Scanning Capacitance Microscope (SCM)

1. Theory

• Definition: A scanning capacitance microscope uses a conductive AFM tip on an oxidized semiconductor as a nanoscale MOS capacitor and measures the change of capacitance with an applied AC bias, dC/dV, at each point (Bruker; Schaadt and Yu).
• Carrier sensitivity: In depletion, dC/dV is larger for lightly doped material and changes sign between n- and p-type, giving 2-D maps of carrier type and relative concentration (Bruker; Marchiando et al.).
• Detection: A resonant UHF capacitance sensor converts attofarad capacitance changes into frequency shifts read by a lock-in amplifier (Bruker; Schaadt and Yu).
• Quantification: Converting dC/dV to concentration needs calibration standards or simulation because the response depends on tip, oxide and bias (Schaadt and Yu; Marchiando et al.).

2. Working Principle

• Sample preparation: A thin insulating layer, about 10 $\mathrm{nm}$ in Marchiando’s model, lets the tip form a MOS structure (Marchiando et al.).
• Sensor: An LC resonator near 900 $\mathrm{MHz}$ to 1 $\mathrm{GHz}$ coupled to the tip detects capacitance through frequency shifts (Bruker; Schaadt and Yu).
• Modulation: A kilohertz to 100 $\mathrm{kHz}$ AC bias modulates depletion, and the lock-in output gives dC/dV in polarity or magnitude mode (Schaadt and Yu; Bruker).
• Contact mode: Topography and dC/dV are acquired together (Bruker).

3. Applications

• 2-D dopant profiling: Junction position, diffusion and effective channel length in transistors, with 10 to 30 $\mathrm{nm}$ resolution (Duhayon et al.).
• Wide-gap materials: AlGaN/GaN heterostructures and SiC defects (Schaadt and Yu; C-AFM page).
• Junction delineation: Locating p-n junctions, though the position shifts with DC bias (Duhayon et al.).

Capacitance Detection

Name	Formula	Related Formulae	Variables/Constants
Capacitance sensor	$V_{so}=c\Delta f,\Delta f\approx {\frac{df}{dV}|}_{V_{dc}}{V}_{ac}\sin {\omega }_{ac}t$	$\frac{df}{dV}=g\left(f,C\right)\frac{f}{C}\frac{dC}{dV}\approx g_0\frac{f_d}{C}\frac{dC}{dV}$	$V_{so}:sensoroutput$ $c:conversionconstant$ $\Delta f:resonanceshift$ $f_d:drivefrequency$ $\begin{array}{r}{g}_0:frequencysensitivity(about0.5);\\ SchaadtandYu:theseequations,polarity\\ andmagnitudelock-inmodes,sensornear\\ 900\mathrm{MHz},250\mathrm{mV}ACbiasat100\mathrm{kHz};\\ Bruker:UHFsensorat880to1050\mathrm{MHz}(1\\ GHzinafigure),kilohertzACbias,Qas\\ resonancefrequencyoverhalf-maximum\\ width,sensitivityof1\times 10^{-22}Fperroot\\ hertz\end{array}$ $\begin{array}{r}(computed:1\times 10^{-22}Fperroothertzina1\\ \mathrm{kHz}bandwidthis3.2\mathrm{zF})\end{array}$
Depletion capacitance and dC/dV	$\frac{1}{C^2}=\frac{1}{C_{ox}^2}+\frac{2\left(V-V_{FB}\right)}{q{\epsilon }_{s}N{A}^2}$	$\frac{dC}{dV}=-\frac{C^3}{q{\epsilon }_{s}N{A}^2}(\text{depletion, n-type sign opposite to p-type})$	$C:tip-oxide-semiconductorcapacitance$ $C_{ox}:oxidecapacitance$ $A:effectivearea$ $N:carrierconcentration$ $\begin{array}{r}{\epsilon }_s:semiconductorpermittivity;MOS\\ depletionrelations(LCRMeterandC-V\\ page;derivativecomputed);Bruker:C-V\\ polarityinvertingforp-type,slope\\ largerforlowconcentration\end{array}$ $\begin{array}{r}(computed:atfixedC,|dC/dV|\propto 1/N,so\\ lighterdopinggiveslargersignal)\end{array}$
Contact area and accumulation capacitance	$A\approx \pi {\left(r_{tip}\sin \varphi \right)}^2$	$C_{a,fit}=a+b{r}_{tip}^2,a=10.7\mathrm{aF},b=0.0038aF/n{\mathrm{m}}^2;C_a\approx 0.022aF/n{\mathrm{m}}^2{r}_{tip}^2$	$r_{tip}:apexradius$ $\varphi :bluntnessangle$ $\begin{array}{r}{C}_a:accumulationcapacitance;Schaadtand\\ Yu:theserelations,simulatedradii30to\\ 90\mathrm{nm},sideangles15to25degrees,\\ bluntness5to40degrees,typicalapex10\\ to30\mathrm{nm},13\mathrm{nm}Al0.26Ga0.74Nat1\times 10^{18}on\\ GaNat1\times 10^{16}\mathrm{c}{\mathrm{m}}^{-3},Co/Crtip4.9\mathrm{V}andAl\\ contact4.1\mathrm{V}workfunctions(seetheQ/A)\end{array}$ $\begin{array}{r}(computed:a13\mathrm{nm}AlGaNbarrierwith{\epsilon }_r=\\ 9.5gives0.0065aF/n{\mathrm{m}}^2,times\pi gives\\ 0.020aF/n{\mathrm{m}}^2{r}^2,matchingtheexpected\\ 0.022)\end{array}$

