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52 January/February 2014 U.S Government work not protected by U.S. Copyright O n 29 December 1959 at the annual meeting of the American Physical Society, Richard Feynman gave a lecture at the California Institute of Technology titled “There Is Plenty of Room at the Bottom: An Invitation to Enter a New Field of Physics.” This memorable lecture has since become very famous as it predicted and envisioned the current era of nanoscience and nanotechnology. The atomic Atif Imtiaz, Thomas Mitchell Wallis, and Pavel Kabos Digital Object Identifier 10.1109/MMM.2013.2288711 Date of publication: 21 January 2014 Atif Imtiaz ([email protected]), Thomas Mitchell Wallis, and Pavel Kabos are with the Physical Measurement Laboratory, National Institute of Standards and Technology, Boulder, Colorado, United States. FOCUSED ISSUE FEATURE CURT SUPLEE FROM NIST Near-Field Scanning Microwave Microscopy

Near-Field Scanning Microwave Microscopy: An Emerging Research Tool for Nanoscale Metrology

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52 January/February 2014U.S Government work not protected by U.S. Copyright

On 29 December 1959 at the annual meeting of the American Physical Society, Richard Feynman gave a lecture at the California Institute of Technology titled “There Is Plenty of Room at the Bottom: An Invitation

to Enter a New Field of Physics.” This memorable lecture has since become very famous as it predicted and envisioned the current era of nanoscience and nanotechnology. The atomic

Atif Imtiaz, Thomas Mitchell Wallis, and Pavel Kabos

Digital Object Identifier 10.1109/MMM.2013.2288711Date of publication: 21 January 2014

Atif Imtiaz ([email protected]), Thomas Mitchell Wallis, and Pavel Kabos are with the Physical Measurement Laboratory, National Institute of Standards and Technology,

Boulder, Colorado, United States.

FOCUSED

ISSUE FEATU

RE

cu

rt

su

ple

e f

ro

m N

Ist

Near-Field Scanning Microwave Microscopy

January/February 2014 53

level represents a totally new world of fresh opportu-nities for design and engineering due to the new phys-ics available at such a small scale. Feynman mentions this in his lecture, “Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics” [1]. This new physics allows the manipulation of matter atom by atom. As Feynman further states, “The principles of physics, as far as I can see, do not speak against the possibility of maneuver-ing things atom by atom. It is not an attempt to violate any laws; it is something, in principle, that can be done; but in practice, it has not been done because we are too big” [1]. Feynman was right, and quantum mechanics continues to play a crucial role in miniaturization of technology. But advances in nanotechnology are not based purely on knowledge of the theory. Today we are realizing that all this “plenty of room at the bot-tom” has brought a great need for complex and inge-nious metrology tools that accompany our knowledge of quantum mechanics. These metrology tools are necessary for atomic-scale manipulation as well as the characterization of each atom and its interaction with the environment. Feynman’s lecture envisioned the need for significantly improved metrology tools. For example, he discussed improving the electron micro-scope by 100-fold. Today, in addition to the scanning electron microscope (SEM), we have the atomic force microscope (AFM), the scanning tunneling micro-scope (STM), and the near-field scanning optical microscope (NSOM), among many other metrology tools used for the advancement of nanotechnology [2]–[4], which Feynman did not foresee. These metrology tools also function as a platform for engineering novel atomic- and molecular-scale devices. This means per-forming logical operations with a single atom or mol-ecule, manipulation of DNA molecules for information storage, or putting together nanomachines [2]–[4].

The near-field scanning microwave microscopy (NSMM) is one of many such innovative tools used to study bulk samples, thin films, and nanoscale materi-als and devices [5]–[29]. The goal of NSMM is to bring quantitative broadband measurements at radio (RF) and microwave frequencies to the available “room at the bottom,” i.e., to make RF and microwave mea-surements down to the molecular and atomic scale. The bandwidth of these quantitative measurements should be in the range of about 100 MHz to 300 GHz. RF and microwave frequencies are the backbone of many technologies. Some of the important applica-tions of RF and microwaves are communications, computing, and remote sensing, to name a few. For example, the current geostationary satellite links operate with subbands in the frequency range of 2–20 GHz for both uplink and downlink communica-tion [30]. Cellular communication works in the range of 700 MHz to about 2.7 GHz [30]. A typical computer processor works at frequencies near 3 GHz. The clock

frequency for digital superconducting computing circuits has been measured at 770 GHz [31]. Airport radar, marine radar, and missile guidance systems work in the range of 8–12 GHz [32]. For the foresee-able future, these technological sectors will remain of prime interest. The miniaturization that Feynman envisioned will require new RF and microwave mea-surement tools such as NSMM to characterize, engi-neer, and optimize nanomaterials and nanodevices. Apart from the technological sectors, there are many interesting problems in fundamental and applied physics that will benefit from a steady and continu-ous development of NSMM. One of the areas of inter-est here is the next generation of possible devices. For example, “beyond complementary metal oxide semi-conductor (CMOS)” engineering research is searching for novel computing devices that will consume much less power while they perform much faster than the current devices. Candidate devices include electron-charge- and electron-spin-based devices, bioinspired devices, magneto-resistive devices, and superconduc-tor-based devices [9], [30], [32]. The clock frequency is expected to be in the gigahertz range, implying that NSMM may be used to study the device characteristics as well as the characteristics of interconnects. Another potential application area is the design of novel mate-rials for engineering and manufacturing applications. Here, possible directions are the characterization of materials such as graphene, carbon-60 molecules (C60, also called bucky-balls), carbon nanotubes (CNTs, also known as bucky-tubes), ferromagnetic materials, fer-roelectric materials, and life-science materials (such as proteins and DNA) [2]–[4], [32], [33]. For example, single-walled CNT films have been shown to provide very good shielding in the range of 10 MHz–30 GHz [34], which has a potential application in protecting electronics circuits from electromagnetic interference in both ground and air applications.

