research article a comprehensive analysis of plasmonics

Hindawi Publishing CorporationAdvances in OptoElectronicsVolume 2013 Article ID 793253 10 pageshttpdxdoiorg1011552013793253

Research ArticleA Comprehensive Analysis of Plasmonics-Based GaAsMSM-Photodetector for High Bandwidth-Product Responsivity

Narottam Das1 Farzaneh Fadakar Masouleh2 and Hamid Reza Mashayekhi2

1 Department of Electrical and Computer Engineering Curtin University Perth WA 6845 Australia2 Department of Physics University of Guilan Rasht 41335-1914 Iran

Correspondence should be addressed to Narottam Das narottamdascurtineduau

Received 29 April 2013 Revised 10 August 2013 Accepted 22 August 2013

Academic Editor Jung Huang

Copyright copy 2013 Narottam Das et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A detailed numerical study of subwavelength nanogratings behavior to enhance the light absorption characteristics in plasmonic-based metal-semiconductor-metal photodetectors (MSM-PDs) is performed by implementation of 2D finite-difference time-domain (FDTD) algorithmDue to the structure design and changes in the device physical parameters various deviceswith differentgeometries are simulated and compared Parameters like nano-grating height and duty cycle (DC) are optimized for rectangularand taper subwavelengthmetal nanogratings onGaAs substrate and their impact on light absorption below the diffraction limits areconfirmedThe calculated light enhancement is sim327-times for an optimized device in comparison with a conventional MSM-PDThis enhancement is attributed to the plasmonic effects in the near-field region

1 Introduction

Periodic nanostructures can produce an efficient light trans-mission and absorption by excitation of surface plasmons(SPs) [1] and their potential practice (or application) inoptical communication system has made them an interestingtype of devices [2] The continuing progress in plasmonicinteraction with nanostructures and their outstanding designinstruction in metal-semiconductor-metal photodetectors(MSM-PDs) has developed a unique context for future-generation optoelectronic systems such as optical fiber com-munication systems high speed chip-to-chip interconnectsand high-speed sampling [3] The conventional MSM-PD isa symmetrical device which is equivalent to two back-to-backconnected Schottky diodes on a semiconductor substrate [4]such as GaAs which as a direct band gap semiconductor col-lects and emits photons more efficiently than indirect semi-conductors such as Si and Ge [5] To create a Schottky junc-tion some essential properties must be satisfied such as typeand quality of metal and semiconductor along with the shapeand size of the interface [6] A significant amount of illumina-tion on top of a conventional MSM-PD is reflected and thelight absorption is reduced considerably in devicersquos activeregion Fabrication of nanogratings on top of the metal fin-gers on conventional MSM-PDs can avoid the unwanted

reflection and exhibit notable light transmission By tailoringthe electrodes structure surface with metal nanogratingsMSM-PDs can be modified for the light absorption and themodification process strongly depends on the corrugationparameters Recently different shapes of one-dimensional(1D) nanostructured surfaces have been developed in whichnoble metals such as gold (Au) are used for nanogratingstructuring When an electric field (or a voltage) is appliedbetween the electrodes and the devicersquos active region is underillumination then the electric carriers (ie electrons andholes) are generated and drifted towards the opposite elec-trodes due to the electric field and can form a photocurrentImprovement of recombination between electrons and holescan lead to enhance the light absorption in the subwavelengthaperture region [3 7 8] Over the decade an interesting effectof light interactingwithmetallic structures has been revealedFor sufficiently small nanograting period higher order dif-fractions are suppressed and only the zero order diffraction ispresent There has been a considerable and growing interestto clarify all phenomena corresponding to the improvementin light absorption via nanoscale structuring recently [9ndash12]The main motivation is to come up with a practical methodfor avoiding the undesirable light reflection from the sur-face of the electrodes and enhance the light transmission

2 Advances in OptoElectronics

120596

120596p

ckz

radic120576d

120596p

radic1 + 120576d

Re kz

1205962 = 1205962p + c2k2

ksp =120596

c( 120576998400m120576d

120576998400m + 120576d)12

Figure 1The dispersion relation of nonradiative SPs on the right ofthe light line and dispersion relation of radiative SPs on the left ofthe light line

efficiency through the subwavelength aperture It is usefulto describe the SP dispersion relation as shown in Figure 1To have propagating bound SPs the wave vector componentmust be real along the interface Any light cannot be used forSP generation because the real part of the wave vector in the119911-direction exceeds that of free light (120596 = 119888119896) as shown inFigure 1 and a coupling mechanism is required

In the presence of a transverse magnetic (TM) polarizedlight the SPs exist along ametal-dielectric interfaceThere areseveral techniques to excite the SP waves such as prism cou-pling and grating coupling For the case of semiconductorsprism coupling is not very much advantageousThe attentionshould be paid to prism refractive index which is hardlyhigher than popular semiconductors used for correspondingresearches [13 14] In particular this study presents the effectsof nanograting structures on theMSM-PD device Optimiza-tion of subwavelength nanogratings shape and pitch is verymuch important to generate the zero-order diffraction wavesThus the subwavelength nanogratings can be represented as ahomogeneousmediumwith optical properties determined bythe nanograting geometry [15]When the nanograting periodis within the order of the light wavelength the light wavemaybe resonant and reflects into the structure hence the higherdiffraction orders will be suppressed and resonant reflec-tion occurs for the zero-order diffraction waves [16ndash18] Themetallic nanogratings can exhibit absorption anomalies Oneof these particularly remarkable anomalies is observed for119901-polarized light only and is due to the surface plasmonpolariton (SPP) excitations [19]The light incident on the one-dimensional metallic nanogratings composed of subwave-length slits is converted into the propagating SPPs that canabsorb the light efficiently in extremely thin (10 nm to morethan 100 nmrsquos thick) layers The coupling of light to thestructure in the form of the SPPs is obtained with the utilityof periodicity There are two distinct mechanisms to producethe transmission of light in 1Dmetal nanogratingwith narrowslits which are the excitation of horizontal and verticalsurface resonances The horizontal surface resonances are

excited by the periodic structure of the nanogratings Thevertical surface resonances have relations with Fabry-Perotresonances of the fundamental TM guided wave in the slits[1] Two vertical resonances existing on the slit walls cancompose a fundamental waveguide mode which satisfies theFabry-Perot condition and reflects repeatedly from both endsof the slit Therefore the guided modes can be excited alongvertical direction evanescent coupling mechanism accountsfor this activation [20] The responsibility of these two effectson extraordinary optical transmission (EOT) is still underdebate However it is indicated that both mechanisms areimportant in the EOT [21] Concentrating the light in smallareas (plasmonic lenses) with the assistance of extremelythin layers [22] the EOT is a unique phenomenon which isinduced by the SP assisted multiple diffractions coupling theSPs into the aperture and conversion back into near-field atthe exit side of the aperture The role of SP modes is essentialto clarify the EOT of light through the slits In the EOT theaperture transmits more light than the standard aperture the-ory The EOT can occur whenever some specific conditionsare satisfied that is the slit width must be much smaller thanthe incident light wavelength the periodicity has to be in therange of wavelength and it can lead to outstanding results ifthe light is normally incident to the structurersquos surface Sub-wavelength apertures have also been used to concentrate lightefficiently into the deep subwavelength regions