Quantification and Resolution

Name	Formula	Related Formulae	Variables/Constants
Signal dynamic range	$\frac{{\left(dC/dV\right)}_{10^{15}}}{{\left(dC/dV\right)}_{10^{19}}}\approx 2(\text{Si, }{r}_{tip}=50\mathrm{nm})$	$N\left(x,y\right)=f_{cal}^{-1}\left[\frac{dC}{dV}\left(x,y\right)\right]$	$\begin{array}{r}{f}_{cal}:calibrationfunctionfromstaircase\\ standardsorsimulation;SchaadtandYu:\\ dC/dVpeakheightvaryingbyabouta\\ factorof2over1\times 10^{15}to1\times 10^{19}\mathrm{c}{\mathrm{m}}^{-3}\\ (OCR-garbledrange)fora50\mathrm{nm}apex,\\ calibrationsampleswithwell-defined\\ layersproposedfortip-shapeestimation;\\ Marchiandoetal.:calibrationby\\ simulatedconversioncurvesrelatingdC/dV\\ todopantdensity\end{array}$ $\begin{array}{r}(computed:afactorof2overfourdecades\\ isabout0.075decadesofsignalper\\ decadeofdoping,soa5percentsignal\\ errorisaboutafactorof2indoping)\end{array}$
Lateral resolution	$d_{SCM}\approx r_{tip}+\text{a few nm}$	$\text{larger }A\Rightarrow \text{larger signal but poorer resolution}$	$\begin{array}{r}{d}_{SCM}:lateralresolution;Bruker:absolute\\ resolutiongenerallyafewnanometres\\ greaterthanthetipradius,depending\\ alsoonoxidethickness;SchaadtandYu:\\ increasedpeakheightfromlargercontact\\ offsetbypoorerlateralresolution,\\ nanoscaletipstructureinfluencing\\ spectrastronglyandmacroscopicshape\\ muchless\end{array}$ $\begin{array}{r}(computed:a20\mathrm{nm}apexresolvesabout25\\ \mathrm{nm};a60\mathrm{nm}bluntedapexabout65\mathrm{nm})\end{array}$
Oxide capacitance of the tip	$C_{ox}=\frac{{\epsilon }_{ox}\pi r^2}{t_{ox}}$	$t_{ox}\approx 10\mathrm{nm},r\approx 10\mathrm{nm}(\text{model values})$	$\begin{array}{r}{C}_{ox}:oxidecapacitanceunderacontactof\\ radiusr\end{array}$ $\begin{array}{r}{t}_{ox}:oxidethickness;parallel-plate\\ estimate(computed);Marchiandoetal.:\\ about10\mathrm{nm}oxideand10\mathrm{nm}tipradiusin\\ theirmodel;Bruker:resolutiondependent\\ onoxidethickness\end{array}$ $\begin{array}{r}(assumed:r=20\mathrm{nm},t_{ox}=2\mathrm{nm};computed:\\ C_{ox}=21.7\mathrm{aF},soanassumed1\times 10^{-3}\\ modulationis22\mathrm{zF},aboutseventimesthe\\ 3.2\mathrm{zF}noisein1\mathrm{kHz})\end{array}$

