Tip-Enhanced Raman Spectroscopy - Semantic Scholar...ago. First the invention of tip-enhanced Raman spectroscopy (TERS) made it possible to combine the spectral information of Raman

Seite 1 von 1

Physik-Department Walther-Meiÿner-Institut Bayerische Akademie

Lehrstuhl E23 für Tieftemperaturforschung der Wissenschaften

Tip-Enhanced Raman Spectroscopy

Master's Thesis

David Hoch

Supervisor: PD Dr. habil. Rudi Hackl

Garching, September 2015

Technische Universität München

Contents

1 Introduction 1

2 Near-Field Optics 3

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Diraction limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3 Evanescent waves and surface plasmons . . . . . . . . . . . . . . . . . . . 9

3 Raman Scattering 17

3.1 Conventional Raman scattering . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Principles of high resolution Raman scattering . . . . . . . . . . . . . . . 22

3.2.1 Field distribution and associated Raman enhancement . . . . . . 23

3.2.2 Contrast gain in near-eld Raman scattering . . . . . . . . . . . . 30

3.3 Tips suitable for TERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 Scanning Probe Microscopy 37

4.1 Atomic force microscope . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2 Scanning tunnelling microscope . . . . . . . . . . . . . . . . . . . . . . . 39

5 Setup 43

5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2 General setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.3 Scanning probe microscopes . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.3.1 Settings and parameters . . . . . . . . . . . . . . . . . . . . . . . 46

5.3.2 Tip fabrication technique . . . . . . . . . . . . . . . . . . . . . . . 47

5.4 Optics setup and simulations . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.4.1 Parabolic mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.4.2 Imaging optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.4.3 Excitation optics . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.4.4 Stray light collection optics . . . . . . . . . . . . . . . . . . . . . 57

6 Measurements 67

I

Contents

6.1 Experiments on Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.2 Experiments on YBCO . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

7 Summary 75

8 Bibliography 77

9 Acknowledgement 83

II

1 Introduction

In solid state physics the investigation of various excitations is of great interest. Spec-

troscopic methods are powerful tools for this issue. In conventional Raman spectroscopy

one analyses inelastically scattered photons in the visible range. In solids the light can

couple to excitations like phonons, magnons, density waves and superconducting gap

excitations. By observing the behaviour of these excitations one can gain deeper insight

into, e.g., the mechanism of high Tc superconductors [1].

The Raman light contains information of a sample volume, that is determined by the

penetration depth of light and the area illuminated by the laser. As it is unavoid-

ably integrated over all the collected Raman light of the illuminated sample volume,

the lateral resolution in conventional Raman measurements cannot be better than a

diraction limited spot size of the focussed laser beam being about half the wavelength

of the excitation laser. In contrast, scanning probe techniques provide sub-nanometer

resolution [2] but are insensitive to many of the excitations of interest. However, there

are several structures of interest the dimensions of which are far below the diraction

limit, such as grain boundaries in crystals, skyrmions, surfaces of topological insulators,

single molecules and their functional groups or the two-dimensional electron gas in het-

erostructures. A very interesting heterostructure is LaAlO3/SrTiO3 (LAO/STO) where

magnetic and superconducting states might coexist at the interface [3].

All these problems seemed to defy the investigation with optical methods not so long

ago. First the invention of tip-enhanced Raman spectroscopy (TERS) made it possible

to combine the spectral information of Raman measurements with the very high reso-

lution of a scanning probe microscope (SPM). This technique works by utilizing optical

near-eld eects at the SPM probe. Near-elds occur at every illuminated or radiat-

ing surface or aperture within subwavelength distances and denote the non-propagating

content of an electromagnetic eld [4]. The principle is also used in scanning near-

eld optical microscopy (SNOM/NSOM) [5] where the optical conductivity, a response

function complementary to that of light scattering experiments, is obtained in nm-sized

volumes. By this it is possible to optically resolve structures in the nanometer and even

the sub-nanometer regime [6, 7].

TERS is not the only technique combining Raman measurements with near-eld tech-

1

CHAPTER 1. INTRODUCTION

niques. Other applications of near-eld Raman scattering are for example surface-

enhanced Raman spectroscopy (SERS) [8], hole-enhanced Raman spectroscopy (HERS)

[9] and shell-isolated nanoparticle-enhanced Raman spectroscopy (SHINERS) [10]. The

mechanism behind all these techniques is that the electric eld of the excitation laser is

highly enhanced in the vicinity of nanometer-sized metallic structures. These structures

can be rough surfaces (SERS [8]), holes in the sample surface (HERS [9]) and also the

sharp end of the tip of a scanning probe microscope, as realized in TERS. The great

advantage of TERS, compared to the other methods, is that one can study not only

thin lms or molecules, adsorbed on a prepared substrate, with molecular resolution

but also bulk crystals with arbitrary surface properties.

In our setup we can use an atomic force microscope (AFM) and a scanning tunnelling

microscope (STM) for both collecting topographic data of the sample and enhancing

the Raman signal directly at the scanning tip.

For silicon for instance, the typical enhancement factor is of the order of 105 [7] and the

ratio between a diraction limited far-eld volume and the enhanced near-eld volume

is of about the same order of magnitude. Thus the laser has to be perfectly focused onto

the sample surface to allow the clear distinction between the conventional Raman signal

and the enhanced signal. This is often done with the help of a microscope objective

lens [11], but can also be achieved with a parabolic mirror. Setups with high numerical

aperture paraboloids already exist in ultrahigh vacuum [7, 12]. In the presented setup,

a half parabola with a solid angle of π is used. It is mounted in a UHV cryostat and

provides eective stray light collection. This entirely new conguration, using a half

parabola as a focusing and collection element, has not been implemented before and

allows access to polarization dependent measurements at low temperatures.

The ambition of this master's thesis was to solve the main technical problems in assem-

bling this setup and, if possible, doing rst measurements to provide a proof of principle

of this conguration. The rst goal was reached quite eectively but the latter one could

not be provided yet due to unexpected technical complicities.

In chapter 2 the optical resolution limit is derived and the origin of near-eld optics

due to evanescent waves and surface plasmons is explained. Chapter 3 starts with the

explanation of conventional far-eld Raman spectroscopy and continues with high reso-

lution Raman scattering as TERS and links it with the previously described near-eld

eects at a SPM tip. In chapter 4 the principles of the atomic force microscope and

the scanning tunnelling microscope which are integrated in our setup are pointed out.

Chapter 5 gives a detailed explanation of our setup and the results of simulations with

the optics simulation software Zemax [13]. Chapter 6 explains the measurements done

up to now and chapter 7 nally gives a conclusion of the work done in regard of this

thesis.

2

2 Near-Field Optics

2.1 Introduction

At some time in the history of optics, when optics theory was more and more devel-

oped, it was realized that there is a lower limit for the spatial resolution. This diraction

limit, dependent on the wavelength of light, was formulated by Abbe in 1873 [14] and

Rayleigh in 1879 [15]. This resolution limit already has a close relation to Heisenberg's

uncertainty principle, formulated in 1927. Highly resolving techniques were invented,

such s confocal microscopy [16] and nonlinear optics, but it was not possible to break

the diraction limit before the application of near-eld techniques. Near-eld optical

microscopy was rst proposed by E. H. Synge in 1928 [17]. He described a very small

aperture, smaller than the wavelength of light, being scanned over a sample surface.

The resulting spot is not limited by diraction. At this time, this could not be realized

experimentally. Without knowing Synge's paper, O'Keefe again proposed the similar

idea in 1956 [18]. Then rst in 1972, Ash and Nichols were able to experimentally realize

this method in the microwave regime, using a 1.5mm aperture. At illumination with

10 cm waves, they reached a resolution of λ/60 [19]. Finally in 1984, after the invention

of scanning probe microscopy, an IBM group published the rst subwavelength images

at optical frequencies [20]. The rst patent on TERS is from 2006 [21, 22].

The basic principle of near-eld optics is the presence of evanescent waves. An evanes-

cent wave is the counterpart to a propagating wave and, as it is not propagating, decays

exponentially. This key property enables the connement of light to theoretically arbi-

trarily low dimensions. The basic principles of this technique, shall be briey outlined

in the following [23].

The dispersion relation of propagating light in free space is

hω = chk (2.1)

with the angular frequency of the photon ω, the speed of light c, the reduced Planck

constant h and the wavevector k =√k2x + k2

y + k2z .

3

CHAPTER 2. NEAR-FIELD OPTICS

Heisenberg's uncertainty principle states that

∆hkx ·∆x ≥ h/2 (2.2)

and links the the connement in x-direction ∆x with the spread of the corresponding

wavevector component kx. This means that

∆x ≥ 1

2∆kx. (2.3)

That sets a lower limit for ∆x, as the maximal value for kx can be the free space

wavevector k =√k2x + k2

y + k2z :

kx,max = k =2π

λ(2.4)

Note that this has to be corrected by the numerical aperture NA of the focusing lens in

a real optical system. The numerical aperture is a dimensionless number and describes

the ability of an optical element to focus or collect light. It is dened as follows:

NA = n · sin(α), with the index of refraction n of the medium, surrounding the optical

element and the maximal half-angle α, under which the light can enter or exit the

element. However,

∆x ≥ λ

4π(2.5)

and looks almost like the Rayleigh diraction limit. The only way of getting kx larger

than k is to make one of the other components, e.g. kz, imaginary. Inserting this

imaginary component into the expression for a plane wave shows the price, one has to

pay for the high connement:

eikzz = e−|kz |z (2.6)

is an exponentially decaying, so-called evanescent wave. Note that in case of an innite

free space, the wave would be exponentially increasing in the other direction. As this

has no physical meaning, evanescent waves only occur at the interface of two materials

with dierent refractive indices n which divide the innite free space into two half

spaces. They are created by total internal reection or by surface plasmons at an

metal-dielectric interface. These evanescent waves can be made propagating, either by

frustrated internal reection or by scattering of the surface plasmons o structures much

smaller than the wavelength of light. So, generally speaking, the Rayleigh limit can be

overcome at an inhomogeneity in space.

4


surface normalincident ray

n 1

n 2

plane of incidence

Figure 2.1 Denition of the plane of incidence of a ray, intersecting an inhomogeneity in space.n1 and n2 are the respective refractive indices of the two half spaces.

2.2 Diraction limit

Without access to the evanescent modes of the spatial spectrum of the observed sam-

ple, the diraction limit is a hard boundary for optical resolution. This means that

the detector necessarily needs the information of the naturally non propagating wave

components to break the resolution limit. By looking at the angular spectrum repre-

sentation for arbitrary z of an electromagnetic wave [23] one nds that only waves with

spacial frequencies in the interval [0...k] can propagate to a detector:

E(x, y, z) =

∞∫∫−∞

E(kx, ky; 0)ei[kxx+kyy±kzz]dkxdky. (2.7)

The magnetic eld H has the same form and can be written by replacing E by B. It

follows from k =√k2x + k2

y + k2z that kz must be imaginary for a spatial resolution of

k2x + k2

y > k2, so two regimes can be distinguished:

k2x + k2

y ≤ k2 : ei[kxx+kyy]e±i|kz |z (plane waves) (2.8)

k2x + k2

y > k2 : ei[kxx+kyy]e−|kz ||z| (evanescent waves). (2.9)

This shows the nature of plane and evanescent waves. The former can freely propagate to

the detector and the latter are exponentially decaying in direction of the surface normal

of an inhomogeneity in space (see Fig.2.1), the location where they arise. The evanescent

waves can, in principle, cover an innite spatial bandwidth, but are practically limited

by the fact that the decay length of the eld gets shorter for higher frequencies.

With the limitation of all k-components being real, we can calculate the diraction limit

of far-eld optics. Therefor we look at the point spread function, which is a measure of

the resolving power of an optical system. It describes the spread of a point source in

the image plane. The point source is a δ-function with an innite spectrum of spatial

frequencies in the object plane. On propagating from the source to the image, all

5


frequency components k2x + k2

y > k2 are lost, which directly results in a nite size of the

image.

The eld of an electric dipole, the smallest radiating electromagnetic unit, reads

E(r) =ω2

ε0c2

←→G (r, r0) · µ. (2.10)

r0 is the dipole location, µ is the dipole moment, ω = 2πf the angular frequency and←→G the dyadic Green's function. Here, the Green's function describes the mapping of an

arbitrarily oriented electric dipole from the source to the image. As we are looking at a

diraction limited system, we only let to contribute far-eld components of the eld to←→G . The result has the form of a 3 x 3 matrix, being multiplied by the dipole moment.

A detailed derivation can be found in [23].

|E|2 is now chosen to denote the point spread function, as this is the relevant criterion

for optical detectors. We dene the numerical aperture as NA = n · sin(θmax) and the

transverse magnication as M = nn′f ′

fwith θmax the maximum angle, under which light

can enter the objective and n, n′, f, f ′ the refractive indices and focal lengths on object

and image side, respectively. The optical axis is orientated along the z-axis. For a dipole

orientation µ = µx · ex (ex is the unit vector along the x-direction), the paraxial point

spread function in the image plane is

limθmaxπ/2

|E(x, y, z = 0)|2 =π4

ε20nn′µ2x

λ6

NA4

M2

[2J1(2πρ)

2πρ

]2

, ρ =NAρ

Mλ(2.11)

with J1 the rst order Bessel function, λ the wavelength of light and ρ =√x2 + y2.

The term in the brackets is known as the Airy function. Fig. 2.2 shows the electric

eld density in terms of the Airy function. The spot is elliptically shaped, the larger

NA, the higher the ellipticity. The width of the point spread function, e.g. the distance

from the optical axis in the image plane, to the position where the point spread function

becomes zero, is called the Airy disc radius and is found to be ∆x = 0.6098MλNA

. Note

that this result coincides with the Abbe diraction limit.

The point spread function along the optical axis is:

limθmaxπ/2

|E(x = 0, y = 0, z)|2 =π4

ε20nn′µ2x

λ6

NA4

M2

[sin(πz)

πz

]2

, z =NA2z

2n′M2λ(2.12)

with z the distance from the image plane along the optical axis. The width of this point

spread function, ∆z = 2n′M2λ

NA2 , is the depth of the eld.

Orientating the dipole along the optical axis (µ = µznz) leads to the point spread

6


(a) )c()b(z =0 z =0

E || 2

0 0.5 1–0.5–10

1

0 1 2 15.001–ρ ΝΑ / Μ λ ρ ΝΑ / Μ λ

r =0

z NA 2 / (M 2 λ2n’) –0.5–1 1.5

Figure 2.2 Point spread functions of a dipole moment in the image plane (a and c) and alongthe optical axis z, at the image (b). The ordinate is the value of |E|2. The solid (black)curves are the paraxial approximation, the dashed (red) and dotted (green) curves are exactsolutions for a NA = 1.4 objective lens. (a) Dipole is orientated in x-direction. The abscissadenotes the x-axis (dashed curve) and the y-axis (dotted curve) in the image plane (z=0).(b) Dipole is orientated in x-direction. The abscissa denotes the optical axis with the imageplane located at zero. (c) Dipole orientated along z-direction (optical axis). The abscissadenotes an arbitrary axis in the image plane. The abscissa is given in terms of the argumentof the Bessel function divided by 2π (a and b) or in terms of the argument of the sine dividedby π (c). Figure taken from [23].

function in the image plane

limθmaxπ/2

|E(x, y, z = 0)|2 =π4

ε20nn′µ2x

λ6

NA6

M2

[2J2(2πρ)

2πρ

]2

, ρ =NAρ

Mλ(2.13)

These calculations map a single point emitter from the source to its image. The distance

∆r‖ =√

∆x2 + ∆y2 of two point emitters, which can be barely distinguished in the

image plane, denes the resolution limit. The point spread function of these two emitters

overlap in the image plane, as illustrated in Fig. 2.3. We can dene the boundary to

indistinguishability, as the separation of the maxima of the two point spread functions

in the image plane by the width of one of them. Thus, a narrow point spread function

leads to a better resolution.

