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Keysight TechnologiesScanning Microwave Microscopy for Quantitative Imaging of Biological Samples Including Live Cells

Application Note

IntroductionThe Scanning Microwave Microscope (SMM) merges the nanoscale imaging capabilities of an atomic force microscope (AFM) with the high-frequency broadband (from MHz to GHz) impedance measurement accuracy of a vector network analyzer (VNA) (Figure 1). The typical frequency range of the combined SMM is between 1-20 GHz (Huber et al. 2010). It allows characterizing electric, dielectric, and magnetic properties of materials at microwave frequencies with nanometer lateral resolution. Using the microwave signal, impedance nanoscale imaging and doping profiling can be performed. Typically the SMM is operated in reflection mode, whereby the ratio of the reflected and incident electromagnetic waves, the so called S11 scattering parameter, is measured by the VNA at each pixel of the AFM tip-sample contact point. As such a microwave image is generated pixel by pixel, simultaneously to the topographical image. Imaging speeds are fast resulting in a typical acquisition time of one minute per image. There are mainly two different imaging modes in SMM. The first is quantitative dopant profiling by means of differential capacitance (also called dC/dV), which is a widely used technique for semiconductor failure analysis and detecting leakages in solid state devices with nanometer resolution (Huber et al 2012). The dC/dV mode relies on a low frequency (kHz) modulation of the GHz S11 signal using the Dopant Profile Measurement Module (DPMM). It allows tuning the semiconductor depletion zone with low frequency and probing the doping concentration through the native oxide interface at GHz frequency. The second SMM mode which is mainly used in life science is complex impedance imaging and it is based directly on the scattering S11 signal at GHz frequency (Gramse et al 2014).

Figure 1. SMM sketch (upper panel) and equivalent electric circuit at the tip/sample interaction (lower panel). SMM impedance matching network consists of half-wavelength resonator, 50 Ω shunt resistor, and coaxial cable. The lower panel presents a 3D geometrical model of a cell in contact with the fully metallic AFM probe. Equivalent electric circuit is composed of cantilever stray capacitance (Cstray), tip/cone capacitance (Ccone), and tip/sample capacitance (Cpar) in parallel with cell conductance (loss, 1/Gpar). A thin layer of native SiO2 on top of doped silicon (Si++) forms the substrate.

Resonator Coax

ReflectionVNA

Air

Cell

03 | Keysight | Scanning Microwave Microscopy for Quantitative Imaging of Biological Samples Including Live Cells - Application Note

Complex impedance imaging with nanometer precision and low impedance values has proved to be a powerful tool for materials science applications (Hoffmann et al 2014; Kasper et al 2014a). In particularly, the capability of sub-surface imaging of buried nanoscale structures has been demonstrated, as well as conductivity measurements of 2D layers (Gramse et al 2015). Recently, the high frequency characterization of biological materials has attracted considerable interests, as SMM represents a convenient non-invasive evanescent imaging technique that complements AFM (Tuca et al 2016). While AFM measures the surface topography, the SMM can see inside materials (eg cell nucleus and organelles) using the electromagnetic wave penetration capabilities at GHz frequency. In the following we present calibrated complex impedance measurements of bacteria and cells, complex permittivity measurements of single bacteria at 20 GHz, and live cell imaging in liquid media. Furthermore we present augmented SMM solutions where the standard SMM mode is extended with other electronic measurement devices from Keysight (eg the dielectric probe kit, or the electronic calibration unit ECal) that opens new and advanced SMM measurement capabilities. Finally, we combine SMM with the Keysight EMPro 3D modeling capabilities at GHz frequencies that can be used to calculate E-fields and complex impedance values inside cells in order to assist quantitative SMM data interpretation.

SMM complex impedance for biological applications

Complex impedance calibration: basic workflowAn SMM S11 complex impedance calibration workflow has been recently developed where no calibration sample is required (Figure 2). From the measured S11, calibrated capacitance and resistance images of metallic, dielectric, biological or semiconducting materials are obtained. For bio-applications silicon substrates are used to adhere cells, bacteria, viruses or membranes. S11 approach curves in order to calculate the three error coefficients in a standard S11 black box calibration. A low frequency EFM approach curve is used to measure the capacitance change with the distance when the cantilever approaches the sample surface. In the case of bio-samples the approach curves are done on the silicon substrate. Using this black-box calibration procedure the complex S11 images are converted to impedance images (Figure 2 & 3).

