Farina Et Al Nanoscale 2011

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Disentangling time in a near-field approach to scanning probe microscopy

Marco Farina,*a Agnese Lucesoli,a Tiziana Pietrangelo,b Andrea di Donato,a Silvia Fabiani,a

Giuseppe Venanzoni,a Davide Mencarelli,a Tullio Rozzia and Antonio Morinia

Received 13th May 2011, Accepted 29th June 2011

DOI: 10.1039/c1nr10491h

Microwave microscopy has recently attracted intensive effort, owing

to its capability to provide quantitative information about the local

composition and the electromagnetic response of a sample. None-

theless, the interpretation of microwave 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 electro-

magnetic waves allows us to disentangle each contribution, providing

images with striking quality and unexplored scenarios for near-field

microscopy.

Scanning probe microscopes constitute a broad class of devices

sharing a common feature: a probe performs a scan in close prox-

imity to the sample surface. Depending on the type of probe, the

system records variations of some physical parameters arising from

the short range interaction between the sample surface and the

probe.1

In the seminal work by Ash and Nicholls in 1972 (ref. 2) micro-

waves were proposed as a possible interaction medium; at first glance

the use of electromagnetic waves looks constrained by the diffraction

limit (or Abbes limit) relating the resolution of an imaging system to

the wavelength, which is centimetric for microwaves. However in

microscopy this limit is circumvented by exploiting the near-field (or

evanescent field) of a probe or of an antenna.2 Near-field decays

exponentially from the source and is therefore an excellent way to

probe a sample at a very high resolution.

In the aforementioned paper the authors achieved a resolution of

l/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 in ref. 3.Microwave microscopy however has many unpaired potentialities,

not yet fully exploited, owing to its capability to perform local

quantitative measurements of electromagnetic properties such as

dielectric constant and conductivity.46 Broadband measurements of

these parameters would open the possibility to perform local

microwave spectroscopy. The latter might be especially attractive for

biological applications as many cellular structures have polar prop-

erties, giving rise to phonon excitation when irradiated by the time-

varying electromagnetic field: basically the applied electric fieldslightly deforms the structure in a periodic manner and vibration

resonances can occur, possibly in the microwave, millimetre and sub-

millimetre wave range.79Yet, local microwave spectroscopy could be

an intriguing tool for the characterization of quantum-mechanical

properties of structures such as carbon nanotubes or nanoribbons.10

We should mention that microwaves were also used as a powerful

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 a sharp tip,

kept in close proximity to the sample to be investigated, since the

electromagnetic field diverges in proximity to an ideal metal edge; an

alternative widely used approach is to use an aperture. However inboth cases the microwave source acts at the same time as an antenna,

radiating in the complex environmentof themicroscope. 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 the 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 this 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 is modeled mostly as a capaci-tanceand to work at specific frequencies where all the surrounding

interactions can be safely modeled as an unwanted parasitic capaci-

tance to be removed. Of course, this approach is sound only insofar

as a microwave signal is generated at a single specific frequencythe

resonant frequencythus losing many of the attractive possibilities

offered by this kind of microscopy. A more holistic approach which is

being investigated by many researchers, including ourselves (see

ESI, Materials and methods, where some hints about our calibra-

tion solution are reported), involves the idea of calibration, namely

a multi-step procedure exploiting the measurement of a set of known

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

aDIBET, Universita Politecnica delle Marche, Via Brecce Bianche, 60131Ancona, Italy. E-mail: [email protected]; Tel: +390712204837bDept. of Neuroscience and Imaging, Universita G. dAnnunzio, Via deiVestini, I-66100 Chieti, Italy. E-mail: [email protected]; Tel:+3908713554554

Electronic supplementary information (ESI) available: Materials andmethods, Fig. S1S7, Table 1, and Videos S1S4. See DOI:10.1039/c1nr10491h

