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  • 4/7/2016

    1

    ECE532221st CenturyElectromagnetics

    Instructor:Office:Phone:EMail:

    Dr.Raymond C.RumpfA337(915)7476958rcrumpf@utep.edu

    Synthesizing Geometries for 21st Century Electromagnetics

    Holographic Lithography

    Lecture #17

    Lecture 17 1

    Lecture Outline Photolithography Two beam interference Multiple beam interference Holographic lithography Beam synthesis Near-field nano-patterning

    Lecture17 Slide2

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    2

    Photolithography(Fabrication of a Rib Waveguide)

    What is Photolithography

    Lecture17 4

    Usuallyultravioletlightisusedtoexposeaphotosensitivematerial.Fornegativetonephotoresists,theresistbecomespolymerizedwherethelightdoseexceedsathreshold.Apositivetonephotoresistbecomespolymerizedwherethelightdoseisbelowathreshold.

    Photolithographyistypicallyusedtofabricatesmall2Dfeaturesfromthinfilm.

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    3

    Close-Up View of Wafer

    Lecture17 Slide5

    Typically,westartwithacleanedfusedsilicasubstrate.A4waferiscommoninresearchlabs.Fusedsilicahasn = 1.52.

    Silicasubstrate

    4wafer

    flat

    Deposition of High-Index Layer

    Lecture17 Slide6

    Second,alayerofhighindexmaterialisdepositedontothesiliconwafer.Acommonprocessisplasmaenhancedchemicalvapordeposition(PECVD).Acommonhighindexmaterialissiliconnitride(SiN)whichhasn = 1.9.

    SilicasubstratewithSiN

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    4

    Spin Coat Photoresist

    Lecture17 Slide7

    Third,aphotoresist isspunontothewaferusingaspinner.Acommonphotoresist isPMMA.

    SilicasubstratewithSiNandphotoresist

    Develop Photoresist

    Lecture17 Slide8

    Fourth,theresistisexposedtoultravioletradiationthroughamaskinthepatternoftheeventualopticalintegratedcircuit.Theexposedresististhenwashedawayleavingbehindtheunexposedresist.

    SilicasubstratewithSiNanddevelopedphotoresist

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    5

    Plasma Etch

    Lecture17 Slide9

    Fifth,thewaferisetchedusingaplasmaetchingprocess.BoththeresistandSiN areetched,buttheremainingresistpreventetchingoftheSiN materialdirectlyunderneath.

    Waferafteretchingprocess

    Clean Wafer

    Lecture17 Slide10

    Sixth,thewaferiscleanedbyremovingtheremainingresist.Theopticalintegratedcircuit(andourribwaveguide)iscomplete!

    RibWaveguide

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    6

    Two Beam Interference

    Electric Field Amplitude

    Lecture17 12

    Theelectricfieldassociatedwitheachoftwoseparatebeamsis1 2

    1 2 and jk r jk rE e E e

    Theoverallelectricfieldresultingfromtheinterferenceofthesetwobeamsis

    1 2 total 1 2jk r jk rE r E e E e

    1k

    2k

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    7

    Beam Intensity

    Lecture17 13

    Theintensityisessentiallythemagnitudesquaredofthetotalelectricfield.

    1 222

    total 1 2 0

    2 2

    0 1 2

    *1 2

    0

    1 2

    *1 2

    1 1 1 cos2 2

    impedance of the medium1

    21

    2

    Phase

    jk r jk rI r E r E e E e I V K r

    I E E

    V E EI

    K k k

    E E

    Overallintensity

    Visibility

    Gratingvector

    Phase

    2k

    1k

    Visibility

    Lecture17 14

    Beamsthatareorthogonallypolarizedwillnotinterfereandwillhavezerovisibility.

    Beamsthatarenotorthogonallypolarized,butnotcompletelythesame,willinterferewithmoderatevisibility.

    Beamswiththesamepolarizationwillhave100%visibility.Thatis,theinterferencewillhavecompletelydarkregionsandcompletelybrightregions.

    increasingvisibility

    V=0

    V=1.0

    V=0.5

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    Induced Grating Vector

    Lecture17 15

    Whentwobeamsinterfere,theresultingintensityisasinusoidalpatternwithaperiodandorientationthatcanbecharacterizedbyagratingvector.K

    Thewavevectorsofthebeamsandtheinducedgratingvectorformatrianglewherethegratingvectorconnectsthetipsofthewavevectors.

    2k

    1k

    K

    Conclusions on Two-Beam Interference The lines of the induced grating bisect the

    wave vectors. A small angle between the wave

    vectors produces a long period interference pattern. There is no upper limit to how long the period can be.

    A large angle between the wave vectors produces a short period interference pattern. There does exists a lower limit on the period.

    Lecture17 16

    max

    min 0

    2

    2 22

    K k

    n

    0

    min 2refractive index of the photoresist

    nn

    Aflattriangle

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    9

    Multiple Beam Interference

    Electric Field Amplitude

    Lecture17 18

    SupposewehaveN beamsoverlappinginthesamevolumeofspaceandproducinginterference.