A considerable development has been reported for theEOT throughmetallic grating with very narrow slits [23]TheSPPs and subwavelength apertures in metallic thin films arealways involved with this phenomenon but the details arestill under investigation [7 9 16] The SPs can be efficientlyexcited in the nanostructured noble metals since they almosthave free-electron behavior [24] The noble metal nanotex-tured structures have special properties to produce local-ized regions of high energy concentration and show largerenhancement for extraordinary optical absorption (EOA)This effect and its underlying mechanism have importantapplications in photolithography and near-field microscopy

The absorption enhancement caused by the excitation ofSPPs is associatedwith the incident photons and their interac-tion with the nanogratings whereas Fabry-Perot resonancesare included in transmission absorption process through thesubwavelength slits In addition the light is mostly reemittedfrom a very small area surrounding the aperture whichis associated with the properties of the Fabry-Perot cavityresonances for symmetric SPP modes of the slit

Themain objective of this research is to find out the radia-tion behavior through the nanoscale device Finite-differencetime-domain (FDTD) simulation tool is a full wavemodelingtechnique that demonstrates significant light-capturing per-formance through the periodic 1D slit arrays [25] for thedesign of ultrafast MSM-PDs [3] The FDTD algorithm wasoriginally proposed by Yee in 1966 [26] and introduces amodeling technique to solve the Maxwellrsquos curl equations intime domain It can directly calculate the value of 119864 (electricfield intensity) and 119867 (magnetic field intensity) at differentmesh points in the computational domain denoted by (119894 119895 119896)with respect to Ampere and Faradayrsquos laws (Maxwell equa-tions) Since then it has been used for several applications

Advances in OptoElectronics 3

and many extensions of the basic algorithm developed [27]Currently the FDTD method is widely used for electromag-netism computations such as fields and resonant modes

2 Nanostructured MSM Photodetector Design

A plasmonics-based MSM-PD structure has three separateregions or parts namely the incident region (themetal nano-gratings) the grating area and the subwavelength aperturesregion and the transmission region (the substrate) Thenanoscale gaps between the interdigitated electrodes in theMSM-PDs result in a huge increase in bandwidth and reduc-tion in dark current whereas the conventional PIN photode-tectors with similar sized active areas are unable to achievethat amount of light

The momentum of SPs can be easily changed by addingthin layers of material on the metal surface or by changingthe dielectric constant of the material deposited on it Herethe gold (Au) metal nanogratings were deposited on top ofthe underlayer containing subwavelength apertures and theunderlayer is just on the semiconductor (GaAs) substrateswhile the whole structure is surrounded by airWhen the sur-face is corrugated the electromagnetic radiation can be cou-pled with the SPPs Incident photons on a corrugated surfacecan induce diffraction by addition or subtraction of multiplesof nanograting vector 119896119892 = 2120587Λ where Λ is the gratingperiod Therefore the nanocorrugations should satisfy thedispersion relation by providing the momentum differenceas in (1) which is governed by the momentum selection rules(ie occurring only at a specific angle for a givenwavelength)For the TM polarization diffraction orders will be in theclassical mount where all diffraction orders are in the planeof incident The SPP charge density waves are confined tothe metal-dielectric interface and can only be excited with 119901-polarized electromagnetic radiation where themagnetic fieldis along the 1Dnanograting corrugations (119867119910)Thismeans incase of a one-dimensional nanograting the corrugations arethe grooves of infinite length in the 119910-direction Here thenanogratings are called the continuous nanogratings withrectangular (or tapered) cross-section because they are placedon a thin layer of the same metal to fabricate the modifieddevice structure The linearly polarized incident radiationof light with appropriate frequency and angle of incidentsatisfies the dispersion relation equation hence the SPP dif-fraction occurs [28] The coupling of incident electromag-netic wave to the SPs on the nanograting assisted MSM-PDstructure surface is shown in Figure 2

The TM polarized wave is required to excite the propa-gating SP waves when the 119911-component of the light 119896-vectormatches with the SP 119896-vector because only the TM polar-ization has electric field component in the same direction assurface normal To represent the influence of electric field inorganizing electric charges and dipoles in the medium weintroduce electric displacement field 119863 = 1205760120576119903119864 betweentwo isotropic media where 1205760 is the vacuum permittivity and120576119903 is the relative (dielectric) permittivity Here the gold hascomplex dielectric permittivity in the form of 120576119898 = 120576

1015840

119898+ 119894120576

10158401015840

119898

from which the real part has been used The dielectricpermittivity of air is 120576119889 The real part of gold dielectric

Surface plasmon

Semiconductor substrate Subwavelength apertureMetal nanogratings

120579

k

120573

120601

z

X

Figure 2 A symmetric diagram of a plasmonic-based MSM-PDstructure with rectangular-shaped nanogratings on interdigitatedelectrodes and semiconductor substrate Here the gold nanograt-ings are on the substratemade fromGaAs EOTwill occur as a resultof SP-light interactions

permittivity has negative value at optical wavelength Theelectric displacement field derived fromMaxwellrsquos equation iscontinuous across the interface With the continuous normalcomponent of 119863 across the interface and the permittivitysign difference for metal and dielectric the electric fieldchanges direction passing through two different media Thischaracteristic will only be satisfied if there is a normal com-ponent for electric field across two regions The polarizationis described with regard to the electric field configuration ofthe incident light with respect to the surface normal (angle 120573)as shown in Figure 2 The wave is purely TE polarized when120573 = 1205872 and purely TM polarized when 120573 = 0 The angle120601 represents the direction of the plane of incidence suchthat the nanograting is in the classical mount in this modelwhere all the diffracted orders remain in the 119909-119911 plane andthe plane of incidence is normal to the nanograting grooves(120601 = 0) Besides when the grooves are parallel to the plane ofincidence the nanograting is in the conical mount (120601 = 90)

In periodic subwavelength structures the nanogratingsare deposited on top of the underlayer from the same metal(such as gold) The absorption enhancement can be achievedby the SPP resonant excitations in the subwavelength regionHere the FDTD method is used to specify the TM polarizedplane wave via Poynting vector The SPPs are evanescentwaves which are generated by the interaction between thesurface electron densities and the electromagnetic fieldswhilst trapping the light power inside the surface Since the SPmodes have longer wave vectors than the light waves with thesame energy the SPwaves are nonradiative on smoothmetal-lic surfaces and cannot propagate in nonmetallic media Oneway to excite the SPPs is the nanograting coupling techniquein which the incident radiation is coupled into the SPPs usinga periodic surface corrugation [17] The nanograting groovesare perpendicular to the 119909-direction and its dimensions andgeometry are optimized to couple the light near the designwavelength that is providing the missing momentum inorder to make the SPPs propagate along the 119911-direction Ina metal-dielectric interface the SPP wave vector matching


condition for a metal nanograting can be defined with somechanges to the well-known prism resonance condition [29]Hence the SPP propagating constant or wave vector withmetal nanograting period of Λ is given by [13 16 30]

120596

119888

sin (120579) plusmn 2120587119897Λ

= 119896sp =120596

119888

radic

120576

1015840

119898120576119889

120576

1015840119898+ 120576119889

(1)

where Λ is the metal nanograting period 120596 is the angularfrequency of the incident light wave 119888 is the speed of light invacuum 120579 is the angle between the incident light and the nor-mal and 119897 is an integer

