Corona-Kelvin Metrology

1. Theory

• Definition: Corona-Kelvin metrology deposits measured doses of ions from a corona discharge on a wafer surface and measures the resulting surface voltage with a vibrating Kelvin probe, building a C-V curve without any contact (Semilab paper; Edelman et al.).
• Quasi-static: The capacitance is $\Delta Q_C/\Delta V$ for each charge step, a low-frequency characteristic (Semilab paper).
• Voltage components: The surface voltage is the sum of a work-function term, the semiconductor surface barrier and the dielectric voltage; light flattens the barrier so the parts can be separated (USF patent).
• Outputs: Dielectric capacitance and EOT, flat-band voltage, total charge, interface trap density, leakage and doping profiles (USF patent; Edelman et al.; Semilab paper).

2. Working Principle

• Corona source: A high-voltage needle ionizes air; ions thermalize and land with negligible energy, so the dielectric is not damaged (Semilab paper).
• Kelvin probe: A vibrating electrode 1 to 2 $\mathrm{mm}$ in diameter, nulled by a backing voltage, reads the contact potential with sub-millivolt precision (Semilab patent; Pina-Galan).
• Charge monitoring: Each dose is measured in situ, and the wafer is returned to the same pre-charging potential before each step (Semilab paper).
• Illumination: Strong light collapses the surface barrier on silicon, giving it from the dark-light difference (USF patent).

3. Applications

• Gate and passivation dielectrics: EOT, charge and interface traps on blanket wafers, replacing MOS and mercury-probe C-V (Edelman et al.).
• SiC MOS: Interface traps and stress-induced charge in SiC dielectrics (USF patent).
• Wide-gap epitaxy: Doping profiles in SiC, Ga2O3, GaN and AlGaN/GaN 2DEG structures (Semilab paper).
• Inline monitoring: About 30 wafers per hour for 12 sites (Semilab patent).

Corona Charging and Kelvin Probe

Name	Formula	Related Formulae	Variables/Constants
Surface voltage decomposition	$V_{CPD}={\Phi }_{ms0}+V_{SB}+V_{OX}$	$\Delta V_{CPD}=\Delta V_{SB}+\Delta V_{OX}$	$\begin{array}{r}{V}_{CPD}:contactpotentialdifferencereadby\\ theKelvinprobe\end{array}$ ${\Phi }_{ms0}:probe-semiconductorwork-functionterm$ $V_{SB}:semiconductorsurfacebarrier$ $\begin{array}{r}{V}_{OX}:dielectricvoltage;USFpatent:these\\ relations,thework-functiontermdropping\\ outofchangeswithcharging\end{array}$ $\begin{array}{r}(computed:inaccumulation\Delta V_{SB}\approx 0,so\\ thewholechangeappearsacrossthe\\ dielectric)\end{array}$
Corona charge and capacitance	$C=\frac{\Delta Q_C}{\Delta V},Q_C=\sum \Delta Q_C$	$1q/c{\mathrm{m}}^2=1.602\times 10^{-19}C/c{\mathrm{m}}^2$	$\begin{array}{r}C:differential(quasi-static)capacitance\\ perarea\end{array}$ $\Delta Q_C:coronachargeincrement$ $\begin{array}{r}\Delta V:surface-voltagechange;Semilab\\ paper:thermalizedcoronaionsdeposited\\ withnegligiblekineticenergy,increments\\ setbypolarityanddose,potential\\ compensationbeforeeachstep,in-situ\\ chargemonitoring,negativechargingfor\\ n-typeandpositiveforp-type,\\ quasi-staticlow-frequencycapacitance;\\ Semilabpatent:deepdepletionfromabout\\ 1\times 10^{12}to1\times 10^{13}q/\mathrm{c}{\mathrm{m}}^2,depositionabout1\mathrm{s}\\ orless,initialsurfacechargeabout\\ 1\times 10^{11}q/\mathrm{c}{\mathrm{m}}^2\end{array}$ $\begin{array}{r}(computed:1\times 10^{12}q/\mathrm{c}{\mathrm{m}}^2=1.6\times 10^{-7}C/c{\mathrm{m}}^{2}and\\ 1\times 10^{13}q/\mathrm{c}{\mathrm{m}}^2=1.6\times 10^{-6}C/c{\mathrm{m}}^2)\end{array}$
Vibrating Kelvin probe	$i\left(t\right)=\left(V_{CPD}-V_b\right)\frac{d{C}_p}{dt}$	$i=0\text{when}{V}_b=V_{CPD}$	$i:probecurrent$ $V_b:backing(nulling)voltage$ $\begin{array}{r}{C}_p:probe-to-surfacecapacitance;\\ Pina-Galan:currentfromtheoscillating\\ capacitance,writteni=(V_{CPD}+V_b)dC/dtwith\\ thenullat{V}_b=-V_{CPD},theoppositesign\\ conventiontothisrow;Semilabpatent:\\ electrodevibratingamillimetreorless\\ abovethewafer,1or2\mathrm{mm}diameter,time\\ constantabout5m/s,0.2\mathrm{mV}precision,\\ range-100to+100\mathrm{V};USFpatent:\\ resolutionbelow0.1\mathrm{mV}(seetheQ/A)\end{array}$ $\begin{array}{r}(computed:0.2\mathrm{mV}ona20\mathrm{V}readingis\\ 1\times 10^{-5}ofthesignal)\end{array}$