The reader may be puzzled by the use of micro-wave frequencies for nanometer-length scale mea-surements. In free space at 300 GHz, the wavelength of an electromagnetic wave is 1 mm, and yet a typical crystal lattice size is on the order of 1 nm. This means that for a wavelength of 1 mm in free space, the required spatial resolution to image atoms by NSMM is 1 millionth of this wavelength. This raises a ques-tion: how can such a comparatively large wavelength measure something over six orders of magnitude smaller? From the perspective of classical optics, the

The atomic level represents a totally new world of fresh opportunities for design and engineering due to the new physics available at such a small scale.

54 January/February 2014

best resolution that can be obtained is on the order of half of the wavelength (Abbe’s limit). We need to break this classical limit in order to achieve nano-meter-scale spatial resolution. Is it possible to break this resolution limit? The answer to this puzzle lies in the physics of the fields and radiation generated by a local oscillating source [35]. Due to the wide-spread usage of communication and broadcasting

systems, engineers and scientists are focused mostly on far-field radiation when they think about spatial resolution. For the far field, the relevant distances r^ h are much larger than the size D^ h of the oscillating source and the wavelength m^ h of the electromagnetic wave. D and m can usually be ignored for every-day communications and broadcasting systems. It is in this regime that Abbe’s resolution limit applies. However, there are two other regimes: the first is the intermediate zone, where ,D r% + m and the second is the near field, where D r% % m or D r# % m [6], [35]. For NSMM, we are interested in the near field with D r# % m [6]. In NSMM, the dimension of the oscillating source D is given by the effective radius of the probe. As a result, the word “probe” replaces the word “oscillating source.” In the near field, the spa-tial resolution is dictated by D and r rather than by the wavelength of the incident electromagnetic wave. With experimental dexterity and smart engineering, we can make D and r quite small. Furthermore, the structure of the electric and magnetic fields may be quite complex; nevertheless, they can be considered quasistatic, meaning that the fields have the spatial extent similar to the static fields with simple-har-monic time dependence [35]. The shape of the probe and the electromagnetic properties of the surround-ing region determine the shape of the fields. By designing a probe with the right dimension in the nanometer range, these fields can also be localized, which leads to localized microwave currents in the sample or device under test (DUT). This allows for the storage of the reactive energy and dissipation of power in small volumes of the sample. Based on such physics, a typical NSMM consists of a very sharp probe integrated into the experimental apparatus; different mechanisms are used to bring this probe in close proximity to the sample.

Experimental MethodThe basic components of an NSMM include a micro-wave source, a resonator attached to the probe, and the apparatus for detection of the signal coming from the sample. The schematic for a typical laboratory NSMM is shown in Figure 1. The vector network analyzer (VNA) generally may be used as both the microwave source and the detector. A resonator can be built by use of a coaxial microwave cable that is connected to the source via a decoupling capacitor (labeled decou-pler in Figure 1). The probe is connected at the other end of the resonator to couple to the sample during measurement. With the source power fixed, most of the signal reflects back (see “Microwave Scattering-Parameter Measurements”) to the source when the frequency is swept, i.e., the magnitude of the com-plex scattering parameter S11 is close to unity. If the frequency of the source matches one of the resonant frequencies of the resonator, then S11 is minimized,

ac SignalDirectional

Coupler

Decoupler

Probe

Sample

Res

onat

or

VNAPort 1 Port 2

Figure 1. The basic schematic for a typical NSMM. The resonator is coupled to the sample via a sharp probe at one end and is connected to the source and detector (VNA ports) via a decoupling capacitor at the other end. Port 1 can act as a source and a detector or alternatively can be used as a source while port 2 is used as a detector. Both detection schemes are shown in the schematic.

The miniaturization that Feynman envisioned will require new RF and microwave measurement tools such as NSMM to characterize, engineer, and optimize nanomaterials and nanodevices.

January/February 2014 55

signifying that most of the energy at this frequency is being stored in the resonator. Since S11 is the quan-tity that is directly measured by the system, NSMM typically needs to be operated at or near these reso-nant frequencies. When there is no sample present, the resonator has an open boundary condition on both sides. The wavelength of the modes of the resonator occur at / , ,…L N N2 1 2resonatorm= =^ h with the spacing in frequency given by /c L2 rresonator:f . The length of the resonator Lresonator^ h is known and c is the speed of light and rf is relative permittivity which is one for air and two for Teflon dielectric. Alternatively, if the sam-ple is also connected to the second port of the VNA, then we can measure the scattering parameter S21 as well as .S11 The sample is connected to the coaxial cable via a special plate with a hole drilled into it that holds a coaxial cable flush with the sample surface. A

directional coupler can be added to record the ac sig-nal returning from the resonator for further signal-processing, as shown in Figure 1.

As discussed earlier for the near field, the probe must be brought close to the sample such that the con-dition D r# % m is met. There are different techniques available to accomplish this. The options include STM feedback circuits as well as AFM feedback circuits such as beam-bounce and tuning-fork techniques. During scanning, these different techniques perform what is called the “distance following of the sample” [6]. This means that the probe is made to track the topography of the surface (see “Distance-Following Feedback Techniques”) by use of the feedback circuit (for example, AFM or STM). The probe follows the topography of the sample while either being in soft contact involving very light force (on the order of a

Microwave Scattering-Parameter Measurements

The general idea of a microwave scattering-parameter measurement is that a well-characterized electromagnetic wave (fixed frequency, power, etc.) is incident on a device under test (DUT) or sample, which can be an actual device or simply a material of interest. The incident wave interacts with the DUT, resulting in transmitted and reflected waves that can be detected to investigate the properties of the DUT.

In the case of a two-port microwave system with the incident power from port 1, the reflected signal is labeled S11 while the transmitted signal is labeled

.S21 For the types of material systems typically studied with NSMM, both signals contain information about the complex quantities of conductivity ( )i1 2v v- , permittivity ( )i1 2f f- , and permeability ( ) .i1 2n n- One of the major challenges in this field is the construction of appropriate theoretical models in order to extract this information from S11 and .S21

A good understanding of both the interaction of the incident electromagnetic wave and the physics of the DUT are needed to extract quantitative physical data from the measurement.

