NANOSTRUCTURES FOR DESIGN AND OPTIMIZATION OF PLASMONIC BIOSENSORS - - PowerPoint PPT Presentation

SIMULATION OF PERIODIC NANOSTRUCTURES FOR DESIGN AND OPTIMIZATION OF PLASMONIC BIOSENSORS

Niccolò Michieli CNISM and Department of Physics and Astronomy «G.Galilei» - University

• f Padua

Nanostructures Group

LIGHT-MATTER INTERACTION BIOSENSORS

PLASMONICS

• Biosensor => transduce biological (and chemical) signal into

a set of useable informations (composition, concentration...)

• Light-matter interactions are the main physical

phenomena exploited to this aim.

• Particularly, Nanotechnology and Nanoscience

can yield important advantages:

• size of analytes: 0.1-1000 nm
• energetic and roto-vibrational transitions => nanometric wavelenghts
• ptical technology, sources and detectors
• (noble) metals nanostructures support coherent

free charges oscillations

LIGHT-MATTER INTERACTION BIOSENSORS

Biosensors Labeled SERS Hot Spots Fluorescence Light Management Specific Absorption Light Management ... Label-free Refractive index Localized Plasmons Surface Plasmos Surface modification ...

Nanotriangles Nanoholes

PLASMONICS – SURFACE AND LOCALIZED PLASMONS

Plasmons Surface Plasmons Localized Plasmons

• Propagating modes
• Coupling by prism or grating
• Poor Field Confinement
• Low absorption
• Extremely sensitive to

surrounding index changes

• Confined modes
• Direct coupling
• Strong Field Confinement
• High absorption
• Extremely sensitive to

(geometrically) small changes in surround

SURFACE PLASMON POLARITONS

• Wave equation (Helmhotz’s Equation) at metal-dielectric interface:

𝜖2𝑭(𝑨) 𝜖𝑨2 + 𝑙0

2𝜁 − 𝑙𝑦 2 𝑭 = 𝟏

• Putting the Boundary Conditions, the dispersion relation results:

𝑙𝑦 = 𝑙0 𝜁1𝜁2 𝜁1 + 𝜁2

• Direct coupling forbidden!!
• Coupling methods:

LOCALIZED PLASMONS – QUASI-STATIC APPROXIMATION

• Laplace Equation with Boundary Conditions:

𝛼𝟑𝝔 = 𝟏

• Solutions given by a Spherical Harmonics Expansion:

𝜚 𝑠, 𝜄 = 𝐵𝑚𝑠𝑚 + 𝐶𝑚𝑠− 𝑚+1 𝑄𝑚 cos 𝜄

∞ 𝑚=0

• Resulting Polarizability:

𝛽 = 4𝜌𝑆3 𝜁 − 𝜁𝑛 𝜁 + 2𝜁𝑛

• Resulting Electric Field in Quasi-Static (dipolar) Approximation:

𝑭 = 𝑭𝟏 + 1 4𝜌𝜁0𝜁𝑛 𝑙2 𝒐 × 𝒒 × 𝒐 𝒇𝒋𝒍𝒔 𝒔 + 3𝒐 𝒐 ∙ 𝒒 − 𝒒 1 𝑠3 − 𝑗𝑙 𝑠2 𝒇𝒋𝒍𝒔

𝜁 = −2𝜁𝑛 Resonance!!

Far Field Near Field

BEYOND QUASI-STATIC APPROXIMATIONS

Exact solutions of the electromagnetic problem only exists for a few particular cases:

• Spherical isolated particles: Mie theory

Multipole expansion (quadrupoles, ottupoles,...)

• Ellipsoidal particles: Gans theory
• Spherical interacting particles: Generalized Multiparticle Mie (GMM)

For all other geometries: Discretization (DDA, FEM, FDFD, FDTD) Typical observed features:

500 600 700 800 900 1000 2 4 6 8 10 12 14

Extinction Efficiency Wavelength (nm)

46 48 50 52 54 56 58 60 62 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Reflectance Angle (°)

HOW TO EXPLOIT PLASMONICS FOR BIOSENSORS?

Sensors SERS Hot Spots Transmission/ Extinction Resonances Peaks Reflection Propagating Modes

Nanohole Arrays Nano Triangles

NANOSTRUCTURES SELF-ASSEMBLY - NSL

2a. 1.

SiO2 NS (30-1000 nm)

Nano Triangles

NANOSTRUCTURES SELF-ASSEMBLY - NSL

2a. 1.

SiO2 NS (30-1000 nm)

2b.

Nano Triangles Nano Hole Arrays

2D PERIODIC STRUCTURES: THE HONEYCOMB LATTICE

All the structures taken in count are periodic, with a «honeycomb» lattice.