Novotny and Hecht [23] obtain hereby a resolution limit of:

∆r‖,min =λ

πn. (2.14)

As every optical system is additionally limited by the numerical aperture, the corrected

resolution limit has to account for the maximum angle under which the rays can exit

the optical system:

∆r‖,min =λ

πNA. (2.15)

7


E exc

enalp egamienalp tcejbo

M ∆r∆r

Figure 2.3 Illustration of the resolution limit. Two very close radiating point sources in theobject plane generate overlapping point-spread functions in the image plane. Figure takenfrom [23].

Abbe and Rayleigh formulate the resolution limit quite similar. Abbe, for example,

states that the maximum of one point spread function should coincide with the rst

minimum of the other one. As already mentioned, the result is the Airy disc radius:

RA = 0.6098λ

NA. (2.16)

In contrast, the Rayleigh criterion originally comes from calculations with grating spec-

trometers and not from microscopy.

There are possibilities to further shift the resolution limit to smaller structures, e.g.

with prior knowledge like dipole orientation, or by selective excitation. In confocal mi-

croscopy, a pinhole is set in front of the detector. The confocal point spread function

is then the square of the point spread function in normal microscopy. This leads to

slightly increased transverse resolution and high axial (longitudinal) resolution. Nor-

mal microscopy itself has no axial resolution. The numerical aperture can be further

exhausted, e.g. by 4Pi microscopy [24], using two objectives at the top and the bottom

of the sample. But all these techniques are still limited by diraction.

For really breaking the resolution limit and gaining arbitrarily high resolution, the spa-

tial frequencies, associated with evanescent waves, must be carried into the detector

plane.

8


-1 0 1 2

0.2

0.4

0.6

0.8

1

-20

r|| / λ

|Ex|

z = 0

-2 0 2 4

0.1

0.2

0.3

0.4

0.5

-40

k|| / k

|Ex|× 4

× 64

eld distribution (a) (b)

0.2

0.4

0.6

0.8

1

0

|Ex|

1 2 30z / λ

eld decay

(c)

spatial spectrumz = 0

Figure 2.4 Distribution of a conned Gaussian eld in the source plane z=0. The solid curvedisplays the connement ω0 = λ, the dashed curve ω0 = λ/2 and the dash-dotted curveω0 = λ/8. (a) Field distribution in real space, (b) spatial spectrum in reciprocal space and

(c) the corresponding eld decay along the optical axis z. r‖ =√x2 + y2 and k‖ =

√k2x + k2

y

lie perpendicular to the optical axis. The better the connement in real space, the broaderis the spectrum of spatial frequencies and the faster does the eld decay along the opticalaxis. The shaded area in (b) denotes the region of evanescent spatial frequencies. Figuretaken from [23].

2.3 Evanescent waves and surface plasmons

The intention of this chapter is to describe the inuence of evanescent elds on mi-

croscopy and spectroscopy and then link this description with the theory of plasmon

dispersion at a metal-dielectric interface.

Fig. 2.4 illustrates, that the connement of the light source below the diraction limit

broadens the spacial spectrum beyond the propagating frequencies into the evanescent

spectrum. See also Fig. 2.5, which shows the corresponding experimental conguration.

Note, that z = 0 denotes the sample surface and the position of the light source is −z0.

As the light source has to couple to the sample for using evanescent waves, near-eld

optical experiments are limited to surface investigations, as the decaying eld does not

reach the bulk.

Picking up the angular spectrum representation from equation 2.7, we get the electric

eld of the source in the surface plane of the sample [23]:

Esource(x, y, 0) =

∞∫∫−∞

Esource(kx, ky;−z0)ei[kxx+kyy+kzz0]dkxdky. (2.17)

When requiring that z0 λ, the eld interacting with the sample still contains evanes-

cent eld components. This is illustrated in Fig. 2.6. The spectrum can also be

9


Figure 2.5 Sketch of a near eld optical microscope.The source is at −z0, the sample plane atz=0 and the detector plane lies at z∞ in the far eld region. ni is the refractive index inthe respective region. Figure taken from [23].

expressed as the sum over discrete spatial frequencies, represented by delta functions:

Esource(kx, ky, 0) =

∞∫∫−∞

Esource(kx, ky; 0)δ(kx − kx)δ(ky − ky)dkxdky. (2.18)

Just looking at the transmission through the innitely thin sample, represented by the

transmission function T(x,y) in real space and directly writing down the convolution of

T and Esource in Fourier space gives us:

Esample(κx, κy, 0) =

∞∫∫−∞

T (κx − kx, κy − ky)Esource(kx, ky,−z0)eikzz0dkxdky. (2.19)

In the last step, we let the wave propagate to the detector, being located in the far eld

region at zinf :

Edetector(κx, κy, zinf) =

∞∫∫−∞

Esample(κx, κy, 0)e(κxx+κyy)eiκzzinfdkxdky. (2.20)

As the source eld was written in terms of discrete spatial frequencies, the source

wavevector k‖ shifts the sample wavevector k′‖: κ‖ = k‖ + k′‖. This is visualised in

Fig. 2.7. δ(k‖) represents a plane wave at normal incidence and does not shift the

original spectrum. δ(k‖ − k) represents the edge case of a plane wave, incident par-

allel to the surface.This shifts the frequency range [k...2k] into the detection window.

Spatial frequencies from δ(k‖ − 2k) on, represent evanescent waves, further shifting the

10


E source(z = –z0) E source(z = 0)

–k k 2k –k k 2kk k

Figure 2.6 Upon propagation from source to sample, E attenuates for higher |k‖|. The region|k‖| ≤ k denotes propagating wave components. The delta functions in the right picturerepresent the spectrum in terms of discrete spatial frequencies. Figure taken from [23].

k

k

k

Figure 2.7 Convolution of sample transmission and source eld. A far-eld detector only hasaccess to the range k‖ = [−k...k]. But as the near-eld components of the source are presentat the sample, evanescent wave components are shifted into the detection range. Figuretaken from [23].

frequency range, being detectable in the far-eld.

As only plane waves reach the detector, k‖ + k′‖ = κ‖ ≤ ωcn3e3 (with the unit vector

e3), so that for k‖,max ≈ π/L, with aperture diameter L,

k′‖,max ≈∣∣∣πL± 2πNA

λ

∣∣∣. (2.21)

The last term can be neglected for L λ. In contrast, for L λ, the resolution is

limited by the diraction limit.

How and where do evanescent waves appear and how can they be coupled into a de-

tector? As mentioned above, evanescent waves do never occur in homogeneous media,

but always when light interacts with inhomogeneities [25]. Wolfgang Dieter Pohl was

the rst who broke the resolution limit of light in 1982 and thus founded the eld of

nano-optics, leading to plasmonics. This eld provides the theoretical explanation of the

11


enhancement eect in TERS. Pohl observed that every self-illuminating or illuminated

object has electromagnetic near- and far-elds at its surface [4]. He describes it colorful

as a skin of light, surrounding these objects and being bound to it, and as drops of light

that occur at small apertures.

Evanescent waves particularly occur at total internal reection in a prism. Although

all the power is reected above a critical angle of incidence, there is an exponentially

decreasing near-eld penetrating the volume with lower refractive index n. As all the

power is reected, there can be no energy transport perpendicular to the surface. Nev-

ertheless, the evanescent wave does contain energy [23]. If the prism is coated with

a thin layer of metal, then it is possible that the light excites surface plasmons (SP).

The same happens when a metal is illuminated from the low-refractive index half-space.

The precondition is that the frequency of the light matches the plasma frequency of the

metal. Thus most appropriate metals for near-eld experiments in the optical regime

are gold, silver and copper. Surface plasmons are the quasiparticles of an oscillating

free electron gas in a metal. The coupling mechanism between this collective electron

motion and the propagating light is similar to that in the radio frequency regime. Field

enhancement is a phenomenon in antenna theory, as the antenna concentrates the elec-

tromagnetic energy into a small space with high energy density. So the vast knowledge

in the rather old eld of antenna technology can be transferred to the optical regime.

The surface plasmons greatly enhance the electric eld in the near-eld regime. When

describing the charge motion of surface plasmons together with the resulting electro-

magnetic eld, one speaks of surface plasmon polaritons (SPP). SPP are bound to the

surface. They are delocalized in plane, but do not radiate at planar interfaces. However,

they can scatter at structures smaller than their wavelength. By this, they become ra-

diating and are called localized surface plasmons (LSP). This is the crucial eect being

exploited for example for SERS and TERS. The required scattering at small structures

is the reason why a rough surface structure is needed in SERS and a sharp tip for TERS.

As the size of these structures localizes the scattering area they dene its resolution.

We will now discuss the plasmon dispersion relation, shown in Fig. 2.8, to get a deeper

insight in the coupling mechanism between the radiative and non-radiative domain. A

full derivation can be found in [23, 26, 27].

Photon and plasmon dispersion base on solutions of Maxwell's equations at planar

metal-dielectric interfaces and the Drude model, stating that the free electrons in a

metal oscillate 180 out of phase relative to the driving electric eld. An electric eld

leads to a displacement r of the electron e, leading to a dipole moment µ = er. Summing

all the l dipole moments of the free electrons results in the macroscopic polarization per

unit volume P = lµ, which can be expressed as P(ω) = ε0χeE(ω). From the electric

displacement eldD(ω) = ε0ε(ω)E(ω) = ε0E(ω)+P(ω) we get the frequency-dependent

12


ñ

Figure 2.8 Plasmon dispersion relation curves. Bulk plasmons can be excited when the photonfrequency matches with the crossing point of the dispersion curves of the bulk plasmon andof the incident light (green and dotted line, respectively). This is only possible when theangle of incidence is smaller than the critical angle: θi < θc. Excitation of surface plasmonsis only allowed at an angle of incidence being larger than the critical angle: θi > θc. Anotherway to satisfy momentum conservation at the excitation of an surface plasmon is addingthe reciprocal GP = 2πn/a of the grating constant a to the wavevector. Figure adaptedfrom [26].

13


dielectric function of the metal ε(ω) = 1+χe(ω). ε describes the optical properties of the

metal and the adjacent dielectric and thus is the material-dependent parameter dening

the surface plasmon dispersion.

To get this dielectric function, we start with the Drude-Sommerfeld model for the free

electron gas

me∂2r

∂t2+meΓ

∂r

∂t= eE0e

−iωt, (2.22)

where e and me are the charge and eective mass of the free electrons and E0 and ω

the amplitude and frequency of the applied electric eld. Γ = vF/l is the damping term

with the Fermi velocity vF and the mean free path l between two scattering events of the

electrons. The ansatz r(t) = r0e−iωt leads to the dielectric function of the free electrons

εDrude(ω) = 1−ω2p

ω2 + iΓω(2.23)

The volume plasma frequency ωp equals√ne2/meε0. It appears that this model gives

quite good results for the optical properties of metals, but can be improved by also

taking bound electrons into account, which take part at interband transitions when

excited by photons in the visible range. So we look at the equation of motion for bound

electrons:

m∂2r

∂t2+mγ

∂r

∂t+ αr = eE0e

−iωt (2.24)

m is the eective mass of the bound electrons, γ is the damping constant and α is

the spring constant of the potential. Solving this equation and using the correlation

P(ω) = ε0(ε(ω)− 1)E(ω) we thus get the dielectric function for interband transitions:

εInterband(ω) = 1 +ω2p

(ω20 − ω2)− iγω

(2.25)

where ωp =√ne2/mε0, with n the density of the bound electrons, ωp as analogy to the

plasma frequency in the Drude model and ω0 =√α/m. The dielectric function can

now be gained by summing up the terms of the Drude-Sommerfeld model and of the

interband transitions:

ε1(ω) = εDrude(ω) + εInterband(ω) = 2− ω2P

ω2 + Γ2+

ω2P (ω2

0 − ω2)

(ω20 − ω2)2 + γ2ω2

+iω

(ω2PΓ

ω4 + Γ2ω2+

ω2Pγ

(ω20 − ω2)2 + γ2ω2

)(2.26)

Fig. 2.9 shows the real and imaginary parts of the dielectric function of gold, separately.

The model is compared with experimental data, which are plotted in the same gure.

Model and experiment coincide quite good but suer from the negligence of higher-

energy interband transitions. So an oset of 6 is added to the terms of the interband

14


600 800 1000 1200

− 60

− 50

− 40

− 30

− 20

− 10

10

1

400 600 800 1000 1200

2

3

4

5

wavelength [nm]

wavelength [nm]

Johnson & Christy

Theory

Im(

)Re

()

Figure 2.9 Dielectric function of gold. Open circles: experimental values from [28]. Squares:model of the dielectric function, including free-electron contribution and a single interbandtransition. The imaginary and real part are shown in the upper and lower panel, respec-tively. Note that the abscissae scale dierently. Figure taken from [23].

transition in Fig. 2.9. However, the model starts to fail below wavelengths of about

500 nm.

It can be clearly seen, that the real part of ε is purely negative and the imaginary part is

positive. This leads to a strong imaginary part of the refractive index Im(n) = Im(√ε)

and thus to a low penetration depth in the metal. The imaginary part of ε indicates

the dissipation of energy by ohmic losses due to the motion of the electrons.

We can insert the dielectric functions ε1 and ε2 of the metal and the dielectric, respec-

tively, into a homogeneous solution of Maxwell's equation:

∇×∇× E(r, ω)− ω2

c2ε1,2(r, ω)E(r, ω) = 0 (2.27)

As there are no solutions for s-polarized light it is sucient to consider only p-polarized

waves. This can be explained by the need of an out-of-plane component to drive electrons

from the bulk to the surface. Applying boundary conditions like continuity of Eparallel

and Dperp (relative to the surface plane) at the interface, one obtains the dispersion

15


relation of the surface plasmon:

k2‖ =

ε1ε2ε1 + ε2

ω2

c2(2.28)

The results of Eq. 2.28 are plotted in Fig. 2.8 for a metal-vacuum or, still with sucient

precision, metal-air boundary.

The normal component of the wavevector is:

k2j,z =

ε2jε1 + ε2

ω2

c2j = 1, 2 (2.29)

Be aware that ε1 = ε′1 +iε′′1 and k‖ = k′‖+ik′′‖ are complex, while ε2 is assumed to be real.

The real part of k‖ determines the wavelength of the surface plasmon and its imaginary

part describes the damping. So

λSPP =2π

k′‖≈

√ε′1 + ε2ε′1ε2

λ. (2.30)

For ε2 = 1 and ε1,Ag = −18.2 + i0.5 and ε1,Au = −11.6 + i1.2 at the wavelength of the

excitation light λ = 633 nm, 1/e intensity propagation length of the surface plasmon is

about 60µm and 10µm, respectively. Equation 2.29 yields the decay lengths for silver

and gold in metal (air), which are 23 nm (421 nm) and 28 nm (328 nm), respectively [23].

With this information about the dispersion relation of the plasmon, we can continue the

discussion of Fig. 2.8. The light line of the propagating light and the dispersion curve of

the surface plasmon do not cross each other. The wavevector of the surface plasmon is

at a given frequency always larger than that of the freely propagating light. So a plane

wave alone can never excite a surface plasmon, as energy and momentum conservation

have to be fullled. However, there are two ways to tilt the light line, in order to obtain

the required intersection. First, the refractive index n in the light line equation can be

increased further. This is done by taking evanescent elds into account, which occur

at total internal reection (TIR). Second, the missing momentum can be gained using

a grating or other nano structure by adding its grating constant to the wavevector of

light: k′‖ = k‖ + 2πn/a, with the grating constant a [26].

