Spreading Resistance Profiler (SRP)

1. Theory

• Definition: A spreading resistance profiler steps two closely spaced probes down a shallow bevel ground through the doped layers and measures the resistance between them at each point, giving resistivity and carrier density against depth (Solecon; Measurlabs).
• Spreading resistance: Current from a small contact spreads into the sample, so the resistance is proportional to the local resistivity, $\rho /2a$ for two disk contacts (Dickey and Ehrstein).
• Calibration: Because the effective contact radius and barrier are not known, resistance is converted to resistivity with a calibration curve from standards (Semilab; Solecon).
• Active carriers: The method measures electrically active dopants, unlike SIMS, which measures atoms (Solecon).

2. Working Principle

• Bevel: The sample is lapped at 0.5 to 5 degrees, magnifying depth by up to about a hundred times (Measurlabs; computed).
• Probing: Two tungsten carbide probes, conditioned to carry many microcontacts, are stepped along the bevel under controlled load (Measurlabs; Semilab).
• Small voltage: About 5 $\mathrm{mV}$ is applied, below the thermal voltage, so the contact behaves linearly (Solecon; linearity my reading).
• Correction and conversion: Multilayer corrections and mobility tables turn the readings into carrier density (Dickey and Ehrstein; Solecon).

3. Applications

• Epitaxial layers: Doping and thickness, where SRP is the preferred method (Solecon).
• Device profiles: p-n junction location in bipolar and CMOS structures (Measurlabs).
• Implant activation: Comparison with SIMS shows incomplete activation (Solecon).
• Deep structures: Power-device and substrate profiles deeper than 500 $\mu \mathrm{m}$ (Solecon).

Spreading Resistance

Name	Formula	Related Formulae	Variables/Constants
Spreading resistance of one contact	$R_{sp}=\frac{\rho }{4a}$	$R_{meas}=2R_{sp}+R_c\approx \frac{\rho }{2a}(\text{two probes})$	$\begin{array}{r}{R}_{sp}:spreadingresistanceunderaflat\\ circularcontactonasemi-infinitesample\end{array}$ $\rho :localresistivity$ $a:effectivecontactradius$ $R_{meas}:measuredtwo-proberesistance$ $\begin{array}{r}{R}_c:barrierandproberesistance;Dickey\\ andEhrstein:R=\rho /2afortwodisks,soone\\ contactis\rho /4a(computed);Solecon:a\\ pairofcloselyspacedprobessteppeddown\\ thebevelwithabout0.005\mathrm{V}applied\end{array}$ $\begin{array}{r}(assumed:a=2\mu \mathrm{m};computed:\rho =1\Omega \mathrm{cm}\\ gives{R}_{sp}=1250\Omega and{R}_{meas}about2500\Omega )\end{array}$
Calibration curve	$\rho =f_{cal}\left(R_{meas}\right)\text{(log-log curve from standards)}$	$R_{meas}=K\left(\rho \right)\frac{\rho }{2a}$	$\begin{array}{r}{f}_{cal}:empiricalcalibrationfrombulk\\ standardsofknownresistivity,K(\rho ):\\ correctionforbarrierandmicrocontact\\ effects;Semilab:resistanceconvertedto\\ resistivitywithacalibrationcurve,\\ probescoveredwithmicrocontactsand\\ conditionedwithaGorey-Schneider\\ grinder,calibrationonlywhenneeded;\\ Solecon:calibrationstandards;Kform(my\\ reading);DickeyandEhrstein:errorsfrom\\ barrierresistance,probecalibrationand\\ probestability\end{array}$ $(computed:at5\mathrm{mV},2500\Omega draws2\mu \mathrm{A})$
Measurement current and range	$I=\frac{V}{R_{meas}},V\approx 5\mathrm{mV}<\frac{k_{B}T}{q}$	${\rho }_{max}\approx 2a{R}_{max}=2a\frac{V}{I_{min}}$	$I:probecurrent$ $\begin{array}{r}V:appliedvoltage,k_{B}T/q:thermalvoltage\\ (25.9\mathrm{mV}at300\mathrm{K})\end{array}$ $\begin{array}{r}{I}_{min}:smallestmeasurablecurrent;Solecon:\\ 0.005\mathrm{V},about8decadesofresistivity\\ andconcentration,lessreliableabove\\ 1000andespecially5000\Omega \mathrm{cm};Semilab:\\ nopracticallimitsoncarrierdensity\\ range,conductivitytype,orientationor\\ depth,andaniPCIVoptionforveryhigh\\ resistancewithcurrentsbelow1\times 10^{-11}\mathrm{A};\\ voltagebelowthethermalvoltagetokeep\\ thebarrierlinear(myreading)\end{array}$ $\begin{array}{r}(computed:1000\Omega \mathrm{cm}draws2\mathrm{nA}and5000\\ \Omega \mathrm{cm}0.4\mathrm{nA};1\times 10^{-11}\mathrm{A}reaches500\mathrm{M\Omega },\\ about2\times 10^5\Omega \mathrm{cm})\end{array}$