Dielectric Parameters

Name	Formula	Related Formulae	Variables/Constants
Dielectric capacitance and EOT	$C_{OX}^{-1}=\frac{\Delta V_{CPD}}{\Delta Q_C}(\text{accumulation})$	$EOT=\frac{3.9{\epsilon }_0}{C_{OX}},C^{-1}=C_{OX}^{-1}+{\left(C_{SC}+C_{it}\right)}^{-1}$	$C_{OX}:dielectriccapacitanceperarea$ $EOT:equivalentoxidethickness$ $\begin{array}{r}{C}_{SC},C_{it}:space-chargeandinterface-trap\\ capacitances;USFpatent:inverseslopein\\ accumulationandtheseriesrelation,\\ example{C}_{OX}=6.67\times 10^{-8}F/c{\mathrm{m}}^{2}on4H-SiC;\\ Edelmanetal.:EOTtobelow1\mathrm{nm}with\\ corrections,unaffectedbywater\\ adsorptionandairbornemolecular\\ contamination;US6,680,621:EOTisthe\\ SiO2thicknessgivingthesame\\ capacitance,C_{OX}={\epsilon }_0{\epsilon }_{ox}/T\end{array}$ $\begin{array}{r}(computed:6.67\times 10^{-8}F/c{\mathrm{m}}^{2}isanEOTof51.8\\ \mathrm{nm})\end{array}$
Flat band and total charge	$C_{FB}=\frac{C_{OX}{C}_S}{C_{OX}+C_S},C_S=\frac{{\epsilon }_s{\epsilon }_0}{L_D}$	$L_D=\sqrt{\frac{k_{B}T{\epsilon }_s{\epsilon }_0}{q^{2}N}},Q_{tot}=-Q_C\left(V_{FB}\right)$	$C_{FB}:flat-bandcapacitance$ $C_S:flat-bandsemiconductorcapacitance$ $L_D:extrinsicDebyelength$ $N:doping$ $\begin{array}{r}{Q}_{tot}:totaldielectriccharge;USFpatent:\\ theseequations,flatbandidentifiedon\\ theC-Q_{C}curve,coronachargeatflatband\\ giving{Q}_{tot},example{C}_{FB}=4.75\times 10^{-8}F/c{\mathrm{m}}^{2}for{N}_D\\ =5\times 10^{15}\mathrm{c}{\mathrm{m}}^{-3}4H-SiCanda4.3\mathrm{V}flat-band\\ shiftafterFowler-Nordheimstress;\\ Semilabpaper:flatbandon\\ dielectric-coveredwafersusingLED\\ illumination;signof{Q}_{tot}(myreading:the\\ coronachargeatflatbandbalancesthe\\ dielectriccharge)\end{array}$ $\begin{array}{r}(assumed:{\epsilon }_s=9.7for4H-SiC;computed:L_D\\ =52.7\mathrm{nm},C_S=1.63\times 10^{-7}F/c{\mathrm{m}}^{2}and{C}_{FB}=\\ 4.73\times 10^{-8}F/c{\mathrm{m}}^2,matchingthepaten{t}^{\prime }s\\ 4.75\times 10^{-8})\end{array}$
Leakage from voltage decay	$J=C_{OX}\frac{dV}{dt}(\text{charge held, no contact})$	$E_{ox}=\frac{V_{OX}}{EOT}$	$\begin{array}{r}J:leakagecurrentdensity,dV/dt:\\ surface-voltagedecayrate\end{array}$ $\begin{array}{r}{E}_{ox}:dielectricfield;US6,680,621:J_{LEAK}=\partial \\ Q_c/\partial t=C_{ox}(\partial V/\partial t-\partial V_{SB}/\partial t),barrierterm\\ neglectedhere;Edelmanetal.:\\ correctionsneededforultra-thin\\ dielectrics\end{array}$ $\begin{array}{r}(computed:6.67\times 10^{-8}F/c{\mathrm{m}}^{2}decayingat1\mathrm{mV}\\ persecondleaks6.7\times 10^{-11}A/c{\mathrm{m}}^2)\end{array}$