    1 21 2, , N

    jk rjk r jk rNE e E e E e

    TheinterferencebetweenallN beamsisthesumofalltheconstituentbeams

    total1

    n

    Njk r

    nn

    E r E e

    1k

    2k

    3k

    4k

    5k

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    10

    Beam Intensity

    Lecture17 19

    ItfollowsthattheintensityoftheinterferenceofallN beamsis

    2 12

    total 01 1 1

    2

    01

    *

    0

    *

    1 1 1 cos2 2

    impedance of the medium1

    21

    2

    Phase

    n

    N N Njk r

    n ij ij ijn i j i

    N

    nn

    ij i j

    ij i j

    ij i j

    I r E r E e I V K r

    I E

    V E EI

    K k k

    E E

    Overallintensity

    Visibilityoftheinterferencebetweentheith andjth beams

    Gratingvectoroftheinterferencebetweentheith andjth beams

    Phaseoftheinterferencebetweentheith andjth beams.Thistermcontrolstheoffsetoftheinterferencepattern.

    ,Overall visibility ij

    i jV V

    Beam Amplitude Vs. Intensity

    Lecture17 20

    ElectricFieldAmplitude InterferenceIntensity

    AerialImage

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    11

    Induced Grating Vectors

    Lecture17 21

    Eachpairofwavevectorsinducesonesinusoidalinterferencepatterncharacterizedbyagratingvector.FortheinterferenceofN beams,thenumberofinducedgratingvectorsis

    2

    # 's2

    N NK

    Wavevectors

    Gratingvectors

    ExampleIfweinterferefivebeams,weget

    25 5 10 gratings2

    Holographic Lithography

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    12

    What is Holographic Lithography?

    Lecture17 23

    Holographiclithographyisalmostalwaysperformedbyinterferingfouropticalbeams.

    Aerialimage

    Latentimage

    4 Beams = 6 Gratings

    Lecture17 24

    Ifweinterferefourbeams,wegetsixplanargratings.2 24 4# gratings 62 2

    N N

    Theseare

    1 2 12

    1 3 13

    1 4 14

    2 3 23

    2 4 24

    3 4 34

    k k K

    k k K

    k k K

    k k K

    k k K

    k k K

    NotethatKij inducesthesamegratingasKji soonlyoneofthesehastobeconsidered.

    21K

    31 K

    41 K

    32 K

    42 K

    43 K

    number of beamsN

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    Determining Lattice Symmetry

    Lecture17 25

    Weknowfrompreviouslecturesthatanyofthe14Bravais latticescanbeuniquelydescribedbythreelatticevectors.

    Thereciprocallatticevectorscanbeinterpretedasgratingvectors.

    Weonlyneedthreegratingvectorstodeterminethesymmetryoftheinducedlattice,butwehavesix.Wechooseanythreethatcontaininformationfromallfourwavevectors.Thesethreedeterminethesymmetryoftheinducedlattice.

    1 2 12

    1 3 13

    1 4 14

    k k K

    k k K

    k k K

    1 2 12

    1 3 13

    2 3 23

    k k K

    k k K

    k k K

    1 2 12

    2 3 23

    2 4 24

    k k K

    k k K

    k k K

    Mostcommonchoice Anothervalidchoice Incorrectchoice

    4Where is ?k

    Four Beams All 14 BravaisLattices

    Lecture17 26

    Usingjustfourbeams,allfourBravais latticescanbeformed.

    Why?Fromtheoryjustpresented,wecanproduceanythreegratingvectorsthatwewantfromjustfourbeams.

    Fromsolidstatephysics,all14Bravais canbedescribedbythreegratingvectors.

    How?Determiningwhatfourbeamsareneedediscalledbeamsynthesis.

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    14

    Lattice Chirp

    Lecture17 27

    Latticesformedbyholographiclithographyareinherentlychirped.Thisisduetoabsorptionofthephotoresist.Lowabsorptionandhighcontrastresistshelpreducechirp,butitisalwayspresent.

    RaymondC.RumpfandEricG.Johnson,"Fullythreedimensionalmodelingofthefabricationandopticalpropertiesofphotoniccrystalsformedbyholographiclithography,"JournaloftheOpticalSocietyofAmericaA,Vol.21,No.9,pp.17031713,Sept.2004.

    Beam Synthesis

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    15

    Step 1 Design the Unit Cell

    Lecture17 29

    ThebeamsynthesisprocedurebeginsbychoosingaBravais latticeandcalculatingitsreciprocallatticevectors.

    Itisusuallymoststraightforwardtobeginbydefiningtheaxisvectorsofthedirectlatticetocontrolsizeandorientationoftheunitcellmoreintuitively.

    1

    2

    3

    0 00 00 0

    a xa ya z

    ExampleAcubicphotoniccrystalwithlatticeconstant willhavetheseaxisvectors.

    Step 2 Choose the Lattice Symmetry

    Lecture17 30

    Theprimitivetranslationvectorscanbecalculatedfromtheprimitiveaxisvectorsifthesymmetryofthelatticeisknown.

    1 1

    2 2

    3 3

    1 0 00 1 00 0 1

    t at at a

    1 1

    2 2

    3 3

    1 2 1 2 1 21 2 1 2 1 21 2 1 2 1 2

    t at at a

    1 1

    2 2

    3 3

    0 1 2 1 21 2 0 1 21 2 1 2 0

    t at at a

    1 1

    2 2

    3 3

    1 2 1 2 01 2 1 2 00 0 1 2

    t at at a

    1 1

    2 2

    3 3

    1 1 3 1 31 3 1 3 1 31 3 1 1 3

    t at at a

    Simple

    BodyCentered

    FaceCentered

    BaseCentered

    Trigonal

    Ourchoiceforfacecenteredcubic(FCC)example

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    16

    Step 3 Calculate the Reciprocal Lattice Vectors

    Lecture17 31

    Thereciprocallatticevectorscanbecalculateddirectlyfromthedirectlatticevectorsusingthefollowingequations:

    2 3 3 1 1 2