Scanning Microwave Impedance Microscope (sMIM)

1. Theory

• Definition: A scanning microwave impedance microscope sends a low-power microwave signal, typically near 3 $\mathrm{GHz}$, to a shielded AFM tip and measures the reflected signal, which depends on the local tip-sample admittance (Bruker; EDFA).
• Two channels: The imaginary part (sMIM-C) follows capacitance and permittivity; the real part (sMIM-R) follows loss and conductivity (Bruker; EDFA).
• Near field: The tip is far smaller than the wavelength, so the interaction is quasi-static and confined to a volume set by the tip size (Zhong et al.; Lai et al.).
• Carrier profiling: Adding an AC sample bias gives dC/dV and dR/dV, like SCM but without needing sample grounding (Bruker; EDFA).

2. Working Principle

• Probe: A coaxially shielded cantilever tip of radius below 50 $\mathrm{nm}$ reduces stray capacitance (Bruker).
• Matching: An impedance-matching network or quarter-wave resonator couples the tip to a 50 $\Omega$ line (Zhong et al.; EDFA).
• Demodulation: The reflected wave is mixed down into in-phase and quadrature outputs giving sMIM-R and sMIM-C (Bruker; Lai et al.).
• Scanning: Contact or PeakForce tapping at forces below 100 $\mathrm{pN}$ maps topography and both channels together (Bruker).

3. Applications

• Dopant mapping: SRAM, IGBT and image-sensor cross-sections over $1\times 10^{14}$ to $1\times 10^{20}$ $\mathrm{c}{\mathrm{m}}^{-3}$ (Bruker; Zhong et al.).
• Failure analysis: Locating gate-oxide point defects or contamination and dopant defects invisible to electron and optical microscopy (EDFA).
• Buried and dielectric structures: Subsurface oxide under nitride, permittivity quantification (Bruker; Zhong et al.).
• Nanomaterials: Carbon nanotubes, nanoparticles and phase-change nanoribbons (Bruker; Zhong et al.).

Admittance and Response

Name	Formula	Related Formulae	Variables/Constants
Tip-sample admittance	$Y=G+j\omega C$	$\Delta S_{11}\propto \Delta Y\Rightarrow \text{sMIM-R}\propto \Delta G,\text{sMIM-C}\propto \Delta C$	$Y:tip-sampleadmittance$ $G:conductance$ $C:capacitance$ $\omega :angularfrequency$ $\begin{array}{r}{S}_{11}:reflectioncoefficient;Bruker:\\ reflected3\mathrm{GHz}signalcarries\\ permittivityandconductivity,sMIM-Cand\\ sMIM-Rchannelsrelatedtopermittivity\\ andconductivity;EDFA:sMIM-Crelative\\ capacitanceandsMIM-Rrelative\\ resistivityofthevolumeunderthetip;\\ Laietal.:admittanceY=1/Zcomputed\\ forthetip;G+j\omega Cform(myreading)\end{array}$ $\begin{array}{r}(computed:at3\mathrm{GHz}a0.075\mathrm{aF}changeis\\ anadmittanceof1.4\mathrm{nS})\end{array}$
Lumped response to sample resistance	$Y=\frac{j\omega C_c}{1+j\omega R_s{C}_c}$	$\mathrm{Re}Y\text{peaks at}\omega R_s{C}_c=1$	$C_c:tip-samplecouplingcapacitance$ $\begin{array}{r}{R}_s:effectivesampleresistance;Laiet\\ al.:lumped-elementdescriptionofthe\\ probe;thisR-Cmodelanditspeaked\\ sMIM-RresponsewithmonotonicsMIM-C(my\\ reading;peakpositioncomputed);Zhonget\\ al.:quasi-staticmodelaccuratefortip\\ capacitance,MIM-Cpeakagainst\\ permittivity\end{array}$ $\begin{array}{r}(assumed:C_c=1\mathrm{fF},a=25\mathrm{nm};computed:\\ thepeakfallsat{R}_s=53\mathrm{k\Omega },about0.53\\ \Omega \mathrm{cm}via\rho =4a{R}_s)\end{array}$
Quasi-static and penetration conditions	$r_{tip}\ll \lambda =\frac{c}{f}$	$\lambda =30\mathrm{cm}\text{at}1\mathrm{GHz}$	$\begin{array}{r}\lambda :free-spacewavelength;Laietal.:\\ quasi-staticanalysisvalidbecausethe\\ probeisfarsmallerthanthe30\mathrm{cm}\\ wavelengthat1\mathrm{GHz};Bruker:tipradius\\ below50\mathrm{nm};Zhongetal.:GHzoperation,\\ quasi-staticmodel\end{array}$ $\begin{array}{r}(computed:\lambda =10\mathrm{cm}at3\mathrm{GHz},twomillion\\ timesa50\mathrm{nm}tip)\end{array}$