This journal is The Royal Society of Chemistry 2011 Nanoscale

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frequency range; this allows the evaluation of the error network

modeling any electromagnetic interaction between parts of the

microscope and its analytical removal from the raw measurement.5

However even this idea is faced with several open issues, among

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 changing samples as in ref. 5, it is very

difficult to ensure that no modification in the part modeling the

microscope (the error network) has occurred. (3) The surroundingcan change or move with time and with temperature, and those

modifications cannot be neglected when working on the nanometric

scale. (4) Defining the error network may be difficult, as the tip and

the 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 to simply perform an inverse Fourier-trans-

form 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 with

time, mimicking a kind of measurement known as Time-Domain

Reflectometry, used in ground penetrating radar or in signal integ-rity 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 microwave signals when compared to the time-scale

involved in microscopy: if we sweep the signal frequency between

0 andfmax, 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 when compared to the time required

for the light to travel across 1 nmin 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 the time-domain

is never used in this framework. Nonetheless in this work we show

how time can still be conveniently used.

Let us consider a microwave probe: assumejust to simplifycalculationsit is 1.5 cm long (it would include some part of

a microwave connector). The microwave signal would travel along

the probe much like along a transmission line: the total back and

forth travel path of the wave involved in the measurement of the

reflection coefficient would be 3 cm; in air, the signal would cover this

distance in 100 picoseconds. Now the interaction between the probe

andthe sample will induce some additional delays: the simplest model

of the probe-to-sample interaction is a capacitance, and a trans-

mission 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 topog-

raphy and surface composition. The point is that we can appreciate

such variations in the pulse obtained by the inverse Fourier-trans-form, in spite of the frequency limit. What actually limits our capa-

bility is the system dynamics and the noise, namely how well we can

detect small changes in the reconstructed (reflected) pulse.

Actually, this application of time does not even require the above

assumptions (long transmission line and signal bandwidth compa-

rable 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 just a convenient expedient to present data, simpli-

fying 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. A 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

of quality.

However the major issue of near field microscopy is that near field

and far field interactions generally coexist; in fact the waves radiatedby the probe reach the sample following multiplepaths, some of them

interacting with the surrounding (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 the contributions, in time they can be at least

partially disentangled, as the distance between the probe and the

sample is in the nanometre range while the distance between the

probe and parts of the microscope is in the centimetre range. The

time-domain transform provides a set of synthetic echoes and, in

some intuitive sense, thefirst 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 a non-localinteraction with the sample itselfbringing for example images

about its tiltingand some from the surroundings. Hence, after

converting data in thetime-domain, it is possibleto focus on a specific

interaction (see ESI, Fig. S1). Most importantly, the whole proce-

dure is a post-processing that can be done off-line on existing data,

not requiring modifications to the instrument.

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

band microwave microscope (Fig. 1; see ESI, Video S1 showing the

setup) exploiting a Scanning Tunneling Microscope (STM) and

a Vector Network Analyzer, the latter being used to perform

measurements of the microwave signal (up to 70 GHz) with high

dynamics. However it should be stressed that ultra-wideband is not

strictly necessary to implement our time-domain microscopy, asshown in the Materials and methods section (see ESI, e.g.Fig. S5):

we just need to measure the reflection coefficient over a finite set of

frequencies in order to take at least some of the advantages 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 platinumiridium STM tip, fed by a capacitively coupled

coaxial line, is also used as the microwave source. The choice of the

STM in this system has some advantages: among others, the STM tip

is naturally a good microwave probe, the STM is intrinsically

contact-less, and STM by itself easily allows atomic resolution. The

major drawback is the need for a conducting sample; howeverGuckenberger et al. in ref. 12 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.

Fig. 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 this case 0.7 fF). Number and

parameters of lines are adjusted to fit experimental data, andFig. 2(b)

reports the comparison between measured data and the model.

In order to demonstrate the concept, we have transformed the

reflection coefficient in time and evaluated the difference between

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data obtained by modifying the tip-to-sample capacitance from 0.7 to0.701 and then to 0.702 fFmodeling a change in a feature of the

sample (topography or composition)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. This

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

83 nm for a wave traveling in air). Fig. 3 shows the corresponding

time-plots; it is evident that there are two timeframes: one where the

local interaction dominates and the other where mostly the non-local

effects dominate: local and non-local interactions are distinguishable.

