith the increase of RL when RL is small. However, due to

Figure 3 Output performance of the TENG system with power management circuits. (a) Structure of the TENG utilized in thiscalculation. (b) Equivalent circuits of the whole TENG system. (c) Real-time output voltage curve under CL=10 μF and RL=10 kΩconditions. (d) Real-time output voltage curve under CL=10 μF and RL=100 kΩ conditions.

S. Niu et al.154

the limitation of the maximum voltage that the TENG canprovide, VDC gets to its saturation value when RL is largeenough. VDC has a small dependence on CL when RL is verysmall. When RL increases a little bit (larger than 10 kΩin this case), vripple becomes negligible comparing to VDC.At the same time, VDC becomes independent of CL. This isbecause all of the capacitance shows infinite impedance atDC condition and the total impedance of the parallelbetween RL and CL is always RL. Since VDC only depends onRL and has almost no dependence on CL, the average poweris also only dependent on RL, as shown in Figure 4b. Same asthe case in the simple resistive load, there also exists anoptimum RL at which the largest average DC power isreached, which is because of the impedance match betweenthe load and the TENG. As CL has almost no impact on VDC,both the average power curve and the optimum RL are alsoindependent of CL. However, different from VDC and theaverage power, fr depends on both RL and CL, and decreaseswhen either RL or CL increases. This phenomenon resultsfrom the increase of the decay time constant of such loadcircuit, which equals to the product of RL and CL. Therefore,it seems that larger CL is good for the whole performance ofthe circuit because it has no influence on VDC but can largelyreduce fr. However, larger CL will increase the length of thetransition state and make it more difficult to reach thesteady state, when the whole circuits begin to function.As shown in Figure 4d, for the same RL, it takes less than 5 sto reach steady state when CL is only 10 μF while it takesabout 50 s to reach steady state when CL is 100 μF. This is

because larger capacitance will require larger amount ofcharges to reach the same final voltage.

From the discussion above, we can obtain the followingstrategy for the design of the power management system.First, simulate the whole system with a relative large CL anddifferent RL to obtain the optimum resistance. Second,setting RL at the optimum resistance, simulate the wholesystem with different CL and calculate the fr–CL curve.Third, from the requirement of real application on fr andthe calculated fr–CL curve, choose a minimum CL that meetsthe requirement for fr. Finally, from the optimum resistanceand the load resistance for the real application, design aDC–DC convertor to realize load adaption. From the aboveprocedures, a power management system for TENG can beeasily designed.

Conclusion

In summary, the first equivalent circuit model was proposedand the first integrated simulator for triboelectric nanogen-erator systems is built from this equivalent circuit modeland validated through comparison with the analyticalresults. Utilizing this simulator, we analyzed the perfor-mance of a whole system containing TENG and powermanagement circuits. The DC voltage output is onlyaffected by the load resistor and is almost independent ofthe filter capacitor. Increasing the load resistor can helpincrease the DC voltage output but there exists an optimum

Figure 4 Optimization of the performance of the integrated TENG system. (a) DC voltage under different load resistances and filtercapacitances. (b) Average output power under different load resistances and filter capacitances. (c) Ripple factor under different loadresistances and filter capacitances. (d) Real-time output voltage curve under 100 kΩ load resistance and different filter capacitances.

155TENG integrated system simulation

load resistance at which the energy delivered gets itsmaximum. The ripple factor of the output is determinedby the product of the load resistance and the filtercapacitance. Increasing either of them can reduce theripple factor, but large capacitor will lead to a longertransition state. Based on the above conclusion, we providethe design flow for such power management system. Thisnew simulation method is a standard tool and method ofTENG simulation, which can be applied to any TENGsystems. It will greatly facilitate the future design andoptimization of TENGs. In addition, the discussion of thepower management circuit can serve as a guide in next-stepexperiments for real applications.

Acknowledgment

This research was supported by U.S. Department of Energy,Office of Basic Energy Sciences under Award DEFG02-07ER46394, MANA, the World Premier International Research CenterInitiative (WPI Initiative), MEXT, Japan.

Appendix A. Supporting information

Supplementary data associated with this article can befound in the online version at http://dx.doi.org/10.1016/j.nanoen.2014.05.018.

