Green, TC

Kondala Rao, G

Mitcheson, PD

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MIXED ELECTROMECHANICAL SIMULATION OF ELECTROSTATICMICROGENERATOR USING CUSTOM-SEMICONDUCTOR DEVICE MODELSKondala Rao. G, Paul D. Mitcheson, Tim C. GreenDepartment of Electrical Engineering, Imperial College Lond n, UK.Abstract: In this paper, modeling of semiconductors that are specially designed for power processing the outputof an electrostatic microgenerator is presented and combined with an electromechanical system simulation of anelectrostatic microgenerator. Various analytical expressions have been derived to study the effects of parasiticelements of semiconductor devices on electrostatic microgenerator effectiveness. These expressions are thenused to estimate the likely operating regions (in terms of generator size and the acceleration of the source) overwhich the choice of the electrostatic transduction mechanism is sensible. It is shown that, whilst the electrostatictransducer itself is known to scale well to small sizes, whencombined with the power processing circuit to forma microgenerator, this may not be the case.Keywords: PSpice modeling, Electromechanical Simulations, Electrostatic Microgenerator, Effectiveness.INTRODUCTIONTo design a globally optimised electrostatic micro-generator, combined electromechanical PSpice sim-ulations of electrostatic microgenerators have beenpreviously carried out [1]. However in that work, idealswitch models were used for charging and discharg-ing of the variable capacitor. It is important to useaccurate semiconductor device models instead of idealswitches as it has been shown that the parasitics of thecharge/discharge switches will significantly affect thecapacitor voltage and therefore energy generation [2].In this paper, PSpice modeling of the custom semi-conductor devices (diode and MOSFET) designed in[2] is explained and an end-to-end system level sim-ulations of the Coulomb Force Parametric Generator(CFPG) type electrostatic microgenerator is presented.The effectiveness of an electrostatic microgeneratoris plotted against generator size and input accelerationby assuming the microgenerator is cube shaped and theproof mass occupies half the volume. This is used inidentifying the useful region of operation of a constantcharge electrostatic microgenerator when interfacedwith a power processing circuit.MODELING OF CUSTOMSEMICONDUCTOR DEVICESTo achieve the high level of off-state impedancethat is required to process the electrostatic microgen-erator’s output, semiconductor devices were speciallydesigned with Silicon-On-Insulator (SOI) based tech-nology [2]. Simulations of these devices were carriedin Silvaco (finite element based software). However,these devices need to be modeled in PSpice in orderto allow a complete end-to-end system simulation tobe run. Unfortunately, developing models in PSpiceis not straight forward since these are power devicesand PSpice inbuilt models do not accurately simulatesome of the effects that are present in the powersemiconductor devices (such as high level injection).Fig. 1. Block diagram of Custom diode PSpice modelWhilst physics based models are useful for pa-rameterising component models, they can be largeand therefore slow to run in SPICE. Therefore, inthis work, a look up table based method is used tomodel these custom devices in PSpice. Both diode andMOSFET are modeled using this method. Here, onlythe modeling of the diode is explained. Fig.1 showsthe block diagram of the diode model with look-uptables. For instance, I-V characteristic data points ofthe custom diode are stored in the table. Then, bysensing the voltage between the anode and cathode, thecorresponding current value from the table will flowin the current source. This simulates the diode forwardcharacteristics. PSpice uses linear interpolation forPowerMEMS 2009, Washington DC, USA, December 1-4, 20090-9743611-5-1/PMEMS2009/$20©2009TRF 356data points in the look-up table. However, PSpicewill not extrapolate the characteristic values beyondthe bounds of the stored data points. In order tomaintain the continuity of the characteristics beyondthose specified in the tables, extra components areadded to the model. These are a voltage sourceVx anda resistorRf orward (valid because the series resistance isdominant after a certain forward voltage). The forwardcharacteristics obtained using this model are shownin Fig.2. The PSpice simulation results closely matchwith the Silvaco data points.0 2 4 6 8 10 1200.10.20.30.40.50.60.7Forward Voltage [V]ForwardCurrent[A]  Silvaco dataPSpice model