材料物理112161358.docx

材料物理112161358.docx

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材料物理112161358

Astudyonphononiccrystals

Abstract:

Asisknowntoall,phononiccrystalisanewtypeofacousticfunctionalmaterial,whichisnecessarytobeusedinsomespecialoccasions,thestudyofphononiccrystalscausedagreatdealofattentioninthenationalresearchinstitutes.Thisarticleintroducestheconceptandthebasiccharacteristicsofphononiccrystalsindetail,thephononiccrystaldefectsstatecharacteristics,thephononiccrystalsforbiddenbandmechanismandvariouspotentialapplicationareas（noiseandvibrationreduction）inphononiccrystals.Finally,weprospecttheresearchanddevelopmentofthephononiccrystals.

Keywords:

phononiccrystalsnoiseandvibrationreductionprospect

1Introduction

Thepotentialfieldofsemiconductoratomsarrangesperiodically.Whenthepropagationoftheelectronshappeninthesemiconductor,theinteractionbetweenelectronicsandatomicperiodicpotentialmakessemiconductorelectronicoccupybandgap,whichisabletomanipulatetheflowofelectrons.Onbehalfofthesiliconcrystalsemiconductorhasbroughtarevolutioninscienceandtechnology.Withthedevelopmentofthetransistors,integratedcircuits,large-scaleintegratedcircuitsevenultra-large-scaleintegratedcircuits,semiconductortechnologyhasaprofoundimpactontheprogressofhumancivilization[1,2].

Morethantenyearsago,peoplebegantotouchontheopticalpropertiesofthestructureandfunctionofmaterialsresearch.Theoryandexperimentshaveprovedthatifthedielectricofthematerialisaconstant,thestructureandfunctionintheperiodicvariationintheopticalwavelengthscale,theinteractionofphotonswithperiodicstructuremakesthematerialhasasimilarsemiconductorelectronicband-gapenergybandstructure,calledphotonicbandgap（knownasphotonicbandgap）.Periodicdielectricphotonicbandgapstructureandfunctionofmaterialsarecalledphotoniccrystal（photoniccrystals）.Photonenergyfallsonthelightwavesinthephotonicbandgapcannotbeinthephotonpropagationinthecrystal.Whenthephotoniccrystalexists（orintroduced）pointdefectsorlinedefects,theforbiddenbandoflightwaveswillbelocalizedinthepointdefectoronlyalongthedefectpropagation.Thedesignoftheperiodicstructureofthephotoniccrystalanditsdefects,canartificiallyregulatetheflowofphotons[3].

In1987,theconceptofphotoniccrystalsindependentlyproposedbyE.YabionovithchandS.Johntwo[4].In1991,Yabionovitchverifiedtheexistofmicrowavephotonicbandgapbyexperimental.Photoniccrystalthenquicklybecamephotoelectronandinformationtechnologyresearchinthefieldhotspots.Subsequently,itisdiscoveredthatwhentheelasticwavepropagationexistsinperiodicelasticcompositemedium,itwillhaveasimilarelasticwaveband,therefore,puttingforwardtheconceptofphononiccrystals.Phononiccrystalhasawealthofphysicalconnotationandpotentiallybroadapplicationprospects.Phononiccrystalshavecausedgreatconcernofnationalresearchinstitutions[5].

2Phononiccrystals

2.1Theconceptsandbasiccharacteristicsofphononiccrystals

ThePhononiccrystalisthecyclicalnatureoftheelasticwavebandstructureandfunctionofmaterials[6].Phononiccrystalinternalmaterialcomponent（calledgroups）oftheelasticconstantsandmassdensityparameterscyclicalchanges.Withthebandgapofthematerialcomponentswithdifferentperiodicstructuresintheformofdifferentphononcrystalelasticwavecharacteristicsaredifferent.

Phononiccrystalshavesimilarbasiccharacteristics:

whentheelasticwavefrequencyfallswithinthebandgaprange,theelasticwaveisprohibitionofthedissemination,whenthereexistsapointdefectorlinedefect,theelasticwaveislocalizedatthepointdefects,oronlyalongthedefectpropagation[7].Similarly,thedesignofthethephononiccrystalperiodicstructuredefectscanartificiallyregulatetheflowofelasticwaves.

Elasticwaveiscoupledbylongitudinalandtransversewavesfullvectorwave,threeindependentelasticparametersareineachgroup,thatthemassdensityP,thelongitudinalwavevelocityCiandshearwavewavevelocityCt（inthefluidmedium,Ct=0）;lightwaveisascalarwave,onlyoneindependentelasticparameteristhedielectricconstantineachelement.Thephononiccrystals,therefore,possessingaricherphysicalmeaning[8].Thefollowingliststherelevantcharacteristicsofthe（electronic）crystals,photoniccrystalsandphononcrystalscomparedwiththreestrikingsimilaritiescanbeseenfromthetable,the（electronic）crystals,photoniccrystalresearchmethodsphononcrystalshaveaguidingrole.

