Mercury Probe

1. Theory

• Definition: A mercury probe presses a small, defined area of liquid mercury against a wafer to form a temporary Schottky, MOS or MIS contact, so C-V and I-V measurements can be made without fabricating metal contacts (Polytec; SEMI MF1392).
• Schottky profiling: On bare silicon, the mercury forms a Schottky diode whose depletion capacitance against reverse bias gives the net carrier density against depth (SEMI MF1392).
• Dielectrics: On oxide or high-k films, the mercury acts as a gate, giving MOS C-V and dielectric integrity data (Polytec; Semilab).
• Area: Because doping scales with the inverse square of area, the effective contact area must be calibrated (SEMI MF1392).

2. Working Principle

• Contact formation: Mercury is pushed through a capillary against the wafer held by vacuum; it is refreshed before each contact to keep it clean (Polytec).
• Return contact: A large front-side ring or a back contact closes the circuit (Polytec).
• Measurement: External C-V and I-V meters connect through the probe; bandwidth 1 $\mathrm{MHz}$ standard, 10 $\mathrm{MHz}$ optional, and bias up to 100 $\mathrm{V}$ standard or 1000 $\mathrm{V}$ optional (Polytec).
• Surface treatment: A chemical treatment, different for n- and p-type, is often needed for a good Schottky barrier (SEMI MF1392).

3. Applications

• Epitaxial layers: Doping and thickness of silicon epitaxy on same- or opposite-type substrates (SEMI MF1392).
• Dielectrics: Oxide integrity, high-k films and ferroelectrics (Polytec; Semilab).
• SOI: Pseudo-MOSFET characterization of SOI wafers (Polytec).
• Compound semiconductors: AlGaN/GaN 2DEG sheet charge and pinch-off with a mercury gate (Semilab).

Schottky C-V Profiling

Name	Formula	Related Formulae	Variables/Constants
Schottky depletion capacitance	$C=\frac{{\epsilon }_{s}A}{W},W=\sqrt{\frac{2{\epsilon }_s\left(V_{bi}+V_R-k_{B}T/q\right)}{qN}}$	$\frac{1}{C^2}=\frac{2\left(V_{bi}+V_R-k_{B}T/q\right)}{q{\epsilon }_{s}N{A}^2}$	$\begin{array}{r}C:depletioncapacitanceunderthemercury\\ dot\end{array}$ ${\epsilon }_s:semiconductorpermittivity$ $A:contactarea$ $W:depletionwidth$ $V_{bi}:built-involtage$ $V_R:reversebias$ $\begin{array}{r}N:netdoping;SEMIMF1392:aSchottky\\ barrierdiodeformedwiththemercury\\ contact;Doolittle:C={\epsilon }_{s}A/WwithWgrowing\\ asthesquarerootof{V}_{bi}+V_R(exactform\\ garbledinextraction);the{k}_{B}T/qterm(my\\ reading)\end{array}$ $\begin{array}{r}(assumed:V_{bi}=0.7\mathrm{V};computed:W=1.48\mu \mathrm{m}\\ at1\mathrm{V}and16.1\mu \mathrm{m}at200\mathrm{V}for1\times 10^{15}\mathrm{c}{\mathrm{m}}^{-3}\\ silicon)\end{array}$
Doping profile	$N\left(W\right)=\frac{2}{q{\epsilon }_s{A}^2}{\left[\frac{d\left(1/C^2\right)}{d{V}_R}\right]}^{-1},W=\frac{{\epsilon }_{s}A}{C}$	$\frac{\Delta N}{N}=2\frac{\Delta A}{A},\frac{\Delta W}{W}=\frac{\Delta A}{A}$	$N(W):netcarrierdensityatdepthW$ $\begin{array}{r}\Delta A:areaerror;SEMIMF1392:about4\times 10^{13}\\ to8\times 10^{16}\mathrm{c}{\mathrm{m}}^{-3}(0.1to100\Omega \mathrm{cm}n-type,0.24\\ to330\Omega \mathrm{cm}p-type),profilefromthe\\ depletiondepthat1\mathrm{V}tothatat200\mathrm{V}or\\ about80percentofbreakdown,whichever\\ islower,layersthickerthanthe\\ depletiondepthat2\mathrm{V},epitaxiallayers\\ onsame-oropposite-typesubstratesand\\ bulkwafers;errorpropagation(computed)\end{array}$ $\begin{array}{r}(computed:a2percentareaerrorgivesa\\ 4percentdopingerroranda2percent\\ deptherror)\end{array}$
Resistivity check of the range	$\rho =\frac{1}{qN\mu \left(N\right)}$	$N=4\times 10^{13}\mathrm{c}{\mathrm{m}}^{-3}:{\rho }_n\approx 115,{\rho }_p\approx 325\Omega \mathrm{cm}$	$\begin{array}{r}\rho :resistivity,\mu (N):doping-dependent\\ mobility;SEMIMF1392quotesthe\\ resistivityequivalentsofitsdoping\\ range;Doolittle:R_{sh}=1/(qn\mu t),so\\ \rho =1/(qN\mu )(computed);mobilityvaluesfrom\\ theTCADMobilityModelspage\end{array}$ $\begin{array}{r}(assumed:{\mu }_n=1350and{\mu }_p=480\mathrm{c}{\mathrm{m}}^2/(\mathrm{V}\mathrm{s})\\ at4\times 10^{13}\mathrm{c}{\mathrm{m}}^{-3},{\mu }_n=800\mathrm{c}{\mathrm{m}}^2/(\mathrm{V}\mathrm{s})at8\times 10^{16}\\ \mathrm{c}{\mathrm{m}}^{-3};computed:115and325\Omega \mathrm{cm},and\\ 0.098\Omega \mathrm{cm}at8\times 10^{16}\mathrm{c}{\mathrm{m}}^{-3},consistentwith\\ SEM{I}^{\prime }srange)\end{array}$

