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I love rains.I like staring at moon.I have only one goal, to travel the world.I am good at remembering dates.When I was a kid my dad cut off the TV connection but promised to take me for movies every sunday. from 2008–2012 I have watched every blockbuster and every flop film, some even twice.my most favourite thing to eat is chocolate ice cream.I get feelings for someone easily.I grow outta feelings easily.I am a big Bollywood junkie, I DO remember loads of dialogues and lyrics.I am an astrologer , astrology found me.I am very fascinated by shayari.I want to fall madly in love with someone, doesn't matter if I am able to pursue them or not.I really lack motivation, I procrastinate alot.I want to be a professor .I am fond of air travel ,I like to look at the sky,clouds and down to earth … plus Whenever I look down I think that these thousands of people have their own stories and battles. It makes me realize how small my problems are.I am a McD addict.I listen to music altleast 3 hours a day.I walk for atleast 2 hours a day.I can die for my friendsF. R. I. E. N. D. S is my favourite though.I don't know how to ride a bicycle.I am 5′9+ .I am really good at cursing.If I were a boy, I'd be a gangster.I love gangs of wasseypur.I want to get arrested once in my life.I am damn funny.I talk alot ,many people compare me with geet from jab we met.I talk really fast and mess up words, gibberish.I cook really delicious pink sauce pasta.I wear loose clothes.I was an overweight kid, thanks McD.I love the feeling called love.I wanna be rich, not marry rich.I love Arijit Singh, Atif Aslm and KK as much as I love Nicki Minaj, Ariana Grande & Cardi B.either you'll find me in pyjamas or all dolled up, there's no in between.I love being the center of attention but I am not an attention seeker.I am really witty.I wanna own a pistol.I talk to myself.I am one of the most open minded and frank people you'll ever come across.I am kind and sensitive but also a bad bitch, depends.I smile 24x7.I hate my ance, and keep on trying new products to avoid and remove it. skin care freak.I hate periods.I have pcod.I am a foodie.I wanna have abs.I am mentally strong and emotionally vulnerable.I love wearing traditional clothes more than western outfits.Thankyou for reading about me. :)

first wayC included in A <=>AuC=AC included in A <=> AnC=C(AnB)uC=An(BuC) <=>(AuC)n(BuC)=An(BuC)1)If C included in A then AuC=A then (AuC)n(BuC)=An(BuC)2)If (AuC)n(BuC)=An(BuC) then (AuC)n(BuC)nC=An(BuC)nC(AuC)nC=AnC therefore C=AnC then C included in ANote: (BuC)nC=C=(BnC)uC is absorption axiomIf C included in A then CuA included in AuA so CuA included in A,we know A included in CuA so CuA=AIf CuA= A ,we know C included in CuA so C included in ATherefore C included in A <=> CuA=Asecond way(AuC)n(BuC)=An(BuC) and (AuC)u(BuC)=Au(BuC)<=> (AuC)=A <=>C included in ABecause we know EnD=FnD and EuD=FuD) <=>E=FE=En(EuD)=En(FuD)=(EnF)u(EnD)=(EnF)u(DnF)=(EuD)nF=(FuD)nF=F

AbstractSignificant developmentof silicon carbide (SiC)material for device applicationsnow allows circuitdesigners to more fully exploit its unique properties. The4H-SiC structure provides the most favorablecharacteristics to optimize device speed andpowerhandling capabilities. These include wide bandgap (3.2eV), high dielectric breakdown (3.5MV/cm), and highthermal conductivity (4.9 W/cm-K) [1]. By combiningthese properties, SiC devices are able to achieve fastreverse recovery and highreverse blocking voltages,along with excellent high temperature characteristics(case temperatures above150 C). This makes thesedevices ideally suited to power electronics applications,where high power levels as well as fastswitching arerequired. Many areas dominated by ultrafast recoverysilicon (Si) diodes, might therefore be better suited to theapplication of SiC. In order to verify the efficacy of SiCdevices, temperature dependent measurements weremade on a sample of fast recoverySi and SiC diodes.This paper presents the results of these measurements,comparing critical characteristics of Si and SiC devicesover a range of junction temperatures upto 150 C.I. INTRODUCTIONThe effectiveness of the SiC devices in thiswork is evaluated through comparison with commerciallyavailable Si devices that are the state-of-the-art for highpower switching applications. These devices are ultra-fast soft recovery(FRED), Si diodes manufactured byInternational Rectifier. The SiC devices being examinedare Junction Barrier Schottky(JBS) diodes manufacturedby Cree, Inc. Both of these diode types combine fastactive switching with high reverseblocking voltage(>500 V) [2,3]. The FRED Si diodes were chosen forthis comparison because these