This relation illustrates that the wave vector of a given fre-quency is smaller than the SPP wave vector therefore thelight wave vector should increase with the support of a coup-ling mechanism to provide SPPs which is satisfied by nano-grating structure To trigger SPPs the dielectric permittivityhas to change sign in themetal-dielectric interfaceThemetalpermittivity has to be complex 120576119898 = 120576

1015840

119898+ 119894120576

10158401015840

119898 Therefore the

wave vector is complex The SPP damping while propagatingalong the interface will be determined by the imaginary partof the wave vector parallel component The researchers dem-onstrated their results for noblemetals such as gold and silverinmetal-dielectric interface [31]The values of dielectric con-stant vary for different frequency ranges We are interested inmetals with the large negative real part and a very small imag-inary contribution to the dielectric constant for the designwavelength such as gold Therefore there will be a high fieldconfinement at the interface while the losses remain mini-mum When the plasmonic excitations occur the left side of(1) matches the wave vector of the excited SPP (119896spp) that isthe equivalence of the interaction of incident radiation and119897th diffracted order with the wave vector of SP at the interface

3 Noble Metals and Lorentz-Drude Model

Nowadays it is clear that the realmetals play a very importantrole in EOT because their effect is essential for the SP exci-tation The real metal is characterized by the frequencydependent dielectric permittivity 120576119898 = 120576

1015840

119898+ 119894120576

10158401015840

119898 It consists

of a negative real part 1205761015840119898and a positive imaginary part 12057610158401015840

119898

responsible for light absorption which is obtained from Lor-entz-Drude model The letter 119894 is an imaginary unity thatis radicminus1 and 120576119889 is the dielectric permittivity of the incidencemedium here it is air The condition for the existence of theSP on a flat air-metal interface 1205761015840

119898lt minus1 12057610158401015840

119898≪ |120576

1015840

119898| is fulfilled

for many metals including the silver and gold [32 33]Dielectric and magnetic properties of the material with

nanotextured structure can easily be determined by theimplementation of Lorentz-Drude model [34] Below plasmafrequency the good conductors like silver (Ag) and gold (Au)have negative values for the real part of complex dielectricconstant Therefore it is necessary to define an appropriatemodel to specify the dielectric properties of the materials Acomplex dielectric function for somemetals and surface plas-mas which have good agreement with the experimentallymeasured results can be expressed in the following form [35]

120576119903 (120596) = 120576119891

119903(120596) + 120576

119887

119903(120596) (2)

where the term 120576119903(120596) is the complex dielectric function formetals 120576119891

119903(120596) is referred to as free electron effects and 120576119887

119903(120596)

is associated with bound electron effects This model takesboth the intraband 120576119891

119903(120596) and interband 120576119887

119903(120596) effects into

account for simulations The former Drude model candescribe the transport properties of electrons in good con-ductors and the later Lorentzmodel is a semiquantummodeldescribing bound electron effects The Drude and Lorentzmodel in frequency domain can be written as in the followingform of (3) and (4) respectively

120576

119891

119903(120596) = 1 +

Ω

2

119901

119894120596Γ0 minus 1205962

(3)

120576

119887

119903(120596) =

119872

sum

119898=1

1198661198981205962

119901

120596

2119898minus 120596

2+ 119894120596Γ119898

(4)

where Ω119901 = 119866012120596119901 is the plasma frequency associated

with intraband transitions with oscillator strength 1198660 anddamping constant Γ0 while 119898 is the number of oscillatorswith frequency 120596119898 and 1Γ119898 is the oscillator lifetime [36]The following equation accounts for the complex index ofrefraction and dielectric constant of materials and can berepresented as a combined form [37]

120576119903 (120596) = 120576119903infin +

119872

sum

119898=0

119866119898Ω2

119898

120596

2119898minus 120596

2+ 119894120596Γ119898

(5)

where 120576119903infin is the relative permittivity at infinite frequency119866119898 is the strength of each resonance term Ω119898 is the plasmafrequency 120596119898 is the resonant frequency and Γ119898 is thedamping factor or the collision frequency

OptiFDTD is the first software to employ the Lorentz-Drude model into the FDTD algorithm Here the Lorentz-Drude model for gold is solved with 6 resonant frequencies(multipole dispersion) The simulation is performed over aconstant plasma frequency which depends on the density ofcharge carriers with the amount of 0137188119864+ 17 The reso-nant frequency changes according to the resonance strengthThe Lorentz-Drude material parameters are listed in Table 1

4 Results and Discussion

To study the mentioned effects on the plasmonic-basedMSM-PD structure we adopted the FDTD algorithm withthe aid of Opti-FDTD software package developed by Opti-wave Inc Nanograting assisted MSM-PD is introduced withan important feature of the EOT The concept of plasmoniclens is representedwhich utilizes plasmonic effects to produceSPPs and funnel the energy toward the central focus pointHence the device is enabled to enhance the collection of pho-tocurrent into the near field region [38 39] A set of numericalsimulations are performed to calculate the Poynting vectorwhich is particularly useful in quality light absorption Onlyon metal surfaces electromagnetic wave can propagate inthe form of SPPs We used nanograting coupling techniqueto enhance the device performance The numerical analysisof the corrugated metal surfaces with different nanograting


Table 1 Lorentz-Drude parameters for gold (measured in radiansper second)

Term Strength Resonant frequency Damping frequency0 07600 0000000119864 + 00 0805202119864 + 14

1 00240 0630488119864 + 15 0366139119864 + 15

2 00100 0126098119864 + 16 0524141119864 + 15

3 00710 0451065119864 + 16 0132175119864 + 16

4 06010 0653885119864 + 16 0378901119864 + 16

5 43840 0202364119864 + 17 0336362119864 + 16

shapes is implemented and their performances are comparedPresuming that the full power flow through the slits reachesto the GaAs substrate the optimal absorbed radiation ratio tothewhole incident power can be perceived by a dimensionlessquantity namely the light absorption enhancement factor(LAEF) defined as the ratio of normalized light transmissionthrough the device with the nanogratings to that of the con-ventional type device without the nanogratings [40] Theterm LAEF shows the impact of nanogratings on the qualityof light flux transmitted into the active region of the devicecomparing to the conventional device without the nanograt-ings

We calculated the amount of light flux transmitted intothe slit for the plasmonic-based MSM-PD structure sets withthe rectangular trapezoidal and triangular nanograting pro-files and their behavior are compared Focused ion beam(FIB) lithography technique is used to develop nanofabri-cations and nanogratings are successfully patterned in plas-monic-basedMSM-PDsTheobservation of SEM images rep-resents the nanogratings with taper walls rather than the rect-angular nanogratings [3 41] and the simulation results con-firm the capability of some trapezoidal nanogratings underspecial design which enhances the LAEF more than the rect-angular one while the reverse is true for some other struc-tures Here several numerical simulation results for theenhancement of optical absorption in MSM-PDs are pre-sented