Contact Geometry and Calibration

Name	Formula	Related Formulae	Variables/Constants
Dot and ring in series	$C_{meas}=\frac{C_{dot}{C}_{ring}}{C_{dot}+C_{ring}}\approx C_{dot}\left(1-\frac{A_{dot}}{A_{ring}}\right)$	$A_{ring}\gg A_{dot}\Rightarrow C_{meas}\to C_{dot}$	$\begin{array}{r}{C}_{dot},C_{ring}:capacitancesunderthemeasuring\\ dotandthefront-sidereturnring\end{array}$ $\begin{array}{r}{A}_{dot},A_{ring}:theirareas;Polytec:dot,\\ dot-ring,dot-two-ring,four-dotand\\ linearfour-probeconfigurations;\\ Doolittle:twoseriescapacitors,one\\ substantiallylargerthantheother;\\ area-ratioapproximationforequal\\ depletionwidths(computed)\end{array}$ $\begin{array}{r}(computed:aring20timesthedotarea\\ makesthereadingabout5percentlowif\\ uncorrected)\end{array}$
Area calibration	$A=\sqrt{\frac{2}{q{\epsilon }_s{N}_{ref}}{\left[\frac{d\left(1/C^2\right)}{d{V}_R}\right]}^{-1}}$	$A_{dot}=2\times 10^{-5}\text{to}0.5\text{or}0.8\mathrm{c}{\mathrm{m}}^2,\text{repeatability better than 2 per cent}$	$\begin{array}{r}{N}_{ref}:dopingofareferencewafer;SEMI\\ MF1392:theeffectiveareaisdetermined\\ withpolishedbulkreferencewaferswhose\\ resistivitywasmeasuredbySEMIMF84\\ (four-pointprobe)at23{}^{\circ }C;Polytec:dot\\ area2\times 10^{-5}to0.8\mathrm{c}{\mathrm{m}}^{2}inthefeaturelist\\ but2\times 10^{-5}to0.5\mathrm{c}{\mathrm{m}}^{2}intheoverview(see\\ theQ/A),arearepeatabilitybetterthan2\\ percent;formulafromtheprofile\\ relation(computedrearrangement)\end{array}$ $\begin{array}{r}(computed:2\times 10^{-5}\mathrm{c}{\mathrm{m}}^{2}isadotof50\mu \mathrm{m}\\ diameter;0.5\mathrm{c}{\mathrm{m}}^{2}is8.0\mathrm{mm})\end{array}$