Bevel and Corrections

Name	Formula	Related Formulae	Variables/Constants
Bevel depth scale	$z=x\tan \theta$	$M=\frac{1}{\tan \theta }$	$z:depthbelowtheoriginalsurface$ $x:distancealongthebevelfromitsedge$ $\theta :bevelangle$ $\begin{array}{r}M:depthmagnification;Measurlabs:bevel\\ anglesof0.5to5degrees,twotungsten\\ carbideprobes,minimumdepthresolution6\\ \mathrm{nm},sampleatleastabout100by400\mu \mathrm{m};\\ Semilab:anglechosenbystructure,layer\\ thicknessandresolution,laser\\ bevel-anglemeasurement(BAM)andin-situ\\ BAM;relation(computedfromthebevel\\ geometry)\end{array}$ $\begin{array}{r}(computed:M=115at0.5degreesand11.4\\ at5degrees;6\mathrm{nm}ofdepthis0.69\mu \mathrm{m}\\ alonga0.5degreebevel;a5\mu \mathrm{m}stepis44\\ \mathrm{nm}ofdepth)\end{array}$
Multilayer correction	${\rho }_{true}=\frac{{\rho }_{app}}{CF\left(\frac{t}{a},\rho \left(z\right)\right)}$	$CF\to 1(t\gg a),CF<1(\text{conducting below}),CF>1(\text{insulating below})$	${\rho }_{app}:resistivityfromthecalibrationcurve$ $\begin{array}{r}CF:correctionfactorforcurrent\\ confinementbyunderlyinglayers\end{array}$ $\begin{array}{r}t:remaininglayerthicknessbelowthe\\ probes;DickeyandEhrstein:theSchumann\\ andGardnercorrectionisthemost\\ generallyapplicable,andtheirownscheme\\ usesdifferencesbetweensuccessive\\ measurements;hereCFisdefinedsothata\\ conductinglayerbelowlowersthereading\\ andaninsulatingjunctionorlayerraises\\ it\end{array}$ $\begin{array}{r}(assumed:a=2\mu \mathrm{m};computed:corrections\\ becomeimportantoncethelayerleftbelow\\ theprobesisafewcontactradii,about5\\ to10\mu \mathrm{m},orless)\end{array}$

Conversion and Comparison

Name	Formula	Related Formulae	Variables/Constants
Resistivity to carrier density	$N=\frac{1}{q\rho \mu \left(N\right)}(\text{iterated})$	$\rho =\frac{1}{q\left(n{\mu }_n+p{\mu }_p\right)}$	$\begin{array}{r}N:netcarrierdensity,\mu (N):bulk\\ mobilityatthatdensity;Solecon:SRP\\ convertsresistivitytocarrierdensity\\ usingbulkmobilities,socarrierdensity\\ inpolysiliconisoftenunder-reported,\\ carrierandatomicdensitiesmatchexcept\\ atjunctions,surfacesandincompletely\\ activatedimplants,resultsverifiable\\ withthefour-pointprobe;mobilityfrom\\ theTCADMobilityModelspage\end{array}$ $\begin{array}{r}(assumed:{\mu }_n=1350\mathrm{c}{\mathrm{m}}^2/(\mathrm{V}\mathrm{s})near1\times 10^{15}\\ \mathrm{c}{\mathrm{m}}^{-3};computed:4.6\Omega \mathrm{cm}correspondsto\\ 1\times 10^{15}\mathrm{c}{\mathrm{m}}^{-3}electrons;apolylayerwithhalf\\ thebulkmobilityreadshalfitstrue\\ density)\end{array}$
SRP against SIMS	$\text{SRP: active carriers, about 8 decades};\text{SIMS: atoms, about 3 to 4 decades}$	$N_{active}\le N_{chemical}$	$N_{active}:electricallyactivedopantdensity$ $\begin{array}{r}{N}_{chemical}:totalatomicdensity;Solecon:SRP\\ suitssiliconandgermanium,needsno\\ ultra-highvacuum,givesonlyconductivity\\ typeratherthanspecies,sensesactive\\ speciesalmostexclusively,preferredfor\\ epitaxiallayersanddeepprofilesbeyond\\ 500\mu \mathrm{m},whileSIMSisbetterfor\\ ultra-shallowprofiles\end{array}$ $\begin{array}{r}(computed:8decadescorresponds,for\\ example,to1\times 10^{-3}to1\times 10^5\Omega \mathrm{cm})\end{array}$

Important Questions

Ques: How does spreading resistance profiling work?