Signal Chain and Sensitivity

Name	Formula	Related Formulae	Variables/Constants
Microwave delivery and power	$P\left(\mathrm{mW}\right)=10^{P_{dBm}/10}$	$L_{res}=\frac{\lambda }{4}(\text{quarter-wave resonator})$	$P:microwavepower$ $\begin{array}{r}{L}_{res}:resonatorlength;Bruker:3\mathrm{GHz},\\ default-20\mathrm{dBm}adjustablefrom-10to-40\\ \mathrm{dBm},optimumafewtotensof\mathrm{MHz}from3\\ \mathrm{GHz},coaxiallyshieldedprobebelow50\mathrm{nm}\\ radius;Zhongetal.:tipona\\ quarter-wavelinecriticallycoupledtoa\\ 50\Omega feedthroughanopen-endstub\end{array}$ $\begin{array}{r}(computed:-20\mathrm{dBm}is10\mu \mathrm{W}andtherange\\ is0.1to100\mu \mathrm{W};assumedPTFElinewith{\epsilon }_r\\ =2.1:\lambda /4=1.7\mathrm{cm})\end{array}$
Capacitance sensitivity	$\Delta C_{min}\sim 0.075\mathrm{aF}(\text{EDFA})$	$\Delta C_{min}\sim 0.7\text{to}6\mathrm{fF}(\text{early unshielded probes})$	$\begin{array}{r}\Delta C_{min}:smallestdetectablecapacitance\\ change;EDFA:0.075\mathrm{aF};Bruker:sub-aF\\ withcoaxialshielding,abouttentimes\\ traditionaltechniques;Zhongetal.:0.7\\ \mathrm{fF}forTi/AlnanowireandPtprobes,3\mathrm{fF}\\ barenanowire,6\mathrm{fF}Siprobe(seetheQ/A)\end{array}$ $\begin{array}{r}(computed:0.7\mathrm{fF}over0.075\mathrm{aF}isa\\ factorof9300)\end{array}$
Carrier profiling channels	$\frac{dC}{dV},\frac{dR}{dV}(\text{lock-in at the AC bias})$	$\text{phase of }dC/dV\Rightarrow n\text{ or }p,\text{amplitude}\Rightarrow N$	$\begin{array}{r}Bruker:ACsamplebiasgivesSCM-like\\ dC/dVplusadR/dVchannel,noelectrical\\ contacttothesubstrateneeded,dopant\\ sensitivity1\times 10^{14}to1\times 10^{20}\mathrm{c}{\mathrm{m}}^{-3}onimage\\ sensors;EDFA:phasegivescarriertype,\\ amplituderelatestodoping,nosample\\ grounding,RandCtogether;Zhongetal.:\\ SRAMandstaircaseimaging\end{array}$ $\begin{array}{r}(computed:1\times 10^{14}to1\times 10^{20}\mathrm{c}{\mathrm{m}}^{-3}issix\\ decades)\end{array}$