AccordingtothecrystalstructureofthephononsintheCartesiancoordinatesystem,inthreeorthogonaldirectionsinthecircumferential,periodicphononiccrystalscanbedividedintoone-dimensional,two-dimensional,three-dimensionalphononiccrystals.Scholarsresearchhasbeencarriedoutonsomeofthespecificstructureofphononiccrystals:

aone-dimensionalphononiccrystals,generalperiodiclayeredstructureconsistingoftwoormorematerials;dimensionalphononiccrystals.Usuallyacertaindirectionisparalleltothespaceforthecenteraxisofthecylindermaterial[9],andtheperiodicityofthelatticestructureareformedintheburiedbasematerial,thecylindermaterialcanbeholloworsolid,generallycircularcross-sectionofthecylinder,canalsobesquare.Cylinderarrangementformmaybeasquarearrangement,deltaarrangement,thehexagonalarraylikedimensionalphononcrystalsaregenerallyburiedinabasematerialformedofasphericalscatteringbodyperiodiclatticestructure,periodiclatticestructurescanbeintheformofabody-centeredcubicstructure,face-centeredcubicstructure,hexagonalclose-packedstructure.Figure1showsatypicalschematicblockdiagramofthevariousphononcrystals.

Fig1Phononiccrystalsofdifferentdimensions

2.2Theresearchoverviewofphononiccrystal

Thepropagationcharacteristicsofelasticwavesinlayeredmediaresearchhasbeenfornearly70years’history,whilethephononiccrystalsproposaloftheconceptandthetheoryofphononcrystalwasjustnearly10-yearhistory[10].Phononiccrystalresearches,duetothedifficultiesoftheoreticalresearch,aswellasotherfactors,makingrelativelyslowprogressandthecrystalliteratureoftotalarenomorethan150,accordingtoincompletestatistics.In1992,MMSignalandENEconomoufirstconfirmedintheorythatasphericalscatteringbodyembeddedinamatrixmaterialtoformathree-dimensionalperiodiclatticestructurehavingelasticwavebandgapcharacteristics[11].In1993,M.S.Kushwahaet.alfirstclearphononiccrystalsandtheconcept,andnickelcolumnaluminumalloyformingthecompositedielectricmatrix,calculatedbytheplanewavemethodcanbeobtainedinshearpolarizationdirectionofelasticwaveband.In1995,R.Martinez-Salaet.alintheWestSpainMadrid200yearsago,asculpturemadeflowingmelodyacousticpropertiesresearch,firstconfirmedthepresenceoftheelasticwavebandfromtheexperimentalpointofviewfromthisphononcrystalcausedgreatconcern[12].Phononiccrystalresearchworkfocusesontheformationofthebandgapofphononiccrystalsandphaseshouldthetheoreticalcalculations[13].Inaddition,scholarsarefromvariouscountriesincrystaldefectsphononstatestudy,experimentalresearchhasalsobeenmadegoodprogressinapplicationsofexploreinfancy.

Phononiccrystalresearchareasareinthecountry,WuhanUniversityandGuandongUniversityofScienceandTechnologyhasmadesomeprogress.NationalUniversityofDefenseTechnologyPhotonic/phononiccrystalresearchcenteriscurrentlyengagedinthestudyofphononiccrystals[14].

2.3Researchcontentofphononcrystals

Phononiccrystalresearchesmainlyincludesthreeaspects:

thebandgapofthephononiccrystalmechanism,characteristicsofdefectstatesandapplicationresearches.

2.3.1phononiccrystalbandgapmechanism

Alotoftheoreticalandexperimentalstudieshaveprovedtheexistenceofaphononiccrystalelasticwaveband,Figure2showsatypicalphononcrystalbandstructure,shadedinFigure2istheelasticwavebandgap.

Fig2Anelasticbandgapofatypicalphononiccrystal

Therearetwomorematureaboutthemechanismofelasticwavebandformed,scatteringmechanismsandlocallyresonantmechanisminPrague.Braggscatteringleadedbycrystalbandtheoryinsolidstatephysics,photoniccrystalscomplywiththeBraggscatteringmechanism.Braggscatteringcausedbythebandgapismainlydueto[15]:

thecyclechanginginmaterialpropertieswithelasticwaveinteraction,suchthatcertainfrequenciesofthewavedoesnotcorrespondtothevibrationmodeintheperiodicstructure,whichcannotspread,resultingintheforbiddenband.LargenumberofstudiesofelasticwavebandgapformedliteraturefocusesontheBraggscatteringmechanism,thestudyshowsthattheelasticwavebandgapgeneratescompositemediarelatedcomponentoftheelasticconstants,densityandspeedofsound,andthefillingratioofthecomponent;andlatticestructureandsize.Ingeneral,non-networktypeofthelatticestructurethannetwork-typelatticestructureiseasytoproducethebandgap;elasticcomponentinthecompositedielectricconstant,thegreaterthedifference,themorepronetheforbiddenband[16].Inaddition,thewavelengthoftheelasticwavebandcorrespondingBraggscatteringformesoftheelasticwaveisusuallyassociatedwithperiodicstructure,thesizeparameter（i.e,thelatticesizeorlatticeconstant）equivalenttotheforbiddenbandisconsistentwiththemechanisminconceptwitht