Thermal Oxidation Furnace

1. Theory

• Definition: A thermal oxidation furnace grows SiO${}_2$ by reacting silicon with dry ${\mathrm{O}}_2$ or steam at 800 to 1200 ${}^{\circ }\mathrm{C}$, the range of CityU’s rate tables (CityU; Filipovic).
• Kinetics: Growth follows the Deal-Grove law, linear when the interface reaction limits and parabolic when diffusion through the oxide limits (CityU; Filipovic).
• Rate constants: $B$ and $B/A$ follow Arrhenius laws and depend on ambient, pressure and orientation (Filipovic; CityU).
• Consumption: The oxide grows partly into the silicon, consuming 0.44 of its thickness (CityU).

2. Working Principle

• Grow: Steam oxidizes about 10 times faster than dry oxygen (KTH).
• Steam source: Pyrogenic steam is made by burning hydrogen with excess oxygen, at most 91 per cent steam (RTP oxidation patent).
• Chlorine: HCl or chlorine-bearing gases getter metals and mobile ions (CityU).
• Anneal and cool: Switching to ${\mathrm{N}}_2$ or Ar and cooling faster lowers the fixed oxide charge $Q_f$ (KTH).

3. Applications

• Gate and tunnel oxides: SiO${}_2$ served as the MOS gate oxide until the 45 $\mathrm{nm}$ node; Stanford’s roadmap lists tunnel oxides of 8.5 to 6 $\mathrm{nm}$ (KTH; Stanford).
• Field oxides: Field oxide for LOCOS isolation, near 0.1 to 1 $\mu \mathrm{m}$ thick (KTH; Stanford).
• Pad, screen and masking oxides: Thin oxides used during implant and diffusion (KTH).
• Interface passivation: A forming gas anneal at 350 to 500 ${}^{\circ }\mathrm{C}$ for 30 min lowers $Q_{it}$ from about $10^{11}$ to $10^{10}$ cm${}^{-2}$eV${}^{-1}$ (KTH).

Growth Kinetics

Name	Formula	Related Formulae	Variables/Constants
Deal-Grove growth law	$x_o^2+A{x}_o=B\left(t+\tau \right)$	$A=2D\left(\frac{1}{k_s}+\frac{1}{h}\right),B=\frac{2D{C}^{\ast }}{N_1},\tau =\frac{x_i^2+A{x}_i}{B}$	$x_o:oxidethickness$ $t:time$ $D:oxidantdiffusivityinSi{O}_2$ $k_s:surfacereactionrate$ $h:gas-phasetransfercoefficient$ $\begin{array}{r}{C}^{\ast }:equilibriumoxidantconcentrationin\\ theoxide\end{array}$ $N_1:oxidantmoleculesperunitoxidevolume$ $\begin{array}{r}{x}_i:initialthickness;CityUandFilipovic:\\ equationsaswritten,steady-statefluxF\\ =C^{\ast }/(1/k_s+1/h+x_o/D)\end{array}$ $\begin{array}{r}(myreading:thethreeresistancesin\\ seriesaregastransfer,diffusionand\\ interfacereaction)\end{array}$
Explicit thickness and limits	$x_o=\frac{A}{2}\left[\sqrt{1+\frac{4B\left(t+\tau \right)}{A^2}}-1\right]$	$x_o\approx \frac{B}{A}\left(t+\tau \right)\text{(short)},x_o\approx \sqrt{Bt}\text{(long)}$	$B/A:linearrateconstant$ $\begin{array}{r}B:parabolicrateconstant;CityU:linear\\ limitfor(t+\tau )muchlessthan{A}^2/4B,\\ parabolicfortmuchgreater;Filipovic:\\ B/Aapproximately{C}^{\ast }{k}_s/N_1\end{array}$ $\begin{array}{r}(computed:1\mathrm{h}at1000{}^{\circ }Cgives69\mathrm{nm}dry\\ and435\mathrm{nm}wet,and1.89\mathrm{h}dryfor100\mathrm{nm}\\ frombaresilicon)\end{array}$
Initial dry-oxidation offset	${\tau }_{dry}\left(1000^{\circ }\mathrm{C}\right)=0.37\mathrm{h}$	${\tau }_{wet}=0$	$\begin{array}{r}\tau :timeshiftthatfitsthefastinitial\\ drygrowth;CityUtable:dry\tau =0.027,\\ 0.076,0.37,1.40and9.0\mathrm{h}at1200,1100,\\ 1000,920and800{}^{\circ }C,wet\tau =0atall\\ temperatures;Filipovic:\tau and{x}_{i}as\\ fittingparametersinthethinregime;\\ Stanfordhandout:dryoxidesgrowmuch\\ fasterthanDeal-Grovepredictsforabout\\ 200\mathring{A},MassoudmodeltermwithLabout70\\ \mathring{A}\end{array}$ $\begin{array}{r}(myreading:theoffset\tau standsinfor\\ thisfastinitialgrowth)\end{array}$