Resolution and Imaging Conditions

Name	Formula	Related Formulae	Variables/Constants
Lateral resolution	$d_{sMIM}<30\mathrm{nm}(\text{Bruker}),\approx 1\mathrm{nm}(\text{EDFA})$	$d_{sMIM}\text{can be below}2r_{tip}(\text{near field})$	$\begin{array}{r}{d}_{sMIM}:electricalresolution;Bruker:below\\ 30\mathrm{nm}easily,below20\mathrm{nm}inthe\\ conclusion,p-to-ntransitionbelow10\mathrm{nm}\\ onSRAM;EDFA:resolutionbelowthetip\\ diameter,about1\mathrm{nm}fromaMoirepattern\\ (seetheQ/A)\end{array}$ $\begin{array}{r}(computed:1\mathrm{nm}is50timesfinerthana\\ 50\mathrm{nm}tipradius)\end{array}$
PeakForce sMIM force	$F_{peak}<100\mathrm{pN}$	$\frac{F_{SSRM}}{F_{peak}}\sim 10^4$	$\begin{array}{r}{F}_{peak}:peaktappingforce;Bruker:1to2\mathrm{kHz}\\ tapping,cantileverresonanceabove10\\ \mathrm{kHz},peakforceroutinelybelow100\mathrm{pN}or\\ even50\mathrm{pN},contacttimetenstohundreds\\ ofmicroseconds,CNTsandnanoparticles\\ imaged;SSRMpage:about3.3\mu \mathrm{N}\end{array}$ $(computed:3.3\mu \mathrm{N}over100\mathrm{pN}is33000)$
Subsurface sensing	$C\propto {\epsilon }_{eff}\left(\text{stack under tip}\right)$	${\epsilon }_{Si{O}_2}=3.9,{\epsilon }_{S{i}_3{N}_4}=7.5$	$\begin{array}{r}{\epsilon }_{eff}:effectivepermittivityoftheprobed\\ volume;Bruker:SiO2buried133\mathrm{nm}under\\ Si3N4detectedwith0.4\mathrm{nm}roughness,\\ tungstencontactsabout125\mathrm{nm}tallinan\\ IGBT,pinninglayerabout140\mathrm{nm}thickin\\ imagesensors;Zhongetal.:buried\\ silicondonorpatternsanda10\mathrm{nm}\\ conductiveline\end{array}$ $(computed:thepermittivityratiois1.9)$

Important Questions

Ques: What does sMIM measure?

The local admittance between tip and sample at microwave frequency. Bruker describes a low-power 3 $\mathrm{GHz}$ signal sent to the tip, whose reflection carries the electrodynamic properties of the material beneath it, read as sMIM-C and sMIM-R channels related to permittivity and conductivity. The EDFA article describes sMIM-C as relative capacitance and sMIM-R as relative resistivity of the volume under the tip. Writing the tip admittance, which Lai et al. compute as $1/Z$, as $Y=G+j\omega C$ (my reading), a 0.075 $\mathrm{aF}$ capacitance change at 3 $\mathrm{GHz}$ is an admittance of only 1.4 $\mathrm{nS}$ (computed), which is why matched, shielded probes are used. The tip is two million times smaller than the 10 $\mathrm{cm}$ wavelength (computed), so the interaction is quasi-static, as Zhong et al. note. Reference: Z. Huang, B. Drevniok, P. De Wolf, S. Dixon-Warren, O. Amster, S. Friedman, B. Pittenger, C. Li and Y. Yang, ‘Nanoscale Mapping of Permittivity and Conductivity with Scanning Microwave Impedance Microscopy’, Bruker Application Note AN145 (fetch-tool summary); ‘Scanning microwave impedance microscopy’ article excerpt, Electronic Device Failure Analysis 25(1), February 2023, page 14 (fetch-tool summary; title and authors not shown); K. Lai, W. Kundhikanjana, M. Kelly and Z.-X. Shen, ‘Modeling of a cantilever-based near-field scanning microwave microscope’, arXiv:0801.2137 (Rev. Sci. Instrum. 79, 063703, 2008): admittance Y computed as 1/Z by quasi-static finite-element analysis at 1 GHz, lumped-element probe description valid since the chip is far smaller than the 30 cm wavelength, imaginary contrast scaling roughly with tip diameter, lambda/4 resonator critically coupled to 50 ohm by a tuning stub, IQ mixer with outputs 90 degrees apart giving capacitive and resistive channels, sensitivity down to the aF level, 110 dB gain at 1 kHz bandwidth, 15 mV per aF (fetch-tool summary); Z. Zhong, X. Chen, X. Quan, H. Huan, F. Nian, S. Liang and Y. Yang, ‘Developments and Recent Progresses in Microwave Impedance Microscope’, Front. Phys. 8, 593076 (2020) (fetch-tool summary).

Ques: Why does the sMIM-R signal peak at intermediate conductivity?