There is another eect of sub-wavelength structures on surface plasmons. Surface plas-

mons can, apart from energy dissipation, propagate freely in the interface plane and are

conned in the perpendicular direction. When the surface plasmon scatteres on a small

structure it becomes a localized surface plasmon, conned at the particle, but being able

to radiate into the dielectric. This is similar to the well-established antenna technology,

where the lengths of the antennas are designed in fractions of the wavelength.

16

3 Raman Scattering

This chapter will start with the explanation of common far-eld Raman spectroscopy

and lead to the inuence of near-eld optics on signal enhancement and contrast gain

in TERS.

3.1 Conventional Raman scattering

Raman scattering is the inelastic scattering of photons on crystals and molecules. The

Raman eect was theoretically predicted in 1923 by Adolf Smekal [29] and experimen-

tally discovered by C. V. Raman and K. S. Krishnan [30] in organic liquids in 1928.

Independently from them, G. Landsberg and L. I. Mandelstam [31] found the eect in

quartz in the same year. In 1930 Raman was awarded the Nobel prize for the discovery

of this eect.

Among many other applications utilising the Raman eect, it is a powerful technique

in the study of high temperature superconductors, Heusler compounds and magnetic

textures like Skyrmions. The power of Raman spectroscopy lies in its capability to ex-

plore dierent regions of the Brillouin zone independently, which will be described by

symmetry selection rules later on. This distinguishes Raman spectroscopy from most

other transport and thermodynamic measurements, which measure the mean over the

hole k-space. One drawback is the extremely small scattering cross section, typically a

fraction of about 10−13 [1] of the incoming photons are scattered inelastically. All the

other photons are scattered without any energy shift, the so called Rayleigh scattering.

The Raman eect is a two photon process. The incident photon excites the system

(sample) to an intermediate state, generates an excitation (e.g. phonon) via coupling

and relaxes into a nal state by emission of a scattered photon. This process costs a

certain amount of energy and thus the scattered photon has a lower energy by exactly

the same amount, so it leaves the sample red shifted. The energy dierence of these two

photons is called the Raman shift and gives the opportunity to examine the energies of

various excitations like phonons, magnons, spin or charge density uctuations. It is also

possible to investigate the superconducting gap as breaking up a cooper pair requires

a well dened energy. A scheme of a typical Raman spectrum is shown in Fig. 3.1 for

17

CHAPTER 3. RAMAN SCATTERING

Figure 3.1 Characteristic Raman spectrum of (Y0.92Ca0.08)Ba2Cu3O6.3. It shows the contri-bution from phonons, magnons and electrons. The number of carriers per copper oxideplaquette is p = 0.07. The inset shows the photon polarization and the correspondingFermi surface in the CuO2 plane. Figure taken from [1].

(Y0.92Ca0.08)Ba2Cu3O6.3. The following theoretical introduction is thoroughly described

by Devereaux and Hackl [1].

In Raman spectroscopy the frequency shift of the scattered photon with respect to the

incident photon is measured. A typical spectrum is shown in the schematic gure 3.1.

This frequency shift occurs because the incident photon with dened frequency ωi and

momentum qi is absorbed by the crystal. The crystal is excited from its initial state I to

the virtual state ν. Upon relaxation of the system into a nal state F 6= I, a photon will

be reemitted with dierent energy ωs and momentum qs. Depending on whether an ex-

citation in the crystal was created (Stokes-process) or annihilated (anti-Stokes process),

the nal state will be of higher or lower energy than the initial state, respectively. This

is sketched in an energy diagram in Fig. 3.2. Denoting the energy dierence between I

and F with Ω and the momentum dierence with q, one can formulate the energy and

momentum conservation

hωs = hωi ± hΩ(q) energy conservation (3.1)

hnqs = hnqi ± hq momentum conservation (3.2)

with h being the reduced Planck constant and n the refractive index of the crystal.

The scattering of an electromagnetic eld described by the operator of the vector po-

tential A(ri)) by a system of N electrons is represented by the Hamiltonian

H = H′ + e

2mc

N∑i

[piA(ri) + A(ri)pi

]+

e2

2mc2

N∑i

A(ri)A(ri). (3.3)

18


I

F

Stokes

I

F

Anti-Stokes

(ωi, q

i)

(ωs, q

s)

(Ω, q)

ν ν

(ωi, q

i) (ω

s, q

s)

(Ω, q)

Figure 3.2 Scheme of the energy levels in Raman scattering. An excitation is created (Stokesscattering) or annihilated (anti-Stokes scattering) by an incident photon. The scatteringmedium changes thereby from an initial state I via a virtual state ν to the nal state Fand emits a scattered photon. Figure taken from [32].

H′ is the Hamiltonian with no contribution to the electron-photon-interaction. It de-

scribes the electronic system of a solid. p = −ih∇ is the momentum operator at position

r. A(ri) contains the polarization and the wavevector of the light at position r. e andm

are the charge and the mass of the electron, respectively. The second term couples the

unit charge to a single photon, describing an intraband transition (current response),

and the third term couples the unit charge to two photons, describing an interband

transition with an intermediate state (density response).

The probability of these processes is, described by Fermi's golden rule, stating that the

transition rate R is determined by:

R =1

Z∑I,F

e−βEI |MF,I |2δ(EF − EI − hΩ), (3.4)

with β = 1/kBT , Z the partition function, hΩ the excitation energy and MF,I =

〈F |M |I〉 the transition matrix element with the eective light scattering operator M .

MF,I can be expanded into basic functions φµ of the crystal's irreducible point group,

allowing the study of the polarization dependence of Raman scattering:

MF,I(q→ 0) =∑µ

Mµφµ. (3.5)

For a vanishing momentum transfer from the photon to the sample, which is a valid as-

sumption given that the photon momentum is small compared to the Fermi momentum

of the electrons and that many particle interactions can be neglected, a simplication

of the scattering cross section can be obtained. The transition rate R can thus be

expressed in terms of a density-density correlation function

19


S(q, iΩ) =∑I

e−βEI

Z

∫dτeiΩτ 〈I|Tτρ(q, τ)ρ(−q, 0)|I〉. (3.6)

The density-density correlation function arises from the sum over all possible nal states

and the thermal average of all initial states. It contains the complex time ordering

operator Tτ and the density operator

ρ(q) =∑k,σ

γ(k,q)c†k+q,σck,σ. (3.7)

ρ(q) itself contains the fermionic creation operator c†k,σ and the annihilation operators

ck,σ with the wavevectors k and the spins σ of the electrons, and the scattering amplitude

or Raman vertex

γ(k,q) =∑α,β

γα,β(k,q)eαi eβs . (3.8)

The polarization vectors for incident and scattered light are eα,βi,s . Using the uctuation-

dissipation theorem, S can be written in terms of the dynamical eective density sus-

ceptibility χ:

S(q,Ω) = − 1

π1 + n(Ω, T )χ′′

(q,Ω) (3.9)

with n(Ω, T ) the Bose-Einstein distribution. With the help of the Kramers-Kronig

relations, the Raman susceptibility can be used to calculate the relaxation rates.

Neglecting the conduction band the Raman vertex γ holds in two dimensions:

γ(k,q→ 0) = e∗sm−1eff ei (3.10)

withm−1eff the inverse eective mass tensor of second order. γ is the sum of contributions

which are each related to a certain symmetry. Fig. 3.4 shows the Raman vertices for

the A1g, B1g and B2g symmetries in the case of the cuprates. Note that the scattering

intensity is proportional to γ2. A1g, A2g B1g and B2g are the irreducible representations

(symmetries) of the D4h pointgroup. They correlate with the ingoing and outgoing po-

larizations of the excitation laser and the scattered Raman light, which can be seen in

Fig. 3.3. As shown in Fig. 3.4 the selection rules allow to study dierent regions of the

Brillouin zone independently.

γ is dependent on the momenta and energies of all the involved electrons. For a momen-

tum transfer much smaller than kF and photon energies much smaller than the band

gap, the Raman vertex can be written as

γα,β(k, q → 0) =1

h2

∂2Ek

∂kα∂kβ. (3.11)

20


xxA

1g + B

1g

x’y’A

1g + B

2g

xyA

2g + B

2g

x’y’A

2g + B

1g

RL B

1g + B

2g

RRA

1g + A

2g

Figure 3.3 Polarizations of the incident and scattered light and the related symmetries ofthe Raman vertex in the copper oxide layer of the cuprates. The arrows symbolize thepolarizations and are named with xx, xy etc. The rst symbol stands for the polarizationof the incident light and the second for the one of the scattered light. x′ and y′ mean anorientation diagonal to x and y and R and L stand for right and left circular polarized lightrespectively. Figure taken from [32].

Finally, this links the Raman vertex with the bandstructure of the scattering medium

at Ek.

21


Γ Γ Γ

A1g B1g B2g

Figure 3.4 Raman vertices of some symmetries of the D4h pointgroup. Blue zones are positiveand red zones negative. The dashed lines show the nodes, where the Raman vertex vanishes.Figure taken from [33].

3.2 Principles of high resolution Raman scattering

Limitations of normal Raman spectroscopy occur due to its very low scattering cross

section of about 10−30 cm2 [34, 35] and the spatial resolution limit of light. Eects like

Rayleigh scattering or uorescence are much more intense and need to be separated

from the Raman signal. Surface studies are complicated, as the light penetrates several

100 nm into the sample and gives also signal from the bulk or substrate material. Surface

enhanced Raman spectroscopy overcomes some of these limitations, but suers from

the need of a rough metallic substrate below a very thin sample. The variety of usable

substrate materials is limited, suitable are mainly noble metals but also e.g. alkali metals

[8]. Furthermore, this method is still limited to diraction [36]. The rough surface is

needed to scatter surface plasmon polaritons (SPP) and create the so called localized

surface plasmons (LSP) being responsible for the enhancement eect [8]. The sharp

tip of a scanning probe microscope also acts as an external scattering body for SPP

and is the principle of tip-enhanced Raman spectroscopy. This makes the investigation

of arbitrarily shaped samples possible, especially at bulk materials without a metallic

substrate. As only one scattering body is present the enhanced signal can be assigned to

sub-wavelength areas. Besides this, there are many more eects increasing the Raman

signal or the contrast between near- and far-eld. The most important ones are:

• electromagnetic enhancement

eld-line crowding: The electric eld lines are highly compressed at sharp

metal structures, thus the electric eld is enhanced in the vicinity of the tip

apex and therefore enlarges the number of Raman scattered photons in this

well dened area. This eect is purely geometric and not frequency dependent

like plasmons, so it is even present when the chosen light frequency is dierent

from the plasmon frequency [23].

22


scattering of surface plasmons: The incident laser light excites surface

plasmons (SP) at the tip apex, locally increasing the electromagnetic eld.

As well the scattered Raman light, especially the evanescent modes, creates

SPs, which can propagate into free space when scattering at the tip apex

[23, 26].

• chemical enhancement: Molecular orbitals overlap with those of the tip and

create new energy states for the Raman process, the so called charge transfer

process. Compared to electromagnetic enhancement this eect scales on shorter

ranges [26, 37].

• resonance Raman: If the laser frequency ts to the energy of an electronic tran-

sition in the sample, the Raman signal is also highly enhanced. This eect is not

limited to near-eld enhanced Raman scattering and also occurs in conventional

Raman measurements.

• depolarization eect: The metallic tip partially depolarizes the polarized scat-

tered Raman light. This means that the enhanced signal is not purely polarized

even if the far-eld signal is polarized due to selection rules. This eect can be used

to highly increase the contrast between the far-eld and the near-eld by blocking

the far-eld signal with a polarizer and thus only measuring the depolarized near

eld signal [38, 39, 40].

There are several dierent congurations which allow the excitation light to reach tip

and sample and the stray light to reach the detector. The most common apertureless

designs are shown in Fig. 3.5. However, there are also designs guiding excitation or/and

stray light through a metal coated glass ber. These designs are mostly aperture type,

being more preferable in near-eld microscopy.

Except for chemical enhancement and resonance Raman, which will both not be utilized

in our experiments, the above mentioned eects of signal and contrast enhancement will

be discussed in-depth in the following.

3.2.1 Field distribution and associated Raman enhancement

Although Raman scattering itself is a linear process, the Raman enhancement factor

scales with the fourth power to the incoming electric eld [41, 42]. This is due to the

enhancement of the near-eld intensity scaling quadratically with the incident electric

eld and the eect that the excitation light as well as the scattered light are enhanced.

As already mentioned, the electric eld in vicinity of the tip apex is enhanced by sur-

face plasmons and eld line crowding. Fig. 3.6 shows the surface charge distribution

23


Figure 3.5 Dierent apertureless TERS congurations. The main dierences are the illumina-tion direction and the used focusing element. Figure taken from [11].

at the tip for dierent electric eld vectors. According to this model, the electric eld

must be orientated along the tip axis to expect eld enhancement. Several mathemati-

cal methods exist to calculate the near-eld distribution at nanometer-sized structures.

Mie theory, for example, is the only analytical method to solve Maxwell's equations

completely, but is limited to spherical particles [43]. Quite common for numerical cal-

culations at sharp tips is the nite dierence time domain method (FDTD) [44]. Other

methods are the nite element method (FEM) [45], boundary element method (BEM)

[46] and discrete dipole approximation (DDA) [47]. Various papers have been published

on simulations of eld distribution at metal tips [41, 42, 48, 49]. The problem space

is discretized into so called Yee cells, so space and time are quantized [41]. To save

computation time the cells are small at interfaces and larger in continuous volumes.

Based on Maxwell's equations and the modied Debye model, treating electrons as free

particles with certain relaxation time, eld distributions can be simulated, as can be

seen in Fig. 3.7. Enhancement and decay length depend on tip-radius and geometry,

excitation wavelength, polarization and incidence angle and the substrate and tip ma-

terial.

Tips prepared of thin etched wires provide very high enhancement factors [50, 51], how-

24


x y

x z

x y

x z

+

+

+

+

++

σ

maxσ/21

50nm

Figure 3.6 Charge density distribution at a tip, forming standing waves. Left: Wavevector ofthe excitation light oriented along the tip axis z, electric eld vector along x. The standingwave has a node at the end of the tip. Right: electric eld vector orientated along z,wavevector along x. An accumulation of the surface charge occurs at the tip end, causinga large eld enhancement. Figure taken from [23].

ever, tetrahedral tip shapes as often used in cantilever based AFM cause even stronger

enhancement [52]. Very good results can also be achieved using more sophisticated tip

structures such as so-called bow-tie antennas (see Fig. 3.8), providing "almost perfect

impedance matching" [23].

Fig. 3.9 shows that for shorter wavelengths the plasmonic excitation is dominant

whereas for longer wavelengths eld line crowding outweighs the eect of surface plas-

mons for suciently small tip radii.

The surface charges of the tip form oscillating standing waves (surface plasmons) with

wavelengths shorter than those of light. Fig. 3.6 shows these standing waves for two

dierent polarizations. For an electric eld polarized perpendicular to the tip axis the

charge accumulates at the side of the tip with opposite sign and has a node at the apex,

as shown on the left side of the gure. On the right side, the electric eld is orientated

along the tip axis and drives the electrons to the apex, resulting in high eld enhance-

ment directly at the tip.

Fig. 3.7 presents the results of FDTD calculations for a silver tip with and without a

substrate material in the close vicinity. It indicates clearly, that the sample material

has an enormous eect on the enhancement factor. The indicator is here the maximum

25


Figure 3.7 Electric eld distributions calculated with the nite dierence time domain method.The Yee cell size is not uniform (see text). The silver tip has a radius of curvature of 25 nmand the plane wave has a wavelength of 632.8 nm, incident at an angle of π/3. (a) Goldsubstrate, 2 nm below the tip apex. The ratio between maximum local eld and the incomingeld amplitude is 242. (b) Without any substrate, the maximum eld enhancement is only16. Figure taken from [49].