Dielectric and HEMT Measurements

Name	Formula	Related Formulae	Variables/Constants
Mercury-gate MOS	$C_{ox}=\frac{{\epsilon }_{ox}A}{t_{ox}},EOT=\frac{3.9{\epsilon }_{0}A}{C_{acc}}$	$Q_{eff}=\frac{C_{ox}\left(W_{MS}-V_{FB}\right)}{A}$	$C_{ox}:oxidecapacitance$ ${\epsilon }_{ox}:dielectricpermittivity$ $t_{ox}:thickness$ $EOT:equivalentoxidethickness$ ${\epsilon }_0:vacuumpermittivity$ $\begin{array}{r}{C}_{acc}:accumulationcapacitance;Polytec:MOS\\ andMIScontacts,oxideintegrity\\ monitoring,ferroelectricsamples;\\ Semilab:dielectriccharacterizationand\\ interfaceanalysis;formulasasontheLCR\\ MeterandC-Vpage\end{array}$ $\begin{array}{r}(computed:1\mathrm{nF}undera0.01\mathrm{c}{\mathrm{m}}^{2}dotisan\\ EOTof34.5\mathrm{nm})\end{array}$
HEMT sheet charge with a mercury gate	$n_s=\frac{1}{qA}{\int }_{V_p}^{0}CdV$	$C\approx \frac{{\epsilon }_{b}A}{t_b}(\text{2DEG present}),C\to 0(V<V_p)$	$n_s:2DEGsheetdensity$ $V_p:pinch-offvoltage$ $\begin{array}{r}{\epsilon }_b,t_b:barrierpermittivityand\\ thickness;Semilab:publicationson2DEG\\ sheetcharge,pinch-offvoltageand\\ mercurygatesforAlGaN/GaN;integral\\ (computed:chargeastheintegralof\\ capacitanceovervoltage);Doolittle:\\ depletionchargeastheintegralofcharge\\ densityoverthedepletionwidth\end{array}$ $\begin{array}{r}(assumed:AlGaNwith{\epsilon }_r=9.5and{t}_b=20\\ \mathrm{nm};computed:420\mathrm{nF}persquare\\ centimetre,and1\times 10^{13}\mathrm{c}{\mathrm{m}}^{-2}needsapinch-off\\ ofabout-3.8\mathrm{V})\end{array}$

Important Questions

Ques: Why use a mercury probe instead of evaporated contacts?

Because it gives contact-based C-V and I-V data in minutes, without lithography or metal deposition. Liquid mercury pressed through a capillary forms a Schottky, MOS or MIS contact of defined area, and is refreshed before each contact so it stays clean and does not stick (Polytec). Wafers up to 8 $\mathrm{in}$ are held by vacuum at 28 $\mathrm{in}\mathrm{Hg}$, the minimum sample is 15 by 15 $\mathrm{mm}$, and the edge exclusion can be as small as 2 $\mathrm{mm}$. SEMI MF1392 notes the method may still be destructive through contamination, although repeat measurements on the same specimen are allowed, so measured wafers are usually not returned to the line (my reading). Mercury is toxic, so the systems are closed and the mercury is replaced less than twice a year (Polytec). Reference: Polytec/MDC, ‘CV92M Mercury Probe System’ brochure (fetch-tool summary); SEMI MF1392, ‘Test Method for Determining Net Carrier Density Profiles in Silicon Wafers by Capacitance-Voltage Measurements with a Mercury Probe’, SEMI store abstract (fetch-tool summary).

Ques: How deep and over what doping range can a mercury probe profile?

SEMI MF1392 covers net carrier densities of about $4\times 10^{13}$ to $8\times 10^{16}$ $\mathrm{c}{\mathrm{m}}^{-3}$, from the depletion depth at 1 $\mathrm{V}$ to that at 200 $\mathrm{V}$ or about 80 per cent of breakdown, whichever is lower, and requires layers thicker than the depletion depth at 2 $\mathrm{V}$. For $1\times 10^{15}$ $\mathrm{c}{\mathrm{m}}^{-3}$ with an assumed 0.7 $\mathrm{V}$ built-in voltage, this is 1.48 to 16.1 $\mu \mathrm{m}$ (computed). At $8\times 10^{16}$ $\mathrm{c}{\mathrm{m}}^{-3}$, depletion at 1 $\mathrm{V}$ is only 0.17 $\mu \mathrm{m}$ (computed), and junction breakdown, which Doolittle lists as a profiling limit, cuts the range further at high doping. The stated resistivity equivalents, 0.1 to 100 $\Omega \mathrm{cm}$ for n-type, agree with typical mobilities: 115 $\Omega \mathrm{cm}$ at $4\times 10^{13}$ $\mathrm{c}{\mathrm{m}}^{-3}$ and 0.098 at $8\times 10^{16}$ (computed). Reference: SEMI MF1392, ‘Test Method for Determining Net Carrier Density Profiles in Silicon Wafers by Capacitance-Voltage Measurements with a Mercury Probe’, SEMI store abstract (fetch-tool summary); W. A. Doolittle, ECE 4813 lecture ‘Doping Profiling’, Georgia Tech: C = eps A/W with W growing as sqrt(Vbi - V), doping from the slope of 1/C^2, W = eps A/C, mercury probes as liquid-metal contacts forming two series capacitors one much larger than the other, leakage lowering apparent capacitance, Q = wC/G below 5 not trusted, junction breakdown as a depth limit (fetch-tool summary, equations garbled); W. A. Doolittle, ECE 4813 lecture ‘Resistivity and Sheet Resistance’, Georgia Tech: Rsh = 1/(q n mu t) for a uniform layer (fetch-tool summary).