Interface Traps and Doping

Name	Formula	Related Formulae	Variables/Constants
Surface barrier and interface traps	$V_{SB}=V_{CPD,dark}-V_{CPD,light}$	$\Delta Q_C=-\left(\Delta Q_{SC}+\Delta Q_{it}\right),D_{it}=\frac{\Delta Q_{it}}{q\Delta V_{SB}}$	$\begin{array}{r}{V}_{CPD,light}:readingunderstrongillumination\\ thatflattensthebands\end{array}$ $\Delta Q_{SC}:space-chargechange,Q_{SC}=\pm qN{L}_{D}F(V_{SB})$ $\begin{array}{r}\Delta Q_{it}:interface-trapchargechange;USF\\ patent:theseequations,green2.36\mathrm{eV}\\ lightforSiO2-Si,recoveryinafraction\\ ofasecondforSibutlessthan10per\\ centafter20\mathrm{s}forSiC,soadarkmethod\\ referencedtoflatbandisusedforSiC,\\ incrementsof1\times 10^{11}q/\mathrm{c}{\mathrm{m}}^2,stressresults\Delta \\ Q_{it}=1.22\times 10^{-7}and\Delta Q_t=1.65\times 10^{-7}C/c{\mathrm{m}}^2\end{array}$ $\begin{array}{r}(computed:\Delta Q_{it}=1.22\times 10^{-7}C/c{\mathrm{m}}^{2}is7.6\times 10^{11}\\ \mathrm{c}{\mathrm{m}}^{-2};1\times 10^{11}q/\mathrm{c}{\mathrm{m}}^{2}spreadover0.1\mathrm{eV}of\\ barrierchangeis{D}_{it}=1\times 10^{12}\mathrm{c}{\mathrm{m}}^{-2}\mathrm{e}{\mathrm{V}}^{-1})\end{array}$
Doping profile from corona C-V	$\Delta W=\frac{\Delta Q_C}{q{N}_D}$	$N=\frac{2}{q{\epsilon }_s{\epsilon }_0}{\left[\frac{d\left(1/C^2\right)}{dV}\right]}^{-1}$	$\Delta W:depletion-widthstep$ $\begin{array}{r}{N}_D:doping;Semilabpaper:theseforms,\\ range1\times 10^{14}to2\times 10^{19}\mathrm{c}{\mathrm{m}}^{-3},dosesabout1\times 10^{10}\\ to1\times 10^{12}q/\mathrm{c}{\mathrm{m}}^2,GaNat1\times 10^{12}q/\mathrm{c}{\mathrm{m}}^{2}with\Delta W\\ about0.5\mathrm{nm},low-dopedSiCat2\times 10^{10}q/\mathrm{c}{\mathrm{m}}^2\\ withabout700\mathrm{nm},multilayerSiCandHEMT\\ 2DEGdoseschedules,50incrementsin3\\ minutesagainst30minutesatconstant\\ dose,abouteightfoldfasterHEMT\\ profiles,equivalencewithin0.05percent\\ andagreementwithmercury-probeC-V;USF\\ patent:doping1\times 10^{11}to1\times 10^{18}\mathrm{c}{\mathrm{m}}^{-3}(seethe\\ Q/A);Semilabpatent:photoneutralization\\ timeconstantfordoping\end{array}$ $\begin{array}{r}(computed:1\times 10^{12}q/\mathrm{c}{\mathrm{m}}^{2}over0.5\mathrm{nm}is2\times 10^{19}\\ \mathrm{c}{\mathrm{m}}^{-3};2\times 10^{10}q/\mathrm{c}{\mathrm{m}}^{2}over700\mathrm{nm}is2.9\times 10^{14}\mathrm{c}{\mathrm{m}}^{-3})\end{array}$

Important Questions

Ques: What is corona-Kelvin metrology, and why is it used?