This technique has been applied to a number of samples; Fig. 4

reports as an example a specimen of Highly Oriented Pyrolitic

Graphite (HOPG). The total scanning area is 10 10 mm2, and the

height of the smallest features is in the order of few nanometres. Inparticular Fig. 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 recorded simultaneously. The time-domain image has

not been processed for further improvement, while the STM image

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

removed in post-processing. The STM image quality was limited by

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

noise induced by the microwave cable. The microwave image, on the

other hand, shows a high quality, taking advantage of the underlying

multi-frequency measurement, and is likely to be displaying also

some of the sub-surface HOPG layers. Further pictures, also showing

spectroscopic barrier-height images, are in Fig. S4 (ESI, Materials

and methods, Additional data). Fig. 5 shows a similar comparison for

mouse myotube C2C12 fixed in paraformaldehyde on the HOPG

substrate (see ESI, Materials and methods; also shown in Fig. S6,

a zoom); the right image is the STM (Set Point: 1 pA, bias voltage:

8 V), while the left image is the simultaneous microwave scan (X

band) at a time instant.

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

(bottom).

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

data (b). Parameters are given in Table S1 (in the ESI, Materials and

methods). TL are transmission lines.

Fig. 3 Differences in the time-domain reflection coefficient: there are

time-frames where the local interaction dominates (left rectangle, near

time) and where a non-local interaction, mediated by the far-field,

dominates (right rectangle, far time).


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Note that this scan is quite challenging for our STM head, as 1 pA

is the minimum current allowed. The microwave image highlights

details partially hidden in the STMscan, in particular over the border

of the cell membrane; note that microwaves seem to discriminate well

the region between cells, having different reflectivities. Images show

part of theconnective structures around the fibers and some details of

the membranes. This is even more evident in living C2C12 cells

(Fig. S7 in the ESI, Materials and methods, area 35 35 mm2

). It isalso useful to follow the time evolution in Videos S3, S4 and S5

(ESI) showing, respectively, the reflected signal changes in time for

the HOPG, the fixed and the living C2C12.

In conclusion, our work proves that the time-domain

approach discloses unexpected developments for the near-field

microscopy.

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. Castagna for reviewing the paper

and L. Palma for running measurements reported in S3.

Notes and references

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2 E. A. Ash and G. Nicholls, Super-resolution aperture scanningmicroscope,Nature, 1972, 237, 510512.

3 S. Kalinin and A. Gruverman,Scanning Probe Microscopy, Springer,New York, 2007.

4 A. Imtiaz and S. M. Anlage, A novel STM-assisted microwavemicroscope with capacitance and loss imaging capability,Ultramicroscopy, 2003, 94, 209212.

5 D. Karbassi, et al., Quantitative scanning near-field microwavemicroscopy for thin film dielectric constant measurement, Rev. Sci.Instrum., 2008, 79, 094706.

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7 C. K. Sun, T. M. Liu and H. P. Chen, US Pat., 2009/0237067A1,2009.

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

nanometres).

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

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8 F. H. Westheimer, Why nature chose phosphates,Science, 1987,235,11731178.

9 D. L. Woolard, et al., Submillimeter-wave phonon modes in DNAmacromolecules, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat.Interdiscip. Top., 2002, 65, 051903.

10 V. V. Talanov, et al., Few-layer graphene characterization by near-field scanning microwavemicroscopy, ACS Nano, 2010, 4, 38313833.

11 S. L. Stranick and P. S. Weiss, Alternating current scanningtunnelling microscopy and nonlinear spectroscopy, J. Phys. Chem.,1994, 98, 17621764.

12 R. Guckenberger, et al., Scanning tunnelling microscopy ofinsulators and biological specimens based on lateralconductivity of ultrathin water films, Science, 1994, 266, 15381540.


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Farina Et Al Nanoscale 2011