Fig. 2. Diode forward characteristics with look-up table basedPSpice modelThe diffusion and depletion capacitance characteris-tics of the custom diode are also stored in the look-uptables and are used to calculate the dynamic currentsource value by usingi = C(V)× dVdt . This currentsource therefore represents the parasitic capacitanceof the custom diode. Thereby, complete behavioralmodeling of the custom diode has been achieved inan accurate and computationally efficient way.ELECTROSTATIC MICROGENERATORSYSTEM SIMULATIONS0 0.02 0.04 0.06 0.08 0.1−101x 10−3y(t)0 0.02 0.04 0.06 0.08 0.10123x 10−4z(t)0 0.02 0.04 0.06 0.08 0.10100200Time [s]Vcap(t)Fig. 3. Simulation resultsImperial College Energy-harvesting Simulator(ICES) toolkit [3] models are used to modelmechanical parts of the CFPG microgenerator systemand the transducer. The half-bridge converter that isproposed in [2] is used as power processing circuit.For simplicity, a load is not attached to the powerconverter output. Various simulation studies havebeen carried out and typical waveforms of inputexcitation (y(t)), proof mass displacement (z(t)) andthe Variable capacitor voltage(Vcap(t)) are shown inFig.3. It has been observed that the semiconductordevice parasitic elements significantly effecting thevariable capacitor voltage due to charge sharing andleakage.Whilst these time domain simulations could beused to optimise the system, an analytical approachis required to speed up the process. This analysis willnow be presented.ANALYSIS OF ELECTROSTATICMICROGENERATOR’s VOLTAGE WITHPARASITICSIn this section, a Coulomb Damped Resonant Gen-erator (CDRG) type electrostatic microgenerator isconsidered for analysis and the variable capacitorvoltage expressions (with and without parasitic ele-ments) are derived. These expressions are then used inestimating the coupling effectiveness of the microgen-erator and power conversion circuit efficiency. Finally,the effectiveness of the microgenerator is calculatedunder different operating conditions.The optimal coulomb force of the CDRG withdisplacement constraint is given in [1] by:Foptcz=Y0ω2mωc|U |√1(1−ωc2)2− 1ω4c(ZlY0)2(1)whereU =sin( πωc )1+cos( πωc ), Yo is input excitation amplitude,m is mass of the generator proof-mass,Zl is peakinternal displacement,ω is angular frequency of thegenerator frame motion andωc = ωωn andωn is gener-ator natural frequency.At resonance (ωc = 1), the optimal force is constantand Eq. 1 simplifies to:Foptcz= 0.7854mYoω2 (2)The electrostatic force between parallel plates of acapacitor for a given separation of 2Zl is given by:357Felectrostatic=12εAplate(Vplate2Zl)2(3)WhereVplate is capacitor voltage andAplate is the areaof the parallel plate.The electrostatic microgenerator will be operatingunder optimal conditions, if the electrostatic force isequal to the coulomb force. Therefore, equating Eq. 2and Eq. 3, we see that the maximum capacitor voltageis:Vplate = 4.212×105(2Zl)√mYoω2Aplate(4)The above equation can be further simplified byassuming the microgenerator is cube shaped with sidelength ofLc and proof mass occupies half of the cubevolume. Therefore,m= ρL3c2 , Aplate= L2c, 2Zl =Lc2 , ρ =19300Kg/m3 (gold) andAcc=Y0×ω2. By substitutingthese values, the maximum capacitor plate voltage issimplified to:Vplate = 2.07×107√L3cAcc (5)Eq. 5 gives the microgenerator maximum voltageas a function of generator size and input acceleration.This is the ideal voltage since it is derived assumingthere are no parasitic elements connected to the mi-crogenerator capacitor.When interfaced with a power processing circuit,the voltage generation of the microgenerator will beaffected due to the parasitic elements such as offstate leakage current and junction capacitance. In thispaper, only parasitic capacitance is considered. Usinganalysis from [4] the junction capacitance can beexpressed as:Cj =Asemi2√2qεV0−VNd (6)whereCj is junction capacitance,Asemi is area ofthe semiconductor,V0 is built in potential and V isoperating voltage,Nd is carrier doping density.When the semiconductor devices are designed bychoosing a doping density which minimises the on-state conduction losses per unit area (Nd = 14×1022VBm−3)[5], the junction capacitance is given by:Cj =1.1×10−3Asemi√(V0−Voperation)VB(7)whereVoperation, VB are operating voltage and voltageblocking capacity of a semiconductor respectively.Assuming the semiconductors are designed to blockthe maximum voltage of the microgenerator (given inEq. 5), the semiconductor junction capacitance can beexpressed as:Cj =2.377×10−7Asemi√(Vo−Voperation) [L3cAcc]14(8)The charge balance