By measuring the resistance between two probe tips at many depths on a bevel. Current from a small contact of radius a spreads into the sample, and Dickey and Ehrstein give $\rho /(2a)$ for two disk contacts, so each contributes $\rho /(4a)$ (computed). For 1 $\Omega \mathrm{cm}$ and an effective radius of 2 $\mu \mathrm{m}$, that is about 2500 $\Omega$ (assumed radius; computed). Solecon applies about 5 $\mathrm{mV}$, below the 25.9 $\mathrm{mV}$ thermal voltage, which should keep the metal-semiconductor contact linear (my reading). Stepping the probes down a polished bevel turns position along the surface into depth, giving resistivity against depth, which a calibration curve and mobility tables convert to carrier density (Solecon; Semilab). Reference: D. H. Dickey and J. R. Ehrstein, NBS Special Publication 400-48, 1979: two-disk relation R = 2V/I = rho/2a, calibration curve from bulk silicon specimens of known resistivity with the proper crystallographic orientation, Schumann and Gardner correction most generally applicable, Dickey-Ehrstein scheme using differences between successive measurements, errors from barrier resistance, probe calibration and probe stability (fetch-tool summary); Solecon Laboratories, ‘SRP and SIMS’ comparison page (fetch-tool summary); Semilab, ‘Spreading Resistance Profiling’ product category page (fetch-tool summary).

Ques: Why is the sample bevelled, and what depth resolution results?

To stretch the depth scale beyond the probe size. A bevel at angle $\theta$ maps a distance x along the surface to depth $x\tan \theta$, magnifying depth by $1/\tan \theta$: 115 times at 0.5 degrees and 11.4 at 5 degrees, the range Measurlabs uses (computed). With 5 $\mu \mathrm{m}$ steps on a 0.5 degree bevel, each step is 44 $\mathrm{nm}$ of depth, and Measurlabs quotes a minimum depth resolution of 6 $\mathrm{nm}$, corresponding to 0.69 $\mu \mathrm{m}$ along the bevel (computed). Semilab notes that the angle depends on the structure, layer thickness and wanted resolution, and measures it with a laser sensor or in situ, because depth accuracy is only as good as the angle. Shallow angles need very flat polishing and a defined bevel edge. Reference: Measurlabs, ‘Spreading resistance profiling (SRP) measurement’ service page (fetch-tool summary); Semilab, ‘Spreading Resistance Profiling’ product category page (fetch-tool summary).

Ques: Why is a calibration curve used rather than the spreading resistance formula?

Because the real contact is not a flat disc of known radius. A probe touches through many microcontacts, and Semilab conditions its probes with a Gorey-Schneider grinder to keep that surface reproducible; Dickey and Ehrstein list barrier resistance, probe calibration and probe stability among the error sources. The formula $\rho /(2a)$ therefore gives the trend but not the number. Instead, bulk standards of known resistivity, usually measured by the four-point probe, are probed with the same tips to build a log-log curve of resistance against resistivity, recalibrated only when needed (Semilab; Solecon). Dickey and Ehrstein require standards of the proper crystallographic orientation. Results can be cross-checked against four-point-probe sheet resistance (Solecon). Reference: Semilab, ‘Spreading Resistance Profiling’ product category page (fetch-tool summary); D. H. Dickey and J. R. Ehrstein, NBS Special Publication 400-48, 1979: two-disk relation R = 2V/I = rho/2a, calibration curve from bulk silicon specimens of known resistivity with the proper crystallographic orientation, Schumann and Gardner correction most generally applicable, Dickey-Ehrstein scheme using differences between successive measurements, errors from barrier resistance, probe calibration and probe stability (fetch-tool summary); Solecon Laboratories, ‘SRP and SIMS’ comparison page (fetch-tool summary).

Ques: Why do thin layers and shallow profiles need corrections?

Because the current spreads into a volume a few contact radii deep, so what lies below influences the reading. On a thick uniform layer the calibration applies directly, but when the layer left under the probes is only a few radii thick, about 5 to 10 $\mu \mathrm{m}$ for a 2 $\mu \mathrm{m}$ radius (computed), a conducting layer underneath lowers the resistance and an insulating junction or substrate raises it. Dickey and Ehrstein call the Schumann and Gardner correction the most generally applicable, and their own scheme derives correction factors from differences between successive measurements on the profile. For very shallow implants, carriers also diffuse from high- to low-doped regions on the bevel surface, called carrier spilling, which distorts junction positions; Solecon notes SIMS is better for ultra-shallow profiles. Reference: D. H. Dickey and J. R. Ehrstein, NBS Special Publication 400-48, 1979: two-disk relation R = 2V/I = rho/2a, calibration curve from bulk silicon specimens of known resistivity with the proper crystallographic orientation, Schumann and Gardner correction most generally applicable, Dickey-Ehrstein scheme using differences between successive measurements, errors from barrier resistance, probe calibration and probe stability (fetch-tool summary); Solecon Laboratories, ‘SRP and SIMS’ comparison page (fetch-tool summary).