Figure 2. SMM sketch (upper panel) and complex impedance calibration (lower panel). The main SMM compo-nents are the AFM cantilever with standard laser deflection readout, the impedance matching network as well as the VNA for GHz signal readout. The VNA measures the S11 amplitude and phase images. Based on a standard VNA three error parameter black-box calibration the conductance and capacitance images are derived.

Impedancematching network

Vectornetworkanalyzer

VNAAFM

Complex S11 - parameter

Blackboxcalibration


After calibration, the topography crosstalk between the topography image and the capacitance image is removed, allowing the subtraction of the cantilever based stray capacitance from the local AFM tip capacitance. The stray capacitance is thereby extracted from the linear part of the S11 approach curve, and the topography-influenced values are subtracted pixel-by-pixel from the raw capacitance values. The impedance calibration method is available as a script in Pico Café (Keysight PicoCafe). Figure 3 shows the calibration script graphical user interface, which allows selecting the most appropriate equivalent electrical network model.

Figure 3. Graphical User Interface (GUI) of the Picoscript for the automated complex impedance calibration with SMM. The upped panel shows the GUI window that allows importing the EFM/SMM approach curve to calibrate the image. The lower panel shows an example of calibrated Capacitance (fF) and Conductance (µS) images obtained using the script. The script allows the user to select the most appropriate equivalent electrical RC model (red circles on the right). The advantage of this calibration workflow is that no specific calibration sample is required and that the calibration can be performed on the bare conductive substrate (eg silicon) where the cells and bacteria are adhered.

SMM calibration script

Calibrated images shown in the script GUI


Complex impedance of bacteria: capacitance and complex permittivityThe SMM was used to measure Escherichia coli (E. coli) bacteria in air and in liquid using intermittent contact mode for imaging soft materials (Figure 4) (Tuca et al 2016). Quanti-tative SMM calibration is achieved resulting in complex impedance images of bacteria in air including capacitance (aF; attoFarad) and conductance (μS; microSiemens) images. E. coli bacteria were immobilized onto a silicon substrate and imaged with the SMM either in the dry state or in buffer solution. Figure 4, upper panel, shows an ensemble of bacteria spread over the surface of Si and SiO2 pillars while the lower panel shows two individual bacteria on Si. The topography images show E. coli bacteria with lengths of 2-3 μm and a height of 300-350 nm. The SMM raw data includes the VNA amplitude image showing a good contrast between the bacteria, SiO2 pillars and the Si substrate. The calibrated capacitance images show individual bacteria with a capacitance ranging from 20-100 aF depending on the tip diameter and the frequency. The capacitance of the bacteria as well as the SiO2 pads is lower than the capacitance of the substrate. This is consistent assuming a simple parallel plate capacitor model where the capacitance decreases with increasing distance of the tip and the substrate. The conductance channel shows no variation between bacteria and substrate (data not shown), which is expected from the non-conductive SiO2 pads and indicates that the bacteria have no electrical loss under the measurement conditions.

In a subsequent study we quantified the electric permittivity of single bacterial cells at microwave frequencies and nanoscale spatial resolution (Biagi et al 2016) (Figure 5). Calibrated complex impedance and admittance images have been obtained at 19 GHz and analyzed with a methodology that removes the non-local topographic cross-talk contributions and thus provides quantifiable intrinsic dielectric images of the bacterial cells. Results for single E-coli provide a relative electric permittivity of ε = 4 in dry conditions and ε = 20 in humid conditions, with no significant loss contributions. The ability of microwaves to penetrate the cell membrane opens an important avenue in the microwave label-free imaging of single cells with nanoscale spatial resolution.

Figure 4. GHz images of single bacteria. Multitude of E. coli bacteria imaged with the SMM in air. The first column shows the AFM topography image, the second column shows the raw SMM S11 amplitude image. The last column shows the calibrated capacitance map overlaid on the 3D topography image.

