Disentangling Time in a Near-Field Approach to the Scanning Probe Microscopy

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This journal is The Royal Society of Chemistry [year] [journal], [year], [vol], 0000 | 1

Disentangling Time in a Near-Field Approach to the Scanning ProbeMicroscopy

Marco Farina*a, Agnese Lucesoli

a, Tiziana Pietrangelo

b, Andrea di Donato

a, Silvia Fabiani

a, Giuseppe

Venanzonia, Davide Mencarelli

a, Tullio Rozzi

a, Antonio Morini

a

Received (in XXX, XXX) Xth XXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XX5

DOI: 10.1039/b000000x

Microwave Microscopy attracted recently intensive efforts,

owing to its capability to provide quantitative information

about the local composition and the electromagnetic response

of a sample. Nonetheless, the interpretation of microwave10

images remains a challenge as the electromagnetic waves

interact with the sample and the surrounding in a multitude

of ways following different paths: microwave images are a

convolution of all contributions. In this work we show that

examining the time evolution of the electromagnetic waves15

allows to disentangle each contribution, providing images

with striking quality and unexplored scenarios for near-field

microscopy.

Scanning Probe Microscopes constitute a broad class ofdevices sharing a common feature: a probe performs a scan in20

close proximity of the sample surface. Depending on the type

of probe, the system records variations of some physical

parameters arising from the short range interaction between

sample surface and probe1.

In the seminal work by Ash and Nicholls in 1972225

microwaves were proposed as a possible interaction medium;

at a first glance the use of electromagnetic waves looks

constrained by the diffraction limit (or Abbe's limit) relating

the resolution of an imaging system to the wavelength, which

is centimetric for microwaves. However in microscopy this30

limit is circumvented by exploiting the near-field (or

evanescent field) of a probe or of an antenna2. Near-field

decays exponentially from the source and is therefore an

excellent way to probe a sample at very high resolution.

In the aforementioned paper the authors achieved a35

resolution of /60 with a signal at 10 GHz, but more recent

works have achieved atomic resolution. A complete review of

the state-of-the-art may be found in3.

Microwave microscopy however has many unpaired

potentialities, not yet fully exploited, owing to its capability to40

perform local quantitative measurements of electromagnetic

properties such as dielectric constant and conductivity4,5,6.

Broadband measurements of these parameters would open the

possibility to perform local microwave spectroscopy. The

latter might be especially attractive for biology applications as45

many cellular structures have polar properties, giving rise to

phonon excitation when irradiated by time-varying

electromagnetic field: basically the applied electric field

slightly deforms the structure in a periodic manner and

vibration resonances can occur, possibly in the microwave,50

millimeter and sub-millimeter wave range7,8,9. Yet, local

microwave spectroscopy could be an intriguing tool for the

characterization of quantum-mechanical properties of

structures such as carbon nanotubes or nanoribbons10. We

should mention that microwaves were also used as a powerful55

approach to perform the Scanning Tunneling Microscopy on

non-conducting samples, by exploiting the harmonics

generated by the non-linear tunnel junction11 and achieving

atomic resolution.

The simplest way to generate decaying fields is to use a60

sharp tip, kept in close proximity of the sample to be

investigated, since the electromagnetic field diverges in

proximity of an ideal metal edge; an alternative widely used

approach is to use an aperture. However in both cases the

microwave source acts at the same time as an antenna,65

radiating in the complex environment of the microscope.

Focusing on the tip approach, it is apparent how the latter is

unable to selectively "illuminate" only the desired area under

its sharp vertex, because it is basically an antenna exciting

any sort of electromagnetic wave and interacting with all the70

regions of the microscope and of the sample. Any microwave

image will be inevitably the convolution of all those

interactions; consequently the interpretation of data and the

accurate modeling of the source/sample/microscope

interaction are still open issues limiting the scope of this75

powerful technique.