are the only Si devicesthat combine high reverse blocking voltage and fastrecovery time, comparable to SiC JBS diodes. Thispresentation will be broken down into two categories foreach material. These consist of low (6-8 A) and high(25-30 A) current rated devices. Each of the diodesbeing studiedhas a reverse breakdown voltage in therange of 500 to 700 V. Experimental data being takenincludes reverse-recovery, reverse-biased capacitance,and forward/reverse current/voltage characteristicmeasurements. Each of these measurements is made at arange of temperatures. The data derived from thesemeasurements are used to make direct comparisons of theSi and SiC device. In this presentation the focus will beon the experimental designand interpretation of theresponse for each device. The results of the temperaturedependent measurements are analyzed and contrasted.This effort to characterize SiC JBS diodes is part of theArmy initiative to investigate fast switching of devices inhigh current density power electronics applications.II. EXPERIMENTALAPPROACHThere are three primary experimental areas forthis work. First, forwardand reverse current-voltage(curve-tracer)measurements were performed. Next,capacitance was measured under reverse bias for the Siand SiC diodes. Finally, active switching (reverserecovery) measurements were taken for each device inthis study. Allof these data were measured from 25 C to150 C, at 25 C increments. Experimental temperaturewas varied in an ovenduring the curve-tracer andcapacitance measurements, while a variac-controlledhotplate was used to control temperature during thereverse recoverytests.Various challenges were encounteredduring themeasurement processes, including minimizing theinductance introduced by wire connectionsin theexperimental setups. Thiswas particularlysignificant inthe reverse recovery setup, where optimizing the fall-time (di/dt) of the input switch signal is critical toaccurately assessing the recovery time of the device.Stray inductance also impacted the high forward current(25-30 A) diode measurements. For these high currentmeasurements, the curve-tracer must be in its high powermode, which utilizes narrow delta input pulses. The highfrequency composition of these steep, short pulsesmagnified the distorting effect of lead inductanceson theIV curves. This necessitated particulareffort andingenuityto minimize wire lengthsduring thetemperature dependent measurements.U.S. Government work not protected by U.S. copyright. 1217Figure 1. Reverse Recovery Circuit DiagramFigure 1 details the setup for the reverserecovery measurements. A fast (5 ns), high power metaloxide semiconductor field effect transistor (MOSFET) isused to switchthe current path in the circuit. TheMOSFET is manufactured by DEI, and rated at 24 A and1000 V. Initially, with the MOSFET on, current flows inthe outer circuitloop, and the diode under test is reversebiased. The MOSFET is then switched off, removing thesource potential from the circuit. The high inductance ofthe test-device loop maintains current flow in this part ofthe circuit, so that the diode is now forward biased. TheMOSFET is then switched back on, which causes thesource potential to reverse bias the diode again. At thispoint, reverserecovery of the diode begins. The minoritycarriers in the junction flow from cathode to anode untilthe device recovers its steady-state characteristics.(a)(b)III. RESULTS AND COMPARISONBoth the Si and SiC devices have fast recoverystructures, which make use of an N-region designed tominimize switching time. The diodes are both designedto provide over 500 V reverse blocking voltage, alongwith fast reverse recovery. Each is also designed tominimize leakage current in their off states. Figure 2gives the reverse recovery current density versus time forthe low current Si and SiC diodes. The 8 A SiFREDdiode displays a clear increase in recovery time and peakreverse current density as the device temperatureincreases. The 6 A SiC JBS diode shows almost nochange with temperature.