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Recent Advances in Scanning Microwave Impedance Microscopy
(sMIM) for Nano-Scale Measurements and Industrial Applications
Stuart Friedman*, Oskar Amster, and Yongliang Yang
PrimeNano, Inc., 407 S California Ave, Suite 5, Palo Alto, CA USA 94306
ABSTRACT
Scanning Microwave Impedance Microscopy (sMIM), a new electrical measurement mode for AFM, has shown
significant success in the imaging and characterization of electrical properties at 10's of nm length scales. We describe
the underlying principles of sMIM and illustrate electrical property imaging capabilities on technologically relevant
materials such as graphene, carbon nanotubes and ferroelectric optical crystals. Additionally we presente current
research on quantitative metrology and provide examples of a proximity modulation method to measure both bulk and
thin-film dielectrics.
Keywords: Microwave Impedance Microscopy, AFM, dielectric, conductivity, quantitative, nano-scale
1. INTRODUCTION
Scanning Microwave Impedance Microscopy (sMIM) is a promising new technique that produces images of the
electrical properties of materials with nano-scale resolution. Coupled with the precise topographic imaging capabilities
of Atomic Force Microscopy – AFM, (widely used in semiconductor metrology, biomedical research, and many other
industrial field), not only the topography but also the function of materials and devices can be probed, adding a new
dimension to scanning probe microscopy. The ability to directly image the local variation of a sample’s permittivity and
conductivity at the 10’s of nm length scale has stimulated new areas of research. Researchers studying graphene, CNT’s,
ferroelectric domains, and many other interesting materials are actively using this technique to gain new understanding
of materials systems behaviors.
The natural progression and general interest in the research and engineer community is to extend the sMIM capabilities
of quantitative measurements, providing local values of conductivity and dielectric constant. With the benefit of AFM
scanning probe capabilities, the sMIM can be operated in a proximity modulation manner to measure the local values of
conductivity and dielectric constant. It uses air as reference and measures the sMIM signal difference between the tip in
air and contact with the sample to realize quantitative sMIM scanning.
In this paper we describe the underlying principles of sMIM and illustrate electrical property imaging capabilities on
technologically relevant materials such as graphene, carbon nanotubes and ferroelectric optical crystals. We also present
current research on quantitative metrology and provided examples of a proximity modulation method to measure both
bulk and thin-film dielectrics.
2. SMIM AND QUANTITATIVE SMIM
2.1 sMIM
Figure 1 illustrates the basic principles of sMIM measurements. The microwave electronics generate 3GHz microwave
signals that are coupled through a custom micro-fabricated coaxial transmission line to the AFM tip. The microwave
signals interact with the nanoscale volume of material beneath the tip apex (volume is comparable with the dimension of
tip apex) and the reflected microwave signals are measured by the electronics. The reflected amplitude and phase depend
on the local dielectric and conductivity of the sample. The microwave electronics process these microwave signals and
produce two output signals corresponding to the real (sMIM-R) and imaginary (sMIM-C) parts of the dielectric constant
of the sample. Figure 1b shows the simulated sMIM outputs as a function of Si sample conductivity beneath the tip apex.
The MIM-C signal, which is proportional to the tip-sample capacitance, is a monotonic function of the Si conductivity,
while the MIM-Re signal, related to resistive loss, peaks at intermediate conductivity. More details can be found in Ref
[1]. One should note that this technique is based on a near-field interaction at GHz frequency so the spatial resolution is
*
Corresponding author: [email protected]
(b)
(a)
microwave
electronics
sMIM-C
sMIM-R
MIM signals (arb. unit)
determined by the tip apex size (currently it is about 50 nm) and not the microwave wavelength. The shielded cantilever
probe design greatly reduces parasitic tip-sample coupling that leads to topographical artifacts and environmental noise
pickup2.
sMIM-C
sMIM-R
-2
10
-1
10
0
10
1
10
Conductivity ( S/m)
2
10
3
10
Figure 1. Microwave Impedance Microscopy. a. sMIM block diagram. b. Simulated sMIM outputs as function of silicon
sample conductivity.