Topography

Topography

Microwave Amplitude

Microwave Amplitude

Capacitance

Capacitance

Capacitance

Topography

Cross-talk

19 GHz

Figure 5. Complex permittivity (dielectric constant ε) of single bacteria at 19 GHz. The cross-talk was

removed by finite element modeling.


Cell conductivity at humidity and living cell imaging in buffer solutionFigure 6 shows the topography and calibrated capacitance and conductivity images of single Chinese Hamster Ovary (CHO) cells acquired in air (upper row) and in liquid (middle row; living cell) (Tuca et al 2016). Due to their large dimensions, they can be easily spotted on the silicon substrate and individually scanned in contact mode. The to-pography images show a diameter of roughly 30μm and a height of more than 1μm. The obtained capacitance variation is induced by cell dielectric properties that are different from the Si substrate dielectric properties. Figure 6, lower panel, shows the microwave interaction at the tip/sample contact point using EMPro finite element modeling (FEM). A 3D cell-like structure has been implemented in CAD (computer-aided design) including the cell nucleus, three vacuoles, and a 10nm thick membrane. The simulated values of admittance were obtained at different frequencies and positions over the cell, in order to investigate how different cell compartments influence the electric field distribution. Different dielectric values were used for the individual cell compartments including the lipid bilayer of the cell membrane (εr=3.2), the cell nucleus with DNA (εr=8) and a protein vacuole (εr=3). Depending on the cell and tip geometry, the simulated tip-cell complex admittance (admittance Y is the inverse of the impedance Z, Y=1/Z) was determined as roughly Y=110 + j250 μS (micro-Siemens), which translates to conductance values of roughly 50 μS and capacitance values of 500 aF. Those modeled EMPro values fit very well to the experimental SMM results.

Figure 7 shows a set of CHO cell measurements with controlled variation of the ambient humidity, ranging from low humidity (2% RH) to high humidity (60% RH). The calibrated conductance values obtained at low humidity are in the order of 10-20μS, whereas the values obtained at high humidity vary between 30-200μS, which can be explained with the variation of the conductivity based on the water content in the cells.

Figure 6. Upper panel: Cell complex impedance imaging in air and liquid. Individual CHO (Chinese Hamster Ovary) cell imaged in air in intermittent contact mode showing topography, calibrated capacitance and conduc-tance. Centre Panel: SMM images of individual ARPE-19 (Arising Retinal Pigmented Epithelia) cell on Si++/SiO2 substrate and imaged in liquid solution of medium, serum, and antibiotics. Lower panel: Tip-cell interaction with 3D EMPro model (left) and simulation of E-field over cell surface and penetration into the cell (right).

Topography

Topography

Capacitance

Raw PNA ampitude

Conductance

Raw PNA phase


Figure 7 lower right panel shows the variation of the complex permittivity of different aqueous solutions (pure water, PBS, and HBSS) with respect to frequency ranging from 1-20 GHz, recorded with the dielectric probe kit (Tuca et al 2016). The choice of the three solutions should match the cell buffer solutions. The real part ε’ of the water dielectric constant thereby decreases from ε’water=78 at 2 GHz to ε’water=40 at 20 GHz. The imaginary part of the water relative permittivity ε” is proportional to the conductivity σ, based on σ=2πfε”ε0, where ε0 is the permittivity of free space, and f is the frequency. The dielectric probe measurements reveal a low value of the imaginary part of the relative permittivity (εwater’’<10, σwater<1S/m) at low frequency (2 GHz) and a high value (εwater’’ =35, σwater=40S/m) at high frequency (20 GHz). The SMM cell conductivity can now be compared to the water conductivity at 20 GHz. The SMM conductivity σ can be obtained from the conductance G in a simple first order approximation from the volume of the cell in contact with the SMM tip, and applying the relation σ = G * l/A, where A is the contact area and l is the cell height obtained from the topography image. The effective conductivity obtained from the SMM cell conductance, at f=20 GHz, is σcell=18 S/m and effective εcell’’=15, which is in the range of the bulk water permittivity. Accordingly, the cell conductivity behavior at different frequencies and ambient humidity is similar to bulk water properties, corroborating the hypothesis that water is adsorbed on the cells’ surface and that it is responsible for the microwave energy dissipation over the cells.