(a)(b)Figure 3. Reverse recovery of high current(a)Si and (b)SiC diodesFigure 3 gives the same comparison for the highcurrent diodes. The 25 A Si device again suffers amarked increase in recovery time and peak reversecurrent density, while the 30A SiC diode showsnegligible effect. The corresponding reverse recoverypower dissipation forthe high current Si and SiC diodeshas been derived from this data. The SiC diodedissipates just over 1 kW, both at25 C and 150 C, whilethe Si diode’s peak power dissipation rises to 5.8 kW at150 C. A summary of the active switching dataat 150 Cis given inTable 1, located at the end of this paper.These results clearly indicate the superiority of the SiCJBS diodes compared to theSi FRED devices at hightemperature. The SiC to Si ratio of total reverse recoverycharge densityis over 8 forthe high current devices and30 for the lowcurrent devices. The power dissipated inFigure 2. Reverse recovery of low current Si, SiC diodes25AmpSi FREDDiodeReverseRecovery-100-50050100150200-200 -100 0 100 200 300Time (ns)Current Density (A/cm2)25 C50 C75 C100 C125 C150 C30 Amp SiC JBS Diode Reverse Recovery-50050100150200250300350-200 -100 0 100 200 300Time (ns)CurrentDensity (A/cm2)25 C50 C75 C100 C125 C150 C8 Amp SiFRED Diode Reverse Recovery-500-400-300-200-1000100200300-50 0 50 100 150 200 250Time(ns)CurrentDensity(A/cm2)25 C50 C75 C100 C125 C150 C6 Amp SiC JBS Diode Reverse Recovery-2-101234567-50 0 50 100 150 200 250Time (ns)Current (amps)25 C50 C75 C100 C125 C150 C1218the Si diodes is approximately five times greater than forthe SiC diodes,as shown in figure 4 below.(a)(b)Energy loss for the Si FRED devices isdetermined to be almost three times more thanfor SiC inthe low current diodes and four times more in the highcurrent diodes. The device structures of the Si and SiCboth provide good characteristics at ambient temperature.The SiC diodes tend to have somewhat lower recoverytime, reverseleakage current, and forward voltage drop.For example, the ambient forward current-voltage slopesmeasured on the curve tracer indicate that the specificresistance for the 30 A SiC JBS diode is 0.6 ohm-mm2.The forward response of the 25 ASi FRED diode gives avalue of 1.1 ohm-mm2as its specific resistance.A pronounced difference in the response of thetwo device types,under reverse bias, is observed withincreasing temperature. The reverse current-voltagecharacteristics, shown in figure 5, offer dramaticillustration of this contrastingbehavior as temperaturerises. Above 100 C, the Si diodes suffer a drasticincrease in reverse bias current, while the leakage currentdensity of the SiC diodes is essentially unchanged. Itshould benoted thatthe reverse leakage current for the Sidiode is below 1 mA, even at 125 C. While this is twoorders of magnitude above the normal Si diodeperformance, it does not preclude meaningful reverserecovery measurements, as indicated in figure 3a.(a)(b)Temperature effects under reverse bias can alsobe seen in the response of such parameters as devicecapacitance. Measurement of the diode capacitance as afunction of reverse bias voltage is necessary to modelthese devices. Preliminary measurements of this criticalparameter were conducted on the high currentdiodesFigure 4. Power dissipation for high current diodes.Figure 5. Comparison of reverse leakage current densityHighCurrentSi FREDDiodeActiveSw itchingPow erDissipationatTem perature01000200030004000500060000 50 100 150 200Time(ns)Power(W)25 C150 CHigh Current SiC JBSDiodeActiveSwitchingPow erDissipation at Temperature01000200030004000500060000 50 100 150 200Time(ns )Power(W)25 C150CSiC-32Reverse CurrentDensityvsVoltage-25-20-15-10-505-800 -700 -600 -500 -400 -300 -200 -100 0Voltage (volts)C ur re ntD e ns (A /s qm )25 C50 C75 C100 C125 C25 A Si FREDDiodeReverseBiasResponse-25-20-15-10-505-800 -600 -400 -200 0Voltage(volts)CurrentDens(A/sqm )25 C50 C75 C100 C125 C1219being considered. These data are represented in figure 6.As before, the Si diode undergoes significant increases incapacitance with temperature, while the SiC diode showslittle or no significant change in its response.(b)(a)IV. CONCLUSIONThe preceding results support the conclusionthat 4H-SiCdiodes havevastly superiorhightemperature characteristics compared to Si devices.Even the state-of-the-art fast recovery Si diodesexamined here suffer drastic degradation of theirswitching performance in the temperature rangesrequired by power electronics applications, while theSiC JBS diodes show little or no effect.The inherent material properties of 4H-SiC,especially its wide bandgap structure, are responsiblefor its excellent high temperature performance. SiChas triple the bandgap energy of Si(3.2 eV vs 1.1 eV).This mitigates the effects of high temperature onminority carrier conduction during reverse recoveryinSiC devices. In addition, SiC has about six times thebreakdown field of Si, allowing for high reverseblocking voltages, even in fast recoverystructures.Finally, the three fold higher thermal conductivity ofSiC minimizes the effects of high temperature up to atleast 150 C, as opposed to Si, where dramatic increasesin reverse recovery chargeand leakage current areobserved above 100 C.The SiC data presented here will be expandedon in the near future to develop SABER and/orPSPICE device models. This will provide a betterunderstanding of performance and failure mechanisms,and give a more comprehensive characterization