Because loss is largest when the sample resistance matches the coupling reactance. In a lumped model the tip couples through capacitance $C_c$ to a sample resistance $R_s$, giving $Y=j\omega C_c/(1+j\omega R_s{C}_c)$ (my reading; Lai et al. treat the probe with lumped elements). Insulators ($R_s$ large) give little loss; metals ($R_s$ small) short the capacitor and give large but lossless capacitance. The real part peaks at $\omega R_s{C}_c=1$, while sMIM-C rises monotonically with conductivity. For an assumed 1 $\mathrm{fF}$ and 3 $\mathrm{GHz}$, the peak falls at 53 $\mathrm{k\Omega }$, about 0.53 $\Omega \mathrm{cm}$ for a 25 $\mathrm{nm}$ contact (computed estimate). The two channels together therefore resolve the ambiguity of a single peaked curve (my reading). Reference: K. Lai, W. Kundhikanjana, M. Kelly and Z.-X. Shen, ‘Modeling of a cantilever-based near-field scanning microwave microscope’, arXiv:0801.2137 (Rev. Sci. Instrum. 79, 063703, 2008): admittance Y computed as 1/Z by quasi-static finite-element analysis at 1 GHz, lumped-element probe description valid since the chip is far smaller than the 30 cm wavelength, imaginary contrast scaling roughly with tip diameter, lambda/4 resonator critically coupled to 50 ohm by a tuning stub, IQ mixer with outputs 90 degrees apart giving capacitive and resistive channels, sensitivity down to the aF level, 110 dB gain at 1 kHz bandwidth, 15 mV per aF (fetch-tool summary).

Ques: How sensitive is sMIM to capacitance: 0.075 aF or 0.7 fF?

The values come from different probes and eras. The EDFA article reports a measured capacitance sensitivity of 0.075 $\mathrm{aF}$, and Bruker states sub-aF sensitivity with coaxially shielded probes, about ten times better than traditional techniques. Zhong et al. review earlier MIM probes with minimum sensitivities of 0.7 $\mathrm{fF}$ for Ti/Al-coated nanowire and Pt probes, 3 $\mathrm{fF}$ for a bare nanowire and 6 $\mathrm{fF}$ for a silicon probe, about 9300 times worse than 0.075 $\mathrm{aF}$ (computed). For current shielded commercial probes, the sub-aF figures are more likely, while the femtofarad values describe unshielded or prototype tips where stray capacitance dominates (my reading). Lai et al. quote aF-level sensitivity, 15 $\mathrm{mV}$ per aF, at a 1 $\mathrm{kHz}$ bandwidth, so values should be compared at the same bandwidth. Reference: ‘Scanning microwave impedance microscopy’ article excerpt, Electronic Device Failure Analysis 25(1), February 2023, page 14 (fetch-tool summary; title and authors not shown); Z. Huang, B. Drevniok, P. De Wolf, S. Dixon-Warren, O. Amster, S. Friedman, B. Pittenger, C. Li and Y. Yang, ‘Nanoscale Mapping of Permittivity and Conductivity with Scanning Microwave Impedance Microscopy’, Bruker Application Note AN145 (fetch-tool summary); Z. Zhong, X. Chen, X. Quan, H. Huan, F. Nian, S. Liang and Y. Yang, ‘Developments and Recent Progresses in Microwave Impedance Microscope’, Front. Phys. 8, 593076 (2020) (fetch-tool summary); K. Lai, W. Kundhikanjana, M. Kelly and Z.-X. Shen, ‘Modeling of a cantilever-based near-field scanning microwave microscope’, arXiv:0801.2137 (Rev. Sci. Instrum. 79, 063703, 2008): admittance Y computed as 1/Z by quasi-static finite-element analysis at 1 GHz, lumped-element probe description valid since the chip is far smaller than the 30 cm wavelength, imaginary contrast scaling roughly with tip diameter, lambda/4 resonator critically coupled to 50 ohm by a tuning stub, IQ mixer with outputs 90 degrees apart giving capacitive and resistive channels, sensitivity down to the aF level, 110 dB gain at 1 kHz bandwidth, 15 mV per aF (fetch-tool summary).

Ques: What lateral resolution does sMIM achieve?