Figure 3.8 SEM micrograph of a bow-tie antenna made of gold. It has a gap distance of 30 nm.The arrow points to the gap between the two triangles, which is the area with highest eldenhancement. Figure taken from [53].

26


Figure 3.9 Spectral variation of the local electric eld amplitude enhancement at the tip apexfor dierent tip radii (dierently coloured lines). The peak at lower wavelengths is due toplasmon excitation and the shoulder at higher wavelengths is due to eld line crowding.Figure taken from [48].

local eld enhancement M = |Elocal||Eincident|

. Note that the Raman enhancement that can

be detected in the far-eld scales with the fourth power to M . According to [49], for

a single silver tip with an apex radius of 25 nm, M equals 16 (Raman enhancement

ξ = 6.6 · 104). If, in contrast, the tip is set 2 nm above a gold substrate, M equals 242

(ξ = 3.4 · 109). Similar results are found in [48]. For a single gold tip with the same

radius of curvature of 25 nm, M and ξ are 20 and 1.6 · 105, respectively. For such a

tip set at d = 2 nm above the gold substrate, the near-eld coupling leads to M = 189

(ξ = 1.8 ·109). If d is increased to 5 nm, Emax decreases by 70% (ξ by 99%) and becomes

fully negligible at d = 20 nm. Simulating the enhancement with dierent substrate ma-

terials (at d = 1 nm), M becomes 352 (Au), 232 (Pt) and 68 (SiO2).

In Fig. 3.10, the enhancement of the electric eld (M), the intensity (M2) and the

Raman signal (M4) are plotted against the tip-substrate distance. The enhancement

decreases rapidly with the distance, indicating that the distance control is a key require-

ment in TERS measurements.

In additional calculations the dependence of the eld enhancement on the angle of in-

cidence was studied [41]. The rather surprising results can be seen in Fig. 3.11. One

would expect that the maximum enhancement occurs when the light is polarized along

the tip axis. However, the calculations with p-polarized light (electric eld vector par-

27


Figure 3.10 Dependence of enhancement on tip-substrate distance. The silver tip is held withvariable distance over a gold substrate. The angle of the incident light is similar to thatin Fig. 3.7. Black: eld enhancement M , red: intensity enhancement M2, green: TERSenhancement M4. Figure taken from [41].

Figure 3.11 Dependence of eld enhancement on the angle of incidence of the plane waverelative to the tip axis. Parameters are as in Fig. 3.10. Figure taken from [41].

28


Figure 3.12 (a) Maximum eld enhancement as a function of the tip radius. Inset: spatialeld distributions for dierent tip radii. (b) Normalised eld and Raman enhancement asa function of lateral displacement along a horizontal line on gold substrate, 1 nm below agold tip with a radius of 25 nm. The parameters are as in Fig. 3.10. Figure taken from [41].

allel to plane of incidence) show that after a maximum at an angle between tip axis and

kinc of about 50 degrees the enhancement decreases again. This eect is only showing

up when the tip is close to a substrate. The reason is that the vertical eld amplitude

of the reected light also becomes larger, but with the phase shifted by π with respect

to that of the incident eld. Due to interference, the enhancement decreases again. As

expected, the enhancement of s-polarized light is very small, as the phase matching

condition of the surface plasmon polariton is not met.

The tip size does basically not have much inuence on the eld enhancement factor

as apparent in Fig. 3.12 (a). First when reaching very small radii, the enhancement

increases rapidly due to eld line crowding. The smaller the radius of curvature, the

higher the lightning rod eect, leading into a eld singularity for innitely sharp tips

[48]. Demming et al. [42] calculate a stronger eect of the tip radius on the enhance-

ment factor, which might be caused by their dierent design with bottom illumination

through the substrate. Also the eect of s-polarized light is stronger in these calcula-

tions, but still below that of the p-polarized light.

As a rule of thumb the resolution is about half the tip radius [54]. A more detailed

result [49] is shown in the inset of Fig. 3.12 (a). The spatial resolution can be dened

as the full width of half maximum (FWHM) of the Raman enhancement. For all shown

tips, the resolution is easily beyond 50% of the radius. Fig. 3.12 (b) shows the eld and

Raman enhancement as a function of lateral displacement, making clear that the focus

of the Raman light collection optics must match the tip cone position exactly.

The model can be improved, by taking into account the tip-cone angle [48]. This group

also includes the shape of the wave fronts of the incident light in TERS congurations.

29


3.2.2 Contrast gain in near-eld Raman scattering

Apertureless TERS setups with side illumination optics suer from the simultaneous

collection of far-eld and near-eld scattered light. Therefore the near-eld signal is

obtained by subtracting a far-eld spectrum from the tip-enhanced one. However, the

near-eld signal is enhanced by several orders of magnitude whereas the scattering

volume, from which the near-eld signal originates, is several orders of magnitude smaller

than the far-eld scattering volume. The resulting ratio of near-eld and far-eld signal

can thus be easily below one. It is obvious that the discrimination of near-eld and

far-eld signal is crucial for TERS measurements. Several parameters and eects have

to be considered, which have either to be suppressed or utilized, including:

• the ratio of near-eld and far-eld scattering volume,

• the tip and substrate dependent enhancement factor,

• the far-eld suppression by utilization of the depolarization eect,

• a smaller eective spot size of the far-eld by using sub-wavelength sized samples

or by introducing a pinhole in the collection optics as well as

• other signal sources, such as light emission from tip-sample tunnel junctions.

The last point, light emission from tunnel junctions, was dealt with by [26]. Surface

plasmon modes within the tip-sample cavity can also be excited by tunnelling electrons

and emit a characteristic spectrum of light. This eect is quite small compared to the

others, so it should be legitimate to neglect it in most of the Raman measurements.

The contrast c is the ratio between the near-eld and far-eld scattered light detected

in the spectrometer,

c =InfIff

=ItotalIff− 1 =

Vnf · νVff

, (3.12)

with Vnf and Vff the near-eld and far-eld scattering volumes and ν the enhancement

factor. ν is mainly dependent on the dielectric functions of tip and sample, the tip shape

and the plasmonic coupling between tip and sample as discussed above. Let's set g to

105 [7] for an example calculation with a gold tip close to a silicon sample. Highly precise

focusing with a spot diameter of 500 nm, a scattering depth in Si in conventional Raman

of 500 nm and a near-eld volume of 102 ·2.5 nm3 lead to a ratio of the scattering volumes

on the order of 10−5 (scattering depths also taken from [7]). The resulting contrast is

about one, so a clear signal discrimination is possible. Note, however, that we assumed

a very small far-eld spot and a tip with good enhancement properties. Slight oxidation

of tip or sample can already decrease the contrast signicantly.

Only if an additional aperture is added the far-eld content can be suppressed further.

30


Figure 3.13 Sketch of a pinhole blocking aberrated rays that do not originate from the focusof the parabola on the left and therefore are not suciently collimated.

The aperture can be a pinhole which is set into the optical path of the collection optics

(Fig 3.13). Only light that comes exactly from the focus of the microscope objective or

parabolic mirror will be perfectly collimated and then focused onto the pinhole. Thus,

the pinhole blocks all the light from the outer regions of the laser spot on the sample

and therefore minimizes the eective spot size. Alternatively, the sample can be chosen

to be smaller than the laser spot, acting like an additional aperture by itself. This is

the case for single molecules being present in the spot. The latter actually gives a real

sub-diraction limited signal in the far-eld.

However, there is another eect which is outweighing the tip enhancement in TERS

measurements [40] and being discussed in many papers [38, 39, 40, 55, 56]. It is the eect

of the tip depolarizing the polarized light scattered from the sample. By blocking the

predominant polarization with a polarizer, the far-eld Raman signal will be suppressed

eectively. The T2g mode of silicon at 520 cm−1 was enhanced by a factor of 8.6 by far-

eld suppression with a polarizer [39]. Also another group increased the contrast of this

mode from originally 0.2 to 9, being a factor of 45 [55].

Ossikovski et al. [56] present a phenomenological model for the eective scattering

tensor R′′k of phonon mode k for the tip-sample system,

R′′k = A′TR′kA′, (3.13)

with R′k the far-eld polarizability tensor and A the phenomenological tip amplication

tensor, both in the laboratory reference frame. The resulting eld intensity is

ITERS ∝∑k

|vTs T ′′k vi|2 (3.14)

with vs,i the incident and scattered electric eld vectors, respectively.

The model is rened by taking the average over several scattering tensors and intensi-

31


ties, calculated with dierent amplication tensors, to take the tip orientation and form

into account. The results coincide quite well with the experimental spectra (Fig. 3.14).

The scattered light is not generally fully depolarized. [38] and [39] study the degree of

depolarization (DOP), dependent on dierent parameters such as the excitation wave-

length and laser power. They state

DOP =

√S2

1 + S22 + S2

3

S0

, (3.15)

where Sx are the Stokes vector components. 0 ≤ DOP ≤ 1, increasing from unpolarized

to fully polarized light.

Fig. 3.15 impressively shows the eect of depolarization on the contrast. Conventional

far-eld Raman spectra of c-Si(100) already show a substantial polarization depen-

dence due to selection rules (a). The dierent phonon modes at 300 cm−1 520 cm−1 and

980 cm−1 are not equally inuenced by the polarization, but show huge dierences. In

panel (b) the polarization conguration with the lowest phonon intensity (same polar-

ization for incident and scattered light) is compared for the cases tip retracted and in

contact. Here, tip in contact means that the tip is close enough to the sample so that the

feedback loop controls the distance. This distance is held constant while scanning. The

phonon modes are enhanced quite dierently. The one at 500 cm−1 increases by factor of

8.6 and is the most enhanced one. It appears that the depolarization eect takes eect

over a rather long tip-sample distance. Raman intensities that can be attributed to the

depolarization eect decay at increasing tip-sample distances. This decay length is very

long compared to that of the enhancement eect. Merlen et al. [39] measured a decay

length of 215 nm for the 520 cm−1 mode of silicon at an experimental setting where this

mode appeared due to the depolarization eect. In contrast, signals attributed to the

enhancement eect usually decay over 10 to 20 nm.

The ability to gain polarization resolved spectra according to the selection rules when

simultaneously utilizing the depolarization eect is not trivial and requires further dis-

cussion.

32


Figure 3.14 (a) Raman intensity of the 521 cm−1 phonon mode of silicon as a function of theincident polarization. The analyser was oriented according to s-polarization. Points andlines symbolize experimental and calculated values, respectively. Squares and the solid lineshow the behaviour with the tip close to the sample. Circles and the dotted line mark thesetup with the tip withdrawn. (b) Experimental and calculated contrast ratios from (a).Figure taken from [56].

33


(a)

(b)

Figure 3.15 Raman spectra of c-Si(100) for various polarizations in excitation and detection.(a) Tip retracted. The most intense phonon is at 520 cm−1 for crossed polarizations. Whenexcitation and detection polarizations are equal, this phonon mode is suppressed. (b)Conventional Raman spectrum (tip retracted) and tip-enhanced Raman spectrum (tip incontact). The baselines are subtracted for better comparability. Both polarizers are orientedfor S polarization. The formerly suppressed phonon mode is enhanced by a factor of 8.6when the tip is within the near-eld range of the laser spot on the sample surface (tip incontact). Inset: The same spectra without baseline subtraction. Figure taken from [39].

34


3.3 Tips suitable for TERS

Having good tips is crucial for the resolution in scanning probe microscopy and TERS.

STM tips are quite easy to produce as it simply requires a single atom at the end of the

tip, which is usually already given when cutting a metal tip at an angle. AFM tips are

more sophisticated to produce, because not only the foremost atom plays a role in the

tip-sample interaction. Here, the resolution is given by the size of the tip end. Sharp

cantilever tips can be bought from the shelf, but when using a tuning fork, as in our

case, the tips have to be etched by oneself with optimized production parameters to

obtain symmetric and sharp tips.

To provide high enhancement factors in TERS the dielectric response of the tip material

must match the excitation frequency of the laser. Most commonly used tip materials in

TERS are silver and gold [11, 42]. Silver, with a resonance peak around 500 nm, is best

for use with green laser light, whilst the gold resonance matches with red light. Silver

provides higher enhancement factors than gold, as the imaginary part of its permittivity

is smaller, but it oxidizes rapidly in air. Furthermore, gold tips are easier to etch and

one usually gains much smaller tip diameters. Beside etching, coating a sharp tip made

from other materials with gold or silver provides usable tips.

Various tip geometries are in use, including cantilever tips with tetrahedral shape and

bow tie shaped tips. The tips used in our setup have a smooth concave tapered shape

as shown in Fig 5.6 (b).

35

4 Scanning Probe Microscopy

Scanning probe microscopy (SPM) is a branch of microscopy that scans the sample sur-

face with an essentially atomically sharp, tip (probe) and is not limited by diraction

such as optical (far-)eld microscopes or the scanning electron microscope (SEM). Ana-

logue to the optical case, one can formulate the point spread function for the scanning

probe microscope (correlating to the probe-sample interaction volume), which is a mea-

sure of the resolving power of the system. To a good approximation the resolution is

the full width at half maximum (FWHM) of the point spread function. For optical mi-

croscopes the resolution limit is approximately λ/2. The SEM has a resolution between

1 nm and 20 nm. Using high-resolution transmission electron microscopes (HRTEM) a

sub-50 pm resolution was reported [57]. However, the increasingly high energy density

in a sharply focused electron beam sets a practical lower limit. In SPM lateral atomic

resolution is possible, theoretically even orbital resolution, and in vertical direction a

resolution of several picometers can be achieved.

The most common SPMs are the scanning tunnelling microscope (STM) and the atomic

force microscope (AFM). The STM was invented at IBM Zürich in 1981 by Gerd Bin-

ning and Heinrich Rohrer [58] and the AFM later in the early 1980's by Gerd Binnig

[59]. For this, they were awarded the Nobel Prize in 1986 [60]. So far, there is a long list

of other types of SPMs, which are either variations of the primary ones (e.g. magnetic

force microscope) or work on basis of new concepts (e.g. scanning thermal microscope).

37

CHAPTER 4. SCANNING PROBE MICROSCOPY

4.1 Atomic force microscope

In an AFM the spatial variation of the tip-sample interaction is measured to gain a to-

pographic image of the sample surface. Several forces with dierent interaction ranges

are eective when the tip is brought close to the sample. There are short range chem-

ical forces with a range of fractions of nanometers, the van-der-Waals force (several

nanometers) and possibly also long range forces like electrostatic and magnetic forces

with eective ranges up to 100 nm [61]. The interaction between two atoms can be

described quite well by the empirical Lennard-Jones potential,

VLJ = 4ε

[(σr

)12

−(σr

)6], (4.1)

where σ and ε are material dependent parameters. The term with the exponent of 6

is mainly related to the attractive van-der-Waals force. The exponent reduces to 2 in

case of spherical tips in the vicinity of a at surface. The term with the exponent of

12 corresponds to the repulsive Pauli interaction, which predominates below a certain

distance.

There are a few methods to detect these forces. In our experiment we use a tuning fork,

vibrating at its resonance frequency (see Fig. 4.1(a)). The tip, mounted on the tuning

fork, is brought closer to the sample with a xyz-piezo positioning system. Once the

interaction forces start to aect the resonance frequency up to a certain threshold value

one can start scanning over the sample surface. The threshold value is typically set to

about 80 % of the initial driving frequency. This value is a compromise between the fast

response of a low threshold and the risk that the tip crashes into the sample, when too

much damping is required. One way is to measure the change of phase and amplitude of

the vibration of the tuning fork and translate this directly into the dierence of height of

the sample structure (constant height mode). Alternatively one can use a feedback loop

to keep the amplitude at its threshold value via the piezo positioners (constant force

mode). Here, the regulation of the piezos corresponds to the topographic structure of

the sample. The latter is used in our setup. Another method is the use of a cantilever,

whose deection due to the interactions follows Hooke's law as shown in Fig. 4.1(b).