Figure 7. Cell conductivity at different humidity. SMM equivalent electric circuit model of the tip-cell interaction (upper left). Calibrated cell conductance images measured at different ambient humidities (lower left). Inset shows cell topography. Real and imaginary parts of water complex permittivity, 0.1M PBS and HBSS buffers as a function of frequency, over the range 1-20 GHz (lower right), experimentally obtained using VNA and dielectric slim probe kit from Keysight (upper right).

CHO Conductance with varying humidityComplex permittivity

Frequency, GHZ

Resonator Coax PNAAFM


Additional SMM techniques

Sub-surface imaging: seeing below the surface. SMM can use the penetration capabilities of GHz microwaves to perform non-destructive in-depth imaging of structures located underneath the sample surface (Gramse et al 2015). This capability, named as sub-surface imaging, is an important benefit when the area of interest is buried under the sample surface. Calibrated sub-surface imaging was shown on a silicon dopant sample covered with dielectric layers of SiO2 (100–400 nm thickness). The electrical properties of doped silicon structures buried under oxides with more than 400 nm thickness were obtained. Sub-surface imaging can be used also for bio-samples including individual cells to locate internal structures below the cell membrane.

Quantitative materials properties including resistivity/conductivity. Based on the S11 complex impedance calibration workflow, the SMM images are converted into capacitance and resistance. Using a tip–sample analytical model that includes tip radius, microwave penetration skin depth, and semiconductor depletion layer width, the resistivity of the device can be extracted from the calibrated SMM resistance as recently demonstrated (Brinciotti et al 2015). The method has been tested on two doped silicon samples and in both cases the resistivity and doping concentration are in quantitative agreement with the data-sheet values over a range of 10−3 Ω*cm to 101 Ω*cm, and 1014 atoms* cm-3 to 1020 atoms*cm-3, respectively. The lateral resolution of SMM is limited by the AFM tip probe apex radius while the bulk penetration is mainly determined by the skin-depth. The skin depth and therefore the microwave penetration depth can be changed by varying the SMM frequency. In this way, frequency dependent depth profiling can be realized with the SMM, and can be applied also for bio-samples.

Capacitance-voltage spectroscopy for further physics investigations. SMM capacitance images can be acquired at different DC tip-bias voltages, and C-V (capac-itance-voltage) curves can be determined (Brinciotti et al 2016). While this is typically used in semiconductor and materials research applications, C-V curves can be also acquired on cells including the investigation of the membrane potential and ion-channels in supporting bilayers.


Augmented SMM: SMM combined with other Keysight productsKeysight’s broad test and measurement products portfolio can be leveraged to augment SMM with other high precision instruments, leading to advanced nanoscale measure-ment solutions unique in the industry.

SMM + ECal for advanced impedance calibrationUsing the electronic calibration kit (ECal) in combination with the SMM, a new and advanced calibration method for nanoscale complex impedance imaging is presented, which does not require any calibration samples (Kasper et al, 2016). Instead, the vector network analyser (VNA) and the corresponding electronically switched calibration (ECal) capabilities in combination with time domain gating and microwave network modelling are used to de-embed the full system (Figure 8).

Based on this workflow the measured complex reflection S11 signal can be directly split into the reactive (capacitive) and lossy (conductive) sample behavior. Nano Schottky diodes on a semiconductor substrate as well as biological cells were measured to demonstrate that the sample conductance and susceptance correspond directly to S11

amplitude and phase, respectively. This advanced workflow of quantitative impedance calibration can have various applications starting from semiconductor failure analysis to novel 2D materials and biological cells in liquid environment.