2.2 Quantitative sMIM
In the proximity modulation method, microwave reflection measurements are taken with the tip in contact (as in Figure
2a) and with the tip retracted to a point where the measurement is independent of the local properties of the sample under
the tip (as in Figure 2b). The contact measurement is identical to the measurement made when generating typical sMIM
images of spatial variations in sample permittivity and conductivity. As simulated electrical potential distribution near
the tip show, the contact measurements are sensitive to the sample and the air near the tip apex. The retracted
measurements are unique to this quantitative method. Unlike in AC or tapping mode AFM imaging, where the tip moves
10’s to 100’s of nm above the surface, in this mode the tip is typically moved ~1um above the surface so that the tip only
effectively measure the surrounding air as shown in figure 2b. The difference between these two measurements (contact
and retracted) cancels out electronics drift and largely isolates the signal from the tip apex. It provides a quantitative
value proportional to the local conductivity and dielectric constant.
(a)
Tip
Air
Substrate
(b)
Figure 2. Illustration of the quantitative sMIM with proximity modulation method. The electrical potential distributions near
the tip are simulated by COMSOL multi-physics.
These measured quantitative values are dependent on parameters such as tip radius that do vary. We have included
calibration steps, based on simple standards such as bulk dielectrics, into our measurement protocol. The calibration data
has been shown sufficient to correct for parameters such as tip radius, allowing the quantitative measurements to be
converted to units of conductivity and permittivity.
3. STUDYING ELECTRICALPROPERTIES USING SMIM TECHNOLOGY
3.1 Graphene
Figure 3 shows the sMIM images on a graphene sample. There are no topographic features on the AFM image (figure
3a). While from the sMIM image, three different graphene domains have different conductivities. Figure 3c shows the
line profile of a blue line in figure 3(b). The width of the conductivity transition is about 15 nm, which reflects the
spatial resolution of sMIM technique.
(c) -2.4
sMIM signal (V)
-2.5
-2.6
-2.7
15 nm
-2.8
-2.9
-3.0
0
50
100
150
200
Distance (nm)
Figure 3. Testing results on graphene sample. (a) AFM topography. (b) sMIM image, (c) profile of blue line in (b) show the
spatial resolution of sMIM. Courtesy Haomin Wang, Shanghai Institute of Microsystem and Information Technology,
Chinese Academy of Sciences.
Figure 4 shows the testing results on another graphene sample. There is no noticeable difference on the graphene piece
labeled with a red circle in Figure 4a. While in the sMIM images showing the conductivity information, different regions
have different conductivities.
Figure 4. Testing results on graphene sample. (a) AFM topography. (b) sMIM-C and (c) sMIM-R images show the graphene
with different conductivities. Courtesy Prof Minghui Lu, Nanjing University.
3.2 CNT
Carbon nanotubes (CNT) have proven to be of high interest for a wide range of research and industrial applications 3. A
great deal of attention has been focused on CNT’s for advanced microelectronics and thermal transfer implementations 4.
There are a wide range of methods for producing CNT’s that also result in a range of properties 5. sMIM’s high
sensitivity to the electrical properties makes it well suited for investigation of the varying properties of CNT’s. Figure 5
shows the images on CNT sample. By comparing the AFM topography image and sMIM image, one can see significant
different between the physical features and conductivity. The CNTs in box A and B have the same topography features
but very different conductivities.
Figure 5. Testing results on carbon nanotubes sample. (a) AFM topography. (b) sMIM image shows different CNTs have
different conductivities. Courtesy Eric Seabron and Prof. William L. Wilson, Frederick Seitz Materials Research
Laboratory, University of Illinois at Urbana-Champaign.
3.3 Ferroelectrics
Ferroelectric materials have been widely used in nano-scale transistor devices6. In recent years, the ferroelectric domain
walls have become the subject of intense scientific research8. In particular, the unexpected electrical conduction at
ferroelectric domain walls9 is highly attractive because of the possibility to create and control nano-scale 1D/2D
conductive paths in wide band gap insulators. Current research often relies on conductive atomic force microscopy (CAFM), in which the measured signals are affected by the domain structure and Schottky barrier 8. sMIM is an ideal
technique to study these materials as it measures local conductivity properties without disturbing the material properties
and altering the intrinsic properties.
Figure 6. Conductive domain walls on LiTaO3. (a) Schematic of sample structure. (b) AFM topography image of LiTaO3.
(c) sMIM dC/dV image. Conductive domain walls are bright in (e) MIM-Im and (f) MIM-Re images. Courtesy Prof ZhiXun Shen, Stanford University and Prof. Minghui Lu, Nanjing University.