41 Effect of Nanograting Height on the LAEF In this subsec-tion we have calculated the amount of light flux transmittedinto the slit for 4 different rectangular nanograting heightsand presented the LAEF spectra in Figure 3 The peak wave-length behaves like a sinusoidal manner and wavelength (120582)is red shifted as the ridgersquos height increases The duty cycle is60 while the nanograting period is kept constant at 810 nmThe subwavelength aperture width and height are kept con-stant at 50 nm and 20 nm respectivelyTheTMmode of lightwas perpendicularly incident on the groove profiles Theheight of the ridge is an effective parameter as different sets ofresults show significant changes in the amount of light trans-mitted into the active area of the MSM-PD with the variationof nanogratings height There are some interpretations toanalyze the curvesThe SPPs coupling process and the follow-ing expected absorption can easily occur for higher gratingsand reduces after certain heights This light absorption has amaximum for a specific wavelength in the spectra which

varies in different heights For amesh step size of 120575119909 = 10 nmthe green curve represents about 26-fold absorption enhance-ment the maximum LAEF for 120 nm nanograting heightFigure 3 For the wavelengths higher than the peak theamount of LAEF decreases and the reason might be the inci-dent light coupling into radiative SPs more than bound ones

Several sets of numerical analysis are carried out to illus-trate the effect of trapezoidal-shaped nanograting height anddemonstrated the height at which the resonance transmissionis maximum The simulations are performed for 4 differentnanograting heights of 100 120 140 and 160 nmwith the sub-wavelength aperture width of 50 nm and the underlayerthickness of 20 nm The results are shown in Figure 4 TheLAEF is 263 times in its maximum for the green curve repre-senting the 140 nm nanograting height for the duty cycle of60 Hence tapered nanogratings height at maximum lightabsorption is higher than the optimum height of its rect-angular counterpart while its resonant wavelength is blueshifted

42 Effect of Duty Cycles on the LAEF This subsectiondiscussed the effect of duty cycles on the LAEF of the nanos-tructured MSM-PDs The nanograting profile which is madeof gold on the GaAs substrate can change the absorptionenhancement Hence for 2 similar nanogratings with thediscrepancy in profile shapes the LAEF can be differentWe specify the optimum duty cycle for trapezoidal and rect-angular-shaped nanograting profiles with an optimumheightof 140 nm and 120 nm respectively The transmission spectraare calculated with 120575119909 = 10 nm mesh step in the FDTDsimulation

We calculated the LAEF spectra in rectangular-shapednanograting structures for different duty cycles such as from30 to 90 as shown in Figure 5 while the subwavelengthaperture width has been kept constant at 50 nm the under-layer thickness and the nanograting height were 20 nm and120 nm respectively It can be inferred that the peak wave-length is different for each specific duty cycle and the max-imum LAEF occurs for 40 duty cycle with the amount ofsim327 It is clear that the duty cycle can affect the peak wave-length as well as the amount of light flux transmitted into theactive area of the MSM-PDs

The optimum duty cycle has also been specified for trape-zoidal-shaped nanograting profile with the subwavelengthaperture width and thickness of 50 nm and 20 nm respec-tively In this case the maximum LAEF is obtained sim315 for40DCwhich is the same duty cycle as the optimumDC forrectangular-shaped nanogratings

The results shown in Figures 5 and 6 illustrate that theamount of LAEF is a function of duty cycle which growsgradually towards the 40 DC and drops down dramaticallytowards 90 DC for both the structures and the peak wave-lengths are red-shifted for the higher duty cycles In thecase of the rectangular and trapezoidal nanograting profilesdesigned with their optimum nanograting height and dutycycle nanostructures with normal walls perform betterTherefore the amount of power (energy) transmitted into theactive region not only depends on the nanogratings height


0

5

10

15

20

25

30

06 07 08 09 1 11 12 13 14

LAEF

Nanograting heightrectangular profile

Wavelength (120583m)

80nm100nm

120nm140nm

Figure 3 LAEF spectra for rectangular nanogratings with differentheights Here DC is 60 and subwavelength aperture width is50 nm

0

5

10

15

20

25

30

06 08 1 12 14

LAEF

Nanograting heighttrapezoidal profile

100nm120nm

140nm160nm


Figure 4 LAEF spectra for different nanograting heights of trape-zoidal profiles Here DC is 60 and subwavelength aperture widthis 50 nm

but also depends on the amount of duty cycles Besides forrectangular-shaped nanograting profile 100 DC indicatesthat the whole structure is like a conventional MSM-PD withthe underlayer thickness of about 140 nm the resulting thick-ness is the sum of underlayer thickness and the nanogratingheight while for trapezoidal shaped nanogratings there willbe triangular grooves between the trapezoidal ridges for 100DC Figure 7

In plasmonic-based MSM photodetector design withnanogratings more photons have the chance of penetrationand concentration into the devicersquos active region via narrowslits of nanograting assisted MSM-PDsTherefore it is useful

0

5

10

15

20

25

30

35

06 07 08 09 1 11 12 13 14

LAEF

Duty cycle

30DC40DC50DC60DC

70DC80DC90DC100DC


120nm rec-grating height

Figure 5 LAEF spectra for different duty cycles in MSM-PD withrectangular nanogratings Here the nanograting height is 120 nmand subwavelength aperture width is 50 nm

0

5

10

15

20

25

30

35

06 07 08 09 1 11 12 13 14

LAEF

Duty cycle

30DC40DC50DC60DC

70DC80DC90DC100DC


140nm trap-grating height

Figure 6 LAEF spectra for different duty cycles in trapezoidalnanograting assisted MSM-PD Here the nanograting height is140 nm and subwavelength aperture width is 50 nm

Semiconductor

Semiconductor

Underlayer

RidgesGrooves

Figure 7Cross-section of rectangular and trapezoidal nanogratingswith duty cycle of 100


30405060

708090100

06 07 08 09 1 11 12 13 14Wavelength (120583m)

0

05

1

15

2

25

3Li

ght r

eflec

tion

fact

or

Reflection spectrum rectangular nanograting

(a)

30405060

708090100

0

05

1

15

2

25

3

06 07 08 09 1 11 12 13 14

Ligh

t refl

ectio

n fa

ctor

Reflection spectrum trapezoidal nanograting


(b)

Figure 8 Light reflection spectra for rectangular (a) and trapezoidal (b) plasmon-assisted MSM-PDs with different duty cycles Here thesubwavelength aperture width and heights are kept constant at 50 nm and 20 nm respectively

to make a comparison between the amount of electromag-netic radiation which is reflected back and the amount ofabsorbed light in the substrate Here we introduce the lightreflection factor which is defined as the amount of lightreflected from the device with the nanogratings normalizedto the amount of reflected light from the surface of con-ventional type device without the nanogratings Figure 8shows the calculated reflection spectrum of rectangular andtrapezoidal nanograting profiles for normal incidence incomparison to the transmission spectrum presented for thesimilar devices with aforementioned parameters in Figures 5and 6 respectively The curves show the reflection spectrumcalculated above the central slit for different duty cyclesLess reflection is observed for nanogratings with verticalwalls considering the range of the light reflection factorfor both rectangular and trapezoidal nanogratings Besidesthe interval between the maximum and minimum reflectionfactors is sim04 and 11 for the rectangular and trapezoidalnanograting profiles respectivelyThe reflectance peak growswith the increase of duty cycle up to 80 and it falls for 90in the rectangular nanograting profile while in the case oftrapezoidal nanogratings the maximum reflectance peak isfor 50 duty cycle

43 Effect of Subwavelength Aperture Width on the LAEF Inthis subsection the effect of subwavelength aperture widthson the light absorption enhancement of different nanogratingprofiles in MSM-PDs is discussedThe aperture width is verysmall compared to the incident light wavelength (1205820) hencesymmetric and fundamental SPmodeswill propagate into theslit The simulation results for 3 different nanograting grooveshapes with the variation of subwavelength aperture widthand the cross-section profiles of the grating structures areshown in Figure 9 Apart from the shape of nanogratings and