A way to obtain C-V data without a gate. A corona discharge deposits ions on the wafer; they thermalize in air and land with negligible kinetic energy, so the surface is not damaged, and a vibrating Kelvin probe measures the surface voltage after each dose (Semilab paper). The ratio of charge step to voltage step gives a quasi-static capacitance, and stepping from accumulation to depletion builds a full C-V curve. Edelman et al. present it as a replacement for MOS and mercury-probe C-V on blanket wafers, with EOT below 1 $\mathrm{nm}$, unaffected by water adsorption and airborne molecular contamination that trouble optical thickness methods. Because no gate is made, measurements can follow each process step, at about 30 wafers per hour for 12 sites (Semilab patent). Reference: Semilab, academic paper summarized in SEMI Standards Watch, September 2024 (variable-dose corona-Kelvin C-V on wide-gap materials) (fetch-tool summary); P. Edelman et al., ‘Non-Contact C-V Measurements of Ultra Thin Dielectrics’, Eur. Phys. J. Appl. Phys. (abstract only) (fetch-tool summary); Semilab, US Patent 12,027,430, ‘Semiconductor doping characterization method using photoneutralization time constant of corona surface charge’ (first 100000 characters read) (fetch-tool summary).

Ques: How does the Kelvin probe measure surface voltage without touching?

By vibrating a small electrode above the surface and nulling the resulting current. The electrode and wafer form a capacitor whose value changes as the electrode vibrates; any potential difference between them drives a current $(V_{CPD}-V_b)d{C}_p/dt$, which a backing voltage $V_b$ drives to zero, so the backing voltage equals the contact potential difference (Pina-Galan, who writes the current with the opposite sign of $V_b$, so the null falls at $V_b=-V_{CPD}$). Semilab’s patent describes an electrode 1 or 2 $\mathrm{mm}$ in diameter, vibrating a millimetre or less above the wafer, with a time constant of about 5 $m/s$, 0.2 $\mathrm{mV}$ precision and a range of -100 to +100 $\mathrm{V}$. On a 20 $\mathrm{V}$ reading, 0.2 $\mathrm{mV}$ is one part in $1\times 10^5$ (computed). Since only changes are analysed, the probe’s own work function drops out (USF patent). Reference: E. A. Pina-Galan, ‘Mathematical analysis of the operation of a scanning Kelvin probe’, arXiv:1907.07465, 2019: i(t) = (V_CPD + V_b) dC/dt, null and off-null methods, V_b = -V_CPD at zero output (fetch-tool summary); Semilab, US Patent 12,027,430, ‘Semiconductor doping characterization method using photoneutralization time constant of corona surface charge’ (first 100000 characters read) (fetch-tool summary); E. I. Oborina and A. Hoff, US Patent 8,803,533, ‘Noncontact determination of interface trap density for semiconductor-dielectric interface structures’, University of South Florida, 2014 (fetch-tool summary).

Ques: How are EOT, flat band and total charge obtained?

From the shape of the charge-voltage curve. In accumulation the surface barrier hardly changes, so the slope $\Delta V/\Delta Q_C$ is the inverse dielectric capacitance (USF patent); the patent’s SiC example, $6.67\times 10^{-8}$ $F/c{\mathrm{m}}^2$, is an EOT of 51.8 $\mathrm{nm}$ (computed). The flat-band capacitance follows from the Debye length, $C_{FB}=C_{OX}{C}_S/(C_{OX}+C_S)$; for $5\times 10^{15}$ $\mathrm{c}{\mathrm{m}}^{-3}$ 4H-SiC with an assumed permittivity of 9.7 this gives $4.73\times 10^{-8}$ $F/c{\mathrm{m}}^2$ (computed), matching the patent’s $4.75\times 10^{-8}$. The corona charge needed to reach that capacitance equals, with opposite sign, the total dielectric charge. After Fowler-Nordheim stress the patent found a 4.3 $\mathrm{V}$ flat-band shift. On wafers with dielectrics, LED illumination helps locate flat band (Semilab paper). Reference: E. I. Oborina and A. Hoff, US Patent 8,803,533, ‘Noncontact determination of interface trap density for semiconductor-dielectric interface structures’, University of South Florida, 2014 (fetch-tool summary); Semilab, academic paper summarized in SEMI Standards Watch, September 2024 (variable-dose corona-Kelvin C-V on wide-gap materials) (fetch-tool summary).