Operating Modes

Name	Formula	Related Formulae	Variables/Constants
Bias selection	$V_{ac}\approx 0.25\text{to}2\mathrm{V},f_{ac}\approx 10\text{to}100\mathrm{kHz}$	$V_{dc}\text{set near flat band for maximum dC/dV}$	$V_{ac},f_{ac}:ACmodulationamplitudeandfrequency$ $\begin{array}{r}{V}_{dc}:DCbias;SchaadtandYu:250\mathrm{mV}at100\\ \mathrm{kHz};Fiorenzaetal.ontheC-AFMpage:2\\ VACat100\mathrm{kHz}onSiC;Marchiandoetal.:\\ 0.1to5Vat1to10\mathrm{kHz},surfaceheld\\ nearflatbandwiththebiassetfromthe\\ dC/dVpeakinalightlydopedregion\end{array}$ $\begin{array}{r}(computed:Fiorenz{a}^{\prime }s2Viseighttimes\\ Schaad{t}^{\prime }s250\mathrm{mV}amplitude)\end{array}$
Polarity and magnitude modes	$\text{phase}=0\text{or}180^{\circ }\Rightarrow \text{carrier type}$	$\left|V_{so}\right|\approx \frac{1}{2}\left|c{g}_0{f}_d\frac{1}{C}\frac{dC}{dV}{V}_{ac}\right|$	$\begin{array}{r}SchaadtandYu:polarity(signed)and\\ magnitudemodesandthemagnitude\\ expression;Fiorenzaetal.(C-AFMpage):\\ phasechangingfrom180to-180degrees\\ acrossantiphaseboundariesin3C-SiC;\\ Duhayonetal.:junctiondelineation,with\\ thejunctionshiftingabout30\mathrm{nm}pervolt\\ ofDCbias\end{array}$ $\begin{array}{r}(computed:thesignalscaleslinearlywith\\ V_{ac}untilthemodulationspansthewhole\\ depletionrange)\end{array}$

Important Questions

Ques: How does SCM detect capacitance changes of attofarads?

With a resonant UHF sensor and lock-in detection. The tip, oxide and semiconductor form a tiny capacitor coupled to an LC resonator near 900 $\mathrm{MHz}$ to 1 $\mathrm{GHz}$; a capacitance change shifts the resonance, and the sensor output is proportional to the shift (Schaadt and Yu; Bruker). An AC bias, for example 250 $\mathrm{mV}$ at 100 $\mathrm{kHz}$, modulates the depletion width, so the lock-in output at that frequency is proportional to dC/dV. Bruker gives a sensitivity of $1\times 10^{-22}$ F per root hertz, 3.2 $\mathrm{zF}$ in a 1 $\mathrm{kHz}$ bandwidth (computed). A 20 $\mathrm{nm}$ contact on 2 $\mathrm{nm}$ oxide has about 21.7 $\mathrm{aF}$ of oxide capacitance, so a modulation of one part in a thousand is about 22 $\mathrm{zF}$, seven times the noise (assumed values; computed). Reference: D. M. Schaadt and E. T. Yu, ‘Scanning capacitance spectroscopy of an AlxGa1-xN/GaN heterostructure field-effect transistor structure: Analysis of probe tip effects’, J. Vac. Sci. Technol. B 20, 1671 (2002) (fetch-tool summary); Bruker, ‘SCM Principles of Operation’, Dimension Icon help pages hosted by KTH Nanolab (fetch-tool summary).