NSMM allows for coupling high-speed signals locally to nanodevices and nanomaterials. Nanodevices and nanomaterials of interest present complex impedances to the DUTs. In the case of NSMM, these complex quantities have to be ideally measured at the nanometer scale and with impedances on the order of the quantum of resistance, . kR 25 8Q X= [38]. For an intuitive understanding of the quantum of resistance, consider a quantum wire, i.e., a wire so small that Heisenberg’s uncertainty principle of E t h# +D D applies to it where ED is change in energy, tD is change in time and h is the Plank constant.

The Ohm’s law /R V ID= where V is voltage and I is current can be written for such wire as / ( / )V e tD D , where e is the electronic charge. This can be rewritten as / / /e V t e E t e h e2 2 2# #D D D D= =

. k25 8 X= , which is the value of quantum resistance. This presents an additional challenge related to NSMM, as the characteristic impedance of typical microwave transmission lines are 50X [39]. Reflection coefficient for a typical nanodevice is

/ .R R50 50 0 996Q Q- + = . As a result, less than 1% of the original signal must be measured, which leaves much room for innovation in new avenues of measurement. For example the resonant technique that we describe in this article is used to enhance the signal-to-noise ratio for the measured signal.

Reference[S1] T. M. Wallis, K. Kim, D. S. Filipovic, and P. Kabos, “Broadband

metrology of nanofibers to enable RF interconnects,” IEEE Micro-wave Mag., vol. 12, no. 7, pp. 51–61, Dec. 2011.

Figure S1. The basic idea of an RF two-port measurement also used with NSMM. A DUT is illuminated with incident microwave signal and the reflected and transmitted signals are measured to study DUT.

DUT

Incident

Transmitted

Reflected

The NSMM Provides Microscopic Method toImage Complex v, Complex f, Complex n of theDUT/Sample at Near-Atomic Scale

56 January/February 2014

Distance-Following Feedback Techniques

In order to achieve high spatial resolution and good signal-to-noise ratio with NSMM, one of several different distance-following mechanisms may be employed. These mechanisms keep NSMM probe either in soft-contact with the sample or at a height that is one nanometer to a few nanometers above the sample. Three common mechanisms are 1) tunneling-current-based feedback, 2) optical beam-bounce based feedback, and 3) tuning-fork-based feedback. Here we will discuss only the feedback mechanisms used commonly with NSMM.

Figure S2 shows a schematic of an (a) AFM and (b) STM and their respective experimental methodologies. An AFM employs an optical beam-bounce-based feedback, which consists of a mechanically sharp tip attached to a cantilever (typically made of silicon). The tip comes in contact with the sample and then either the tip or sample can be scanned laterally. The forces between the tip and sample are dependent on their characteristics and include Van der Waals, electrostatic, chemical,

and capillary forces among many others. These forces can be attractive or repulsive in nature. The overall force curve between the tip and sample is shown in the figure. The attractive region is due to the Van der Waals forces and is the region where scanning is done in noncontact mode (shown with the dashed green box). However, so far, NSMM has been used only with contact-mode AFM (shown with dashed red box). The dominant force in this region is repulsion due to the overlap of atomic orbitals at this close distance between the tip and sample. A beam-bounce feedback circuit keeps the force between the tip and the sample constant. As the tip is scanned laterally, the changes in local force between the tip and sample are detected via a four-quadrant photo-detector that receives the reflected laser light from the back of the cantilever. The error signal from the cantilever is then converted into a topography map. This technique may be used on metallic, semiconducting or insulating samples.

Figure S2. The basic physics behind the two important distance-following feedback mechanisms used with NSMM. (a) The atomic force microscope (AFM) and (b) the scanning tunneling microscope (STM).

Tip

Sample

Tip

Sample

(a) (b)

LaserDetector

Contact Mode(Repulsive Forces)

Noncontact Mode(Attractive Forces)

Tunnel-CurrentSTM

FeedbackCircuitAFM

FeedbackCircuit

Quantum-Mechanical Tunnel Current(This Current Decays Very Fast with Change in Tip-to-Sample Distance)

Tip-to-Sample Distance (nm)0 1 2 3Tip-to-Sample Distance

Tip

-to-

Sam

ple

For

ce

0

Tun

nel-C

urre

nt (

nA)

0.75

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0.25

0

January/February 2014 57

few nanonewtons) or while hold-ing the probe above the surface at a distance of a few atoms (1 nm in case of STM). In addition to the topographic mapping via distance following, the electromagnetic interaction of the probe with the sample is being recorded simulta-neously by measuring .S11 In this way, the sample is studied nonde-structively while maintaining a spatial resolution on the order of few nanometers.

In Figure 2, a homemade NSMM is shown that utilizes a tuning fork mechanism for dis-tance following. The resonator is made out of a commercially avail-able Micro-coax UT-085 semirigid coaxial cable. The conductor for the semirigid coaxial cable is cop-per, and the dielectric is Teflon [polytetrafluoroethylene (PTFE)]. At the very end of the resonator, a probe is attached that is also made from the same UT-085 cable. The inner conductor has been removed and replaced by a spe-cial copper or stainless steel capil-lary of matching diameter that is used as the holder of a very sharp tip. This configuration creates a tip socket, which makes the tip replacement an easy task. The res-onator is then connected to port 1 of the VNA, as shown by the dark black line representing a coaxial cable in Figure 2. The tuning fork

The STM, on the other hand, works on the principles of the quantum-mechanical tunnel current and functions as the tunnel-current-based feedback for NSMM. This current is a very small current (on the order of nanoamperes) and can flow if voltage is applied between two closely spaced metal electrodes. The separation between the electrodes is at atomic scale distances (on the order of 1 nm or less). In the case of STM, the tip acts as one electrode and the sample as the other. There is a feedback circuit used to maintain a constant tunnel current between the tip and the sample. This tunnel current drops off exponentially with an increase in the tip-to-sample separation, as shown in figure. As the tip scans across the sample, the local electron density of

states is measured and converted into the surface-topography map.