Sources range from about 30 $\mathrm{nm}$ to about 1 $\mathrm{nm}$. Bruker states that sMIM easily achieves electrical resolution below 30 $\mathrm{nm}$, below 20 $\mathrm{nm}$ in its conclusion, and resolved a p-to-n transition narrower than 10 $\mathrm{nm}$ on an SRAM, with tips below 50 $\mathrm{nm}$ radius. The EDFA article reports resolution below the tip diameter because sMIM is a near-field measurement, and about 1 $\mathrm{nm}$ measured on a Moire pattern, 50 times finer than a 50 $\mathrm{nm}$ radius (computed). The 10 to 30 $\mathrm{nm}$ range is more likely for routine semiconductor cross-sections, while 1 $\mathrm{nm}$ applies to periodic contrast on ideal samples, where a sharp asperity carries most of the signal (my reading). Reference: Z. Huang, B. Drevniok, P. De Wolf, S. Dixon-Warren, O. Amster, S. Friedman, B. Pittenger, C. Li and Y. Yang, ‘Nanoscale Mapping of Permittivity and Conductivity with Scanning Microwave Impedance Microscopy’, Bruker Application Note AN145 (fetch-tool summary); ‘Scanning microwave impedance microscopy’ article excerpt, Electronic Device Failure Analysis 25(1), February 2023, page 14 (fetch-tool summary; title and authors not shown).

Ques: How does sMIM profile dopants, and how does it compare with SCM?

By measuring dC/dV with an AC sample bias, as SCM does, plus resistance channels. Bruker notes that with AC sample bias sMIM provides SCM-like carrier profiling and adds a dR/dV channel for nonlinear resistive behaviour, without electrical contact to the substrate. The EDFA article states that the dC/dV phase indicates carrier type and the amplitude relates to doping, and that sMIM needs no sample grounding and collects R and C together. Bruker reports dopant sensitivity from $1\times 10^{14}$ to $1\times 10^{20}$ $\mathrm{c}{\mathrm{m}}^{-3}$ on image sensors, six decades (computed), broader than the factor of 2 signal change of SCM over four decades on the SCM page. Zhong et al. cite SRAM and staircase imaging. Reference: Z. Huang, B. Drevniok, P. De Wolf, S. Dixon-Warren, O. Amster, S. Friedman, B. Pittenger, C. Li and Y. Yang, ‘Nanoscale Mapping of Permittivity and Conductivity with Scanning Microwave Impedance Microscopy’, Bruker Application Note AN145 (fetch-tool summary); ‘Scanning microwave impedance microscopy’ article excerpt, Electronic Device Failure Analysis 25(1), February 2023, page 14 (fetch-tool summary; title and authors not shown); Z. Zhong, X. Chen, X. Quan, H. Huan, F. Nian, S. Liang and Y. Yang, ‘Developments and Recent Progresses in Microwave Impedance Microscope’, Front. Phys. 8, 593076 (2020) (fetch-tool summary).

Ques: Can sMIM image soft or buried structures?

Yes, with PeakForce tapping and its subsurface sensitivity. Bruker combines sMIM with PeakForce tapping at 1 to 2 $\mathrm{kHz}$, peak forces routinely below 100 $\mathrm{pN}$ or even 50 $\mathrm{pN}$, and contact times of tens to hundreds of microseconds, imaging carbon nanotubes and nanoparticles. That force is about 33000 times below the 3.3 $\mu \mathrm{N}$ of SSRM (SSRM page; computed). Because the microwave field penetrates into the stack, Bruker detected SiO2 with permittivity 3.9 buried 133 $\mathrm{nm}$ under Si3N4 of permittivity 7.5, a ratio of 1.9 (computed), on a surface with 0.4 $\mathrm{nm}$ roughness. Zhong et al. cite imaging of buried silicon donor patterns. Zhong et al. note the strong penetration of microwaves, which lets sMIM probe internal structure. Reference: Z. Huang, B. Drevniok, P. De Wolf, S. Dixon-Warren, O. Amster, S. Friedman, B. Pittenger, C. Li and Y. Yang, ‘Nanoscale Mapping of Permittivity and Conductivity with Scanning Microwave Impedance Microscopy’, Bruker Application Note AN145 (fetch-tool summary); Z. Zhong, X. Chen, X. Quan, H. Huan, F. Nian, S. Liang and Y. Yang, ‘Developments and Recent Progresses in Microwave Impedance Microscope’, Front. Phys. 8, 593076 (2020) (fetch-tool summary).