Ques: Why does contact area accuracy matter so much?

Because the extracted doping scales with the inverse square of the area. In $N=2/[q{\epsilon }_s{A}^{2}d(1/C^2)/dV]$, an area error of 2 per cent gives a doping error of 4 per cent and a depth error of 2 per cent (computed). A mercury contact’s area depends on surface tension, capillary condition and the wafer surface, so it is not known from the capillary diameter alone. SEMI MF1392 therefore determines the effective area with polished bulk reference wafers whose resistivity was measured by the four-point probe method of SEMI MF84 at 23 ${}^{\circ }\mathrm{C}$; rearranging the profile equation gives the area from the known doping (computed). Polytec quotes an area repeatability better than 2 per cent, so doping repeatability of about 4 per cent is the practical limit (computed). Reference: SEMI MF1392, ‘Test Method for Determining Net Carrier Density Profiles in Silicon Wafers by Capacitance-Voltage Measurements with a Mercury Probe’, SEMI store abstract (fetch-tool summary); Polytec/MDC, ‘CV92M Mercury Probe System’ brochure (fetch-tool summary).

Ques: Is the largest dot area 0.5 or 0.8 square centimetres?

The Polytec CV92M brochure gives both values. Its overview says the dot can have an area of $2\times 10^{-5}$ to 0.5 $\mathrm{c}{\mathrm{m}}^2$, while the feature list gives $2\times 10^{-5}$ to 0.8 $\mathrm{c}{\mathrm{m}}^2$. The smallest dot corresponds to about 50 $\mu \mathrm{m}$ in diameter, and 0.5 and 0.8 $\mathrm{c}{\mathrm{m}}^2$ to 8.0 and 10.1 $\mathrm{mm}$ (computed). The more likely reading is that the standard heads reach 0.5 $\mathrm{c}{\mathrm{m}}^2$ and an optional large-area head reaches 0.8 $\mathrm{c}{\mathrm{m}}^2$, since the feature list usually covers the full option range (my reading). Large dots suit lightly doped material and thick dielectrics, where capacitance per area is low; small dots suit thin, leaky dielectrics, where total capacitance and leakage current must stay manageable (my reading). The exact head should be checked with the supplier. Reference: Polytec/MDC, ‘CV92M Mercury Probe System’ brochure (fetch-tool summary).

Ques: Why does the front-side ring affect the reading?

Because the ring contact is also a capacitor, in series with the dot. With both contacts on the front, the measured capacitance is $C_{dot}{C}_{ring}/(C_{dot}+C_{ring})$; for equal depletion widths this is about $C_{dot}(1-A_{dot}/A_{ring})$, so a ring 20 times the dot area reads about 5 per cent low if uncorrected (computed; Doolittle describes the arrangement as two series capacitors, one substantially larger than the other). Large rings, forward bias on the ring, or a back contact reduce the error, and software usually corrects for the area ratio. A front ring is needed when the substrate is of opposite type or has an insulating backseal, cases SEMI MF1392 handles with separate fixtures. Polytec offers dot, dot-ring, dot-two-ring and four-dot heads for these configurations. Reference: SEMI MF1392, ‘Test Method for Determining Net Carrier Density Profiles in Silicon Wafers by Capacitance-Voltage Measurements with a Mercury Probe’, SEMI store abstract (fetch-tool summary); Polytec/MDC, ‘CV92M Mercury Probe System’ brochure (fetch-tool summary); W. A. Doolittle, ECE 4813 lecture ‘Doping Profiling’, Georgia Tech: C = eps A/W with W growing as sqrt(Vbi - V), doping from the slope of 1/C^2, W = eps A/C, mercury probes as liquid-metal contacts forming two series capacitors one much larger than the other, leakage lowering apparent capacitance, Q = wC/G below 5 not trusted, junction breakdown as a depth limit (fetch-tool summary, equations garbled).

Ques: Why is surface preparation needed for Schottky mercury C-V?