For more technical details and an elaborate discussion on both STM and AFM, please see [S2]. For more historical and nonmathematical treatment of STM and AFM, please see [S3]. For original work on STM and AFM, please see [S4] and [S5].

References[S2] C. J. Chen, Introduction to Scanning Tunneling Microscopy, 2nd

ed. London, U.K.: Oxford Univ. Press, 2008.[S3] H. C. Von Baeyer, Taming the Atom: The Emergence of the Vis-

ible Microworld. New York: Random House, 1992.[S4] G. Binnig and H. Rohrer, “Scanning tunneling microscopy,” Surf.

Sci., vol. 126, no. 1-3, pp. 236–244, Mar. 2, 1983.[S5] G. Binnig, C. F. Quate, and C. Gerber, “Atomic force microscope,”

Phys. Rev. Lett., vol. 56, no. 9, pp. 930–933, 1986.

Probe(Sharp Tip)

Resonator

Bias Tee

Port 1 Port 2

VNA

Sample

Sharp Tip

CxCout

ZSample

Microwaves

Sample

Not to Scale

dc Signal for STM

C L

Tuning Fork

Figure 2. A homemade NSMM system built at NIST. This system performs distance following with a tuning fork. The resonator is made by use of a commercially available coaxial cable. The inset shows a typical model used to understand the tip-to-sample interaction.

58 January/February 2014

mechanism keeps the tip roughly 10 nm above the sample. A bias-tee has been added to the system, allowing the dc tip-sample current to be monitored simultaneously. The sample holder is attached to a z -stage for the motion in z -direction which provides for a scan range of 25 nm with 0.2-nm resolution. The z -stage is mounted on a closed-loop x y- stage with 100-nm range and 2-nm resolution in both x and y directions [36]. The system also has multichannel, fiber-coupled sources for illuminating the sample with different laser wavelengths, which has been used for measurements of photovoltaic samples [36].

The inset of Figure 2 shows a typical model of a probe and sample interaction. The sample presents a complex-impedance Zsample to the probe. The capaci-tance between the inner conductor and the sample is labeled as ,CX and the one between the sample and the outer conductor is labeled as .Cout This Cout is in series with CX where Cout is much larger than CX so it can be safely ignored. Zsample is sample dependent and has to be modeled for each sample differently.

NSMM probe can be in the form of a cantilever or a sharpened wire that is either chemically etched

or cut with a standard wire cutter to give it a very sharp end. The probes in the form of cantilevers and chemically etched wires are commercially avail-able for purchase. The cut probes can be made in a laboratory setting with minimal training. The SEM micrograph for a commercially prepared platinum probe by Rocky Mountain Nanotechnology is shown in Figure 3(a) for purposes of illustration. The probe is commercially available from Rocky Mountain Nanotechnology in Utah and compatible with com-mercial AFMs, such as the systems built by Agilent

0.0 0.45 0.9 1.35 1.80 2.25

(a)

(b)

-Df (MHz)0.0 0.45 0.9 1.35 1.80 2.25

1,720 nm

1 cm

Figure 4. (a) Frequency-shift image of US$.25 coin taken with a 480-nm diameter center-conductor coaxial probe at an operating frequency of 9.572 GHz. Subwavelength features are present even though the operating wavelength matches the diameter of the coin. (b) The topographic surface plot of the coin, which has been constructed using the frequency shift data shown in (a). (Printed with the permission of American Institute of Physics from C. P. Vlahacos et. al. Appl. Phys. Lett. 72, 1778 (1998) [8].)

500 nm

500 nm 200 nmi

R 1 20 nm

(a)

(b)

Figure 3. (a) SEM images of a commercial NSMM probe showing the large-scale structure of the tip and magnified section of the working-end of the probe. The probe is made of platinum. (b) The opening angle of the probe is shown for the commercially available tip. In the orange box is a high-magnification SEM of a homemade tip made of platinum-iridium wire. The white circle labeled R represents the radius of the tip which for a new tip it is less than 20 nm.

The basic components of an NSMM include a microwave source, a resonator attached to the probe, and the apparatus for detection of the signal coming from the sample.

January/February 2014 59

Technologies. The sharp end of the probe comes in close proximity to the sample and serves as a work-ing end of the probe since it illuminates the sample with microwaves. The crucial parameters for the probe that dictate the spatial resolution for NSMM is the radius of curvature R of the sharp end (or alter-natively the opening angle i of the probe, as shown in Figure 3(b), for the commercial probe). The inset of Figure 3(b) shows a typical homemade sharp tip made of platinum-iridium wire. The two parameters i and R have a close relationship with each other because a probe with very small i will also have a very small R . However, we cannot continue to reduce i or R indefinitely because the capacitance between the tip and sample (denoted as CX in the inset of Figure 2) has to remain large enough to get a good signal-to-noise ratio. On the other hand, increasing i or R arbitrarily will compromise the spatial reso-lution. This requires a trade-off between signal-to-noise and spatial resolution. This R has to be used as the fitting parameter in electromagnetic models for the system since it is very difficult to monitor its shape in situ and values can be anywhere from 20 nm (for a new tip) to 200 nm (for a significantly used blunt tip).

There are three necessary tasks for the proof-of-principle for NSMM operation that must be dem-onstrated. The first is to show the success of the near-field microscopy in breaking Abbe’s limit. The second is to show the atomic-scale spatial resolution achieved with NSMM. The third is to provide clear evidence that NSMM is capable of studying with high spatial resolution the frequency-selective materials contrast. We shall address each one of these issues in the following section.