0

2

4

6

8

10

12

14

16

18

20

06 07 08 09 1 11 12 13 14

LAEF

Subwavelength aperture width


Taper 500nmTaper 150nmTaper 50nmTriang 500nmTriang 150nm

Triang 50nmRec 500nmRec 150nmRec 50nm

(a)

(b)

Figure 9 LAEF spectra for plasmon-assisted MSM-PDs with dif-ferent aperture widths for rectangular trapezoidal and triangular-shaped nanogratings Here the subwavelength aperture andnanograting heights are kept constant at 60 nm and 100 nm respec-tively


8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(a)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(b)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(c)

Figure 10 Field distribution at the cross-section of trapezoidal (a) and rectangular (b) nanograting assisted MSM-PDs besides conventionaltype device without nanogratings (c) at the subwavelength aperture The calculated total electric field intensity distribution inside the GaAssubstrate is shown using the following parameters gold underlayer thickness of 60 nm grating period of 810 nm and the subwavelengthaperture width of 50 nm

subwavelength aperture widths other structural parametersare invariant The nanogratings are designed with the con-stant period of 810 nm for 9 nanogratings considered on eachside of the slit (subwavelength aperture) The accepted opin-ion is that the light transmission enhancement and improvedabsorption in the semiconductor substrate can be obtainedwhen the subwavelength aperture width ismuch smaller thanthe incident light wavelength (1205820) This condition assists themetal nanogratings in the light transmission and absorp-tion effectively The FDTD simulation results are shownfor 120575119909 = 10 nm mesh size The LAEF spectra are presentedin Figure 9 for the rectangular trapezoidal-shaped with 09aspect ratio and triangular-shaped nanogratings For 60 nmunderlayer thickness 100 nm nanograting height and 50duty cycle the light absorption is minimum for triangular-shaped nanograting The LAEF in 150 nm and 500 nm aper-ture widths for the rectangular profiles is slightly higherthan the trapezoidal ones while the trapezoidal nanogratingshave the ability to improve the light absorptionmore than therectangular nanogratings for 50 nm subwavelength aperture

the narrowest slit width It has been stated that the lightis gradually compacted from the top to the bottom of thetapered grooves therefore the field is gradually enhancedmore effectively than the grooves with normal walls We haveplotted the electric field distribution of these 2 structures toconfirm how this variation influences the amount of LAEFfrom 19 to 167

Figure 10 demonstrates the increase of light absorption intrapezoidal nanograting grooves compared to the rectangularnanogratings with the slit width of 50 nm Also the lightabsorption is calculated within the cross-section of a basicMSM-PDwithout nanogratings on the electrodes to prove itsincompetence in the absence of plasmon polariton excita-tions To assess the plasmonic effects of themetallic nanograt-ing the confinement of light in the subwavelength region canbe determined according to the color bar representing eachpointrsquos electric field strength in the density plot The summa-tion of electric field components shown in Figure 10 confirmsthe better power (energy) concentration in the small sub-wavelength area of trapezoidal grooves in comparison with


the rectangular nanogratings and the conventional typedevice without the nanogratings

5 Conclusion

In conclusion plasmonic-based grating-assistedMSM-PD issupposed to be more efficient in light absorption comparedwith a conventional MSM-PD Based on the SPP interactionand Fabry-Perot resonances the power concentration in thedevice active layer was calculated We have undertaken adetailed investigation of the effects of different nanogratingshapes and other geometrical parameters The analyses werebased on the FDTD simulation results and it shows sim327-times optical absorption in comparisonwith the conventionalMSM-PDs Also the concept of plasmonic lenses has beenintroduced which provides very high optical properties forfuture applications From the density plot the near field con-centration for the case of trapezoidal and rectangular nano-grating structures with optimized parameters are proven tobe more efficient compared with the basic MSM-PDs Thesesimulation results are useful for the design and developmentof high responsivity-bandwidth-product MSM photodetec-tors

References

[1] S Collin F Pardo R Teissier and J Pelouard ldquoHorizontal andvertical surface resonances in transmission metallic gratingsrdquoJournal of Optics A vol 4 pp 154ndash160 2002

[2] E Ozbay ldquoPlasmonics merging photonics and electronics atnanoscale dimensionsrdquo Science vol 311 no 5758 pp 189ndash1932006

[3] NDas A KararMVasiliev C L Tan K Alameh andY T LeeldquoAnalysis of nano-grating-assisted light absorption enhance-ment in metal-semiconductor-metal photodetectors patternedusing focused ion-beam lithographyrdquo Optics Communicationsvol 284 no 6 pp 1694ndash1700 2011

[4] A D Zebentout Z Bensaad M Zegaoui A Aissat and DDecoster ldquoEffect of dimensional parameters on the current ofMSMphotodetectorrdquoMicroelectronics Journal vol 42 no 8 pp1006ndash1009 2011

[5] C Cha Broad-band and scalable circuit-level model of MSM PDfor co-design with preamplifier in front-end receiver applications[PhD thesis] Department of Electrical and Computer Engi-neering Georgia Institute of Technology Atlanta Ga USA2004

[6] T Wijesinghe andM Premaratne ldquoDispersion relation for sur-face plasmon polaritons on a Schottky junctionrdquoOptics Expressvol 20 no 7 pp 7151ndash7164 2012

[7] L Martın-Moreno F J Garcia-Vidal H J Lezec A Degironand TW Ebbesen ldquoTheory of highly directional emission froma single subwavelength aperture surrounded by surface corru-gationsrdquo Physical Review Letters vol 90 no 16 4 pages 2003

[8] NDas A KararMVasiliev C L Tan K Alameh andY T LeeldquoGroove shape-dependent absorption enhancement of 850 nmMSM photodetectors with nano-gratingsrdquo in Proceedings of the10th IEEE Conference on Nanotechnology (NANO rsquo10) pp 289ndash293 Seoul Republic of Korea August 2010

[9] F F Masouleh N Das and H Mashayekhi ldquoImpact of dutycycle and nano-grating height on the light absorption of plas-monics-based MSM photodetectorsrdquo in Proceedings of the 12th

IEEE International Conference on Numerical Simulation ofOptoelectronic Devices pp 13ndash14 Shanghai China 2012

[10] TW EbbesenH J LezecH F Ghaemi TThio and P AWolffldquoExtraordinary optical transmission through sub-wavelenghthole arraysrdquo Nature vol 391 no 6668 pp 667ndash669 1998

[11] H J Lezec A Degiron E Devaux et al ldquoBeaming light froma subwavelength aperturerdquo Science vol 297 no 5582 pp 820ndash822 2002

[12] Y Ding J Yoon M H Javed S H Song and R MagnussonldquoMapping surface-plasmon polaritons and cavity modes inextraordinary optical transmissionrdquo IEEE Photonics Journalvol 3 no 3 pp 365ndash374 2011

[13] S A Maier Plasmonics Fundamentals and ApplicationsSpringer New York NY USA 2007

[14] G T Reed and A P Knight Silicon Photonics An IntroductionJohn Wiley and Sons New York NY USA 2004

[15] D Dhakal Analysis of the sub-wavelength grating in OptiFDTDsimulator [MS thesis] School of Engineering and ScienceJacobs University Bremen Germany 2009