SMM + SMU for advanced voltage spectroscopySMM can be interfaced with the Keysight’s high precision Source Meter Unit (SMU) to simultaneously and accurately measure the DC and RF impedance characteristics of the sample. SMM allows measuring the calibrated capacitance at 1-20 GHz as a function of the tip bias voltage. In this augmented SMM solution, the SMU (Keysight B2900) ensures well defined bias conditions, offering both an accurate DC source as well as precise measurement channels for voltage and current (with a resolution of 100 nV and 100 fA, respectively) (Kasper et al, 2012). This can be useful in the study of voltage properties of cell membranes and ion channels.

Figure 8. SMM-ECal setup including VNA, ECal, 50 Ohm resonator cable and AFM cantilever. In the calibration workflow the calibration planes (dashed vertical lines) are sequentially moved towards the cantilever tip.


Nanoscale modeling with EMPro for data interpretation

Nanoscale modeling with ADS and EMPro: GHz electric field distributionCalibrated SMM experiments can be compared to quantitative modelling using two Keysight software packages, ADS and EMPro (Figure 9) (Kasper et al 2014b; Medina et al 2015). ADS is an electric circuit simulation tool that provides optimisation, tuning, network parameters, and the broadband frequency response for standard electronic components. ADS was used to model the broadband frequency S11 response of the coaxial cables and the impedance matching network, as well as the effect of the AFM tip in contact with different materials samples. The ADS frequency sweep simulations were compared to experimental SMM data and a quantitative agreement has been achieved. With the 3D modeling tool EMPro, calibrated SMM impedance images and electrical E-field distributions can be compared to 3D microwave finite element modelling. As such, 3D electromagnetic full-wave simulations using EMPro can validate the calibrated complex impedance SMM measurements. EMPro supports two simulation engines, Finite Element Modelling (FEM) and Finite Difference Time Domain (FTDT).

Figure 9. SMM modeling with ADS and EMPro. (a) Integrated 2D circuitry model (ADS) and 3D EM design block (EMPro model). (b) 3D CAD model of the cantilever and sample holder. (c) Meshed view in EMPro advanced mode. (d) E-Field distribution at 10 GHz. Here transmission S21 imaging is compared to reflection S11. ADS and EMPro models can be used to study different imaging geometries, measurement parameters like tip-diameter and SMM frequency. Quantitative comparisons can be done with SMM experiments.

In FEM, the structure is included in CAD and meshing is done until the solutions for the Maxwell’s equations in the mesh tetrahedrons converge to a certain threshold. Integrat-ing the obtained electric and magnetic fields, the voltage and current is calculated in each mesh point (Figure 9). The ratio of voltage to current calculated by EMPro at the port gives the impedance, which corresponds to S11. Both EMPro and ADS modelling are used to gain insights into the sub-surface imaging capabilities of bio-samples, oxides and semiconductor materials at different frequencies and different experimental conditions. As such the modelling packages are useful for proper experimental SMM planning as well as further data interpretation at a quantitative level (Oladipo et al 2013).


Figure 10 shows how the 3D-field solver EMPro was used for nanoscale modeling of the E-field and impedance values of the SMM tip-sample system at 19 GHz of individual cells (Tuca et al 2015). The model of the cantilever, tip, substrate, and sample has been simulated at different frequencies, both in air and liquid environment. The results, which show an extremely confined E-field radiated from the tip and probing the sample, qualitatively agree with the experiments. Figure 10 (a) shows the geometric model of the cantilever, the probe tip, and the sample (i.e. cell model) on the substrate. In (b), the electric field distribution is shown over the cell structure, the thin SiO2 pad, and the Si substrate. In (c), the internal structure of the cell is described including cell nucleus, vacuoles, water as internal fluid, cell membrane, and air as surrounding medium. Panel (d) shows a zoom-in on the electric-field distribution at the nanoscale tip-cell contact point. The localized E-field demonstrates the resolution of the SMM in probing the local impedance/admittance of the sample, e.g. cell or bacteria. Also it shows that subsurface imaging can be done with roughly 1 μm of penetration depth which was verified with SMM experimental studies.

Acknowledgements

This work was done by Keysight Labs Linz Enrico Brinciotti, Giorgio Badino, Manuel Kasper, and Ferry Kienberger ([email protected]; Principal Investigator), with support from Johannes Kepler University of Linz (JKU Linz) Silviu Sorin-Tuca, Georg Gramse, and Peter Hinterdorfer.