Because the barrier height and leakage depend strongly on the surface. A leaky or low barrier conducts under reverse bias, so the capacitance reading becomes dominated by conductance, as in a high-D sample on the LCR Meter and C-V page, and the profile is distorted; Doolittle warns that leakage lowers the apparent capacitance in a bias-dependent way and that readings with $Q=\omega C/G$ below 5 should not be trusted. SEMI MF1392 notes that a chemical treatment may be needed to form a reliable Schottky diode and that the chemistry differs for n- and p-type wafers; Semilab lists a study comparing surface preparation methods for mercury Schottky C-V on epitaxial silicon, including a pre-treatment chamber for p-type. Native-oxide thickness and surface charge also shift the apparent built-in voltage. The prepared state can drift with time in air, so the delay between treatment and measurement should be controlled (my reading). Reference: SEMI MF1392, ‘Test Method for Determining Net Carrier Density Profiles in Silicon Wafers by Capacitance-Voltage Measurements with a Mercury Probe’, SEMI store abstract (fetch-tool summary); Semilab, ‘MCV-530 / MCV-530L Mercury Probe System’ product page (specifications tab not read) (fetch-tool summary); W. A. Doolittle, ECE 4813 lecture ‘Doping Profiling’, Georgia Tech: C = eps A/W with W growing as sqrt(Vbi - V), doping from the slope of 1/C^2, W = eps A/C, mercury probes as liquid-metal contacts forming two series capacitors one much larger than the other, leakage lowering apparent capacitance, Q = wC/G below 5 not trusted, junction breakdown as a depth limit (fetch-tool summary, equations garbled); LCR Meter and C-V page of this vault.

Ques: What can a mercury gate measure on dielectrics and HEMT wafers?

Most of what a fabricated capacitor gives. On an oxide or high-k film, the mercury acts as a gate, so accumulation capacitance gives the equivalent oxide thickness, $3.9{\epsilon }_{0}A/C_{acc}$: 1 $\mathrm{nF}$ under a 0.01 $\mathrm{c}{\mathrm{m}}^2$ dot is 34.5 $\mathrm{nm}$ (computed). Flat-band shifts give oxide charge, and I-V ramps test dielectric integrity (Polytec lists oxide-integrity monitoring; the charge relation is on the LCR Meter and C-V page). Semilab lists 2DEG sheet charge and pinch-off voltage for AlGaN/GaN with a mercury gate: integrating capacitance from pinch-off to zero gives the sheet density, so a 20 $\mathrm{nm}$ AlGaN barrier, about 420 $\mathrm{nF}$ per square centimetre, needs about -3.8 $\mathrm{V}$ to deplete $1\times 10^{13}$ $\mathrm{c}{\mathrm{m}}^{-2}$ (assumed permittivity 9.5; computed). Polytec also lists pseudo-MOSFET measurements on SOI and ferroelectric samples. Reference: Semilab, ‘MCV-530 / MCV-530L Mercury Probe System’ product page (specifications tab not read) (fetch-tool summary); Polytec/MDC, ‘CV92M Mercury Probe System’ brochure (fetch-tool summary); LCR Meter and C-V page of this vault.

References

1. Polytec GmbH / Materials Development Corporation, “CV92M Mercury Probe System,” product brochure (date not stated). Available: https://www.polytec.com/fileadmin/website/optical-systems/halbleiter-messtechnik/pdf/CV92M.pdf
2. SEMI, “SEMI MF1392: Test Method for Determining Net Carrier Density Profiles in Silicon Wafers by Capacitance-Voltage Measurements with a Mercury Probe,” standard abstract, SEMI store. Available: https://store-dev2.semi.org/en-jp/products/mf139200-semi-mf1392-test-method-for-determining-net-carrier-density-profiles-in-silicon-wafers-by-capacitance-voltage-measurements-with-a-mercury-probe
3. W. A. Doolittle, “Doping Profiling,” ECE 4813 Semiconductor Device and Material Characterization, lecture 3, Georgia Institute of Technology. Available: https://alan.ece.gatech.edu/ECE4813/Lectures/Lecture3DopingProfiling.pdf
4. W. A. Doolittle, “Resistivity and Sheet Resistance,” ECE 4813 Semiconductor Device and Material Characterization, lecture 2, Georgia Institute of Technology. Available: https://alan.ece.gatech.edu/ECE4813/Lectures/Lecture2ResistivityAndSheetResistance.pdf
5. Semilab, “MCV-530 / MCV-530L Mercury Probe System,” product page. Available: https://research-metrology.semilab.com/products-solutions/mcv-530-mcv-530-l-mercury-probe-system
6. LCR Meter and C-V, page in this vault.

Related pages in this vault: LCR Meter and C-V, Corona-Kelvin Metrology, Spreading Resistance Profiler (SRP), Four-Point Probe, Metal Semiconductor Contacts, MOS Capacitor, Lifetime Testers, Silicon on Insulator (SOI) MOSFET.