[16] H Raether Surface Plasmons on Smooth andRough Surfaces andon Gratings Springer Berlin Germany 1988

[17] D Mawet P Riaud J Baudrand et al ldquoAchromatic optical vor-tex coronagraphwith subwavelength gratingsrdquo in Proceedings ofthe International Coronagraph Workshop pp 69ndash72 PasadenaCalif USA 2006

[18] H Kikuta H Toyota and W Yu ldquoOptical elements with sub-wavelength structured surfacesrdquo Optical Review vol 10 no 2pp 63ndash73 2003

[19] J S White G Veronis Z Yu et al ldquoExtraordinary opticalabsorption through subwavelength slitsrdquo Optics Letters vol 34no 5 pp 686ndash688 2009

[20] D de Ceglia M A Vincenti M Scalora N Akozbek and M JBloemer ldquoEnhancement and inhibition of transmission frommetal gratings engineering the spectral responserdquo 2010 httparxivorgabs10063841

[21] J A Porto F J Garcıa-Vidal and J B Pendry ldquoTransmissionresonances onmetallic gratings with very narrow slitsrdquo PhysicalReview Letters vol 83 no 14 pp 2845ndash2848 1999

[22] T Lopez-Rios D Mendoza F J Garcıa-Vidal J Sanchez-Dehesa and B Pannetier ldquoSurface shape resonances in lamellarmetallic gratingsrdquo Physical Review Letters vol 81 no 3 pp 665ndash668 1998

[23] A Barbara P Quemerais E Bustarret and T Lopez-RiosldquoOptical transmission through subwavelength metallic grat-ingsrdquo Physical Review B vol 66 no 16 Article ID 161403 4pages 2002

[24] R Gordon D Sinton K L Kavanagh and A G Brolo ldquoA newgeneration of sensors based on extraordinary optical transmis-sionrdquo Accounts of Chemical Research vol 41 no 8 pp 1049ndash1057 2008

[25] Y Xie A R Zakharian J V Moloney and M MansuripurldquoTransmission of light through a periodic array of slits in a thickmetallic filmrdquo Optics Express vol 13 no 12 pp 4485ndash44912005

[26] K S Yee ldquoNumerical solution of initial boundary value prob-lems involving maxwellrsquos equations in isotropic mediardquo IEEETransactions on Antennas and Propagation vol 14 p 302 1966

[27] A Bondeson T Rylander and P Ingelstrom ComputationalElectromagnetics Springer New York NY USA 1st edition2005


[28] R Marani M Grande V Petruzzelli and A DrsquoOrazio ldquoPlas-monic bandgaps in 1D arrays of slits on metal layers excited byout-of-plane sourcesrdquo International Journal of Optics vol 2012Article ID 146396 12 pages 2012

[29] M Bera and M Ray ldquoRole of waveguide resonance in coupledplasmonic structures using bimetallic nanofilmsrdquo Optical Engi-neering vol 51 no 10 Article ID 103801 2012

[30] N Zhang R Schweiss Y Zong and W Knoll ldquoElectrochem-ical surface plasmon spectroscopymdashrecent developments andapplicationsrdquo Electrochimica Acta vol 52 no 8 pp 2869ndash28872007

[31] C Genet and T W Ebbesen ldquoLight in tiny holesrdquo Nature vol445 no 7123 pp 39ndash46 2007

[32] A S Vengurlekar ldquoExtraordinary optical transmission throughmetal filmswith subwavelength holes and slitsrdquoCurrent Sciencevol 98 no 8 pp 1020ndash1032 2010

[33] B Sturman E Podivilov andM Gorkunov ldquoTheory of extraor-dinary light transmission through arrays of subwavelengthslitsrdquo Physical Review B vol 77 no 7 Article ID 075106 2008

[34] R Umeda C Totsuji K Tsuruta and H Totsuji ldquoAn FDTDanalysis of nanostructured electromagnetic metamaterialsusing parallel computerrdquo Materials Transactions vol 50 no 5pp 994ndash998 2009

[35] A D Rakic A B Djurisic J M Elazar and M L MajewskildquoOptical properties ofmetallic films for vertical-cavity optoelec-tronic devicesrdquo Applied Optics vol 37 no 22 pp 5271ndash52831998

[36] M Bordovsky P Catrysse S Dods et al ldquoWaveguide designmodeling and optimization from photonic nanodevices tointegrated photonic circuitsrdquo in Integrated Optics DevicesMaterials and Technologies VIII 65 vol 5355 of Proceedings ofSPIE San Jose Calif USA May 2004

[37] B Ung Study of the interaction of surface waves with a metallicnano-slit via the finite-difference time-domain method [MSthesis] Laval University Quebec Canada 2007

[38] J A Schuller E S BarnardW Cai Y C Jun J SWhite andML Brongersma ldquoPlasmonics for extreme light concentrationand manipulationrdquo Nature Materials vol 9 pp 193ndash204 2010

[39] Y Fu and X Zhou ldquoPlasmonic lenses a reviewrdquo Plasmonics vol5 no 3 pp 287ndash310 2010

[40] R Grote R M Osgood J E Spanier and B Nabet ldquoOpti-mization of a surface plasmon enhancedmetal-semiconductor-metal photodetector onGalliumArseniderdquo in Proceedings of theFrontiers in Optics OSA Technical Digest (CD) (Optical Societyof America) Paper FThY3 Rochester NY USA October 2010

[41] N Das A Karar C L Tan K Alameh and Y T Lee ldquoImpact ofnanograting phase-shift on light absorption enhancement inplasmonics-based metal-semiconductor-metal photodetect-orsrdquo Advances in Optical Technologies vol 2011 Article ID504530 8 pages 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



120596

120596p

ckz

radic120576d

120596p

radic1 + 120576d

Re kz

1205962 = 1205962p + c2k2

ksp =120596

c( 120576998400m120576d

120576998400m + 120576d)12

Figure 1The dispersion relation of nonradiative SPs on the right ofthe light line and dispersion relation of radiative SPs on the left ofthe light line

efficiency through the subwavelength aperture It is usefulto describe the SP dispersion relation as shown in Figure 1To have propagating bound SPs the wave vector componentmust be real along the interface Any light cannot be used forSP generation because the real part of the wave vector in the119911-direction exceeds that of free light (120596 = 119888119896) as shown inFigure 1 and a coupling mechanism is required