To date, the philosophy adopted to partially overcome this

major problem has been to create resonant structures

involving the tip -whose interaction with the sample ismodeled mostly as a capacitance-, and to work at specific80

frequencies where all the surrounding interactions can be

safely modeled as an unwanted parasitic capacitance to be

removed. Of course, this approach is sound only in as far as a

microwave signal is generated at a single specific frequency -

the resonant frequency-, losing thus many of the attractive85

possibilities offered by this kind of microscopy. A more

holistic approach which is being investigated by many

researchers, including ourselves (see ESI Material and

Methods, where some hints about our calibration solution are

reported), involves the idea of calibration, namely a multi-step90


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This journal is The Royal Society of Chemistry [year] Journal Name, [year], [vol], 0000 | 2

procedure exploiting the measurement of a set of known

samples (or loads, also called "standards") over an arbitrary

frequency range; this allows the evaluation of the error

network modeling any electromagnetic interaction between

parts of the microscope and its analytical removal from the5

raw measurement5.

However even this idea is faced with several open issues,

among the others: 1) One has to be able to create samples

which are well characterized over a frequency range, and

whose measurement can be easily repeated. 2) When changing10

samples as in5, it is very difficult to ensure that no

modification in the part modeling the microscope (the error

network) has occurred. 3) The surrounding can change ormove with time and with temperature, and those modifications

can not be neglected when working at the nanometric scale. 4)15

Defining the error network may be difficult, as tip and sample

interact in a complicated way (multimodal interaction).

In this work we propose to follow a completely different

strand, namely to introduce the concept of time-domain in

near-field microscopy: the idea is simply to perform an20

inverse Fourier-transform of the microwave data, typically the

reflection coefficient (the ratio between complex amplitudes

of reflected and incident signals) measured at one edge of the

tip over a given frequency range. In this way we obtain a

description of how the reflected signal changes in time,25

mimicking a kind of measurement known as "Time-Domain

Reflectometry", used in ground penetrating radar or in signal

integrity applications. Much like what happens with the

diffraction limit, even in this case we are faced with an

apparent limit, related to the slowness of the microwave30

signals when compared to the time-scale involved in

microscopy: if we sweep the signal frequency between 0 and

fmax, the inverse Fourier-transform would provide the

response to a pulse having time width 1/fmax, typically in the

order of tens of picoseconds, really an eternity when35

compared to the time required for the light to travel across 1

nm - in air just 3 attoseconds. Actually, the interaction with

matter introduces quite longer delays, but still the time-scales

apparently do not match, and this is why time-domain is never

used in this framework. Nonetheless in this work we show40

how time can still be conveniently used.

Let us consider a microwave probe: assume -just to

simplify calculations- it is 1.5cm long (it would include some

part of a microwave connector). The microwave signal would

travel along the probe much like along a transmission line: the45

total back and forth travel path of the wave involved in the

measurement of the reflection coefficient would be 3cm; in

air, the signal would cover this distance in 100 picoseconds.

Now the interaction between the probe and the sample will

induce some additional delay: the simplest model of the50

probe-to-sample interaction is a capacitance, and a

transmission line terminated on a capacitance is equivalent to

a longer open line (for a given frequency). Variations of this

capacitance appear as variations of the delay, reflecting both

changes in topography and surface composition. The point is55

that we can appreciate such variations in the pulse obtained by

the inverse Fourier-transform, in spite of the frequency limit.

What actually limits our capability is the system dynamics and

the noise, namely how well we can detect small changes in the

reconstructed (reflected) pulse.60

Ethernet Cable

Vector Network Analyzer

SPM

controller/Feedback

Coax Cable

Pt/Ir tip

Tunnel current

Voltagesour

ceSample

XYZ piezo

Fig.1Broadband setup (top) and detail of the STM/SMM tip (bottom)

Actually, this application of time does not even require the65

above assumptions (long transmission line and signal

bandwidth comparable to the travel time); this is evident when

considering a single tone, where the small change in the phase

of the reflection coefficient is a measure of the same time-

delay. In this framework the time domain is consequently just70

a convenient expedient to present data, simplifying

understanding. In the limit case of a homogeneous sample, for

example, differences in time will map differences in

topography; the additional intriguing information is provided

by the penetration of microwaves under the sample surface. A75

further advantage is that the reflection coefficient in time is a

real quantity, while in frequency it is a complex one: in the

latter case, informative images will either appear in amplitude

or phase plot when changing the frequency, and sometimes

information spreads between the two, with a deterioration of80

quality.