Figure 6 shows the scanning results on LiTaO3. The sample is z-cut LiTaO3 crystal with up and down domains (Figure
6a). The sample surface is flat except for polishing scratches and occasional contamination particles (Figure 6b). The
ferroelectric domain configuration can be observed in the nonlinear dC/dV image (figure. 6c) and the contrast represents
opposite polarizations of the two domains. In the MIM images (Figures 6d and e), the domain walls are more conductive
than the domains. Further sMIM and theoretical studies revealing the conductivity in the domain walls is in process and
will be published soon.
It is worth noting that sMIM is sensitive to the variations in conductivity near the surface and measures these changes
using applied potentials in the mV range. In contrast, conductive AFM is sensitive to the conductivity along the entire
path of current flowing from the tip to the ground electrode and often utilizes applied potential of a few volts.
4. QUANTITATIVE SMIM WITH PROXIMITY MODULATION
4.1 Proximity Modulation on Bulk Dielectrics
Figure 7 shows the quantitative sMIM results on a variety of bulk dielectric samples with dielectric constants between
2.5 and 300. As outlined in section 2.2, the experimental results are derived from measurements with the tip in contact
with and raised 1 micron above the sample. The measured data are compared to theoretical values obtained from
modeling. The model included the following steps:
1.
Finite element modeling to determine the capacitance and resistance of the tip—sample interface. As described
in Section 2.2 the model is run both for the tip in contact and raised above the sample.
2.
Microwave circuit modeling of the passive components interfacing the tip to the electronics.
3.
Detailed modeling of the microwave electronics module.
This first principles model predicts the output video signals for a given sample permittivity, conductivity and geometry.
There are no fitted parameters in the model. When nominal values for tip radius, microwave power and electronics gain
are used, there is a slight offset between the measured results and modeled values. In Figure 5 the modeled values (red
squares and line) were scaled by 1.4x so that the modeled value at  = 10 matches the trendline of the experimental
values (blue diamonds). The factor of 1.4 is well within the range produced by expected tip radius and microwave
power/gain variations. Once normalized in this fashion, the dielectric data matches the model quite well.
Figure 7. The calculated and measured signals for a variety of dielectric samples with ε between 2.5 and 300. The model
results were normalized to the experimental data at ε =10 to correct for tip size and micro-wave power.
The systematic trend seen in Figure 7 is the first step towards a quantitative metrology technique. Measurements also
need to be repeatable. The measurement stability was demonstrated by selecting three locations on a bulk dielectric
(strontium titanate) and collecting data from each location in sequence. The locations were separated by approximately
15 um so the tip disengaged and moved ~15 um between each measurement. These measurements by design include
many sources of variability: variation in the local permittivity (presumably quite low for the single crystal sample),
variation in surface finish and/or contamination, variation due to tip motion and variation in tip/sample contact. The
combined effect of all of these sources of variation was less than 3%, as shown in Figure 8.
Figure 8. Eleven measurements taken by cycling through 3 locations (e.g. 1 2 3 1 2 3 1 2 3 1 2) on a strontium titanate
sample ( = 300). Data include variation due to: time, stage and tip movement, and variation of sample properties (3
locations).
The sMIM signal for strontium titanate is higher in Figure 8 than in Figure 7. As mentioned previously, the difference in
un-normalized measurements is expected as the data were collected on different days with different probes. By
normalizing these kinds of measurements to a measurement from a standard, such as bulk SiO 2 or Al2O3, the probe-toprobe variability can be canceled.
4.2 Proximity Modulation on Thin Films
In this section we investigate measurement of the permittivity and thickness of low-k thin films, using a series of SiO2
thin films as calibration standards. The electric field distribution in thin film samples impacts our measurements so the
method outlined in section 4.1 is not sufficient. Instead simulations are used to account for changes in the field
distributions. In this example we used COMSOL multiphysics FEM software to simulate the tip sample admittance as a
function of film thickness and permittivity. Microwave circuit analysis indicates that the sMIM signal is proportional to
the tip-sample admittance. Figure 9a plots the measured sMIM-C versus the imaginary part of the COMSOL calculated
tip-sample admittance for the three SiO2 calibration films of different thicknesses. The linear relationship seen in Figure
9a confirms this relationship between tip-sample admittance and the proximity modulation sMIM signal. As a result, the
curve in figure 9a can be used as a calibration for quantifying properties of an unknown film. Here we give two
examples, one for an unknown dielectric constant and one for an unknown thickness.