In the presence of a transverse magnetic (TM) polarizedlight the SPs exist along ametal-dielectric interfaceThere areseveral techniques to excite the SP waves such as prism cou-pling and grating coupling For the case of semiconductorsprism coupling is not very much advantageousThe attentionshould be paid to prism refractive index which is hardlyhigher than popular semiconductors used for correspondingresearches [13 14] In particular this study presents the effectsof nanograting structures on theMSM-PD device Optimiza-tion of subwavelength nanogratings shape and pitch is verymuch important to generate the zero-order diffraction wavesThus the subwavelength nanogratings can be represented as ahomogeneousmediumwith optical properties determined bythe nanograting geometry [15]When the nanograting periodis within the order of the light wavelength the light wavemaybe resonant and reflects into the structure hence the higherdiffraction orders will be suppressed and resonant reflec-tion occurs for the zero-order diffraction waves [16ndash18] Themetallic nanogratings can exhibit absorption anomalies Oneof these particularly remarkable anomalies is observed for119901-polarized light only and is due to the surface plasmonpolariton (SPP) excitations [19]The light incident on the one-dimensional metallic nanogratings composed of subwave-length slits is converted into the propagating SPPs that canabsorb the light efficiently in extremely thin (10 nm to morethan 100 nmrsquos thick) layers The coupling of light to thestructure in the form of the SPPs is obtained with the utilityof periodicity There are two distinct mechanisms to producethe transmission of light in 1Dmetal nanogratingwith narrowslits which are the excitation of horizontal and verticalsurface resonances The horizontal surface resonances are

excited by the periodic structure of the nanogratings Thevertical surface resonances have relations with Fabry-Perotresonances of the fundamental TM guided wave in the slits[1] Two vertical resonances existing on the slit walls cancompose a fundamental waveguide mode which satisfies theFabry-Perot condition and reflects repeatedly from both endsof the slit Therefore the guided modes can be excited alongvertical direction evanescent coupling mechanism accountsfor this activation [20] The responsibility of these two effectson extraordinary optical transmission (EOT) is still underdebate However it is indicated that both mechanisms areimportant in the EOT [21] Concentrating the light in smallareas (plasmonic lenses) with the assistance of extremelythin layers [22] the EOT is a unique phenomenon which isinduced by the SP assisted multiple diffractions coupling theSPs into the aperture and conversion back into near-field atthe exit side of the aperture The role of SP modes is essentialto clarify the EOT of light through the slits In the EOT theaperture transmits more light than the standard aperture the-ory The EOT can occur whenever some specific conditionsare satisfied that is the slit width must be much smaller thanthe incident light wavelength the periodicity has to be in therange of wavelength and it can lead to outstanding results ifthe light is normally incident to the structurersquos surface Sub-wavelength apertures have also been used to concentrate lightefficiently into the deep subwavelength regions

A considerable development has been reported for theEOT throughmetallic grating with very narrow slits [23]TheSPPs and subwavelength apertures in metallic thin films arealways involved with this phenomenon but the details arestill under investigation [7 9 16] The SPs can be efficientlyexcited in the nanostructured noble metals since they almosthave free-electron behavior [24] The noble metal nanotex-tured structures have special properties to produce local-ized regions of high energy concentration and show largerenhancement for extraordinary optical absorption (EOA)This effect and its underlying mechanism have importantapplications in photolithography and near-field microscopy

The absorption enhancement caused by the excitation ofSPPs is associatedwith the incident photons and their interac-tion with the nanogratings whereas Fabry-Perot resonancesare included in transmission absorption process through thesubwavelength slits In addition the light is mostly reemittedfrom a very small area surrounding the aperture whichis associated with the properties of the Fabry-Perot cavityresonances for symmetric SPP modes of the slit

Themain objective of this research is to find out the radia-tion behavior through the nanoscale device Finite-differencetime-domain (FDTD) simulation tool is a full wavemodelingtechnique that demonstrates significant light-capturing per-formance through the periodic 1D slit arrays [25] for thedesign of ultrafast MSM-PDs [3] The FDTD algorithm wasoriginally proposed by Yee in 1966 [26] and introduces amodeling technique to solve the Maxwellrsquos curl equations intime domain It can directly calculate the value of 119864 (electricfield intensity) and 119867 (magnetic field intensity) at differentmesh points in the computational domain denoted by (119894 119895 119896)with respect to Ampere and Faradayrsquos laws (Maxwell equa-tions) Since then it has been used for several applications







1015840

119898+ 119894120576

10158401015840

119898


Surface plasmon


120579

k

120573

120601

z

X






120596

119888

sin (120579) plusmn 2120587119897Λ

= 119896sp =120596

119888

radic

120576

1015840

119898120576119889

120576

1015840119898+ 120576119889

(1)



1015840

119898+ 119894120576

10158401015840





1015840

119898+ 119894120576

10158401015840

119898 It consists


119898


119898lt minus1 12057610158401015840

119898≪ |120576

1015840




120576119903 (120596) = 120576119891

119903(120596) + 120576

119887

119903(120596) (2)



119903(120596)


119903(120596) and interband 120576119887



120576

119891

119903(120596) = 1 +

Ω

2

119901

119894120596Γ0 minus 1205962

(3)

120576

119887

119903(120596) =

119872

sum

119898=1

1198661198981205962

119901

120596

2119898minus 120596

2+ 119894120596Γ119898

(4)



120576119903 (120596) = 120576119903infin +

119872

sum

119898=0

119866119898Ω2

119898

120596

2119898minus 120596

2+ 119894120596Γ119898

(5)








1 00240 0630488119864 + 15 0366139119864 + 15

2 00100 0126098119864 + 16 0524141119864 + 15

3 00710 0451065119864 + 16 0132175119864 + 16

4 06010 0653885119864 + 16 0378901119864 + 16

5 43840 0202364119864 + 17 0336362119864 + 16











0

5

10

15

20

25

30

06 07 08 09 1 11 12 13 14

LAEF



80nm100nm

120nm140nm


0

5

10

15

20

25

30

06 08 1 12 14

LAEF


100nm120nm

140nm160nm





0

5

10

15

20

25

30

35

06 07 08 09 1 11 12 13 14

LAEF

Duty cycle

30DC40DC50DC60DC

70DC80DC90DC100DC




0

5

10

15

20

25

30

35

06 07 08 09 1 11 12 13 14

LAEF

Duty cycle

30DC40DC50DC60DC

70DC80DC90DC100DC




Semiconductor

Semiconductor

Underlayer

RidgesGrooves



30405060

708090100

06 07 08 09 1 11 12 13 14Wavelength (120583m)

0

05

1

15

2

25

3Li

ght r

eflec

tion

fact

or


(a)

30405060

708090100

0

05

1

15

2

25

3

06 07 08 09 1 11 12 13 14

Ligh

t refl

ectio

n fa

ctor



(b)




0

2

4

6

8

10

12

14

16

18

20

06 07 08 09 1 11 12 13 14

LAEF





(a)

(b)



8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(a)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(b)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(c)







5 Conclusion


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















1015840

119898+ 119894120576

10158401015840

119898


Surface plasmon


120579

k

120573

120601

z

X






120596

119888

sin (120579) plusmn 2120587119897Λ

= 119896sp =120596

119888

radic

120576

1015840

119898120576119889

120576

1015840119898+ 120576119889

(1)



1015840

119898+ 119894120576

10158401015840





1015840

119898+ 119894120576

10158401015840

119898 It consists


119898


119898lt minus1 12057610158401015840

119898≪ |120576

1015840




120576119903 (120596) = 120576119891

119903(120596) + 120576

119887

119903(120596) (2)



119903(120596)


119903(120596) and interband 120576119887



120576

119891

119903(120596) = 1 +

Ω

2

119901

119894120596Γ0 minus 1205962

(3)

120576

119887

119903(120596) =

119872

sum

119898=1

1198661198981205962

119901

120596

2119898minus 120596

2+ 119894120596Γ119898

(4)



120576119903 (120596) = 120576119903infin +

119872

sum

119898=0

119866119898Ω2

119898

120596

2119898minus 120596

2+ 119894120596Γ119898

(5)