Proof of PrincipleFor the first case we include an experiment in which a US$.25 coin was imaged with a home-built NSMM [8]. The coin has a diameter of about 2.2-cm. The oper-ating frequency was chosen to be 9.572 GHz, which corresponded to the . cm2 2m= dimension for the microwave coaxial cable. By use of a probe of 480 nm in diameter, the lateral sample position was scanned at a fixed tip height of 30 nm above the coin. This design had a frequency-following feedback circuit to keep the source locked at the resonant frequency of 9.572 GHz. As the sample was scanned, the output of the feedback circuit was recorded to create an image of the changes in the resonant frequency [Figure 4(a)]. The topographic image was then constructed from this frequency-shift image as shown in Figure 4(b). This validates the con-cept of NSMM breaking Abbe’s /2m limit as the sub-wavelength features are visible in the frequency-shift and topography images.

For the second case, we include a study of a highly ordered pyrolytic graphite (HOPG) sample performed with NSMM (called NFMM in [29]), which had STM-assisted distance following [29]. In this particular

4.6 0.8

(a)

0.5 nm

-6.5 +6.5

(b)

It (nA) Dfr (kHz)

489 514

(c)

Q

Figure 5. Atomic-resolution images of highly ordered HOPG taken in STM constant height operation. (a) Tunnel current, It, (b) resonance frequency shift, T fr, and (c) quality factor (Q) images. All images were acquired simultaneously at a scan speed of 20 lines/s with a bias voltage of 100 mV. The resonance frequency for measurement is 2.50 GHz. (Printed with the permission of American Institute of Physics from Jonghee Lee et. al. Appl. Phys. Lett. 97, 183111 (2010) [29].)

The goal of NSMM is to bring quantitative broadband measurements at radio (RF) and microwave frequencies to the available “room at the bottom”; i.e., to make RF and microwave measurements down to the molecular and atomic scale.

60 January/February 2014

case, a /4m -resonator was used at a resonant fre-quency of 2.5 GHz and a quality factor of 600. Pt-Ir tips were used for both the STM and NSMM imag-ing, and the resonant frequency and the quality fac-tor were tracked during the imaging with quadrature homodyne detection. The atomic resolution images of HOPG are shown in Figure 5. The STM tunnel current, the frequency shift, and the quality factor images from the microscope were all taken simulta-neously. The subnanometer spatial resolution shown in Figure 5 is attributed to the capacitance variation, which NSMM feedback circuit is able to track due to the distance following by the STM feedback cir-cuit. Without the distance-following mechanism, the probe, which is effectively tens of nanometers, could not have achieved such a high spatial resolution.

For the third case, we include a study of an IMEC [40], [41] variably doped p-type sample with a com-mercially available AFM assisted NSMM (called SMM in [27]). The AFM feedback circuit was used for distance following. The sample is comprised of stripes containing different doping concentrations, as shown in Figure 6. Region A is the bulk silicon, region B has a concentration of 1016 cm-3, region C has 1017 cm-3, region D has 1018 cm-3, region E has 1019 cm-3, and region F has 1020 cm-3. Each doped stripe is roughly 1.5 nm wide. The topographic roughness of the SiOx surface was on the order of 5 nm [Figure  6(b)] in the area of the doped region of interest so the capacitance during a single scan can be considered constant. This makes it an ideal sample because now the predominant contrast in the signal will be due to the material properties (see “Lumped Element Circuit Theory”). The surface was scanned at a fixed frequency during the scan and the dc bias between the tip and the sample, ,V was varied as shown in Figure 6(a). For this particular measure-ment, a special lock-in technique [27] was used to measure the d S11^ h/dV signal. Here a low-frequency modulation signal of 12 kHz is applied to the AFM tip to modulate the reflected microwave S11^ h signal. As shown in Figure 7, at each frequency, the region of maximum signal in d /dVS11^ h is shifting to higher dopant values as the frequency is increased. The region of 1018 cm-3 has no signal contrast at 2.3 GHz (labeled “OFF” in Figure 7). However, at 17.9 GHz it turns ON while the lower doped regions do not show signal contrast at this higher frequency. This brings to light the strength of frequency-dependent measurements with a broadband NSMM, as the fre-quency selectivity allows improved measurement of local material properties.

Calibration To get useful data from NSMM measurements, appro-priate calibration of the system is required. The spe-cific quantity that must be calibrated will depend on

Figure 6. (a) An image of d S11^ h/dV, illustrating the structure of the sample. The solid white vertical lines show the different doped regions (in cm-3): A = bulk silicon (~1015), B = 1016, C = 1017, D = 1018, E = 1019, F = 1020. The dashed black lines demarcate regions of various applied gate voltages that were applied at the tip. (b) The topographic image from contact-mode AFM showing flat topography of the surface. This is further highlighted by the averaged line cut of the topography, which displays ~5 nm of topographic roughness on the surface. (Printed with the permission of American Institute of Physics from A. Imtiaz et. al, J. Appl. Phys., 111, 093727, (2012) [27].)

(a)

d(S

11)/

dV

Tip

-Bia

s

A

12 nm

nm

12 nm

B C

1

0

0.5

D

0.00-0.50-0.75-1.00-1.25-1.50-1.75-2.00-2.25-2.50-2.75-3.00E F

Position (nm)(b)

Line Cut

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ogra

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Edg

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900

800

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January/February 2014 61

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the material sample or DUT as well as the objective of the experiment. Possible quantities include total com-plex impedance, absolute capacitance, complex perme-ability and permittivity, as well as dopant or carrier concentration. In general, the sample (or DUT) always presents NSMM probe with a complex-impedance (see “Microwave Scattering-Parameter Measurements”). Thus, strategies for calibration rely on the measure-ment of well-understood and well-characterized cali-bration samples that present known impedance loads to NSMM.