However the major issue of near field microscopy is that

near field and far field interactions generally coexist; in fact

the waves radiated by the probe reach the sample following

multiple paths, some of them interacting with the surrounding85

(the shield, the microscope body etc.). This is the key point

where operating in the time-domain provides a solution. In

fact, while frequency-domain images are a convolution of all


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the contributions, in time they can be at least partially

disentangled, as the distance between probe and sample is in

the nanometer range while the distancee between probe and

parts of the microscope are in the centimetric range. The time-

domain transform provides a set of synthetic echoes and, in5

some intuitive sense, the first echo comes from the nearest

interaction, namely the informative part of the sample. At

different times, depending on the actual bandwidth of the

excitation, we will receive the echoes from parasitic paths.

Some of them come from non-local interaction with the10

sample itself -bringing for example images about its tilting -

and some from the surroundings. Hence, after converting data

in time-domain, it is possible to focus on a specific interaction(see ESI, supplementary figure S1). Most importantly, the

whole procedure is a post-processing that can be done off-line15

on existing data, not requiring modifications to the

instrument.

In order to prove this concept we have developed an ultra-

wide band microwave microscope (Figure1; see ESI videoS1

showing the setup) exploiting a Scanning Tunneling20

Microscope (STM) and a Vector Network Analyzer, t he latter

Coax

Cc

C1

R1

TL1

C2

R2

TL2

C3

R3

TL3

C4

R4

TL4

C5

R5

TL5

C6

R6

TL6

CsampleRtunnel

Non-Local Interactions Local tip/sampleInteraction

(a)

(b)25

Fig.2Model (a) and comparison between theoretical and measured data

(b). Parameters are in table I (in ESI, Materials and Methods). TL are

transmission lines

being used to perform measurements of the microwave signal

(up to 70 GHz) with high dynamic. However it should be30

stressed that ultra-wideband is not strictly necessary to

implement our time-domain microscopy, as shown in the

Matherial and Methods section (see ESI, e.g. figure S5): we

just need to measure the r eflect ion coeffic ient over a finite set

of frequencies in order to take at least some of the advantages35

from a virtual time-pulse. In our system the STM current is

recorded simultaneously, and is used in the feedback chain in

order to maintain the tip-to-sample distance, while providing

at the same time an STM topographical image of the sample

being characterized. Hence, the conductive Platinum-Iridium40

STM tip, fed by a capacitively coupled coaxial line, is also

used as microwave source. The choice of the STM in this

system has some advantages: among the others, the STM tip is

naturally a good microwave probe, the STM is intrinsically

"contact-less", and STM by itself easily allows atomic45

resolution . The major drawback is the need of a conductingsample; however Guckenberger et al. in11 demonstrated the

possibility to partially overcome this STM limitation by

exploiting a thin water film present on the sample surface and

its peculiar high lateral conductivity.50

Figure 2 shows an equivalent circuit that we propose for the

head: a set of transmission lines, modeling non-local

interactions and enclosure resonances, the coaxial probe and

the local tip-to-sample interaction, modeled as a capacitor (in

Local Interaction

Non- Local Interaction

0

Differenceinreflectioncoefficient(x10-

)

55

Fig.3 Differences in time-domain reflection coefficient: there is a time-

frame where local interaction dominates (left rectangle, "near time") and a

time-frame where non local interaction, mediated by the far-field,

dominates (right rectangle, "far time").

this case 0.7 fF). Number and parameters of lines are adjusted60

to fit experimental data, and Fig. 2(b) reports the comparison

between measured data and model.