(b)
3.6
0.8
3.4
0.7
3.2
Dielectric Constant
Measured sMIM (V)
(a) 0.9
0.6
0.5
0.4
0.3
0.2
0.5
0.6
0.7
0.8
-6
Simulated Admittance (10 S)
3.0
2.8
2.6
2.4
2.2
0.50
0.52
0.54
0.56
0.58
0.60
-6
Simulated Adimittance (10 S)
Figure 9. (a) Measured sMIM versus simulated admittance for three calibration standards (diamonds and red line). Purple
lines show conversion of sMIM from unknown sample to estimated tip-sample admittance. (b) Simulated admittance versus
dielectric constant for a 95 nm thick film. Purple lines show conversion of estimated tip-sample admittance for unknown
sample to dielectric constant.
For the first example we analyze a film of known thickness (95 nm) and unknown dielectric constant. We start with the
measured sMIM proximity modulation signal of 0.34V from the unknown sample. Using the curve in figure 9a from the
three SiO2 calibration standards we determine the unknown sample should have a simulated admittance is 0.55 × 10 -6 S.
COMSOL simulations are then used to evaluate the tip-sample admittance dependence on permittivity for 95 nm thick
films, shown in Figure 9b. From the simulations in Figure 9b we see that the simulated admittance of 0.55 × 10 -6 S is
produced from a film permittivity is 2.6. As a result, we can infer the permittivity of our unknown film is 2.6. Mercury
probe measurements of this film indicated a permittivity in the range of 2.0 to 2.5.
For the second example we analyze a sample of unknown thickness but known dielectric constant = 2.5. Similar to the
example in figure 9, the measured proximity modulation sMIM signal from the unknown sample is 0.59V and from the
SiO2 calibration standard data, the corresponding simulated admittance is 0.63 × 10 -6 S (Figure 10a). Figure 10b
contains COMSOL simulations for films of varying thickness and dielectric constant of 2.5. The simulation for 26 nm
thickness produces the simulated tip-sample admittance that matches the 0.63e-6 siemens inferred from the sMIM
measurement. Optical interferometry measurements of this sample indicate a 19 nm thickness. The sMIM derived
thickness (26 nm) is 40% larger than the interferometer value. We believe one source of the discrepancy is the
semiconducting nature of the doped Si substrate, particularly for these thinner films. Our COMSOL models assume a
metallic boundary under the low-k film. We are working to incorporate a semiconducting boundary in our models.
(a) 0.9
(b) 100
80
Film Thickness (nm)
Measured sMIM (V)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.5
0.6
0.7
0.8
60
40
20
0
0.50
0.55
0.60
0.65
0.70
0.75
-6
-6
Simulated Adimittance (10 S)
Simulated Adimittance (10 S)
Figure 10. (a) Measured sMIM versus simulated admittance. (b) Simulated admittance versus film thickness.
5. SUMMARY
The sMIM technique presented in this paper is a new mode for AFM imaging that enables imaging and measurement of
local electrical properties (ε and σ) at 10’s of nm length scales. It is compatible with conductors, dielectrics,
semiconductors and insulators and requires no special sample preparation. The technique has wide applications in
materials science and nanotechnology research and development. In this paper we described the underlying principles of
sMIM and illustrated electrical property imaging capabilities on technologically relevant materials such as graphene,
carbon nanotubes and ferroelectric optical crystals. For materials such as graphene and carbon nanotubes to fulfil their
technological promise it will be critical to understand the origins of, and ultimately control, their electrical properties.
These electrical properties are not revealed in topographic AFM images and are in fact hard to detect using other
electrical AFM modes, such as conductive AFM, yet are shown quite clearly in the sMIM images, providing valuable
information for research and process development. For materials such as the ferroelectrics, the non-invasive ability to
image high resolution features such as the grain boundaries opens the way to more directly investigate the local
behavior.
Additionally we presented current research on quantitative metrology and provided examples of a proximity modulation
method to measure both bulk and thin-film dielectrics. Both cases utilized a simple calibration procedure relying on 1 to
3 calibration standards to correct for variation in system parameters. For the bulk dielectric experiment, detailed
modeling was used to validate the quantification protocol. For the thin-film experiment a finite element model of the tip
sample interaction was used to account for the electric field variations created by the thin film geometry. Results were
compared to independent metrology results. A contribution from the semiconducting substrate of the thin films needs to
be investigated further.
ACKNOWLEDGEMENTS
Some of this material is based upon work supported by the Department of Energy under Award Number DESC0009586. The authors would like to thank Prof. Mike Kelly for many helpful discussions.
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