For instance, an absolute calibration sample has been designed and measured [19], while a corre-sponding calibration algorithm [25] and a calibration kit [37] have been developed. Using this calibration approach, we have measured a calibrated absolute capacitance in the range of 0.1 to 22 fF with a noise level of 2 aF and an estimated uncertainty of %20! [19] for single frequency measurements. Using the same calibration samples, Hoffman et. al. demon-strated a general procedure for determining a cali-brated complex impedance based on a three-term model [37]. As an alternative approach, Farina et. al. used STM-based NSMM measurements at three different heights above the sample to serve as the reference standards for a one-port calibration [25].

For the calibration of materials properties, the IMEC samples [40] were used with doping concentra-tions in the range of 1015–1020 atoms/cm3. The same special lock-in technique was used to measure the

Lumped Element Circuit Theory for NSMM

Understanding NSMM measurements requires some insight into the interaction of the probe and the sample. The inset of Figure 2 shows the circuit model of the tip-to-sample interaction. As mentioned in the text, the capacitance Cout is so large that it can be safely ignored for the purpose of understanding the measurement. Due to the quasistatic nature of the fields in the near-field regime, the coupling-capacitance Cx can be calculated based on the image-charge method [11]. The working end of the probe is modeled as a sphere above a semi-infinite conducting plane. The values calculated for Cx are in the range of femtofarads, and for particularly sharp tips, nmR 10+^ h can be in the range of attofarads.

To extract information about the sample, a model for Zsample must be developed. Here, knowledge of the sample physics is essential. As an example, in the

figure we show a model for the variably doped silicon sample from IMEC (Figures 6 and 7 in the main text). This sample was measured with the commercially available 5400 AFM by Agilent technologies, which uses a platinum tip in the contact mode. Due to the presence of the oxide layer above the silicon, the tip and sample can be modeled as a metal-oxide-semiconductor (MOS) structure.

The sample is then seen as an RC circuit in series where the capacitances due to the depletion layer Cdepleti no^ h and oxide layer COxide^ h contribute to the total capacitance C total^ h of the circuit. The surface resistance at a given microwave frequency can be calculated as Rs (ratio of the resistivity of the sample to the skin depth at a given frequency), and the material resistance is the sheet resistance of the silicon sample denoted by Rx (ratio of the resistivity of the sample to the thickness of the sample). From the measurement, we extract the circuit-model parameters, which in turn allow for the determination of several quantities of interest such as local mobility n^ h and carrier concentration ncarrier^ h .

References[S6] A. Imtiaz, T. M. Wallis, S.-H. Lim, H. Tanbakuchi, H.-P. Huber, A.

Hornung, P. Hinterdorfer, J. Smoliner, F. Kienberger, and P. Kabos, “Frequency-selective contrast on variably doped p-type silicon with a scanning microwave microscope,” J. Appl. Phys., vol. 111, no. 9, p. 093727, 2012.

[S7] S. M. Anlage, V. V. Talanov, and A. R. Schwartz, “Principle of near field microwave microscopy,” in Scanning Probe Microscopy: Elec-trical and Electromechanical Phenomena at the Nanoscale. New York: Springer-Verlag, 2007, pp. 215–253.

Figure S3. The lumped element model used for the sample from IMEC CAMS (Center for Advanced Metrology Solutions) in Belgium.

Ctotal RS

f(ncarrier, n)

f(~, ncarrier, n)

f(Cdepletion, COxide)Rx

The probe is made to track the topography of the surface (see “Distance-Following Feedback Techniques”) by use of the feedback circuit (for example, AFM or STM).

January/February 2014 63

/Sd dV11^ h signal as already mentioned. Using a knowledge of the doping concentrations of the IMEC samples, we developed the calibration curves for the

/Sd dV11^ h signal based on the FASTC2D software from NIST  [41]. With this method, the doping con-centration of an unknown sample can be extracted by keeping the imaging parameters (analyzer frequency, lock-in parameters, the tip, etc.) constant for the imaging of this new sample. While this technique is tedious, it has been successful in measuring the rela-tive doping concentration with a resolution of better than 20% [41].

Future DirectionsAs described earlier, the measurements require not only high spatial resolution but also systematic varia-tion of other parameters in order to assist the ongoing development of nanoelectronics. These parameters include pressure, temperature, magnetic field, and additional in situ preparations of the sample sur-face. Future nanoelectronics device engineering will also necessitate studies of local transport properties, which may in turn benefit from the use of more than one measurement probe. To this end, a four-probe system built by RHK Technologies Inc. was installed at NIST in early 2013 (as shown in Figure 8). The sys-tem is capable of operating under UHV pressures, a temperature of about 10 K and with an in-plane magnetic field with the field value of about 80 kA/m

(1,000 Oe). Figure 8(b) shows a close-up photograph of the four probes on the sample. All the probes are able to carry the microwave signal to the sample at a frequency of up to 40 GHz. Figure 8(c) shows the atomic scale surface imaging on silicon (111) for this new system.

One potential research direction for NSMM is the measurement of the saline solutions for imag-ing current flow through dielectric and conducting channels. This has potential applications in biologi-cal sciences as well as in the emerging field of nano-biotechnology [6], [42]. The latter draws inspiration for devices and materials from studies of biological systems. The majority of the devices and materials are not simple bulk materials but rather are multilay-ered. This requires that, on the theoretical side, new models be developed for the electromagnetic inter-action between the tip and the stratified media [6], [9]. This also requires that further study be made for imaging the buried structures along the same lines as has been done in reference [13]. In addition, novel tip structures also need to be designed for increasing signal-to-noise and improving spatial resolution. The measured signal by NSMM always has unwanted contribution from the environment in addition to the desired signal from the device or material under test. Further research is needed to find out ways to reduce the contribution of the environment to NSMM signals. One important future direction is to further research a creative idea of time-domain microwave micros-copy as discussed in [43]. Despite these challenges, NSMM will clearly remain an important metrology tool for the advancement of nanoelectronics.

DisclaimerCertain commercial equipment, instruments, or mate-rials are identified in this article to adequately specify the experimental procedure. Such identification does not imply recommendation or endorsement by NIST nor does it imply that the materials used are necessar-ily the best for the purpose.