Ques: Why does dC/dV reveal carrier type and concentration?

Because depletion under the tip depends on doping. In depletion, $1/C^2$ rises linearly with bias at a rate inversely proportional to the doping, so $dC/dV=-C^3/(q{\epsilon }_{s}N{A}^2)$ and, at fixed capacitance, its magnitude scales as $1/N$ (LCR Meter and C-V page; computed). Lightly doped regions therefore give larger signals, as Bruker notes, and the C-V curve inverts for p-type, so the signed signal has opposite polarity for n and p regions. Where the sign changes, a p-n junction lies, which is how SCM delineates junctions in transistors (Duhayon et al.). In polarity mode the lock-in phase gives the sign; in magnitude mode only the size (Schaadt and Yu). Reference: Bruker, ‘SCM Principles of Operation’, Dimension Icon help pages hosted by KTH Nanolab (fetch-tool summary); D. M. Schaadt and E. T. Yu, ‘Scanning capacitance spectroscopy of an AlxGa1-xN/GaN heterostructure field-effect transistor structure: Analysis of probe tip effects’, J. Vac. Sci. Technol. B 20, 1671 (2002) (fetch-tool summary); N. Duhayon, D. Alvarez, P. Eyben, M. Fouchier, M. Xu, T. Clarysse, W. Vandervorst and L. Hellemans, ‘Two dimensional carrier profiling using scanning capacitance microscopy’, ECS meeting abstract 0743 (IMEC): 10 to 30 nm resolution set by tip size and oxide thickness, 2-D profiling of Si devices and III-V lasers, effective channel length of a 0.15 um NMOS, junction position and diffusion, junction delineation, junction shift of about 30 nm/V with DC bias on a 0.5 um transistor (fetch-tool summary).

Ques: Does the measured accumulation capacitance match the tip area?

No, by a factor of about six. Schaadt and Yu fitted the simulated accumulation capacitance as $10.7+0.0038r_{tip}^2$ $\mathrm{aF}$ with radius in nanometres, while expecting about $0.022r_{tip}^2$ $\mathrm{aF}$ from the barrier capacitance of their structure; the expected value checks out, since a 13 $\mathrm{nm}$ AlGaN barrier with permittivity 9.5 gives 0.0065 $aF/n{\mathrm{m}}^2$ and times $\pi$ gives 0.020 (computed). The fitted coefficient is 5.8 times smaller, equivalent to an effective contact radius about 2.4 times smaller than the apex radius (computed), consistent with their contact area $\pi (r_{tip}\sin \varphi {)}^2$ for bluntness angles below about 25 degrees (my reading). The fit with its offset term is the more reliable description of real tips, and the parallel-plate estimate an upper bound. Reference: D. M. Schaadt and E. T. Yu, ‘Scanning capacitance spectroscopy of an AlxGa1-xN/GaN heterostructure field-effect transistor structure: Analysis of probe tip effects’, J. Vac. Sci. Technol. B 20, 1671 (2002) (fetch-tool summary).

Ques: Why is SCM hard to quantify?