Rate Constants

Name	Formula	Related Formulae	Variables/Constants
Arrhenius rate constants	$B=C_1{e}^{-E_1/k_{B}T},\frac{B}{A}=C_2{e}^{-E_2/k_{B}T}$	$\text{dry}:C_1=772\mu {\mathrm{m}}^2/h,E_1=1.23\mathrm{eV},C_2=6.23\times 10^6\mu m/h,E_2=2.00\mathrm{eV}$	$k_B:Boltzmannconstant$ $\begin{array}{r}T:absolutetemperature;Filipovictable\\ for(111)siliconat1atm:wet{C}_1=386\\ \mu {\mathrm{m}}^2/h,E_1=0.78\mathrm{eV},C_2=1.63\times 10^8\mu m/h,E_2=\\ 2.05\mathrm{eV},divide{C}_{2}by1.68for(100);the\\ thesisprintsthe{C}_{2}unitas\mu {\mathrm{m}}^2/hand\\ labelstheB/Aenergies{E}_1\end{array}$ $\begin{array}{r}(computed:at1000{}^{\circ }CdryB=0.0104\mu {\mathrm{m}}^2/h\\ andB/A=0.075\mu m/h;wetB=0.316\mu {\mathrm{m}}^2/hand\\ B/A=1.25\mu m/h)\end{array}$
Tabulated rate constants	$\text{dry }1000^{\circ }\mathrm{C}:A=0.165\mu \mathrm{m},B=0.0117\mu {\mathrm{m}}^2/h,B/A=0.071\mu m/h$	$\text{wet }1000^{\circ }\mathrm{C}:A=0.226\mu \mathrm{m},B=0.287\mu {\mathrm{m}}^2/h,B/A=1.27\mu m/h$	$\begin{array}{r}CityUtables:wetat1200,1100,1000and\\ 920{}^{\circ }C(B=0.720,0.510,0.287,0.203\\ \mu {\mathrm{m}}^2/h),dryat1200to800{}^{\circ }C(B=0.045,\\ 0.027,0.0117,0.0049,0.0011\mu {\mathrm{m}}^2/h;B/A=\\ 1.12,0.30,0.071,0.0208,0.0030\mu m/h)\end{array}$ $\begin{array}{r}(computed:theArrheniusfitdiffersfrom\\ thetableby11percentindryBat1000\\ {}^{\circ }C,20percentindryB/Aat1200{}^{\circ }Cand\\ 15percentinwetBat1200{}^{\circ }C)\end{array}$
Orientation and pressure	${\left(\frac{B}{A}\right)}_{111}=1.68{\left(\frac{B}{A}\right)}_{100},B_{111}=B_{100}$	$B\propto p,{\left(\frac{B}{A}\right)}_{dry}\propto p^{0.7\text{to}0.8},{\left(\frac{B}{A}\right)}_{wet}\propto p$	$\begin{array}{r}p:oxidantpartialpressure;CityU:\\ (111)/(100)ratio1.65to1.75over900to\\ 1100{}^{\circ }C,average1.68,Bnearly\\ orientationindependent,higherpressure\\ allowslower-temperaturegrowth;\\ Filipovic:(110)/(100)=1.45notwell\\ established,pressureexponentsaswritten\end{array}$ $\begin{array}{r}(myreading:B/Adependsonsurfacebond\\ density,Bondiffusionthroughtheoxide)\end{array}$