Ques: How is the interface trap density measured, and why is SiC harder?

By separating the corona charge into the part that changes the space charge and the part captured by interface traps. Strong light flattens the bands, so the surface barrier is the difference between dark and illuminated readings; green light at 2.36 $\mathrm{eV}$ suffices for SiO2 on silicon (USF patent). Each dose then splits as $\Delta Q_C=-(\Delta Q_{SC}+\Delta Q_{it})$, with the space charge known from the doping and barrier, and $D_{it}=\Delta Q_{it}/(q\Delta V_{SB})$. A $1\times 10^{11}$ $q/\mathrm{c}{\mathrm{m}}^2$ step absorbed over a 0.1 $\mathrm{eV}$ barrier change means $1\times 10^{12}$ $\mathrm{c}{\mathrm{m}}^{-2}\mathrm{e}{\mathrm{V}}^{-1}$ (computed). In SiC the wide gap makes the light method fail, because the surface recovers slowly, less than 10 per cent after 20 $\mathrm{s}$ against a fraction of a second for silicon, so the patent uses a dark method referenced to flat band. Reference: E. I. Oborina and A. Hoff, US Patent 8,803,533, ‘Noncontact determination of interface trap density for semiconductor-dielectric interface structures’, University of South Florida, 2014 (fetch-tool summary).

Ques: How does corona-Kelvin profile doping in wide-gap materials?

Like Schottky C-V, but with corona charge in place of a gate. Each dose deepens the depletion layer by $\Delta W=\Delta Q_C/(q{N}_D)$, and the slope of $1/C^2$ against voltage gives the doping (Semilab paper). The paper varies the dose to keep depth steps sensible: $1\times 10^{12}$ $q/\mathrm{c}{\mathrm{m}}^2$ gives about 0.5 $\mathrm{nm}$ in heavily doped GaN, which is $2\times 10^{19}$ $\mathrm{c}{\mathrm{m}}^{-3}$, while $2\times 10^{10}$ $q/\mathrm{c}{\mathrm{m}}^2$ gives about 700 $\mathrm{nm}$ in lightly doped SiC, which is $2.9\times 10^{14}$ $\mathrm{c}{\mathrm{m}}^{-3}$ (computed). Variable doses cut a SiC profile from about 30 minutes to 3 minutes for 50 increments and made HEMT profiles about eight times faster, with dose equivalence within 0.05 per cent and agreement with mercury-probe C-V on SiC, Ga2O3, GaN and AlGaN/GaN. Reference: Semilab, academic paper summarized in SEMI Standards Watch, September 2024 (variable-dose corona-Kelvin C-V on wide-gap materials) (fetch-tool summary).

Ques: Over what doping range does corona-Kelvin work, and how precise is the probe?