Figure 10. 3D electromagnetic FEM model of an AFM-tip in contact with a cell generated with EMPro. (a) CAD geometric model. (b) After meshing the model, EMPro calculates the E-field distribution and the complex impedance values. The E-fields are shown in colour scale including the full cantilever and the three layer stack substrate. (c) CAD model of the AFM-tip in contact with the cell including internal cell structures. The cell diameter is 30 μm with a height of 2.5 μm and a 10 nm thick cell membrane (relative permittivity εr = 3.2). The inside contains a 2 μm spherical nucleus (εr = 3.2) and 200 nm diameter vacuoles (εr = 3.2) all embedded in water (εr varying with frequency based on the Debye model). (d) E-field distribution of the tip-cell system showing the highly localized E-field penetrating into the cell and the contrast conferred by the cell internal structure.


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References

1. Biagi, M.C. et al. (2016), “Nanoscale Electric Permittivity of Single Bacterial Cells at Gigahertz Frequencies by Scanning Microwave Microscopy,” ACS Nano, 10 (1), 280-288.2. Brinciotti, E. et al. (2015), “Probing resistivity and doping concentration of semiconductors at the nanoscale using scanning microwave microscopy”, Nanoscale, 7, 14715-22.3. Brinciotti, E. et al. (2016), “Frequency analysis of dopant profiling and capacitance spectroscopy using Scanning Microwave Microscopy”, submitted.4. Gramse, G. et al. (2014), “Calibrated complex impedance and permittivity measurements with scanning microwave microscopy”, Nanotechnology 25, 145703-11.5. Gramse, G. et al. (2015), “Quantitative sub-surface and non-contact imaging using scanning microwave microscopy”, Nanotechnology 26, 135701-10.6. Hoffmann, J. et al. (2014), “Measuring Low Loss Dielectric Substrates with Scanning Probe Microscopes,” Applied Physics Letters, 105, 013102-6.7. Huber, H.P. et al. (2010), “Calibrated nanoscale capacitance measurements using a scanning microwave microscope”, Rev. Sci. Instr. 81, 113701-98. Huber, H.P. et al. (2012), “Calibrated nanoscale dopant profiling using a scanning microwave microscope”, J. Appl. Phys. 111, 014301-9.9. Kasper, M. et al. (2014a), “Metal-oxide-semiconductor capacitors and Schottky diodes studied with scanning microwave microscopy at 18GHz”, J. Appl. Phys. 116, 184301-8.10. Kasper, M. et al. (2014b), “Electromagnetic Simulations at the nanoscale: EMPro modeling and comparison to SMM experiments”, Keysight Application Note 5991-2907EN.11. Kasper, M. et al. 2016. “An advanced impedance calibration method for nanoscale microwave imaging”, IEEE-MTT conference proceeding June 2016 San Francisco. 4 Pages.12. Keysight PicoCafe: http://www.picocafe.com/types/picoscripts/submission/11713. Medina, P.F. et al. (2015), “Transmission and reflection mode scanning microwave microscopy (SMM): experiments, calibration, and simulations”, Proceedings of the 45th European Microwave Conference, Paris, 654-657.14. Moertelmaier, M. et al. (2014), “Continuous capacitance–voltage spectroscopy mapping for scanning microwave microscopy”, Ultramicroscopy 136, 67–72.15 Oladipo, A. O. et al. (2013), “Three-dimensional finite-element simulations of a scanning microwave microscope cantilever for imaging at the nanoscale”, Appl. Phys. Lett. 103, 213106-10.16. Schweinböck, T. & Hommel, S. (2014), “Quantitative Scanning Microwave Microscopy: A calibration flow”, Microelectronics Reliability, 54, 2070–4.17. Tuca S.S. et al. (2015), “Single E-coli bacteria imaged at 20 GHz using the SMM”, Microscopy & Analysis July/August 2015, page 9-12.16. Tuca S.S. et al. (2016), “Calibrated complex impedance of CHO cells and E. Coli bacteria at GHz frequencies using scanning microwave microscopy,” Nanotechnology, 27, 135702-11.

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