• The lattice can be decomposed in triangles or in exagons.
• It can be seen as a sinlge plane of a HCP crystal.
• The unit cell is a rhomb, which is one third of the unitary

exagon and is composed by two unit triangles.

MODELS SETUP: SOLVING MAXWELL’S EQUATIONS BY FINITE ELEMENTS

• The geometry of the model contains:
• the nanostructure itself
• the substrate under the NS
• the medium over the NS
• PML domains to simulate

infinite semi-spaces.

• The domain is then divided in finite

elements (meshing)

• Dielectric functions of glass and metals

from experimental data (J&C,Palik)

• Helmholtz equation (FT of the wave

equation) is solved point by point for each frequency:

𝛼2𝐹 + 𝑙2𝐹 = 0

NANOTRIANGLES

• The unit cell contains 2 nanotriangles. These are placed in the

centers of the two triangles forming the unit cell.

• The tips of tips of the triangles are faced each-other.
• The exact shape of the monomer is determined by the technique
• f deposition, the quantity of deposed metal, and by (optional)

thermal annealing.

• Nanostructures have been modelized both as snipped prisms

and snipped thetrahedra.

NANOTRIANGLES – RESONANCE TAYLORING

The resonance position (and shape) is strongly dependent on the geometry of the triangles, interactions and surrounding media characteristics. To taylor the resonance, the following parameters are considered:

• The geometric properties of the structures used for

parametrization:

• Lattice constant (dependent on PS nanospheres)
• Triangles side and height (dependent on

deposition parameters)

• Snipping of the tips (dependent on deposition and

annealing)

• Dielectric properties of environment have been considered
• Presence of interfaces (substrates)

NANOPRISMS - GEOMETRY

400 500 600 700 800 900 1000 1100 1200 2 4 6 8 10 12 14 16

Extinction Efficiency Wavelenght (nm)

Base L=200 nm L=300 nm h=30 nm h=45 nm

Larger => Redshift Aspect Ratio Closer to 1 => Blueshift

Base Prism: L=100 nm; h=10 nm; snip=10 nm, silver

400 500 600 700 800 900 2 4 6 8 10 12 14

Single d=120nm c-c d=240nm c-c d=360nm c-c exagon l=120nm snip=20nm snip=30nm

Extinction Efficiency Wavelength (nm)

NANOPRISMS – GEOMETRY AND INTERACTION

Interactions Snipping Base Prism: L=100 nm; h=10 nm; snip=10 nm, silver

NANOPRISMS – SURROUNDING MEDIA/INTERFACE

600 800 1000 1200 1 2 3 4 5 6 7 8 Extinction Cross Section (10

• 14 m

2)

Wavelength (nm)

Air Silica Glass Quartz Glass Silica Glass Interface

n=1.45 n=2.05

NANOTRIANGLES – HOT SPOTS

• Surface Enhanced Raman Spettroscopy (SERS) efficiency is strogly dependent on local

field: 𝐺

𝑇𝐹𝑆𝑇 = 𝐽𝑇𝐹𝑆𝑇

𝐽0 = 𝐹2 𝜕𝑗𝑜 ∙ 𝐹2 𝜕𝑝𝑣𝑢 𝐹0

4

≈ 𝐹4 𝐹0

4

• The presence of plasmonic hot spots can enhance Raman signal up to 14 orders of

magnitude.

• Given the strong dependance, almost all the signal comes from the narrow hot spot

regions.

• To predict the experimental Enhancement Factor, an average over the whole surface is

needed.

• If the analytes are coupled to group that bound preferentially to metals (Sulphur groups),

the average can neglect the (low enhancement) glass surface.

NANOTRIANGLES – HOT SPOTS

400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0

Normalized Values Freespace incident Wavelenght (nm)

Max(E)/E0 Ave(E)/E0 Ave(E

4)/E 4

400 500 600 700 800 900 1000 1100 1200 10 1000 100000 1E7

SERS Enhancement Factor Freespace incident Wavelenght (nm)

𝐹𝐺 = 1.5 ∙ 105

• Localized Plasmons => strong Near Field, decay ≈ 10 − 20 𝑜𝑛
• Sensitivity close to the surface => also a monolayer shifts the resonance
• Simulation of the resonance for different thicknesses and geometries of functionalization

Functionalization

NANOPRISMS - SENSITIVITY

600 650 700 750 800 850 1 2 3 4 Extinction Cross Section (10

• 14 m

2)

Freespace incident Wavelenght (nm)

t=0nm t=1nm t=2nm t=5nm t=10nm

600 700 800 900 1000 1100 0.0 0.2 0.4 0.6 0.8 1.0 Absorption (Arb. Units)