The deection is measured with a laser and a photo diode.

38


Figure 4.1 (a) Tuning fork based AFM. The tuning fork is vibrating at its resonance frequency.Interactions between tip and sample damp the vibration and indicate distance changes.Figure taken from [62]. (b) Cantilever based AFM. The deection of the cantilever due totip-sample interactions is measured by the deection of a laser beam. Figure taken from[63].

4.2 Scanning tunnelling microscope

In scanning tunnelling microscopy (STM) a bias voltage is applied between the tip

and the (conductive) sample and the resulting tunnelling current is measured (see Fig.

4.2). Thus, scanning across the sample surface with a certain bias voltage gives an im-

age, which is formed by the surface landscape geometry and the local density of states

(LDOS). For tip approach and for scanning, xyz-piezo positioners are used. The tip is

approached to the sample until a certain threshold current is measured. In this position

the scanning will start. The sample can be scanned either in the constant height mode,

where tip or sample are moved only in xy-direction parallel to the sample surface. Here

the measured tunnelling current is the indicator for changes in surface topography and

the LDOS. Alternatively, the z-piezo is adjusted via a feedback control so as to keep

the tunnelling current constant. In this mode, the piezo movement reects the surface

topography.

The energy levels of the tunnelling electrons are given by the time-independent Schrödinger

equation in one dimension:

− h2

2m

∂2ψn(z)

∂z2+ U(z)ψn(z) = Eψn(z). (4.2)

Here z is the position of the tunnelling electron between tip and sample. For positive

bias of the tip z is maesured from the tip and vice versa. m is the electron mass, and

U the barrier height. The wavefunctions of the electrons of tip and sample ψt and ψs,

39


Figure 4.2 Sketch of an STM. A bias voltage is applied between the tip and a conductingsample. The tunnelling current, appearing when the distance becomes several nanometers,is measured. A feedback control readjusts the positioning piezo in z-direction to avoidcrashing the tip into the sample and ripping of the tunnelling current. Figure taken from[64].

respectively, are exponentially decaying inside the barrier:

ψt(z) = ψt(0)e±κz (4.3)

ψs(z) = ψs(d)e±κ(d−z) (4.4)

with κ =√

2mφh

and φ the work function, which is assumed to be the same for tip and

sample. d is the barrier thickness, i.e. the tip-sample distance. In case of positive bias

the electrons from the tip tunnel into the empty states on the sample, and vice versa

when U is negative. According to Bardeen's formalism [65], the tunnelling current is

I = (2πe/h)∑t,s

f(Et)[1− f(Es − eV )]|Mts|2δ(Et − Es) (4.5)

with the tunnelling matrix element Mts between states of the tip and surface and the

Fermi function f(E).

Using the wavefuctions ψs and ψt, the tunnelling current is proportional to

I ∝∑|ψt(d)|2|ψs(0)|2exp(−2κd) (4.6)

Including the Terso-Hamann approximation [66] with the assumptions of low temper-

atures, of an s-wave like tip wave function and that the electrons are only tunnelling at

EF , one obtains:

I ∝∑|ψs(r0)|2δ(Es − EF ) (4.7)

with r0 being the distance from the center of curvature of a spherical tip. The sum

represents the surface LDOS at EF , hence the contour map at constant bias voltage

gives access to the local density of states.

40


Generalizing the Terso-Hamann approximation [67] by including a range of states

within an energy window e · V above the Fermi level, with V being the applied voltage

one can describe bias-dependent imaging and spectroscopy,

I ∝∫ EF +eV

EF

ρs(r, E)ρT (r, E − eV )T (E, eV, r)dE, (4.8)

with the electron tunnelling transition probability T and the surface and tip density of

states ρs(r, E) and ρT (r, E− eV ), respectively. Under the assumption that the tip DOS

is constant, one gets at a given energy :

dI

dV∝ ρs(eV )T (eV ) (4.9)

This contains a convolution of the topographic and electronic structure and highlights

bias depending features.

So far we were discussing the tunnelling between two metals but also tunnelling between

the tip and a superconducting sample is feasible [68]. With a STM it is possible to map

the density of states and the energy gap of the superconductor and compare these

results with those from the Raman measurement. In particular the study of high TC-

superconductors and the investigation of the pseudogap and vortex cores is obtainable

both with STM [69] and Raman [70, 71].

41

5 Setup

This chapter describes our setup and the parameters used. The performance and be-

haviour of the setup is simulated with the optics design software Zemax [13].

5.1 Overview

Our TERS setup is designed to simultaneously full the requirements for SPM and Ra-

man scattering on samples such as YBa2Cu3O7 (YBCO), SrTiO3/LaAlO3 (STO/LAO)

or surfaces of topological insulators. Although it is not the only one combining these

facilities our setup is so far unique in its conguration. Whereas most of the other

TERS setups use a microscope objective lens, here a parabolic mirror with high numer-

ical aperture is used for both focusing and collection purposes of laser and Raman light,

respectively. Unlike other parabolic mirror assisted setups where the sample surface

is orientated perpendicular to the mirror axis [7], in this setup the sample surface is

orientated parallel to the optical axis of the mirror. By tilting the sample with respect

to the polarization direction of the incident light, this setup provides access to polar-

ization control in the Raman measurements. The samples are illuminated from the top

as the setup is designed for intransparent samples. The tip, being responsible for the

enhancement, is illuminated from the side and can be controlled via a scanning tun-

nelling microscope setup or a scanning force microscope, optionally. The sample holder

is, together with the scanning probe microscopes, located in a cryogenically pumped

UHV cryostat which can be evacuated to a pressure of 10−8 mbar and cooled down to

temperatures of about 10K. To provide high precision of the scanning probe micro-

scopes the cryostat is mounted on a vibration isolating optical table together with the

optical setup.

As the prove of principle of this setup, due to tip-enhancement, is still outstanding, the

setup is not nalised yet and requires further improvements.

43

CHAPTER 5. SETUP

5.2 General setup

The UHV cryostat and the optics are set on an optical table with vibration isolation

(Newport). Fig. 5.1 shows the arrangement in the laboratory. Inside the cryostat, as

shown in Fig. 5.2, the scanning probe microscope unit and the parabolic mirror are

mounted in an upside down position for technical reasons. One can see the open cryo-

stat with the connected microscope head and the inner optics. A close up top view of

the sample holder is depicted in Fig. 5.3. The topmost layer on the sample holder is

copper to ensure electrical contact with the sample during STM operation. Permanently

installed is a small aluminium block that holds a silicon sample at an angle of 30 with

respect to the plane of the sample holder. When this sample is shifted into the focus of

the parabola, the direct laser reex will hit the parabola and exit the cryostat what is

done for alignment purpose. Next to the aluminium block the samples for the measure-

ments are xed. Currently there are set two silicon samples with dierent doping and

one optimally doped YBa2Cu3O7 sample.

Control and read out of the SPM and the data requires several electronic devices, which

are placed in a rack next to the optical table. This electronics and the microscope unit

were supplied by Attocube and are controlled by a software named Daisy.

The vacuum chamber of the cryostat is evacuated with a turbo pump and dry forepump

(Pfeier, HiCube 80 Eco). In order to remove dirt and moisture from the cryostat and

therefore accelerating the evacuation, the cryostat has to be ushed with nitrogen gas

several times. The appropriate setup with physisorbing gas purier and particle lter

is already installed and a pressure of the order of 10−5 mbar was achieved. In order to

reach UHV conditions the system will have to be baked out what requires the instal-

lation of heating tapes. All infrastructure for cooling exists and will be applied once

room temperature enhancement is veried. Upon cooling the positions of the parabolic

mirror and the tip mount change with respect to the external optics and can be adjusted

by varying the vertical position of the entire cryostat. The precision is close to 1µm.

The laser is mounted on a quick-mount stage which allows the interchange of dierent

lasers between all Raman laboratories with minor adjustment.

44

CHAPTER 5. SETUP

1

32

Figure 5.1 Overview of the lab. The rack on the left hand side houses the (1) electronics forSPM control, (2) the temperature controller and (3) the cryogen level monitor. The opticaltable with the cryostat and the optical components is on the right.

piezo stage for tip control

parabolic mirror

last lens and mirror of Köhler illumination

Figure 5.2 SPM unit in the open cryostat. The lens in the front is part of the Köhler illuminationsetup. The piezo stage for tip control is located in the middle. The parabolic mirror is belowthe piezo stage.

45

CHAPTER 5. SETUP

electric contact for STM measurements

YBCO

silicontilted silicon

Figure 5.3 Microscope image of the sample holder. The topmost layer on the sample holder iscopper to ensure electrical contact to the wire in the upper right corner for STM operation.On the aluminium block on the right, a silicon sample is glued at an angle of 30 withrespect to the plane of the holder to make the direct laser reex hit the parabola and exitthe cryostat for alignment purposes. The two samples on the left are crystalline silicon,xed with silver paint. On top of the left one an optimally doped YBCO sample is xed.

5.3 Scanning probe microscopes

5.3.1 Settings and parameters

The tip for both STM and AFM operation is glued on a quartz tuning fork. Fig. 5.4

shows a microscope image of the tip and the tuning fork. For STM operation one end of

a thin PtIr-wire is xed at the tip to connect the tip and the contact pad on the sample

holder electrically to allow the application of a bias voltage during the measurement.

The bias voltage is typically about 1-2V and the threshold current is around 500 pA

during approach and then increased to 1-1.5 nA for the measurement. In case of AFM

operation, the tuning fork is vibrating with a resonance frequency of 32.768 kHz (see

Fig. 5.5). The damping threshold which is the level the feedback loop tries to maintain

is set to 80-90% of the undamped amplitude of the tuning fork.

The Pt-Ir wire attached for STM measurements is not necessary for AFM measurements

and usually removed for this. However, we found out that the wire shifts the resonance

frequency of the vibrating tuning fork-tip system negligibly. So it will be possible to

perform both types of scanning probe measurements without heating up the cryostat

and breaking the vacuum.

To avoid a crash of tip and sample the operation is not done in constant height mode,

46

CHAPTER 5. SETUP

tip

sample stage

tuning fork

Figure 5.4 Microscope picture of the sample block, the tuning fork and a gold tip glued at itsend.

but in constant current (STM) and constant damping mode (AFM) with variable height.

5.3.2 Tip fabrication technique

The setup for etching the gold tips is shown in Fig. 5.6(a). It was built and optimized

by Nitin Chelwani. The tips are made out of a 100µm thin gold wire which is annealed

at 800C before etching. Annealing removes defects and grain boundaries by increasing

the size of the crystallites in the gold which otherwise would cause non-uniform etching.

As an electrolyte we use 37% fuming hydrochloric acid. The counter electrode is a

platinum ring. The gold wire is in contact with the electrolyte to close the electric

circuit but hardly touches the electrolyte surface. We use pulsed alternating current at

a voltage of 8V with a frequency of 3.03 kHz and a DC oset of 0.4V. The pulses last

30µs and are separated by 300µs. These settings and parameters turned out to provide

the best results but dier between the various groups producing their own tips. Etching

stops automatically when the contact between tip and solution breaks o, leaving a

sharp tip with the desired shape. Tip sharpness varies and may reach radii of below 20

nm with parameters indicated.

Etching silver tips turned out to be more complicated and does still not return the

required results. We started experimenting with silver wires (0.22 mm, 99.99% purity)

and an etching solution out of 14.44mol/l nitric acid and 2mol/l ethanol with a volume

ratio of 1:2. One possibility could be that the tip is overetched before the electric circuit

47

CHAPTER 5. SETUP

2 9 . 0 2 9 . 5 3 0 . 0 3 0 . 5 3 1 . 00 . 0

0 . 5

1 . 0

1 . 5

2 . 0

volta

ge U

(V)

f r e q u e n c y f ( k H z )

v o l t a g e r e s p o n s e o f d r i v e n t u n i n g f o r k

Figure 5.5 Frequency response of the tuning fork - tip system. The voltage output of thepreamplier is drawn as a function of the frequency. The peak position denotes the eigen-frequency. It is shifted to lower frequencies due to damping by the tip and the PtIr wirethat is needed for STM operation.

is interrupted when the contact between tip and solution opens. To avoid this, a labview

program was started to be implemented which stops the power supply as soon as the

current falls below a threshold value close to the end of the etching process. We already

tried out dierent parameters with during and alternating current but didn't reach a

usable tip shape and sharpness yet. However, etching the gold wires is reproducible and

provides very sharp and uniformly shaped tips.

48

CHAPTER 5. SETUP

magn: 500,000

Figure 5.6 (a) Setup for tip etching. The tip is xed in a crocodile clip and dipped into theetching solution. A ring out of a platinum wire acts as cathode. (b) Successfully etched goldtip as seen using an optical microscope. (c) The same tip imaged by a scanning electronmicroscope, used to determine the size of the tip apex.

5.4 Optics setup and simulations

The setup contains optical elements in several light paths, such as the imaging and the

scattering pathways. An overview is shown in Fig. 5.7 in a photo (a) and in a sketch

(b) with the main components being labelled. The whole optics is explained in detail

in the following sections. Many of the optical components were designed and simulated

with the software Zemax.

5.4.1 Parabolic mirror

The parabolic mirror is the crucial element for the contrast gain between near-eld and

far-eld spectrum, but also for the stray light intensity and the view onto the sample.

It is one half of a full paraboloid covering half space, thus has a solid angle of π. The

surface quality is approximately λ/2 at optical frequencies. The diameter of the mirror

is 15mm with a focal length of 8 mm. The sketch in Fig. 5.8 shows the principle of a

parabolic mirror. (a) Collimated light, incident along the optical axis, is focused onto

the focal point of the mirror. (b) Thus, all the light, leaving the focal point and hitting

the mirror, is then parallel. (c) A 30 tilted silicon sample on the sample holder (see

Fig. 5.3) is used for alignment purposes. For alignment of the ber coupling, the tilted

sample is moved into the focus and leads the direct reex back into the mirror. As the

49

CHAPTER 5. SETUP

cryostat

beam splitters

KÖHLERbright fieldillumination

camera

fiber entrance

spectrometerparabolic mirror laser

optical flat

λ/2-waveplatepolarizer

edge filterbeam expander

Figure 5.7 View on the optics setup from top, (a) current photo, (b) sketch with detaileddescription.

50

CHAPTER 5. SETUP

inelastically scattered light is too weak to be observed, the direct reex is a necessary

reference for the rst alignment approach.

Highly precise optical systems require indicators giving information about the actual

alignment quality. The shape of the laser spot on the sample surface only gives a rough

idea of the alignment. For aligning the incident laser beam exactly parallel to the optical

axis of the parabola we use an optical at. An optical at has exactly parallel back and

front planes. Here the precision of the entire area is better than λ/20. The principle

is sketched in Fig. 5.9 (e). The incident beam is split into one intense beam (second

reex) and two low intense beams (rst and third reexes). The intense beam has about

92% of the laser power and is used for the measurements. The other two beams are

used for alignment purpose, their intensity is about 4% of the laser power. Higher order

reexes can be neglected due to their low intensity. The intense beam is blocked during

alignment. A measure of the alignment quality is the overlap of the rst and third

reexes at the sample surface (Fig. 5.9 (a)-(c)). The better the alignment, the better

the overlap and the smaller is the resulting spot size will be. With this indicator we

were able to highly improve the spot quality (Fig. 6.1 in the measurements chapter).

5.4.2 Imaging optics

For the alignment of the Raman optics it is essential to have a live image of the sample

surface. Seeing the laser spot gives information about the illuminated sample area of

interest, the spot size, as well as the quality of the alignment. Misalignment can be in

terms of deviation of the optical path from the optical axis of the mirror and in shift

of the sample out of the focal point. These deviations cannot be seen separately, but

show up altogether in a non-circular and non-uniform spot.