Furnace Chemistry

Name	Formula	Related Formulae	Variables/Constants
Oxidant density and solubility	$N_{1,O_2}=2.2\times 10^{22}\mathrm{c}{\mathrm{m}}^{-3},N_{1,H_{2}O}=4.4\times 10^{22}\mathrm{c}{\mathrm{m}}^{-3}$	$C_{dry}^{\ast }=5.2\times 10^{16}\mathrm{c}{\mathrm{m}}^{-3},C_{wet}^{\ast }=3.0\times 10^{19}\mathrm{c}{\mathrm{m}}^{-3}\left(1000^{\circ }\mathrm{C}\right)$	$\begin{array}{r}CityU:N_{1}values;Filipovic:C^{\ast }at1atm\\ and1000{}^{\circ }C,Ndoubledforwetoxidation;\\ Henr{y}^{\prime }slaw{C}^{\ast }=Hp\end{array}$ $\begin{array}{r}(computed:watersolubilityis577times\\ thatofoxygen,while{N}_{1}isonlydoubled,\\ whichiswhywetgrowthisfarfaster)\end{array}$
Silicon consumption	$x_{Si}=0.44x_o$	$\frac{x_o}{x_{Si}}=2.27$	$\begin{array}{r}{x}_{Si}:thicknessofsiliconconsumed;CityU:\\ 0.44timestheoxidethickness\end{array}$ $\begin{array}{r}(computed:100\mathrm{nm}ofoxideconsumes44\mathrm{nm}\\ ofsilicon,so56percentoftheoxide\\ liesabovetheoriginalsurface)\end{array}$
Pyrogenic steam and chlorine	$2H_2+O_2\to 2H_{2}O$	$\frac{F_{H_2}}{F_{O_2}}\le 1.67\left(\text{safety}\right),\le 2\left(\text{controller cap}\right)$	$\begin{array}{r}F:gasflow;RTPoxidationpatent:\\ torch-generatedsteamlimitedto91per\\ centwith9percentexcessoxygen,H_2:O_2\\ cappedat2bythecontrollerswitha1.67\\ safetyratio;KTH:dry{O}_{2}with1to3per\\ centClgivesacleaneroxide,Clgetters\\ metals;CityU:chlorineconverts\\ impuritiestovolatilechlorides,reduces\\ oxidation-inducedstackingfaultsand\\ mobile-ioncharge{Q}_{m}aftertubecleaning\end{array}$ $\begin{array}{r}(computed:aratioof1.67leaves0.165of\\ eachoxygenmoleculeunburned,giving91\\ percentsteam)\end{array}$

Important Questions

Ques: How does the Deal-Grove model predict oxide thickness?

It balances three fluxes in series, gas transfer, diffusion through the oxide and reaction at the interface, giving $x_o^2+A{x}_o=B(t+\tau )$ (CityU; Filipovic). Thin oxides grow linearly at $B/A$, set by the interface reaction, and thick oxides parabolically at $\sqrt{Bt}$, set by diffusion. With CityU’s 1000 ${}^{\circ }\mathrm{C}$ constants, one hour of dry oxidation from bare silicon gives 69 $\mathrm{nm}$ (including $\tau$ = 0.37 $\mathrm{h}$) and one hour of wet oxidation gives 435 $\mathrm{nm}$ (computed). Growing 100 $\mathrm{nm}$ dry at 1000 ${}^{\circ }\mathrm{C}$ takes about 1.9 $\mathrm{h}$ (computed). The model treats the oxide as a uniform diffusion barrier, so it fits thick oxides well but needs the $\tau$ offset or Massoud’s correction in the thin regime: Stanford notes that dry oxides grow much faster than Deal-Grove predicts up to about 200 angstrom, and Massoud’s extra term fades beyond a length of about 70 angstrom. Reference: City University of Hong Kong, AP6120 course notes, chapter 4, ‘Thermal Oxidation’ (Deal-Grove model and rate-constant tables) (fetch-tool summary); L. Filipovic, ‘Topography Simulation of Novel Processing Techniques’, PhD thesis, TU Wien Institute for Microelectronics, section on the Deal-Grove model (fetch-tool summary); J. D. Plummer, M. D. Deal and P. B. Griffin, EE 212 class handout 10, chapter 6 ‘Thermal Oxidation’ (Stanford, 1999), hosted on the University of Washington EE 528 site (fetch-tool summary).

Ques: Should the tabulated or Arrhenius rate constants be used?

They disagree by up to about 20 per cent. At 1000 ${}^{\circ }\mathrm{C}$ dry, CityU tabulates B = 0.0117 and B/A = 0.071, while Filipovic’s Arrhenius constants give 0.0104 and 0.075 (computed). At 1200 ${}^{\circ }\mathrm{C}$ dry B/A is 1.12 in the table and 0.90 from the fit, and wet B is 0.72 against 0.83 (computed). The Arrhenius constants are a single straight-line fit over the full temperature range, while the tables list values extracted at each temperature, so at a tabulated temperature the table is more likely closer to the measured data (my reading). Between tabulated points the fit is more convenient. Filipovic’s thesis also prints the $C_2$ unit as square micrometres per hour, which must be micrometres per hour for $B/A$ (my reading), so its units should be checked before use. Reference: City University of Hong Kong, AP6120 course notes, chapter 4, ‘Thermal Oxidation’ (Deal-Grove model and rate-constant tables) (fetch-tool summary); L. Filipovic, ‘Topography Simulation of Novel Processing Techniques’, PhD thesis, TU Wien Institute for Microelectronics, section on the Deal-Grove model (fetch-tool summary).