Because the signal changes weakly and non-uniquely with doping. Schaadt and Yu found the dC/dV peak varies by only about a factor of 2 over $1\times 10^{15}$ to $1\times 10^{19}$ $\mathrm{c}{\mathrm{m}}^{-3}$ in silicon for a 50 $\mathrm{nm}$ apex, so a 5 per cent signal error corresponds to roughly a factor of 2 in doping (computed). The response also depends on tip radius and shape, oxide thickness and quality, and DC bias; Marchiando et al. add that the dC/dV peak shifts to higher bias as doping rises and convert signals through simulated calibration curves. Quantitative profiles therefore use calibration staircases measured with the same tip and oxide, or simulations of the tip-sample system, and are cross-checked against SIMS or SRP. Schaadt and Yu recommend well-characterized calibration samples for tip estimation. Reference: D. M. Schaadt and E. T. Yu, ‘Scanning capacitance spectroscopy of an AlxGa1-xN/GaN heterostructure field-effect transistor structure: Analysis of probe tip effects’, J. Vac. Sci. Technol. B 20, 1671 (2002) (fetch-tool summary); J. F. Marchiando, J. R. Lowney and J. J. Kopanski, ‘Models for interpreting scanning capacitance microscope measurements’, Scanning Microscopy 12, 205 (1998), NIST: thin (about 10 nm) insulating layer and 10 nm tip radius modelled, low-frequency modulation 1 to 10 kHz with 0.1 to 5 V depending on oxide and doping, 915 MHz sensing, dC/dV peak in depletion shifting to higher bias with doping, surface held near flat band with the bias set from the dC/dV peak in a lightly doped region, calibration by simulated conversion curves, 2-D and 3-D dopant profiling (fetch-tool summary).

Ques: What lateral resolution can SCM achieve?

About the tip radius plus a few nanometres. Bruker states that absolute resolution is generally a few nanometres greater than the tip radius and depends on oxide thickness. Schaadt and Yu describe typical apex radii of 10 to 30 $\mathrm{nm}$ and simulated tips up to 90 $\mathrm{nm}$ with bluntness that reduces the effective apex to about 60 $\mathrm{nm}$; a sharp 20 $\mathrm{nm}$ apex resolves about 25 $\mathrm{nm}$, a blunted 60 $\mathrm{nm}$ apex about 65 $\mathrm{nm}$ (computed estimate). They note the trade-off directly: a larger contact area raises the peak signal but lowers lateral resolution, and nanoscale tip structure matters much more than the macroscopic shape. Since contact-mode scanning wears tips, resolution degrades over a session, so wear should be monitored with reference samples. Reference: Bruker, ‘SCM Principles of Operation’, Dimension Icon help pages hosted by KTH Nanolab (fetch-tool summary); D. M. Schaadt and E. T. Yu, ‘Scanning capacitance spectroscopy of an AlxGa1-xN/GaN heterostructure field-effect transistor structure: Analysis of probe tip effects’, J. Vac. Sci. Technol. B 20, 1671 (2002) (fetch-tool summary).

Ques: How should the AC and DC bias be chosen?

Small enough to stay in the linear regime, with DC set where dC/dV is largest. The lock-in signal scales with AC amplitude, $|V_{so}|\approx \frac{1}{2}|c{g}_0{f}_d(dC/dV)V_{ac}/C|$ (Schaadt and Yu), so larger amplitude gives more signal; Marchiando et al. quote 0.1 to 5 V depending on oxide thickness and doping. Schaadt and Yu used 250 $\mathrm{mV}$ at 100 $\mathrm{kHz}$; Fiorenza et al., on the C-AFM page, used 2 V at 100 $\mathrm{kHz}$ on SiC, eight times larger (computed), suited to wider gaps and thicker oxides. DC bias shifts the apparent junction, about 30 $\mathrm{nm}$ per volt on a 0.5 $\mu \mathrm{m}$ transistor (Duhayon et al.), so it is set near flat band from the dC/dV peak in a lightly doped region (Marchiando et al.). Reference: D. M. Schaadt and E. T. Yu, ‘Scanning capacitance spectroscopy of an AlxGa1-xN/GaN heterostructure field-effect transistor structure: Analysis of probe tip effects’, J. Vac. Sci. Technol. B 20, 1671 (2002) (fetch-tool summary); J. F. Marchiando, J. R. Lowney and J. J. Kopanski, ‘Models for interpreting scanning capacitance microscope measurements’, Scanning Microscopy 12, 205 (1998), NIST: thin (about 10 nm) insulating layer and 10 nm tip radius modelled, low-frequency modulation 1 to 10 kHz with 0.1 to 5 V depending on oxide and doping, 915 MHz sensing, dC/dV peak in depletion shifting to higher bias with doping, surface held near flat band with the bias set from the dC/dV peak in a lightly doped region, calibration by simulated conversion curves, 2-D and 3-D dopant profiling (fetch-tool summary); N. Duhayon, D. Alvarez, P. Eyben, M. Fouchier, M. Xu, T. Clarysse, W. Vandervorst and L. Hellemans, ‘Two dimensional carrier profiling using scanning capacitance microscopy’, ECS meeting abstract 0743 (IMEC): 10 to 30 nm resolution set by tip size and oxide thickness, 2-D profiling of Si devices and III-V lasers, effective channel length of a 0.15 um NMOS, junction position and diffusion, junction delineation, junction shift of about 30 nm/V with DC bias on a 0.5 um transistor (fetch-tool summary).