Ques: How is microwave power delivered to the tip?

Through a matched, shielded transmission path at low power. Bruker uses a default -20 $\mathrm{dBm}$, 10 $\mu \mathrm{W}$, adjustable from -10 to -40 $\mathrm{dBm}$, 0.1 to 100 $\mu \mathrm{W}$ (computed), with the optimal frequency a few to tens of $\mathrm{MHz}$ from 3 $\mathrm{GHz}$ to match the probe. Zhong et al. describe a tip connected to a quarter-wave section of transmission line forming a resonator, critically coupled to a 50 $\Omega$ feed line through an open-end tuning stub; in an assumed PTFE line that quarter wave is about 1.7 $\mathrm{cm}$ (computed). The EDFA article describes a custom cantilever with matched impedance and shielding. Zhong et al. note that without matching the large mismatch to the 50 $\Omega$ line makes small impedance variations undetectable. Reference: Z. Huang, B. Drevniok, P. De Wolf, S. Dixon-Warren, O. Amster, S. Friedman, B. Pittenger, C. Li and Y. Yang, ‘Nanoscale Mapping of Permittivity and Conductivity with Scanning Microwave Impedance Microscopy’, Bruker Application Note AN145 (fetch-tool summary); Z. Zhong, X. Chen, X. Quan, H. Huan, F. Nian, S. Liang and Y. Yang, ‘Developments and Recent Progresses in Microwave Impedance Microscope’, Front. Phys. 8, 593076 (2020) (fetch-tool summary); ‘Scanning microwave impedance microscopy’ article excerpt, Electronic Device Failure Analysis 25(1), February 2023, page 14 (fetch-tool summary; title and authors not shown); K. Lai, W. Kundhikanjana, M. Kelly and Z.-X. Shen, ‘Modeling of a cantilever-based near-field scanning microwave microscope’, arXiv:0801.2137 (Rev. Sci. Instrum. 79, 063703, 2008): admittance Y computed as 1/Z by quasi-static finite-element analysis at 1 GHz, lumped-element probe description valid since the chip is far smaller than the 30 cm wavelength, imaginary contrast scaling roughly with tip diameter, lambda/4 resonator critically coupled to 50 ohm by a tuning stub, IQ mixer with outputs 90 degrees apart giving capacitive and resistive channels, sensitivity down to the aF level, 110 dB gain at 1 kHz bandwidth, 15 mV per aF (fetch-tool summary).

References

1. Z. Huang, B. Drevniok, P. De Wolf, S. Dixon-Warren, O. Amster, S. Friedman, B. Pittenger, C. Li and Y. Yang, “Nanoscale Mapping of Permittivity and Conductivity with Scanning Microwave Impedance Microscopy,” Bruker Application Note AN145. Available: https://bruker.com/es/products-and-solutions/microscopes/materials-afm/resource-library/an145-nanoscale-mapping-of-permittivity-and-conductivity-with-scanning-microwave-impedance-microscopy.html
2. “Scanning microwave impedance microscopy” (article excerpt), Electronic Device Failure Analysis, vol. 25, no. 1, p. 14, February 2023. Available: http://static.asminternational.org/EDFA/202302/10/
3. K. Lai, W. Kundhikanjana, M. Kelly and Z.-X. Shen, “Modeling and characterization of a cantilever-based near-field scanning microwave impedance microscope,” Review of Scientific Instruments, vol. 79, 063703, 2008; preprint arXiv:0801.2137. Available: https://www.arxiv.org/pdf/0801.2137
4. Z. Zhong, X. Chen, X. Quan, H. Huan, F. Nian, S. Liang and Y. Yang, “Developments and Recent Progresses in Microwave Impedance Microscope,” Frontiers in Physics, vol. 8, 593076, 2020. Available: https://frontiersin.org/journals/physics/articles/10.3389/fphy.2020.593076/full

Related pages in this vault: Scanning Spreading Resistance Microscope (SSRM), Atomic Force Microscope (AFM), Scanning Capacitance Microscope (SCM), Scanning Near-Field Optical Microscope (SNOM) and TERS, Kelvin Probe Force Microscope (KPFM).