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Simiao Niu is a Ph.D. candidate working as agraduate research assistant in School ofMaterials Science and Engineering at theGeorgia Institute of Technology, under thesupervision of Prof. Zhong Lin Wang. Heearned his B.E. degree in the Institute ofMicroelectronics at Tsinghua University in2011 with the highest honors and outstand-ing undergraduate thesis award. His doc-toral research interests include theoretical

and experimental studies on: mechanical

energy harvesting by triboelectric nanogenerators and high-perfor-mance piezotronic and piezo-phototronic sensors based on piezo-electric nanowires.

Yu Sheng (Alvin) Zhou is a Ph.D. candidatesupervised by Prof. Zhong Lin (Z.L.) Wang inSchool of Materials Science and Engineeringat the Georgia Institute of Technology. Hereceived his B.S. in Applied Physics and M.S.in Applied Optics from Beihang University(BUAA). His doctoral research focuses onmechanical energy harvesting and self-pow-ered sensors, scanning probe microscopicstudy on electro-mechanical coupling

(eg. piezotronics) in nano-structured semi-

conductor materials as well as triboelectrification between metaland dielectric materials.

Dr. Sihong Wang is a postdoctoral fellow inProf. Zhong Lin (Z.L.) Wang’s group at theGeorgia Institute of Technology. Heobtained his Ph.D. degree in MaterialsScience and Engineering from the GeorgiaInstitute of Technology in 2014 under thesupervision of Prof. Zhong Lin (Z.L.) Wang,and his B.S. in Materials Science and Engi-neering from Tsinghua University, China in2009. His research mainly focuses on nano-

material-based mechanical energy harvest-

ing and energy storage, self-powered systems, nanogenerator-based sensors and piezotronics.

Ying Liu received her B.S. in physics fromthe Yuanpei program at Peking University in2009 and is a Ph.D. candidate with Prof.Zhong Lin Wang in School of MaterialsScience and Engineering at the Georgiainstitute of Technology. Her main researchinterest is the coupling of mechanics, elec-tronics, and photonics in the same material,which includes piezo-phototronics andtriboelectrics.

Long Lin received his B.S. in MaterialsScience and Engineering from Tsinghua Uni-versity, China in 2010. He is currently a Ph.D. candidate in School of Materials Scienceand Engineering at the Georgia Institute ofTechnology. He is working as a graduateresearch assistant at Prof. Zhong Lin Wang’sgroup. His research mainly focuses on nano-material synthesis and characterization,fabrication of high-output nanogenerators,

self-powered nanosystems, piezo-tronic and

piezo-phototronic effect of semiconductor nanostructures andvarious applications.

Dr. Yoshio Bando is an adjunct professor atUniversity of Tokyo in Japan. He has beenworking on synthesizing new one-dimen-sional inorganic nanomaterials, and clarify-ing their structures and properties. Byutilizing sophisticated TEM, he has discov-ered many new nanotubes and nanowiressuch as BN, MgO, and AlN. He has receivedmany outstanding awards such as the Tsu-kuba Prize in 2005, Academician, World

Academy of Ceramics in 2004, Commenda-

tion Award by the Minister of State for Science and Technology in1998, Academic Award of the Ceramic Society of Japan in 1997,Seto Award of Electron Microscopy Society of Japan in 1994, Scienceand Technology Accomplishment Award by the Minister of State forScience and Technology in 1994. In 2002, he was chosen as one ofthe "Top Thirty Key Persons in Nanotechnology" in Japan by thescientific journal, "Nikkei Science". He is appointed as adjunctmember of the Science Council of Japan (2006). He is now a Fellowof American Ceramic Society and an Editor-in-Chief of Journal ofElectron Microscopy.

Dr. Zhong Lin Wang is a Hightower Chairand Regents’s Professor at the GeorgiaInstitute of Technology. He is also the Chiefscientist and Director for the Beijing Insti-tute of Nanoenergy and Nanosystems, Chi-nese Academy of Sciences. His discoveryand breakthroughs in developing nanogen-erators establish the principle and techno-logical road map for harvesting mechanicalenergy from environment and biological

systems for powering personal electronics.

He coined and pioneered the field of piezotronics and piezo-phototronics by introducing piezoelectric potential gated chargetransport process in fabricating new electronic and optoelectronicdevices. This historical breakthrough by redesign CMOS transistorhas important applications in smart MEMS/NEMS, nanorobotics,human-electronics interface and sensors. Dr. Wang’s entire publica-tions have been cited for over 60,000 times. The H-index of hispublications is 129.