Ques: What do polarity and magnitude modes show?

Polarity mode keeps the sign of dC/dV, distinguishing n- from p-type, while magnitude mode gives only its size, which is more sensitive to small changes but loses type information (Schaadt and Yu). In polarity mode the lock-in phase flips by 180 degrees between carrier types: Fiorenza et al. observed the phase changing from 180 to -180 degrees across antiphase boundaries in 3C-SiC, revealing electrically active defects (C-AFM page). The junction lies where the signed signal crosses zero, though its apparent position shifts with DC bias (Duhayon et al.). Combining both modes with topography lets features be aligned to device structures. For quantitative work, the magnitude-mode expression links the output to sensor and bias parameters (Schaadt and Yu). Reference: D. M. Schaadt and E. T. Yu, ‘Scanning capacitance spectroscopy of an AlxGa1-xN/GaN heterostructure field-effect transistor structure: Analysis of probe tip effects’, J. Vac. Sci. Technol. B 20, 1671 (2002) (fetch-tool summary); Bruker, ‘SCM Principles of Operation’, Dimension Icon help pages hosted by KTH Nanolab (fetch-tool summary).

References

1. D. M. Schaadt and E. T. Yu, “Scanning capacitance spectroscopy of an AlxGa1-xN/GaN heterostructure field-effect transistor structure: Analysis of probe tip effects,” Journal of Vacuum Science and Technology B, vol. 20, no. 4, 2002. Available: https://sites.utexas.edu/etylab/files/2016/01/jvstb_jul02.pdf
2. Bruker, “SCM Principles of Operation,” Dimension Icon help pages, hosted by KTH Nanolab. Available: https://www.nanophys.kth.se/nanolab/afm/icon/bruker-help/Content/AppModules/Operation/SCM/SCMTheory.htm
3. J. F. Marchiando, J. R. Lowney and J. J. Kopanski, “Models for interpreting scanning capacitance microscope measurements,” Scanning Microscopy, vol. 12, no. 1, pp. 205-224, 1998. Available: https://www.ecmjournal.org/smi/pdf/smi98-21.pdf
4. N. Duhayon, D. Alvarez, P. Eyben, M. Fouchier, M. Xu, T. Clarysse, W. Vandervorst and L. Hellemans, “Two dimensional carrier profiling using scanning capacitance microscopy,” Electrochemical Society meeting abstract 0743, 203rd meeting. Available: https://www.electrochem.org/dl/ma/203/pdfs/0743.pdf

Related pages in this vault: Conductive AFM (C-AFM), Scanning Spreading Resistance Microscope (SSRM), Spreading Resistance Profiler (SRP), Scanning Microwave Impedance Microscope (sMIM), LCR Meter and C-V, Atomic Force Microscope (AFM), Kelvin Probe Force Microscope (KPFM), Secondary Ion Mass Spectrometer (SIMS and ToF-SIMS).