The sources give different figures. The Semilab paper quotes $1\times 10^{14}$ to $2\times 10^{19}$ $\mathrm{c}{\mathrm{m}}^{-3}$ for doping profiles, while the USF patent states $1\times 10^{11}$ to $1\times 10^{18}$ $\mathrm{c}{\mathrm{m}}^{-3}$, with embodiments from $1\times 10^{14}$ to $1\times 10^{18}$. For the Kelvin probe, Semilab’s patent gives 0.2 $\mathrm{mV}$ precision and the USF patent a resolution below 0.1 $\mathrm{mV}$. The ranges overlap from $1\times 10^{14}$ to $1\times 10^{18}$ $\mathrm{c}{\mathrm{m}}^{-3}$, where both are likely valid; Semilab’s upper limit of $2\times 10^{19}$ is supported by its GaN measurement, which is computed to be near $2\times 10^{19}$ $\mathrm{c}{\mathrm{m}}^{-3}$, whereas the $1\times 10^{11}$ lower limit in the patent reads as a claim boundary rather than a demonstrated result (my reading). The probe figures differ because precision and resolution are different quantities, and both are adequate for millivolt-level C-V steps (my reading). Reference: Semilab, academic paper summarized in SEMI Standards Watch, September 2024 (variable-dose corona-Kelvin C-V on wide-gap materials) (fetch-tool summary); E. I. Oborina and A. Hoff, US Patent 8,803,533, ‘Noncontact determination of interface trap density for semiconductor-dielectric interface structures’, University of South Florida, 2014 (fetch-tool summary); Semilab, US Patent 12,027,430, ‘Semiconductor doping characterization method using photoneutralization time constant of corona surface charge’ (first 100000 characters read) (fetch-tool summary).

Ques: How does corona-Kelvin measure leakage in thin dielectrics?

By watching the surface voltage decay after charging. With no contact, deposited charge can only leave through the dielectric, so the leakage current density is $C_{OX}dV/dt$: a $6.67\times 10^{-8}$ $F/c{\mathrm{m}}^2$ film decaying at 1 $\mathrm{mV}$ per second leaks $6.7\times 10^{-11}$ $A/c{\mathrm{m}}^2$ (US 6,680,621, which neglects the surface-barrier term in some cases; computed). Charging to higher voltages maps current against field up to tunnelling and Fowler-Nordheim conduction, which the USF patent also uses as a stress. For ultra-thin films, leakage during each measurement step distorts the quasi-static capacitance, so Edelman et al. apply corrections to reach EOT below 1 $\mathrm{nm}$. The decay must be measured at a fixed time after each dose, and illumination effects must be excluded, so results are compared at matched timing (my reading). Reference: US Patent 6,680,621, ‘Steady state method for measuring the thickness and the capacitance of ultra thin dielectric in the presence of substantial leakage current’: J_LEAK = dQc/dt = Cox(dV/dt - dV_SB/dt), EOT as the SiO2 thickness giving the same capacitance (fetch-tool summary); P. Edelman et al., ‘Non-Contact C-V Measurements of Ultra Thin Dielectrics’, Eur. Phys. J. Appl. Phys. (abstract only) (fetch-tool summary); E. I. Oborina and A. Hoff, US Patent 8,803,533, ‘Noncontact determination of interface trap density for semiconductor-dielectric interface structures’, University of South Florida, 2014 (fetch-tool summary).

References

1. Semilab, academic paper on variable-dose corona charge-Kelvin probe C-V, summarized in SEMI Standards Watch, Sep. 2024. Available: https://www.semi.org/en/standards-watch-2024-sep/academic-paper-provided-by-Semilab-inc
2. P. Edelman, A. Savtchouk, M. Wilson, J. D’Amico, J. N. Kochey, D. Marinskiy and J. Lagowski, “Non-Contact C-V Measurements of Ultra Thin Dielectrics,” The European Physical Journal Applied Physics (abstract page). Available: https://research-metrology.semilab.hu/publications/non-contact-c-v-measurements-of-ultra-thin-dielectrics
3. Semilab Semiconductor Physics Laboratory, “Semiconductor doping characterization method using photoneutralization time constant of corona surface charge,” US Patent 12,027,430. Available: https://patents.google.com/patent/US12027430
4. E. I. Oborina and A. Hoff, “Noncontact determination of interface trap density for semiconductor-dielectric interface structures,” US Patent 8,803,533, University of South Florida, Aug. 12, 2014. Available: https://patents.justia.com/patent/8803533
5. E. A. Pina-Galan, “Mathematical analysis of the operation of a scanning Kelvin probe,” arXiv:1907.07465, 2019. Available: https://arxiv.org/abs/1907.07465
6. US Patent 6,680,621, “Steady state method for measuring the thickness and the capacitance of ultra thin dielectric in the presence of substantial leakage current.” Available: https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/6680621

Related pages in this vault: Mercury Probe, LCR Meter and C-V, Lifetime Testers, Kelvin Probe Force Microscope (KPFM), MOS Capacitor, Spreading Resistance Profiler (SRP), Charge Pumping, Thermal Oxidation Furnace.