The illumination method used is known as Köhler illumination [72]. This type of illu-

mination is the predominant technique in scientic microscopy as it provides very even

illumination and high exploitation of light. The image of the light source is completely

defocused in the sample plane, thus the illumination source is not visible in the image.

The setup was designed by Bea Botka. We built up two dierent types of Köhler illumi-

nation, namely bright eld and dark eld illumination. Both are set in the reected-light

mode as we are using intransparent samples but in principle Köhler illumination is also

used in transmitted-light microscopy. The contrast in bright-eld illumination is gained

by absorption of light by the sample or scattering of the light out of the eld of view

of the objective. Only transmitted or directly reected light reaches the image plane.

Whereas in dark-eld illumination transmitted or directly reected light does not reach

the objective and only widely scattered light is forming the image. So far, only the

bright-eld illumination is in use, as we are currently only using at samples.

51

CHAPTER 5. SETUP

parabolic mirror

tip

sample

c)

piezo stage

parabolic mirror

sample

b) tip

piezo stage

parabolic mirror

sample

a) tip

piezo stage

Figure 5.8 Principle of the parabolic mirror. (a) Incident parallel laser light is focused on thesample by the parabolic mirror. (b) The scattered light which reaches the parabolic mirroris collimated and leaves the system as a parallel beam. (c) For alignment purposes, a tiltedsample is moved into the focus to direct the laser reex back to the parabolic mirror andcollimate it again. The direct reex is hence parallel to the incident light.

52

CHAPTER 5. SETUP

silver coating

quartz

b)

Figure 5.9 Adjustment with the optical at. (a) Only the rst reection of the optical atis visible on the sample while the other reections are blocked. (b) The rst and thirdreections are visible. As the system is misaligned, they can be distinguished clearly. (c)The foci of the rst and third beam overlap as the system is well aligned. (d) Spot of mainbeam (second reex). (e) Principle of the optical at from side view. The quartz surfacereects about 4%, the silver coating reects 95% - 98%.

The arrangement of the bright-eld setup is shown in Fig. 5.10. The optical path goes

through the side window of the cryostat. Unlike the observation optics, the illumination

setup does not use the parabolic mirror but instead a at mirror located in the cryostat.

The objective used for observation is facing the parabolic mirror via a beamsplitter,

to be out of the Raman light path. The beamsplitter is removed after alignment since

otherwise 50% of the intensity would get lost.

The resolution of the imaging optics is up to 3µm, but decreases quickly out of the

focal region. In Fig. 5.11 (a) a resolution test target is shown, as it appears through

observation optics. In Fig. 5.11 (b) the tip is close to a silicon sample. The upper

structure is the tip, the lower one its shadow on the sample. The distance between tip

and shadow is a rough indicator for the tip-sample distance.

Whenever the sample is not exactly in the focus of the parabola neither optimal focusing

of the incident laser nor satisfactory imaging of the surface is possible. An analysis of

the arising aberrations is shown in Fig. 5.12 and Fig. 5.13. Fig. 5.14 and Fig. 5.15

intend to explain the distribution of the discretized light eld on the sample surface,

used for ray tracing evaluation and the nature of the ray fan plots in Fig. 5.12, respec-

tively. It was tested with Zemax, if it is possible to further improve the imaging quality

with insertion of additional lenses. But neither circular achromats and aspheres, nor

53

CHAPTER 5. SETUP

CondensorAperture FieldAperture

LED

LED

LEDImage

LED Image

Condensor Aperture(intensity)Field Aperture(illuminated area)

parallelbeams

Achromat, 30 mm focal length


Achromat,100 mm focal length


Plano-Convex,35 mm focal length

mirror30°30°

15°

Cryostat

Figure 5.10 Optical path of the Köhler bright eld illumination. Inset: Photo of the opticalpath, with the main components marked.

cylindrical lenses could improve the image when running the optimization algorithm.

5.4.3 Excitation optics

In this chapter the optical components between the laser and the sample will be dis-

cussed. The arrangement can be seen in Fig. 5.7. It contains a polarizer and a

λ/2-waveplate for proper power and polarization settings. The available solid state

lasers emit at 532 nm (Coherent Sapphire SF), 575 nm (Coherent Genesis MX SLM)

and 659.4 nm (Laser Quantum Ignis-FS).

For distinguishing the radiation from the large far-eld area from the small near-eld

area their ratio must be as small as possible, meaning that the laser spot actually needs

to reach the diraction limit. To minimize the spot, the beam was expanded to reduce

the divergence. The upper limit for the beam diameter is the separation of the split

beams in the optical at. To avoid interferences, the beam diameter must not be larger

than 6.2mm. In Fig. 5.16 a clear beam separation can be seen in panel (a) and the

exceedance of this limit in panel (b).

The following subchapters explain the eect of polarization, tip position and misalign-

ment on the measurements.

54

CHAPTER 5. SETUP

10 µm

50 µm

20 µm

a)

b)

Figure 5.11 Resolution of the imaging optics. (a) Resolution test target on the sample holder.Left: Microscope image. Right: View through observation optics. The width of one linein the blue box is 20µm. (b) Tip and its shadow on the resolution test target. The tipcomes into the eld of view from above, its shadow comes from below. View through theobservation optics.

Polarization

Polarization control is essential to distinguish the information from dierent regions of

the Brillouin zone or to utilize the depolarization eect of the tip (see section 3.2.2).

The polarization is set with polarizers, being set outside of the cryostat. Thus the

incident and Raman light both pass the parabolic mirror between sample and polarizer.

As the polarization is set with respect to the orientation of the crystal axes in the

sample surface and both, parabolic mirror and sample orientation, inuence the desired

settings, it is necessary to understand this relation. A simulation for our setup has been

established in Zemax (gure 5.17 and table 5.18).

In order to provide highest enhancement factors, for example, the highest fraction of

the electric eld must be orientated along the tip axis. Therefor vertical polarization is

required as initial polarization. Raman light polarized along the tip axis will be mainly

vertically polarized after reection at the parabolic mirror (see table). Light polarized

within the sample plane but perpendicular to the optical axis will mainly be polarized

horizontally and light along the mirror axis will leave the cryostat rather unpolarized.

Shadowing eect of the tip

When the tip approaches to the sample, it necessarily moves through the collimating

laser beam close to the focus and creates a shadow on the sample. Fig. 5.19 shows

55

CHAPTER 5. SETUP

the shadow in the far eld spot for several tip positions. Some of the scattered light

from the far eld is as well blocked by the tip. The light distribution right outside the

parabolic mirror is also shown in Fig. 5.19.

spot diagram

ray fan plot

0.2

mm

0.00 ; 0.00 mm 0.00 ; 0.01 mm 0.00 ; -0.01 mm

0.00 ; -0.02 mm 0.00 ; 0.02mm -0.02 ; 0.00 mm

0.02 ; 0.00 mm 0.01 ; 0.00 mm -0.01 ; 0.00 mm

0.02 ; 0.00 mm

0.00 ; 0.00 mm 0.00 ; 0.01 mm 0.00 ; -0.01 mm

0.00 ; -0.02 mm 0.00 ; 0.02mm -0.02 ; 0.00 mm

0.01 ; 0.00 mm -0.01 ; 0.00 mm

Px Px Px

Px Px Px

Px Px Px

Py Py Py

Py Py Py

Py Py Py

ey ey ey

ey ey ey

ey ey ey

ex ex ex

ex ex ex

ex ex ex

Figure 5.12 (Caption next page.)

56

CHAPTER 5. SETUP

Figure 5.12 (Previous page.) Visualization of the aberrations occurring in the observationoptics. The aberrations come mainly from the reection at the parabolic mirror. The upperand lower gures are the spot diagram and ray fan plot in the image plane, respectively.There is one plot for every of the nine eld points, drawn in Fig. 5.14. The coordinateswritten above every plot denote the position of the eld within the sample plane, relative tothe focus. The ray fan plot shows the displacement of the ray relative to the chief ray (seeFig. 5.15 for explanation). The chief ray is located in the center of every plot. The abscissadenotes the position of the ray in the stop plane and the ordinate its deviation from thechief ray in the image plane, for x and y in the two plots, respectively. An aberration-freeeld shows up as a horizontal line in the ray fan plot as the eld from the focus in theupper left corner. The deviation from the horizontal line denotes aberrations. The left plotat (0.00,-0.02) (see Fig. 5.14 for explanation) has the typical shape of coma and the rightplot seems to contain additional spherical aberrations. Compare for example the diagramsof the elds (0.02;0) and (0;0.02), to see that the aberrations are non symmetric. Figuresgenerated with Zemax.

Deviation from optical axis and resulting spot size

An incident beam, not exactly parallel to the optical axis of the mirror, quickly intro-

duces aberrations and a drifted far-eld spot. A vertical shift of the sample increases

the spot size rapidly. How sensitively the system reacts to misalignment is simulated in

Fig. 5.20. Laser tilt leads to a smaller spot on the sample surface, which has a positive

eect on the contrast function but the spot drifts out of the focus within the sample

plane which lowers the Raman light collection eciency. However, during alignment the

sample position and laser tilt are changed iteratively, as there is no separate indicator

for the quality of each of them.

5.4.4 Stray light collection optics

The Raman light is radiated into a solid angle of 2π, half of it being covered by the

parabolic mirror. The mirror collimates the light before it leaves the cryostat and is

coupled into an optical multimode ber and led to a close-by lab with the triple spec-

trometer (T64000 Jobin Yvon). Between the ber exit and the spectrometer a λ/4

waveplate, a polarizer and a λ/2 waveplate are mounted to set the polarization accord-

ing to the preference of the spectrometer. A photo of the corresponding optics and the

spectrometer can be seen in Fig. 5.21.

To separate the laser path from the collection optics, a half waveplate with 70% re-

ection and 30% transmission is used. The laser beam is incident from the rear side

and transmitted, while the Raman light leaving the cryostat is reected towards the

collection optics.

There are direct reexes, e.g. coming from the cryostat windows, which are also coupled

into the ber. These reexes are very intense compared to the Raman light and cause

57

CHAPTER 5. SETUP

Figure 5.13 Wavefront map of the focused eld (a) and the eld defocused by 20µm (b). Thedierence of the real to the ideal wavefront is plotted. The defocused eld indicates comawith tendency to defocus. Figure generated with Zemax.

x

y

0 ; 0-0.01; 0

-0.02 ; 0 0.02 ; 00.01; 0

0 ; 0.02

0 ; 0.01

0 ; -0.02

0 ; -0.01

sample planea) b)

y

x

units in mm

Figure 5.14 (a) All eld positions on the sample, used for simulations with Zemax. The point(0.00 ; 0.00) lies in the focus of the parabola. (b) Drawing of the eld-positions and theemitted light. For better visibility, only four eld points are shown. Figure (b) generatedwith Zemax.

58

CHAPTER 5. SETUP

aperture stop

marginal ray

chief ray

aperture stop

chief ray

a)

b)

object plane

object plane

image plane

image plane

aberrated ray

Figure 5.15 (a) Denition of chief ray and marginal ray. (b) Visualization of the principle ofthe ray fan plot in Fig. 5.12. The length of the red bar at the aperture stop is plotted onthe abscissa. The length of the red bar in the image plane is plotted on the correspondingordinate. The lengths in the ray fan plot are normalized to the size of the aperture stop.

a) b)

Figure 5.16 Zemax calculation of the overlap of the beams in the optical at. View on thedetector in the scattered beam path. The change from 6mm (a) to 8mm (b) beam diametercauses an overlap of the beams, which might cause unwanted interferences. Figure generatedwith Zemax.

59

CHAPTER 5. SETUP

Y

Y

Z

X

input

sample

laser

Z Y

ZX

X

Z

Figure 5.17 Zemax calculation of the polarization change due to the parabolic mirror. Layoutand polarization pupil map on the sample surface. The coordinate systems represent thoseof the laser, the sample and the polarization map, respectively. The input polarization isset to an angle of 20, tilted clockwise from vertical in view along the laser beam. Thepupil map lies within the sample layer. The polarization on the sample is uniform andstays linear. The laser hits the mirror about in the middle of the lower left quadrant.

initial polarization polarisation on the samplehorizontal/vertical X = Y × Z Y = along mirror axis Z = along tip axis

0/1 0.24 0.63 0.711/0 0.77 0.55 0.241/1 0.39 0.84 0.32

Figure 5.18 Polarization vector at the sample for dierent initial polarizations of the incidentlaser. Due to the reversibility of light the table gives also information about the polarizationof the Raman light in the coupling optics. Calculations done with Zemax. The layout usedfor the calculations is similar to that in Fig. 5.17.

60

CHAPTER 5. SETUP

sample irradiance Raman light

layo

utw

ithou

t tip

tip in

focu

stip

shi

fted

by

0.05

mm

to

war

ds th

e m

irror

tip in

0.0

05 m

m

dist

ance

from

sam

ple

cross section (mm) cross section (mm)

inte

nsity

(a.u

.)in

tens

ity (a

.u.)

inte

nsity

(a.u

.)in

tens

ity (a

.u.)

-0.05 -0.025 0 0.025 0.05 -20 -10 0 10 20

inte

nsity

(a.u

.)

-20 -10 0 10 20

-20 -10 0 10 20

-20 -10 0 10 20

-0.05 -0.025 0 0.025 0.05

-0.05 -0.025 0 0.025 0.05

-0.05 -0.025 0 0.025 0.05

Figure 5.19 (Caption next page.)

61

CHAPTER 5. SETUP

Figure 5.19 (Previous page.) This gure shows the eect of the tip on the laser spot on thesample surface (left) and the Raman light (right) by blocking the light when being ap-proached to the sample. In this simulation the full width of half maximum of the unblockedlaser spot is set to about 10µm. The scattered beam outside the cryostat has the size andshape of the mirror surface. The results for dierent positions of the tip are shown. Figuresgenerated with Zemax.

a signal in the spectrum coming from luminescence in the silica ber core. Especially

when the tip is close to the sample, many reections are created and overlay the signal.

This can be seen in Fig. 6.7 of chapter 6 for the case of a YBCO sample. To prevent

this, we introduce an edge lter, blocking the laser line. The OD 6 edge lters cut the

spectrum at 664.2 nm (107 cm−1 with respect to the red laser line, Iridian 660nm LPF)

and at 535.4 nm (119 cm−1 with respect to the green laser line, Iridian 532nm LPF).

For this purpose the coupling optics had to be redesigned as shown in Fig. 5.22. The

blue rays in the gure come from the exact focal point of the parabola. The green rays

come approximately from a point 15µm away from the focus and dene the maximum

spot size used for calculations, here. The resulting eciency of coupling the Raman

light into the ber, calculated with Zemax, is about 64 %. Assumptions are an ide-

ally focusing objective and optimized alignment with the sample in the focus of the

parabola. The pinhole and the edge lter were not included in the simulation. The

pinhole will intentionally lower the eciency by blocking light from the outer part of

the scattering area and suppresses the far-eld portion. The edge lter will additionally

reduce the power by 10%. The misalignment of one lens by 0.5mm reduces the coupling

eciency to 24%. Still mainly the far-eld signal should be aected. The optimization

calculation, applied to the lens positions, is a compromise between maximal coupling

eciency and parallel rays incident at the edge lter.