Wavelenght (nm)

T=5, Absorption T=10, Absorption T=15, Absorption T=20, Absorption T=30, Absorption

Prism

Functionalization

Prism

𝜖𝜇 𝜖𝑈

𝑈=0

= 3.0 𝜖𝜇 𝜖𝑈

𝑈=0

= 5.8

Optimal Coupling to Plasmons => 𝜇𝑆 = 𝑏 − 𝑐 ∙ 𝑑𝑈

𝜖𝜇 𝜖𝑈

𝑈=0

= −𝑐 ∙ ln (𝑑)

NANOTRIANGLES - SUMMARY

• The effects of the geometric properties of the nanostructure have been investigated.
• The resonance can be taylored by tuning 4 parameters:
• Optimization tips for the two applications:

Parameters Lattice Constant Side Lenght Height Snip/Shape Controlled by NS diameter Deposition setup Annealing Effect of Increase Redshift Redshift Blueshift Blueshift Reason Larger Structures AR closer to 1

Less curvature and interaction

Application SERS Refractive Index SENSING Lattice Constant

Dependent on Raman Spectrum of Analytes Dependent on the desired position of

resonance, once fixed other parameters Side Lenght

Longest possible => better t-t coupling

Height Low structures => higher avg field High structures => better coupling to func. Snip/Shape No snip, sharp edges => Hot Spots Moderate snip => more homogeneity Tips Collimation => longer sides, sharper

• edges. Evaporation => homogeneity

(no planets) Higher Aspect Ratio, Annilation to lower defects and strongest t-t coupling

NANOHOLE ARRAYS

• Nanohole Array Parameters:
• Substrate: silica glass (n=1.445)

Computed quantities:

• Transmittance (normal, various

functionalizations)

• Reflectivity (wavelenght and angle

sweeps)

• Local fields

Parameters: Value (nm): Lattice Constant (𝒃𝟏) (HCP) 535 Holes Radius (𝑆) 205 Film height (ℎ) 46 87

𝑏0 ℎ 2𝑆

Substrate Functionalization Film Holes

NANOHOLE ARRAY REFLECTANCE – SENSITIVITY MAPS

Angle (deg) Wavelenght (nm) Reflectance

ℎ = 46 𝑜𝑛

𝜇 = 1140

𝜄

NANOHOLE ARRAY REFLECTANCE – SENSITIVITY MAPS

Angle (deg) Wavelenght (nm) Reflectance

ℎ = 87 𝑜𝑛

𝜇 = 1120

𝜄

NANOHOLE ARRAY - SENSITIVITY MAPS

Reflectance – h = 46 nm Surface: Nanohole Array on Silica (As) Point Plot: Nanohole with Functionalization

REFLECTANCE - ℎ = 46 𝑜𝑛

45 50 55 60 65 70 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95

Reflectance Angle (deg)

T=0 nm T=3 nm T=4 nm T=5 nm T=7 nm T=10 nm T=15 nm

Functional- ization T (nm) Dip Angle (deg) 57.0 3 55.7 4 55.0 5 54.3 7 53.6 10 52.3 15 50.4

𝑇𝑚𝑝𝑞𝑓 = −0.44 𝑒𝑓𝑕/𝑜𝑛

REFLECTANCE - ℎ = 87 𝑜𝑛

Functional- ization T (nm) Dip Angle (deg) 59.1 3 58.2 4 58.0 5 57.7 7 57.0 15 54.9

45 50 55 60 65 70 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00

Reflectance Angle (deg)

T=0 nm T=3 nm T=4 nm T=5 nm T=7 nm T=15 nm

𝑇𝑚𝑝𝑞𝑓 = −0.29 𝑒𝑓𝑕/𝑜𝑛 Experimental h = 100nm: 𝑇𝑚𝑝𝑞𝑓 = −0.18 𝑒𝑓𝑕/𝑜𝑛

400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0 400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0 400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0 400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0 400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0 400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0 400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0 400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0 400 600 800 1000 1200 0.0 0.2 0.4 0.6 0.8 1.0

Rhole=200nm Rhole=150nm

Wavelenght

Transmittance Reflectance Absorbance

Rhole=100nm Nanohole Array. Lattice constant= 535 nm

Wavelenght Wavelenght Wavelenght Wavelenght Wavelenght Wavelenght Wavelenght Wavelenght

NANOHOLE ARRAY - FAR FIELD AND LOCAL FIELD MAPS

Holes

T= 50 nm T= 100 nm T= 150 nm

650 700 750 800 850 900 950 1000 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Transmittance Wavelenght (nm) T=0 nm T=3 nm T=4 nm T=5 nm T=7 nm T=10 nm T=15 nm