equation for a constant chargeoperation is given by:Cg1×Vprecharge+Cp1×Vprecharge=Cg2×Vf inal+Cp2×Vf inal (9)where Cg1, Cg2 are generator initial and fi-nal capacitances(Cg1 = εAplated0 ,Cg2 =εAplate2Zl), Cp1and Cp2 are initial and final parasitic capacitances,Vf inal is final voltage,Vprecharge is precharge voltage(4.13×107d0√L×Acc)and d0 is the initial separa-tion of the plates.After substituting these values in the Eq. 9 andsimplifying; we obtain:2ε0LcVf inal+2.37×10−7Asemi[L3cAcc]14√Vf inal=3.6×10−4[L5Acc]12 +1.5×10−3Asemi√d0Lc(10)Assumingd0 = 1µm, Eq. 10 has been solved ana-lytically for Vf inal using Maple and is given by:Vf inal= 1[L7cAcc]12[8.4×10−6[1.05×1013A2semi−X1+X2]] (11)WhereX1=1.78×1010Asemi√3.5×105A2semi+1.6×105[L5cAcc]+660L2c√(Acc)Asemi(12)X2=2.44×1012L5cAcc+1010L2c√(Acc)Asemi (13)Eq. 11 therefore gives an analytical expression forthe microgenerator voltage when parasitic capacitanceloading is present.System effectiveness is defined as a product ofcoupling effectiveness and circuit efficiency.The coupling effectiveness(Ecoupling) is the ratio ofthe energy that is stored in the capacitor with andwithout parasitic elements present(Ecoupling =V2f inalV2plate)and the complete expression is given by:358Ecoupling= 1Acc2Lc10[1.6×10−23[1.69×1013A2semi−X3+X4]2](14)WhereX3=1.4×109Asemi√1.4×108A2semi+4.05×106[L5cAcc]+66×103AsemiL2cAcc0.5(15)X4= 2.44×1011L5cAcc+4×109AsemiL2cAcc0.5 (16)Circuit efficiency is a conventional efficiency. Inany standard power processing circuit, the first stageof power conversion is transferring energy into aninductor and the efficiency of this stage is limited bythe conduction losses of the switching element. Here,only this stage efficiency is estimated by assumingthat the variable capacitor energy is transferred to theinductor through a resistance (MOSFET on state resis-tance,Rmos f et=2×10−11V2BAsemi) and therefore this analysisprovides an upper bound on circuit efficiency.Coupling effectiveness, circuit efficiency and micro-generator effectiveness are plotted for different cubesizes and input accelerations (see Fig.4, Fig.5 andFig.6 respectively). The optimal semiconductor areahas been chosen for each and every point in order tomaximise the system effectiveness.As can be seen, the effectiveness increases withlength. This is due to the fact that parasitic capacitanceof pn junction is more at low voltages (inverse squareroot characteristics). At higher lengths and higheraccelerations, the effectiveness falls slightly due to theincrease in MOSFET drift region resistance at highervoltages.0.511.522.530.20.40.60.8100.20.40.60.81Acceleration [ms−2]Length of the cube [mm]CouplingEffectivenessFig. 4. Coupling effectiveness of an electrostatic microgeneratorCONCLUSIONSEnd to end system simulations of CFPG type elec-trostatic microgenerator have been presented.The effectiveness of an electrostatic microgeneratorhas been estimated and plotted against generator size012300.510.750.80.850.90.951Acceleration [ms−2]Length of the cube [mm]CircuitEfficiencyFig. 5. Power Circuit Efficiency0.511.522.530.20.40.60.8100.20.40.60.81Acceleration [ms−2]Length of the cube [mm]GeneratorEffectivenessFig. 6. Maximum effectiveness of an electrostatic microgeneratorand input acceleration. This plot is helpful in choosingthe generator size for a given excitation.In the analysis, factors such as off-state leakagecurrent of semiconductor devices and complete powerprocessing circuit are not considered. More accurateeffectiveness can be estimated if these factors are con-sidered. As can be seen, the effectiveness of an electro-static microgenerator attached to a power processingcircuit is relatively poor at small dimensions due tothe relationship between capacitance and voltage in apn junction.REFERENCES[1] Mitcheson, P. D. Analysis and optimization of energy har-vesting micro generator systems PhD thesis Department ofElectrical Engineering, Imperial College London (2005).[2] Stark, B. H., Mitcheson, P. D., Miao, P., Green, T. C.,Yeatman, E. M., and Holmes, A. S. (2006)Power Electronics,IEEE Transactions on21(1), 27–37.[3] Kondala Rao, G., Mitcheson, P. D., and Green, T. C. No-vember 2007 In Proceedings of PowerMEMS 2007 Freiberg,Germany: . pp. 137–140.[4] Streetman, B. G. and Banerjee, S. K. (2006) Solid StateElectronics Devices, Pearson Prentice Hall, USA.[5] Duncan, A. G. and John, G. (1989) POWER MOSFETS:Theory and Applications, John Wiley & Sons, USA.359

Mixed Electromechanical Simulation of Electrostatic Microgenerator Using Custom-Semiconductor Device Models

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