The far-eld content in the Raman signal has to be minimized, which either can be

achieved by a reduced spot size or by the pinhole mentioned above. The reason is that

in this conguration it is not possible to measure the pure near-eld signal. This is only

possible in case of a setup using aperture probes, or when the stray light is collected

through an apertureless probe. Here, the normal far-eld light will always contribute

to the spectrum as well. This can be overcome by measuring a non-enhanced far-eld

spectrum and subtracting it from a tip-enhanced spectrum. This will in principle show

the pure near-eld spectrum. A high contrast between near-eld and far-eld is required

to gain a signicant near-eld spectrum by this way. The contrast c' can be formulated

in terms of the near-eld and far-eld intensities Inear and Ifar:

c′ =IapproachedIretracted

=Ifar + Inear

Ifar= 1 +

InearIfar

(5.1)

It is obvious, that the near-eld intensity must have at least the same order of magnitude

62

CHAPTER 5. SETUP

sample defocus 0 mm 0 mm 0 mm 0.05 mm before focus laser tilt 0 degree 0.1 degree in x 0.2 degree in x 0 degree

sample defocus 0 mm 0 mm 0.05 mm behind focus 0.05 mm before focus

laser tilt 0.1 degree in y 0.1 degree in x and y 0.1 degree in x and y 0 degree

50 micron

Z

X

Figure 5.20 Laser spot size and shape on the sample for dierent degrees of misalignment. Theupper left picture shows the spot for a well aligned system. The other pictures show theeect of sample defocus and deviation of the laser from the optical axis of the mirror onthe spot size and position on the sample surface. The reason why the spot looks dierentfor symmetric sample defocus towards and away from the mirror, is that the divergence ofthe beam causes a focus shift away from the focus of the parabola. Figures generated withZemax.

63

CHAPTER 5. SETUP

Figure 5.21 Photo of optical components and the spectrometer. The ber (orange) comes fromthe lower left, the optical components lead the light into the spectrometer, seen in thebackground. The path implies a polarizer to select a certain polarization, a λ/2 waveplateto tilt the selected polarization into the preferred direction of the spectrometer and a λ/4waveplate to turn linearly polarized light into circular polarized one or vice versa if desired.

as the far-eld, to distinguish them. A typical enhancement factor ν of silicon, for

example, is 105 [7]. Let us now assume that the intensity I is proportional to the

scattering volume times the enhancement factor. For spot diameters of 1500 nm (far-

eld) and 30 nm (near-eld), and penetration depths of 500 nm (far-eld) and 2.5 nm

(near-eld), this leads to the contrast

c = 1 +Vnear · νVfar

= 1 +π · 152 · 2.5 nm3 · 105

π · 7502 · 500 nm3= 1.2. (5.2)

This can be seen as a lower limit for a signicant contrast, and therefore the upper limit

for the far-eld diameter is about 1500 nm, when measuring silicon with this resolution.

The diraction limited diameter of our spot can be estimated as 1µm, by multiplying

the focal length of the parabolic mirror by the divergence of the laser beam. The diver-

gence is initially 1mrad and is reduced by a factor of 8, due to beam expansion, which

is limited by the size of the optical at. So it is expected that the new setup with the

beam expansion will provide the desired contrast. Nevertheless, it is very complicated

to align and reach the actual diraction limit, so a pinhole in the collection optics shall

further lower the eective spot size. The pinhole shall block light, which comes not

exactly from the mirror focus, as this will leave the parabola non-collimated.

The new collection optics with edge lter and pinhole is already planned and has to be

mounted and aligned next.

64

CHAPTER 5. SETUP

edge lter

ber entrance

achromat,19 mm focal length

pinhole

objective

Figure 5.22 Layout of the coupling optics. The blue rays come from the exact focal point ofthe parabola, the green rays come approximately from a point 15µm away from the focus.The resulting eciency of coupling the Raman light into the ber, calculated with Zemax,is about 64 %. The pinhole and the edge lter were not included in the simulation.

65

6 Measurements

This chapter describes the rst measurements performed to demonstrate the envisaged

tip enhancement. So far this was not possible but I spotted several issues which have to

be addressed or solved before a successful experiment will be possible. Unfortunately,

the augmentation of the setup was too time consuming to be nished in the course of

the thesis work. However, several improvements have been implemented which will be

described below.

6.1 Experiments on Silicon

The rst measurements on this setup where made on silicon. The intention was to prove

that conventional Raman measurements are possible with this setup and to improve the

alignment of the collection optics and the ber coupling of the Raman light. In addition

the alignment of the incident laser beam had to be optimized. For this purpose the

optical at described in the previous chapter (see paragraph 5.4.1 and Fig. 5.9) was

used. The black curve in Fig. 6.1 shows the best result after aligning the collection

optics. The intensity gain of the Raman signal after optimizing the incident beam is

shown in red in Fig. 6.1.

The measurements done so far are conventional far-eld Raman measurements with

a spatial resolution given by the laser spot size on the sample surface. To gain sub-

diraction limited resolution the tip of the scanning probe microscope has to be ap-

proached to the sample surface. This requires the control of the tip position and the

tip-sample distance via a feedback loop. Thus the tip approach is always done in either

AFM or STM mode.

The spatial resolution and performance of the scanning probe microscopes were rst

tested without simultaneous Raman measurements. Fig. 6.2 and Fig. 6.3 show an

AFM scan on a resolution test target and a STM scan on a gold sample, respectively.

The AFM measurements on the resolution test target display that the best resolution

achieved was about 50 nm. The resolution is mainly dependent on the apex diameter

of the tip used for the measurement. Fig. 6.3 shows a measurement which was made

67

CHAPTER 6. MEASUREMENTS

Inte

nsity

(cou

nts

s-1 )

Figure 6.1 Si spectra with (red curve) and without (black curve) alignment using the opticalat. The smooth background of the black curve is due to longer integration time. Forexcitation the line at 532 nm was used.

in order to test the performance of the scanning tunnelling microscope. The sample is

a 100 nm thin gold layer, sputtered on a silicon substrate. Panels 1a) and 2a) show the

topography of the sample surface (abscissa and ordinate are the axes of the sample sur-

face and the grey scale denotes the topography). Panel 2a) is thereby a magnication of

the central part of panel 1a). Panels 1b) and 2b) show a line scan (abscissa: horizontal

scan line, ordinate: topography) in backward and forward scanning direction. The scan

lines correspond to the uppermost line of the pictures 1a) and 2a), respectively. As the

sample was not absolutely parallel to the movement of the piezo-scanner, the function

"slope compensation" was on, to correct for the tilt. The applied bias voltage between

tip and sample is 1.344 V and the current which was set to be hold by the feedback

loop was 1-1.5 nA. To provide a stable measurement two parameters can be set in the

feedback loop conguration, the so called P and I values. The appropriate values dier

in every measurement and were set to 0 and 27mHz, respectively. Although the mea-

surement was made at ambient conditions, the performance is already quite good. At

low temperature and in vacuum further improvement can be expected. So far the per-

formance at ambient conditions is sucient for the next step which combines scanning

and light scattering.

While a tip-enhanced spectrum is recorded the tip remains at a single point on the sam-

ple. In case of conductive samples the use of the STM instead of the AFM is preferable.

For STM the near-eld to far-eld signal ratio of the Raman intensity is higher because

the tip is permanently close to the sample while measuring. In contrast, during an AFM

measurement the tuning fork is oscillating and the tip periodically oscillates out of the

68


1.208 μmar

bitr

ary

units

arbi

trar

y un

its

arbi

trar

y un

its

Figure 6.2 Measurements with an atomic force microscope on a resolution test target. Here,the resolution is about 50 nm.

near-eld range of the laser spot. While the far-eld signal is constantly recorded by

the CCD of the spectrometer, the time at which a tip-enhanced signal is measured is

much shorter, resulting in a lower contrast than for STM measurements.

The red curve in Fig. 6.4 shows a conventional Raman spectrum of silicon with the tip

retracted from the sample surface. When the tip is approached to the sample surface,

the intensity of the phonon is reduced rather than enhanced (black curve in Fig. 6.4).

The alignment of the optical setup is the same for both measurements. There is no

indication for tip-enhancement in these spectra. This can be explained by the shadow

the tip creates around the laser spot when approaching. This eect was simulated with

Zemax and is described in the previous chapter (see paragraph 5.4.3 and Fig. 5.19).

The increased background most probably comes from direct reexes of the laser light

at the tip which are coupled into the ber where they cause luminescence. However, we

expect that a tip-enhancement occurs but is overcompensated by the shadow eect.

To measure this enhancement the contrast needs to be highly increased. Thus we con-

tinued the measurements with a YBa2Cu3O7 (YBCO, see Fig. 6.7) sample although its

Raman response is much lower than that of silicon, the much stronger z-axis Raman

matrix element may overcompensate the shadow eect and additionally improve the

near-eld signal.

6.2 Experiments on YBCO

High tip-enhancement is expected for the oxygen apex vibration (A1g symmetry) of

YBCO at 500 cm−1 (see Fig. 6.5) because its matrix element is strongest for zz po-

larization (assumed the crystallographic c-axis being orientated perpendicular to the

69


Figure 6.3 STM measurement on a gold coated silicon surface. The 100 nm thick Au layer wassputtered on silicon substrate. The measurements consist of 100 × 100 data points. Panels1a) and 2a) show the topography of the sample surface, whereat abscissa and ordinate arethe axes of the sample surface and the grey scale denotes the topography. 2a) is therebya magnication of the central part of panel 1a). Panels 1b) and 2b) show a line scan(abscissa: horizontal scan line, ordinate: topography) in backward and forward scanningdirection. The scan lines correspond to the uppermost line of the pictures 1a) and 2a),respectively.

70


4 0 0 4 5 0 5 0 0 5 5 0 6 0 0 6 5 00

4 0

8 0

1 2 0

1 6 0

2 0 0Int

ensity

(cou

nts s-1 )

R a m a n s h i f t ( c m - 1 )

t i p a p p r o a c h e d t i p r e t r a c t e d

Figure 6.4 Silicon spectrum with phonon at 520 cm−1. Red curve: tip retracted; black curve:tip approached. For excitation the line at 532 nm was used.

sample surface). The z direction coincides with the tip axis in which direction the elec-

tric eld of the incident and scattered light is enhanced. Fig. 6.6 sketches this relation

between the directions of the polarization vector of the laser light, the surface plasmon

oscillation and the vibration of the phonon in A1g symmetry. In vacuum the projection

of the polarization vector of the incident laser light onto the z-axis is quite high for p-

polarization (parallel to the plane of incidence). Once again, the agreement of all, light

polarization, surface plasmon oscillation and A1g-phonon vibration, is high. As n2 n1

the projection of the polarization onto the z-axis in the bulk is much smaller and the

excitation of the A1g-phonon is not predominant. Thus the conventional Raman signal

is low for the phonon at 500 cm−1 with respect to the tip-enhanced signal, resulting

high contrast. Aside from that YBCO is not only appropriate for alignment and prove

of principle but also provides unsolved physical problems requiring high-resolution op-

tical measuring methods. Lattice strain occurs at the twin boundary of YBCO. The

dimensions on which this eect occurs are too small to be resolved by conventional spec-

troscopic methods. How far this strain extends into the domains is a question TERS

could answer.

Fig 6.7 shows the conventional Raman spectrum of an optimally doped YBCO sample

measured with our TERS setup. The expected phonon at 500 cm−1 is visible but the

71


Figure 6.5 Crystal structure of YBa2Cu3O7 (YBCO). The black arrows denote the directionof the oxygen apex vibration in A1g symmetry. This phonon is Raman active and has anenergy of 500 cm−1. Figure adapted from [73].

n2

n1

sample

tip

z

E

E

plane of incidence

vacuum

A vibration direction1g

surface plasmon oscillation direction

incident laser light

Figure 6.6 Sketch of the polarization direction of the incident laser light with respect to thetip and sample orientation. The light is p-polarized in this sketch (parallel to the planeof incidence). The refractive index of the sample (n2) is much larger than that of thevacuum (n1), thus the projection of the polarization vector onto the z-axis becomes muchsmaller after entering the bulk. Also the directions of the surface plasmon oscillation andthe A1g phonon are along the z-axis (the crystallographic c-axis is assumed to be orientatedperpendicular to the sample surface).

72


Inte

nsity

(cou

nts

s-1)

Figure 6.7 Spectrum of optimally doped YBa2Cu3O7 (YBCO). For excitation the line at 532 nmwas used. Comparison to the Raman spectrum of silica in the inset indicates that not allfeatures originate from YBCO but seem to come from the silica content in the ber andoverlie the YBCO signal. Inset adapted from [74].

characteristic shape of the spectrum looks more similar to the spectrum of silica (see

inset) than to YBCO, especially for higher wavenumbers. The ber core is made out

of silica so apparently do direct laser reexes cause luminescence in the ber which is

stronger than the YBCO signal.

To solve this problem the laser reexes will have to be blocked before entering the ber.

For that purpose the coupling optics was redesigned and has to be built in the setup

next. The details will be explained in the next section.

6.3 Outlook

Parts of the optics setup have been redesigned (see Fig. 5.22) to increase the contrast

between near-eld and far-eld and have to be aligned next. An edge lter in the

parallel beam path of the collection optics shall block the laser line to prevent direct

reexes from entering the ber. Consequently less silica luminescence will be visible in

the measured spectrum and thus also features with low intensities, as the phonons in

the YBCO spectrum, should be resolvable.

A pinhole shall block light that comes from the outer regions of the laser spot on the

sample because light that comes not exactly from the focus of the parabola does not

73


leave it parallel and will therefore not be focused precisely enough by the objective to

pass the pinhole. This suppresses the far-eld intensity and increases the contrast. A

polarizer after the edge lter shall also give further control on selection rules and shall

increase the far-eld - near-eld contrast due to the depolarization eect discussed in

chapter 3.2.2.

For the case that the new coupling setup will not lead to a sucient increase of the

contrast, it is planned to measure brilliant cresyl blue molecules, as they give a strong

signal.

Further improvement of the quality of the excitation beam can be gained by the use

of a so called shear plate. The shear plate is an indicator for diverging and converging

beams and would provide an optimally parallel beam entering the parabolic mirror.

Another complication is expected when the atomic force microscope will be used on non-

conductive samples. It is not cantilever based but uses a tuning fork, whose amplitude

is several times the expected decay length of the near-eld signal. So in a signicant

fraction of the integration time of the measurement, there will be no near-eld content,

making the achievement of sucient contrast a challenge. To circumvent this problem

we need to avoid counting the photons when the tip is out of the near-eld range. The

incident laser might be triggered at the resonance frequency of the tuning fork, for ex-

ample with an acousto optic modulator (Bragg cell) [75]. Here, sound waves produce a

diraction grating and deect the laser beam out of an aperture periodically.

Further polarization control may be achieved by placing a gold sphere on the tip apex.

Gold particles with a diameter of 100 nm were already mounted at the end of a glass

bre by Kalkbrenner et al. [76].

AFM or STM scans could be a systematic way of nding the area of interest on the

sample. A topographic map or a map of the electronic density of states (DOS), could

help to nd the most interesting spots for the tip-enhanced spectrum. Another way

is to pause the scanning procedure in specic distances and take Raman spectra with

high resolution all over the scanning area. This produces a lot of data, e.g. scanning an

area of 10×10µm2 and taking a Raman spectrum every 100 nm, gives already 10,000

spectra. To better handle this amount of work, it is planned to write a code to perform

the series of measurement automatically. With such a software data evaluation would

be possible in a way that one can click on any pixel of a scanning probe topographic

map and directly gets the corresponding Raman spectrum displayed. An additional

feature would be, to map the intensity distribution of the Raman shift of interest, e.g.

520 cm−1 in case of silicon, instead of the topographic data. This would highly simplify

the data interpretation and makes it easier to gain them and deal with it. The former

Bachelor student Roland Richter already had started with the implementation.

74

7 Summary

The purpose of this thesis was to pursue the development of a setup for doing tip-

enhanced Raman spectroscopy (TERS). This includes construction issues, mainly re-

garding optical components, and rst measurements to provide the prove of principle.

In the described TERS setup an atomic force microscope or a scanning tunnelling micro-

scope can be used to control the tip that allows one to obtain topographic and tunnelling

images. In addition, the metallic tip is used for locally enhancing the incident laser eld

and as an antenna for the scattered light. For sample observation, excitation laser fo-

cusing and stray light collection a half parabola with a solid angle of π is used. It is

mounted in a UHV cryostat. This entirely new conguration, using a half parabola as a

focusing and collection element, has not been implemented before and allows access to

polarization dependent measurements at low temperatures. In addition, the parabola is

used as a mirror for direct observation of the Köhler-type illumunated sample surface.