1 00240 0630488119864 + 15 0366139119864 + 15

2 00100 0126098119864 + 16 0524141119864 + 15

3 00710 0451065119864 + 16 0132175119864 + 16

4 06010 0653885119864 + 16 0378901119864 + 16

5 43840 0202364119864 + 17 0336362119864 + 16











0

5

10

15

20

25

30

06 07 08 09 1 11 12 13 14

LAEF



80nm100nm

120nm140nm


0

5

10

15

20

25

30

06 08 1 12 14

LAEF


100nm120nm

140nm160nm





0

5

10

15

20

25

30

35

06 07 08 09 1 11 12 13 14

LAEF

Duty cycle

30DC40DC50DC60DC

70DC80DC90DC100DC




0

5

10

15

20

25

30

35

06 07 08 09 1 11 12 13 14

LAEF

Duty cycle

30DC40DC50DC60DC

70DC80DC90DC100DC




Semiconductor

Semiconductor

Underlayer

RidgesGrooves



30405060

708090100

06 07 08 09 1 11 12 13 14Wavelength (120583m)

0

05

1

15

2

25

3Li

ght r

eflec

tion

fact

or


(a)

30405060

708090100

0

05

1

15

2

25

3

06 07 08 09 1 11 12 13 14

Ligh

t refl

ectio

n fa

ctor



(b)




0

2

4

6

8

10

12

14

16

18

20

06 07 08 09 1 11 12 13 14

LAEF





(a)

(b)



8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(a)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(b)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(c)







5 Conclusion


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120596

119888

sin (120579) plusmn 2120587119897Λ

= 119896sp =120596

119888

radic

120576

1015840

119898120576119889

120576

1015840119898+ 120576119889

(1)



1015840

119898+ 119894120576

10158401015840





1015840

119898+ 119894120576

10158401015840

119898 It consists


119898


119898lt minus1 12057610158401015840

119898≪ |120576

1015840




120576119903 (120596) = 120576119891

119903(120596) + 120576

119887

119903(120596) (2)



119903(120596)


119903(120596) and interband 120576119887



120576

119891

119903(120596) = 1 +

Ω

2

119901

119894120596Γ0 minus 1205962

(3)

120576

119887

119903(120596) =

119872

sum

119898=1

1198661198981205962

119901

120596

2119898minus 120596

2+ 119894120596Γ119898

(4)



120576119903 (120596) = 120576119903infin +

119872

sum

119898=0

119866119898Ω2

119898

120596

2119898minus 120596

2+ 119894120596Γ119898

(5)








1 00240 0630488119864 + 15 0366139119864 + 15

2 00100 0126098119864 + 16 0524141119864 + 15

3 00710 0451065119864 + 16 0132175119864 + 16

4 06010 0653885119864 + 16 0378901119864 + 16

5 43840 0202364119864 + 17 0336362119864 + 16











0

5

10

15

20

25

30

06 07 08 09 1 11 12 13 14

LAEF



80nm100nm

120nm140nm


0

5

10

15

20

25

30

06 08 1 12 14

LAEF


100nm120nm

140nm160nm





0

5

10

15

20

25

30

35

06 07 08 09 1 11 12 13 14

LAEF

Duty cycle

30DC40DC50DC60DC

70DC80DC90DC100DC




0

5

10

15

20

25

30

35

06 07 08 09 1 11 12 13 14

LAEF

Duty cycle

30DC40DC50DC60DC

70DC80DC90DC100DC




Semiconductor

Semiconductor

Underlayer

RidgesGrooves



30405060

708090100

06 07 08 09 1 11 12 13 14Wavelength (120583m)

0

05

1

15

2

25

3Li

ght r

eflec

tion

fact

or


(a)

30405060

708090100

0

05

1

15

2

25

3

06 07 08 09 1 11 12 13 14

Ligh

t refl

ectio

n fa

ctor



(b)




0

2

4

6

8

10

12

14

16

18

20

06 07 08 09 1 11 12 13 14

LAEF





(a)

(b)



8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(a)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(b)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(c)







5 Conclusion


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1 00240 0630488119864 + 15 0366139119864 + 15

2 00100 0126098119864 + 16 0524141119864 + 15

3 00710 0451065119864 + 16 0132175119864 + 16

4 06010 0653885119864 + 16 0378901119864 + 16

5 43840 0202364119864 + 17 0336362119864 + 16











0

5

10

15

20

25

30

06 07 08 09 1 11 12 13 14

LAEF



80nm100nm

120nm140nm


0

5

10

15

20

25

30

06 08 1 12 14

LAEF


100nm120nm

140nm160nm





0

5

10

15

20

25

30

35

06 07 08 09 1 11 12 13 14

LAEF

Duty cycle

30DC40DC50DC60DC

70DC80DC90DC100DC




0

5

10

15

20

25

30

35

06 07 08 09 1 11 12 13 14

LAEF

Duty cycle

30DC40DC50DC60DC

70DC80DC90DC100DC




Semiconductor

Semiconductor

Underlayer

RidgesGrooves



30405060

708090100

06 07 08 09 1 11 12 13 14Wavelength (120583m)

0

05

1

15

2

25

3Li

ght r

eflec

tion

fact

or


(a)

30405060

708090100

0

05

1

15

2

25

3

06 07 08 09 1 11 12 13 14

Ligh

t refl

ectio

n fa

ctor



(b)




0

2

4

6

8

10

12

14

16

18

20

06 07 08 09 1 11 12 13 14

LAEF





(a)

(b)



8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(a)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(b)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(c)







5 Conclusion


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

5

10

15

20

25

30

06 07 08 09 1 11 12 13 14

LAEF



80nm100nm

120nm140nm


0

5

10

15

20

25

30

06 08 1 12 14

LAEF


100nm120nm

140nm160nm





0

5

10

15

20

25

30

35

06 07 08 09 1 11 12 13 14

LAEF

Duty cycle

30DC40DC50DC60DC

70DC80DC90DC100DC




0

5

10

15

20

25

30

35

06 07 08 09 1 11 12 13 14

LAEF

Duty cycle

30DC40DC50DC60DC

70DC80DC90DC100DC




Semiconductor

Semiconductor

Underlayer

RidgesGrooves



30405060

708090100

06 07 08 09 1 11 12 13 14Wavelength (120583m)

0

05

1

15

2

25

3Li

ght r

eflec

tion

fact

or


(a)

30405060

708090100

0

05

1

15

2

25

3

06 07 08 09 1 11 12 13 14

Ligh

t refl

ectio

n fa

ctor



(b)




0

2

4

6

8

10

12

14

16

18

20

06 07 08 09 1 11 12 13 14

LAEF





(a)

(b)



8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(a)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(b)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(c)







5 Conclusion


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










30405060

708090100

06 07 08 09 1 11 12 13 14Wavelength (120583m)

0

05

1

15

2

25

3Li

ght r

eflec

tion

fact

or


(a)

30405060

708090100

0

05

1

15

2

25

3

06 07 08 09 1 11 12 13 14

Ligh

t refl

ectio

n fa

ctor



(b)




0

2

4

6

8

10

12

14

16

18

20

06 07 08 09 1 11 12 13 14

LAEF





(a)

(b)



8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(a)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(b)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(c)







5 Conclusion


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(a)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(b)

8 85 9 95 10

0

005

01

0

05

1

15

2

25

3

35

4

x-axis (120583m)

z-a

xis (120583

m)

minus01

minus005

(c)







5 Conclusion


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











5 Conclusion


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article a comprehensive analysis of plasmonics

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