References[1] R. P. Feynman. (2013, Nov. 14). There’s plenty of room at the bot-

tom. [Online]. Available: http://www.zyvex.com/nanotech/feyn-man.html

[2] M. Kaku, Visions: How Science Will Revolutionize the 21st Century. New York: Anchor Books, 1998.

[3] K. E. Drexler and M. Minsky, Engines of Creation: The Coming Era of Nanotechnology. New York: Anchor Books, 1990.

(a) (b)

(d)(c)

DUT

4

1

2

3

1 nm

STMChamber

SamplePreparationChamber

SEM Column

Figure 8. (a) A four-probe NSMM installed recently at NIST by RHK Technologies, Inc. The picture shows the entire system: the STM chamber, SEM column, and tip and sample preparation area have been highlighted. (b) The close-up of NSMM probes. (Pictures were taken by Curt Suplee at NIST.) (c) The four probes shown together on one sample. Each probe is capable of carrying a microwave signal up to 40 GHz. (d) The Si (111) surface imaged by the RHK system with clear atomic-scale resolution.

The clock frequency is expected to be in the gigahertz range, implying that NSMM may be used to study the device characteristics as well as the characteristics of interconnects.

64 January/February 2014

[4] K. E. Drexler, Nanosystems: Molecular Machinery, Manufacturing and Computation. New York: Wiley Inter-Science, 1992.

[5] B. T. Rosner and D. W. van der Weide, “High-frequency near-field microscopy,” Rev. Sci. Instrum., vol. 73, no. 7, pp. 2505–2525, 2002.

[6] S. M. Anlage, V. V. Talanov, and A. R. Schwartz, “Principle of near field microwave microscopy,” in Scanning Probe Microscopy: Elec-trical and Electromechanical Phenomena at the Nanoscale. New York: Springer-Verlag, 2007, pp. 215–253.

[7] A. Imtiaz and S. M. Anlage, “A novel STM-assisted microwave microscope with capacitance and loss imaging capability,” Ultra-microscopy, vol. 94, nos. 3–4, pp. 209–216, 2003.

[8] C. P. Vlahacos, D. E. Steinhauer, S. K. Dutta, B. J. Feenstra, S. M. Anlage, and F. C. Wellstood, “Quantitative topographic imaging using a near-field scanning microwave microscope,” Appl. Phys. Lett., vol. 72, no. 14, pp. 1778–1780, 1998.

[9] A. Imtiaz, T. M. Wallis, and P. Kabos, “Near-field scanning micro-wave microscope (NSMM),” in Yearbook of Science and Technology.New York: McGraw-Hill, 2013.

[10] A. Imtiaz, T. M. Wallis, S. H. Lim, J. Chisum, Z. Popovic, and P. Kabos, “Near-field antenna as a scanning microwave probe for characterization of materials and devices,” in Proc. 4th European Conf. Antennas Propagation, Barcelona, Spain, 2010, pp. 1–3.

[11] C. Gao and X.-D. Xiang, “Quantitative microwave near-field microscopy of dielectric properties,” Rev. Sci. Instrum., vol. 69, no. 11, pp. 3846–3851, 1998.

[12] M. A. Fenner, F. Kienberger, H. Tanbakuchi, H.-P. Huber, and P. Hinterdorfer, “Quantitative measurement of electric properties on the nanometer scale using atomic force microscopy,” in Proc. Int. Semiconductor Conf., Dresden, 2011, pp. 1–4.

[13] C. Plassard, E. Bourillot, J. Rossignol, Y. Lacroute, E. Lepleux, L. Pacheco, and E. Lesniewska, “Detection of defects buried in metal-lic samples by scanning microwave microscopy,” Phys. Rev. B, vol. 83, no. 12, p. 121409, 2011.

[14] V. V. Talanov, A. Scherz, R. L. Moreland, and A. R. Schwartz, “A near-field scanned microwave probe for spatially localized electrical metrology,” Appl. Phys. Lett., vol. 88, no. 13, pp. 134106–134106-3, 2006.

[15] J. Kim, K. Lee, B. Friedman, and D. Cha, “Near-field scanning microwave microscope using a dielectric resonator,” Appl. Phys. Lett., vol. 83, no. 5, p. 1032, 2003.

[16] M. Tabib-Azar, D.-P. Su, A. Pohar, S. R. LeClair, and G. Ponchak, “0.4 μm spatial resolution with 1 GHz (m = 30 cm) evanescent micro-wave probe,” Rev. Sci. Instrum., vol. 70, no. 3, pp. 1725–1729, 1999.

[17] T. Machida, M. B. Gaifullin, S. Ooi, T. Kato, H. Sakata, and K. Hirata, “Development of near-field microwave microscope with the functionality of scanning tunneling spectroscopy,” Japan. J. Appl. Phys., vol. 49, p. 116701, Nov. 2010.

[18] A. Imtiaz, T. Baldwin, H. T. Nembach, T. M. Wallis, and P. Kabos, “Near-field microwave microscope measurements to character-ize bulk material properties,” Appl. Phys. Lett., vol. 90, no. 24, pp. 243105–243105-3, 2007.

[19] H. P. Huber, M. Moertelmaier, T. M. Wallis, C. J. Chiang, M. Hochleitner, A. Imtiaz, Y. J. Oh, K. Schilcher, M. Dieudonne, J. Smo-liner, P. Hinterdorfer, S. J. Rosner, H. Tanbakuchi, P. Kabos, and F. Kienberger, “Calibrated nanoscale capacitance measurements using a scanning microwave microscope,” Rev. Sci. Instrum., vol. 81, no. 11, p. 113701, 2010.

[20] A. Hovsepyan, A. Babajanyan, T. Sargsyan, H. Melikyan, S. Kim, J. Kim, K. Lee, and B. Friedman, “Direct imaging of photocon-ductivity of solar cells by using a near-field scanning microwave microprobe,” J. Appl. Phys., vol. 106, no. 11, p. 114901, 2009.