Ques: How does SRP compare with SIMS?

They measure different things and complement each other. SRP senses electrically active dopants almost exclusively and gives only the conductivity type, while SIMS sputters the sample in high vacuum and counts atoms, identifying the species but not whether they are active (Solecon). Solecon gives SRP about 8 decades of resistivity and concentration, for example $1\times 10^{-3}$ to $1\times 10^5$ $\Omega \mathrm{cm}$ (computed), against about 3 decades for SIMS, perhaps 4 in recent work. SRP needs no ultra-high vacuum, is usually cheaper, suits silicon and germanium, is preferred for epitaxial layers and profiles deeper than 500 $\mu \mathrm{m}$, and can be verified with four-point probes. SIMS works on nearly any solid and is better for ultra-shallow profiles. Their difference shows incomplete activation. Reference: Solecon Laboratories, ‘SRP and SIMS’ comparison page (fetch-tool summary).

Ques: Can SRP measure very high resistivities?

Sources differ. Solecon says SRP becomes less reliable above 1000 $\Omega \mathrm{cm}$, especially above 5000 $\Omega \mathrm{cm}$, although it is usually still the best option, while Semilab says it has no practical limits on carrier density range and offers an iPCIV option for very high resistance with currents below $1\times 10^{-11}$ $\mathrm{A}$. At 5 $\mathrm{mV}$ with an assumed 2 $\mu \mathrm{m}$ radius, 1000 $\Omega \mathrm{cm}$ draws only 2 $\mathrm{nA}$ and 5000 $\Omega \mathrm{cm}$ 0.4 $\mathrm{nA}$, while $1\times 10^{-11}$ $\mathrm{A}$ reaches about $2\times 10^5$ $\Omega \mathrm{cm}$ (computed). Both are probably right in their own terms: low-current electronics extend the measurable range, but surface leakage, contact noise and calibration standards become poor at high resistivity, so Solecon’s caution about accuracy is more likely to hold in practice (my reading). Reference: Solecon Laboratories, ‘SRP and SIMS’ comparison page (fetch-tool summary); Semilab, ‘Spreading Resistance Profiling’ product category page (fetch-tool summary).

Ques: Why can SRP under-report carrier density?

Because it converts resistivity to density with bulk mobilities. SRP measures resistivity, and $N=1/[q\rho \mu (N)]$ needs the mobility, which it takes from bulk silicon tables (Solecon); 4.6 $\Omega \mathrm{cm}$ corresponds to $1\times 10^{15}$ $\mathrm{c}{\mathrm{m}}^{-3}$ electrons with a mobility of 1350 $\mathrm{c}{\mathrm{m}}^2/(\mathrm{V}\mathrm{s})$ (assumed mobility; computed). Where the real mobility is lower, as in polysilicon, heavily damaged implants or strained layers, the same resistivity implies more carriers than the bulk table assumes, so the density is under-reported: a poly layer with half the bulk mobility reads half its true density (computed). Solecon also notes that carrier and atomic densities differ near junctions and surfaces and in incompletely activated implants. Mobility models are on the TCAD Mobility Models page. Reference: Solecon Laboratories, ‘SRP and SIMS’ comparison page (fetch-tool summary); TCAD Mobility Models page of this vault.

References

1. Solecon Laboratories, “SRP & SIMS” comparison page. Available: https://solecon.com/sra/srp-sims.html
2. Semilab, “Spreading Resistance Profiling,” product category page. Available: https://semilab.com/category/products/spreading-resistance-profiling
3. D. H. Dickey and J. R. Ehrstein, Semiconductor Measurement Technology: Spreading Resistance Analysis for Silicon Layers with Nonuniform Resistivity, NBS Special Publication 400-48, 1979. Available: https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nbsspecialpublication400-48.pdf
4. Measurlabs, “Spreading resistance profiling (SRP) measurement,” service page. Available: https://measurlabs.com/products/spreading-resistance-profiling-srp-measurement/
5. TCAD Mobility Models, page in this vault.

Related pages in this vault: Four-Point Probe, Secondary Ion Mass Spectrometer (SIMS and ToF-SIMS), Mercury Probe, Scanning Spreading Resistance Microscope (SSRM), TCAD Mobility Models, Scanning Capacitance Microscope (SCM), Corona-Kelvin Metrology, Hall Effect System, Diffused and Implanted Resistors, Beamline Ion Implanter, Diffusion Furnace.