NANOHOLE ARRAY TRANSMITTANCE – ℎ = 46 𝑜𝑛

640 645 650 655 660 0.40 0.42 0.44 0.46 0.48 0.50

Transmittance Wavelenght (nm)

665 670 675 680 685 0.00 0.01 0.02 0.03 0.04 0.05

Transmittance Wavelenght (nm)

860 880 900 920 0.43 0.44 0.45 0.46 0.47

Transmittance Wavelenght (nm)

640 645 650 655 660 0.40 0.42 0.44 0.46 0.48 0.50

Transmittance Wavelenght (nm)

665 670 675 680 685 0.00 0.01 0.02 0.03 0.04 0.05

Transmittance Wavelenght (nm)

860 880 900 920 0.43 0.44 0.45 0.46 0.47

Transmittance Wavelenght (nm)

NANOHOLE ARRAY TRANSMITTANCE – ℎ = 46 𝑜𝑛

Thickness (nm) Peak 1 (nm) Dip (nm) Peak 2 (nm) 647.1 670.1 872.5 3 648.0 672.3 877.0 4 648.2 672.9 879.0 5 648.4 673.5 880.5 7 648.8 674.5 884.0 10 649.5 675.8 888.0 15 650.5 677.7 897.0 Feature 𝝁𝟏 (nm) Sensitivity Feature width (nm) 648 0.21 ~40 672 0.44 ~30 877 1.63 ~100

NANOHOLE ARRAY – WHICH IS THE BEST?

5 10 15 50 52 54 56 58 60 Slope = -0.44 deg/nm

Dip Angle (deg) Functionalization Thickness (nm)

h=46 nm h=87 nm Slope = -0.29 deg/nm

Transmittance, ℎ = 46 𝑜𝑛 Transmittance, ℎ = 87 𝑜𝑛 Reflectance

Method Peak/dip Sensitivity (/nm)

T, ℎ = 46 𝑜𝑛 P1, 𝝁𝟏 = 647 nm 0.21 nm T, ℎ = 46 𝑜𝑛 D1, 𝝁𝟏 = 670 nm 0.19 nm T, ℎ = 46 𝑜𝑛 P2, 𝝁𝟏 = 872 nm 2.09 nm T, ℎ = 87 𝑜𝑛 P1, 𝝁𝟏 = 646 nm 0.21 nm T, ℎ = 87 𝑜𝑛 D1, 𝝁𝟏 = 666 nm 0.44 nm T, ℎ = 87 𝑜𝑛 P2, 𝝁𝟏 = 823 nm 1.63 nm R, ℎ = 46 𝑜𝑛 𝝁𝟏 = 1140 nm

• 0.44 deg

R, ℎ = 87 𝑜𝑛 𝝁𝟏 = 1120 nm

• 0.29 deg

2 4 6 8 10 12 14 16 650 660 670 870 880 890 900 Peak 1 Dip Peak 2

Wavelenght (nm) Thickness (nm)

2 4 6 8 10 12 14 16 640 650 660 670 820 830 840 850 860 Peak 1 Dip Peak 2

Wavelenght (nm) Thickness (nm)

NANOHOLE ARRAYS - SUMMARY

• NHA can be used both in transmittance and in reflectance to build biosensors.
• SERS cannot use NHA due to low enhancement factor (~ 4-5)
• The response can be taylored by tuning 3 parameters:

Parameters Lattice Constant Hole Radius Height Controlled by NS diameter RIE Deposition setup Mode Transmittance Reflectance Hole Radius Larger holes => lower absorption Smaller holes => lower dissipation Height Thin film => higher transmittance and better sensitivity Thick film => lower dissipation Thin film => better sensitivity Tips Thin film and large holes Small holes => better conduction => narrower dip Thin film => better sensitivity

• Optimization tips for the two operative modes:

CONCLUSIONS

• Plasmonic Bio-Sensors design can take great advantage from nanostructures obtained by

NSL

• The design of the nanostructures can be controlled by tuning a small set of parameters, and

simulations give hints on how to obtain best performaces.

• Nanotriangles can be used both for Refractive Index-sensitive and SERS substrates. In

both cases, the agreement with experiment is pretty good, keeping in count the defects on the real samples

• Nanohole arrays can be used both in transmittance and in reflectance
• Reflectance give the best (and most stable against defects) results
• Transmittance is far easier to measure, and it’s usable too
• Simulations show how to tune parameters to get the desired result

Thank You

for your Attention!

Thanks to people, present and past members, of my group: Boris, Carlo, Giovanni P, Giovanni P, Valentina B, Valentina M, Valentina R, Marco, Martina And Tiziana and Giovanni M