The goal was the demonstration of tip-enhancement which is expected to actually oc-

cur but not being veried because of the low contrast to the far-eld spectrum. So

the main focus was placed on the improvement of the alignment. To do so, additional

components were introduced into the setup. The use of an optical at improved the

quality of the excitation laser spot on the sample. So does the beam expansion, widen-

ing the laser from originally 0.75mm to 6mm and thus reducing its divergence by the

same factor. Zemax simulations were done to gain information on the expected coupling

eciency of the collection optics, polarization changes on the beam path and the sen-

sitivity to misalignment. Conventional far-eld Raman measurements were performed

at room temperature. Experiments at low temperature are planned after the demon-

stration of tip enhancement. The far-eld measurements were performed on silicon and

YBa2Cu3O7 (YBCO), for two doping levels in either case. The silicon spectrum can be

recorded with sucient quality. In contrast, the spectrum of YBCO suers from a high

background signal due to silica luminescence in the core of the optical ber. To reduce

this background signal the expansion of the optical setup for collecting the Raman light

was elaborated. This includes an edge lter, a polarizer and an additional pinhole which

are already built in the setup but not yet aligned and tested.

75

8 Bibliography

[1] T. P. Devereaux and R. Hackl, Inelastic light scattering from correlated electrons,

Rev. Mod. Phys. 79, 175 (2007).

[2] C. Bai, Scanning tunneling microscopy and its applications (New York: Springer

Verlag, 2000).

[3] L. Li, C. Richter, J. Mannhart, and R. C. Ashoori, Coexistence of magnetic order

and two-dimensional superconductivity at LaAlO3/SrTiO3 interfaces, Nat Phys 7,

762 (2011).

[4] W. D. Pohl, Das unsichtbare Licht, Physik Journal 12, (2013).

[5] Y. Oshikane, T. Kataoka, M. Okuda, S. Hara, H. Inoue, and M. Nakano, Obser-

vation of nanostructure by scanning near-eld optical microscope with small sphere

probe, Science and Technology of Advanced Materials 8, 181 (2007).

[6] L. Meng, Z. Yang, J. Chen, and M. Sun, Eect of Electric Field Gradient on Sub-

nanometer Spatial Resolution of Tip-enhanced Raman Spectroscopy, Sci. Rep. 5,

(2015).

[7] J. Steidtner and B. Pettinger, High-resolution microscope for tip-enhanced optical

processes in ultrahigh vacuum, Review of Scientic Instruments 78, (2007).

[8] A. Otto, I. Mrozek, H. Grabhorn, and W. Akemann, Surface-enhanced Raman

scattering, J. Phys.: Condens. Matter 4, 1143 (1992).

[9] A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, Nanohole-

Enhanced Raman Scattering, Nano Letters 4, 2015 (2004).

[10] J. F. Li, Y. F. Huang, Y. Ding, Z. L. Yang, S. B. Li, X. S. Zhou, F. R. Fan, W.

Zhang, Z. Y. Zhou, W. Yin, B. Ren, Z. L. Wang, and Z. Q. Tian, Shell-isolated

nanoparticle-enhanced Raman spectroscopy, Nature 464, 392 (2010).

[11] C. Blum et al., Tip-enhanced Raman spectroscopy - an interlaboratory reproducibil-

ity and comparison study, Journal of Raman Spectroscopy 45, 22 (2014).

77

CHAPTER 8. BIBLIOGRAPHY

[12] D. Zhang, X. Wang, K. Braun, H.-J. Egelhaaf, M. Fleischer, L. Hennemann, H.

Hintz, C. Stanciu, C. J. Brabec, D. P. Kern, and A. J. Meixner, Parabolic mirror-

assisted tip-enhanced spectroscopic imaging for non-transparent materials, Journal

of Raman Spectroscopy 40, 1371 (2009).

[13] Zemax LLC (http://www.zemax.com/).

[14] E. Abbe, Beiträge zur Theorie des Mikroskops und der mikroskopischen

Wahrnehmung, Archiv für mikroskopische Anatomie 9, 413 (1873).

[15] L. Rayleigh, XXXI. investigations in optics, with special reference to the spectro-

scope, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of

Science 8, 261 (1879).

[16] M. Minsky, Memoir on inventing the confocal scanning microscope, Scanning 10,

128 (1988).

[17] E. Synge, XXXVIII. A suggested method for extending microscopic resolution into

the ultra-microscopic region, The London, Edinburgh, and Dublin Philosophical

Magazine and Journal of Science 6, 356 (1928).

[18] J. A. O'Keefe, Resolving power of visible light, Journal of the Optical Society of

America 46, 359 (1956).

[19] E. Ash and G. Nicholls, Super-resolution aperture scanning microscope, (1972).

[20] D. W. Pohl, W. Denk, and M. Lanz, Optical stethoscopy: Image recording with

resolution λ/20, Applied physics letters 44, 651 (1984).

[21] R. Hartschuh, A. Kisliuk, N. Lee, D. Mehtani, and A. Sokolov, High contrast tip-

enhanced raman spectroscopy, 2006, WO Patent App. PCT/US2006/005,429.

[22] A. Sokolov, A. Kisliuk, D. Mehtani, R. Hartschuh, and N. Lee, High contrast tip-

enhanced Raman spectroscopy, 2010, US Patent 7,656,524.

[23] L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press,

2006).

[24] S. W. Hell, S. Lindek, C. Cremer, and E. H. K. Stelzer, Confocal microscopy with

an increased detection aperture: type-B 4Pi confocal microscopy, Opt. Lett. 19, 222

(1994).

[25] E. Wolf and M. Nieto-Vesperinas, Analyticity of the angular spectrum amplitude of

scattered elds and some of its consequences, J. Opt. Soc. Am. A 2, 886 (1985).

78


[26] G. Picardi, Ph.D. thesis, Freie Universität Berlin, 2003.

[27] R. Dennig, Master's thesis, Karl-Franzens-Universität Graz, 2014.

[28] P. B. Johnson and R. W. Christy, Optical Constants of the Noble Metals, Phys.

Rev. B 6, 4370 (1972).

[29] A. Smekal, Zur Quantentheorie der Dispersion, Naturwissenschaften 11, 873

(1923).

[30] C. V. Raman and K. S. Krishnan, A New Type of Secondary Radiation, Nature

121, 501 (1928).

[31] G. Landsberg and L. Mandelstam, Eine neue Erscheinung bei der Lichtzerstreuung

in Krystallen, Naturwissenschaften 16, 557 (1928).

[32] H.-M. Eiter, Master's thesis, Technische Universität München, 2008.

[33] T. Böhm, Master's thesis, Technische Universität München, 2012.

[34] J. Wessel, Surface-enhanced optical microscopy, J. Opt. Soc. Am. B 2, 1538 (1985).

[35] J. G. SKINNER and W. G. NILSEN, Absolute Raman Scattering Cross-Section

Measurement of the 992 cm-1 Line of Benzene, J. Opt. Soc. Am. 58, 113 (1968).

[36] J. Steidtner, Ph.D. thesis, Freie Universität Berlin, 2007.

[37] L. Xia, M. Chen, X. Zhao, Z. Zhang, J. Xia, H. Xu, and M. Sun, Visualized method

of chemical enhancement mechanism on SERS and TERS, Journal of Raman Spec-

troscopy 45, 533 (2014).

[38] P. Gucciardi, J.-C. Valmalette, M. Lopes, R. Dèturche, M. L. de la Chapelle, D.

Barchiesi, F. Bonaccorso, C. D'Andrea, M. Chaigneau, G. Picardi, and R. Os-

sikovski, Light depolarization eects in tip enhanced Raman spectroscopy of silicon

(001) and gallium arsenide (001), AAPP | Physical, Mathematical, and Natural

Sciences 89, (2011).

[39] A. Merlen, J. C. Valmalette, P. G. Gucciardi, M. Lamy de la Chapelle, A. Frigout,

and R. Ossikovski, Depolarization eects in tip-enhanced Raman spectroscopy, Jour-

nal of Raman Spectroscopy 40, 1361 (2009).

[40] M. Motohashi, N. Hayazawa, A. Tarun, and S. Kawata, Depolarization eect in

reection-mode tip-enhanced Raman scattering for Raman active crystals, Journal

of Applied Physics 103, (2008).

79


[41] Z. Yang, J. Aizpurua, and H. Xu, Electromagnetic eld enhancement in TERS

congurations, Journal of Raman Spectroscopy 40, 1343 (2009).

[42] A. L. Demming, F. Festy, and D. Richards, Plasmon resonances on metal tips:

Understanding tip-enhanced Raman scattering, The Journal of Chemical Physics

122, (2005).

[43] G. Mie, Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen, An-

nalen der Physik 330, 377 (1908).

[44] M. Futamata, Y. Maruyama, and M. Ishikawa, Local Electric Field and Scattering

Cross Section of Ag Nanoparticles under Surface Plasmon Resonance by Finite

Dierence Time Domain Method, The Journal of Physical Chemistry B 107, 7607

(2003).

[45] J. P. Kottmann, O. J. Martin, D. R. Smith, and S. Schultz, Dramatic localized

electromagnetic enhancement in plasmon resonant nanowires, Chemical Physics

Letters 341, 1 (2001).

[46] F. J. García de Abajo and J. Aizpurua, Numerical simulation of electron energy

loss near inhomogeneous dielectrics, Phys. Rev. B 56, 15873 (1997).

[47] E. Hao and G. C. Schatz, Electromagnetic elds around silver nanoparticles and

dimers, The Journal of Chemical Physics 120, 357 (2004).

[48] W. Zhang, X. Cui, and O. J. F. Martin, Local eld enhancement of an innite

conical metal tip illuminated by a focused beam, Journal of Raman Spectroscopy

40, 1338 (2009).

[49] Z. Yang, Q. Li, F. Ruan, Z. Li, B. Ren, H. Xu, and Z. Tian, FDTD for plasmonics:

Applications in enhanced Raman spectroscopy, Chinese Science Bulletin 55, 2635

(2010).

[50] Y. C. Martin, H. F. Hamann, and H. K. Wickramasinghe, Strength of the electric

eld in apertureless near-eld optical microscopy, Journal of Applied Physics 89,

5774 (2001).

[51] C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P.

Mulvaney, Drastic Reduction of Plasmon Damping in Gold Nanorods, Phys. Rev.

Lett. 88, 077402 (2002).

[52] E. J. Sánchez, L. Novotny, and X. S. Xie, Near-Field Fluorescence Microscopy Based

on Two-Photon Excitation with Metal Tips, Phys. Rev. Lett. 82, 4014 (1999).

80


[53] S. Dickreuter, J. Gleixner, A. Kolloch, J. Boneberg, E. Scheer, and P. Leiderer,

Mapping of plasmonic resonances in nanotriangles, Beilstein Journal of Nanotech-

nology 4, 588 (2013).

[54] B. Pettinger, B. Ren, G. Picardi, R. Schuster, and G. Ertl, Tip-enhanced Ra-

man spectroscopy (TERS) of malachite green isothiocyanate at Au(111): bleaching

behavior under the inuence of high electromagnetic elds, Journal of Raman Spec-

troscopy 36, 541 (2005).

[55] D. Mehtani, N. Lee, R. D. Hartschuh, A. Kisliuk, M. D. Foster, A. P. Sokolov, and

J. F. Maguire, Nano-Raman spectroscopy with side-illumination optics, Journal of

Raman Spectroscopy 36, 1068 (2005).

[56] R. Ossikovski, Q. Nguyen, and G. Picardi, Simple model for the polarization eects

in tip-enhanced Raman spectroscopy, Phys. Rev. B 75, 045412 (2007).

[57] P. Moriarty, Resolution frontiers, 2012, http://nanotechweb.org/cws/article/indepth/

44336, accessed April 13, 2015.

[58] G. Binnig and H. Rohrer, Scanning apparatus for surface analysis using vacuum-

tunnel eect at cryogenic temperatures, 1984.

[59] G. Binnig, C. F. Quate, and C. Gerber, Atomic Force Microscope, Phys. Rev. Lett.

56, 930 (1986).

[60] The Nobel Prize in Physics 1986 (http://www.nobelprize.org/nobel_prizes/

physics/laureates/1986/), accessed August 5, 2015.

[61] F. J. Giessibl, Advances in atomic force microscopy, Rev. Mod. Phys. 75, 949

(2003).

[62] https://nanohub.org, accessed June 8, 2015.

[63] Askewmind, Figure licenced by Wikimedia Commons,

https://commons.wikimedia.org/wiki/File:Atomic_force_microscope_block_

diagram.png#le, accessed June 8, 2015.

[64] http://www.physics.ohio-state.edu, accessed June 8, 2015.

[65] J. Bardeen, Tunnelling from a Many-Particle Point of View, Phys. Rev. Lett. 6,

57 (1961).

[66] J. Terso and D. R. Hamann, Theory of the scanning tunneling microscope, Phys.

Rev. B 31, 805 (1985).

81


[67] I. Fernández Torrente, Ph.D. thesis, Freie Universität Berlin, 2008.

[68] I. Giaever, H. R. Hart, and K. Megerle, Tunneling into Superconductors at Tem-

peratures below 1K, Phys. Rev. 126, 941 (1962).

[69] O. Fischer, M. Kugler, I. Maggio-Aprile, C. Berthod, and C. Renner, Scanning

tunneling spectroscopy of high-temperature superconductors, Rev. Mod. Phys. 79,

353 (2007).

[70] J. K. Freericks and T. P. Devereaux, Raman scattering through a metal-insulator

transition, Phys. Rev. B 64, 125110 (2001).

[71] B. Jankó and J. D. Shore, Electromagnetic response of a static vortex line in a

type-II superconductor: A microscopic study, Phys. Rev. B 46, 9270 (1992).

[72] A. Köhler, Ein neues Beleuchtungsverfahren für mikrophotographische Zwecke,

Zeitschrift für wissenschaftliche Mikroskopie und für Mikroskopische Technik 10,

433 (1893).

[73] R. Hackl, Superconductivity in copper-oxygen compounds, Zeitschrift für Kristallo-

graphie Crystalline Materials 226, 323 (2011).

[74] T. Deschamps, A. Kassir-Bodon, C. Sonneville, J. Margueritat, C. Martinet, D.

de Ligny, A. Mermet, and B. Champagnon, Permanent densication of compressed

silica glass: a Raman-density calibration curve, Journal of Physics: Condensed

Matter 25, 025402 (2013).

[75] Nanoscale Spectroscopy with Applications, edited by S. M. Musa (CRC Press, 2008).

[76] T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, A single gold par-

ticle as a probe for apertureless scanning near-eld optical microscopy, Journal of

Microscopy 202, 72 (2001).

82

9 Acknowledgement

My gratitude belongs to numerous people for their support. Particularly, I would like

to thank

Prof. Dr. Rudolf Gross for giving me the opportunity to work at the Walther-

Meiÿner-Institut,

Dr. Rudi Hackl for providing the topic, his advice and a lot of helpful discussions,

Nitin Chelwani for the very good cooperation and teamwork in the lab and of course

all the o-topic chats,

Andreas Baum, Thomas Böhm and Florian Kretzschmar for all their help and

the productive discussions,

the technical sta for manufacturing many of the parts needed for the setup,

the entire Raman group and all the other colleagues for the great working atmo-

sphere,

and nally my family and friends for their support, their time and their encourage-

ment.

Documents

Tip-Enhanced Raman Spectroscopy - Semantic Scholar...ago. First the invention of tip-enhanced Raman spectroscopy (TERS) made it possible to combine the spectral information of Raman