In order to demonstrate the concept, we have transformed

the reflection coefficient in time, and evaluated the difference

between data obtained by modifying the tip-to-sample65

capacitance from 0.7 to 0.701 and then to 0.702 fF -modeling

a change in a feature of the sample (topography orcomposition)-; a further plot shows the difference produced

by modifying the first transmission line length by just 0.001

degrees from the nominal value of 104 at 10 GHz. This70

models a slight change in the non local interaction (a distance

of 83nm for a wave traveling in air). Figure 3 shows the

corresponding time-plots; it is evident that there is a

timeframe where local interaction dominates, and one mostly

affected by the non-local effects: local and non-local75

interactions are distinguishable.

This technique has been applied to a number of samples;

Figure 4 reports as example a specimen of Highly Oriented


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Pyrolitic Graphite (HOPG). The total scanning area is 10x10

m2, and the height of the smallest features is in the order of

few nanometers. In particular Figure 4 on the left shows the

time-domain image from the microwave microscopy, while on

the right we see the plot of the STM topography recorded5

simultaneously. The time-domain image has not been

processed for further improvement, while the STM image

showed also a relevant plane tilt (order of 1m) that was

removed in post-process. The STM image quality was limited

by the quality of the tip (obtained by wire cutting) and by10

microphonic noise induced by the microwave cable. The

microwave image, on the other hand, shows high quality,

taking advantage of the underlying multi-frequencymeasurement, and is likely to be displaying also some of the

sub-surface HOPG layers. Further pictures, also showing15

spectroscopic barrier-height images, are in figure S4 (ESI,

Material and Methods, Additional data). Figure 5 shows a

similar comparison for mouse myotubes C2C12 fixed in

paraformaldehyde on HOPG substrate (see ESI Material and

Methods; also shown in fig. S6 a zoom); the right image is20

STM (Set Point: 1 pA, Bias Voltage: 8V), while the left image

is the simultaneous microwave scan (X band) at a time instant.

Note that this scan is quite challenging for our STM head, as

1pA is the minimum current allowed. The microwave image

highlights details partially hidden in the STM scan, in25

particular over the border of the cell membrane; note that

microwaves seem to discriminate well the region between

cells, having different reflectivity. Images show part of the

connective structures around the fibers and some details of the

membranes. This is even more evident in living C2C12 cells30

(fig S7 in ESI Material and Methods, area 35x35 m2). It is

also useful to follow the time evolution in videos (ESI) No.3, No.4, No. 5 showing respectively the reflected signal

changes in time for the HOPG, the fixed and the living

C2C12.35

In conclusion, our work proves that the time-domain

approach discloses unexpected developments for the near-

field microscopy.

Fig. 4HOPG in time-domain microwave microscopy (left; max. frequency 20.5 GHz) and simultaneous STM image (right; height in nanometers).40

Fig. 5Comparison for myotubes fixed with paraformaldehyde on HOPG substrate. Left: time-domain microwave image; right: simultaneous STM.


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Acknowledgements

We thank C. Franzini-Armstrong (University of Pennsylvania)

for the suggestions during the preparation of the manuscript.

We are grateful to G. Scoles (Princeton University) for

valuable discussions on the subject. We also thank R.5

Castagna for reviewing the paper, and L. Palma for running

measurements reported in S3.

Notes and referencesa

DIBET, Universit Politecnica delle Marche, Via Brecce Bianche,1060131 Ancona, Italy, Tel. ++390712204837, E-mail: [email protected]. of Neuroscience and Imaging, Universit "G. d'Annunzio", Via dei

Vestini, I-66100 Chieti, Italy, Tel. ++3908713554554, E-mail:

[email protected]

Electronic Supplementary Information (ESI) available: Materials and15

Methods [fig. S1 to S7, table I], Videos S1 to S4, . See

DOI: 10.1039/b000000x/

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Disentangling Time in a Near-Field Approach to the Scanning Probe Microscopy