[21] A. Tselev, N. V. Lavrik, A. Kolmakov, and S. V. Kalinin, “Scan-ning near-field microwave microscopy of VO2 and chemical vapor deposition graphene,” Adv. Funct. Mater., vol. 23, no. 20, pp. 2635 –2645, 2013.

[22] A. Imtiaz, “Quantitative materials contrast at high spatial resolu-tion with a novel near-field scanning microwave microscope,” Ph.D. dissertation, Dept. Physics, Univ. Maryland, College Park, MD, 2005.

[23] J. D. Chisum, “Low-noise instrumentation for near-field micro-wave microscopy,” Ph.D. dissertation, Dept. Elect. Eng., Univ. Colorado, Boulder, CO, 2011.

[24] L. Zhang, Y. Ju, A. Hosoi, and A. Fujimoto, “Microwave atomic force microscopy imaging for nanometer-scale electrical property characterization,” Rev. Sci. Instrum., vol. 81, no. 12, p. 123708, 2010.

[25] M. Farina, D. Mencarelli, A. di Donato, G. Venanzoni, and A. Morini, “Calibration protocol for broadband near-field microwave microscopy,” IEEE Trans. Microwave Theory Tech., vol. 59, no. 10, pp. 2769–2776, 2011.

[26] E. H. Synge, “A suggested method for extending microscopic res-olution into the ultra-microscopic region,” Philos. Mag. Ser. 7, vol. 6, no. 35, pp. 356–362, 1928.

[27] A. Imtiaz, T. M. Wallis, S.-H. Lim, H. Tanbakuchi, H.-P. Huber, A. Hornung, P. Hinterdorfer, J. Smoliner, F. Kienberger, and P. Kabos, “Frequency-selective contrast on variably doped p-type silicon with a scanning microwave microscope,” J. Appl. Phys., vol. 111, no. 9, p. 093727, 2012.

[28] S. Kim, H. Yoo, K. Lee, B. Friedman, M. A. Gaspar, and R. Levicky, “Distance control for a near-field scanning microwave microscope in liquid using a quartz tuning fork,” Appl. Phys. Lett., vol. 86, no. 15, p. 153506, 2005.

[29] J. Lee, C. J. Long, H. Yang, X.-D. Xiang, and I. Takeuchi, “Atomic resolution imaging at 2.5 GHz using near-field microwave micros-copy,” Appl. Phys. Lett., vol. 97, no. 18, pp. 183111–183111-3, 2010.

[30] N. Klein, “Microwave communication systems—Novel ap-proaches for passive devices,” in Nanoelectronics and Information Technology, R. Waser, Ed., 2nd ed. New York: Wiley-VCH, 2005.

[31] W. Chen, V. Rylyakov, V. Patel, J. E. Lukens, and K. K. Likharev, “Rapid single flux quantum T-flip-flop operating upto 770 GHz,” IEEE Trans. Appl. Supercond., vol. 9, no. 2, pp. 3212–3215, 1999.

[32] K. Goser, P. Glösekötter, and J. Dienstuhl, “Nanoelectronics and Nanosystems: From Transistors to Molecular and Quantum Devices. New York: Springer-Verlag, 2004.

[33] I. Bekey, Advanced Space System Concepts and Technologies: 2010 – 2030+. Los Angeles, CA: AIAA, 2003.

[34] H. Xu, S. Anlage, L. Hu, and G. Gruner, “Microwave shielding of transparent and conducting single-walled carbon nanotube films,” Appl. Phys. Lett., vol. 90, no. 18, pp. 183119–183119-3, 2007.

[35] J. D. Jackson, Classical Electrodynamics, 3rd ed. New York: Wiley, 1999.

[36] J. C. Weber, J. B. Schlager, N. A. Sanford, A. Imtiaz, T. M. Wallis, L. M. Mansfield, K. J. Coakley, K. A. Bertness, P. Kabos, and V. M. Bright, “A near-field scanning microwave microscope for charac-terization of inhomogeneous photovoltaics,” Rev. Sci. Instrum., vol. 83, no. 8, p. 083702, 2012.

[37] J. Hoffmann, M. Wollensack, M. Zeier, J. Neigemann, H.-P. Huber, and F. Kienberger, “A calibration algorithm for nearfield scanning microwave microscopes,” in Proc. IEEE Conf. Nanotechnology, Bir-mingham, U.K., Aug. 2012, pp. 1–4.

[38] P. J. Burke, C. Rutherglen, and Z. Yu, “Single-walled carbon nano-tubes: Applications in high frequency electronics,” Int. J. High Speed Electron. Syst., vol. 16, no. 4, p. 977, 2006.

[39] D. M. Pozar, Microwave Engineering, 2nd ed. New York: Wiley, 1998.

[40] S. Magonov and J. Alexander, “Compositional mapping of mate-rials with single-pass kelvin force microscopy,” Agilent Technolo-gies, Application note # 5990-5480EN (Accessed November 15th, 2013).

[41] H. P. Huber, I. Humer, M. Hochleitner, M. Fenner, M. Moertel-maier, C. Rankl, A. Imtiaz, T. M. Wallis, H. Tanbakuchi, P. Hin-terdorfer, P. Kabos, J. Smoliner, J. J. Kopanski, and F. Kienberger, “Calibrated nanoscale dopant profiling using a scanning micro-wave microscope,” J. Appl. Phys., vol. 111, no. 1, pp. 014301–014301-9, 2012.

[42] O. Shoseyov and I. Levy, Eds., NanoBioTechnology: BioInspired Devices and Materials of the Future. New York: Humana Press Inc. 2010.

[43] M. Farina, A. Lucesoli, T. Pietrangelo, A. di Donato, S. Fabiani, G. Venanzoni, D. Mencarelli, T. Rozzi, and A. Morini, “Disentangling time in a near-field approach to scanning probe microscopy,” Nanoscale, vol. 3, no. 9, pp. 3589–3593, 2011.