Ques: Why is wet oxidation so much faster than dry oxidation?

Mainly because water is far more soluble in SiO${}_2$. Filipovic gives equilibrium concentrations at 1000 ${}^{\circ }\mathrm{C}$ and 1 atm of $5.2\times 10^{16}$ $\mathrm{c}{\mathrm{m}}^{-3}$ for ${\mathrm{O}}_2$ and $3.0\times 10^{19}$ $\mathrm{c}{\mathrm{m}}^{-3}$ for ${\mathrm{H}}_2\mathrm{O}$, a ratio of 577 (computed), while the oxidant needed per unit oxide only doubles, from $2.2\times 10^{22}$ to $4.4\times 10^{22}$ $\mathrm{c}{\mathrm{m}}^{-3}$ (CityU). Since $B=2D{C}^{\ast }/N_1$, the parabolic constant rises from 0.0117 to 0.287 $\mu {\mathrm{m}}^2/h$ at 1000 ${}^{\circ }\mathrm{C}$, about 25 times (computed). KTH puts steam oxidation at about 10 times faster than dry oxidation, consistent with this, and recommends dry oxygen with 1 to 3 per cent chlorine for a cleaner oxide. Pyrogenic steam is made by burning hydrogen with excess oxygen; an RTP patent caps its torch at 91 per cent steam with 9 per cent excess oxygen. Reference: L. Filipovic, ‘Topography Simulation of Novel Processing Techniques’, PhD thesis, TU Wien Institute for Microelectronics, section on the Deal-Grove model (fetch-tool summary); City University of Hong Kong, AP6120 course notes, chapter 4, ‘Thermal Oxidation’ (Deal-Grove model and rate-constant tables) (fetch-tool summary); C. Henkel and M. Ostling, IH2655 Lecture 5, ‘Thermal Oxidation of Silicon’, KTH Royal Institute of Technology (2012) (fetch-tool summary); US patent 5,935,650, ‘Method of oxidation of semiconductor wafers in a rapid thermal processing (RTP) system’ (USPTO full text) (fetch-tool summary).

Ques: How do orientation and pressure change the growth rate?

Orientation changes the linear constant only. CityU measures a (111)/(100) $B/A$ ratio of 1.65 to 1.75 over 900 to 1100 ${}^{\circ }\mathrm{C}$, averaging 1.68, while $B$ is almost independent of orientation because diffusion through amorphous oxide does not see the substrate. Filipovic adds a (110)/(100) ratio of 1.45, noted as not well established, which matters for FinFET sidewalls (my reading). Pressure raises $C^{\ast }$: $B$ scales linearly with partial pressure, wet $B/A$ also linearly, and dry $B/A$ as $p^{0.7}$ to $p^{0.8}$ (Filipovic). High-pressure oxidation therefore lets thick oxides grow at lower temperature, reducing dopant diffusion (CityU). At 10 atm, wet growth in the parabolic regime would be ten times faster (computed). Reference: City University of Hong Kong, AP6120 course notes, chapter 4, ‘Thermal Oxidation’ (Deal-Grove model and rate-constant tables) (fetch-tool summary); L. Filipovic, ‘Topography Simulation of Novel Processing Techniques’, PhD thesis, TU Wien Institute for Microelectronics, section on the Deal-Grove model (fetch-tool summary).

Ques: What do silicon consumption and chlorine mean for a furnace process?

The oxide grows into the silicon: CityU gives a consumed thickness of 0.44 times the oxide, so 100 $\mathrm{nm}$ of oxide consumes 44 $\mathrm{nm}$ of silicon and rises 56 $\mathrm{nm}$ above the original surface (computed). This step height and a volume expansion of 2.27 times (computed; Stanford quotes about 2.2 times) causes stress at LOCOS edges and limits oxidation of narrow fins (my reading). Chlorine additions convert metallic impurities into volatile chlorides, suppress oxidation-induced stacking faults, and chlorine tube cleaning reduces mobile-ion charge (CityU). After growth, switching to nitrogen or argon and cooling faster lowers the fixed oxide charge, and a forming gas anneal at 350 to 500 ${}^{\circ }\mathrm{C}$ reduces interface traps about tenfold (KTH). Reference: City University of Hong Kong, AP6120 course notes, chapter 4, ‘Thermal Oxidation’ (Deal-Grove model and rate-constant tables) (fetch-tool summary); J. D. Plummer, M. D. Deal and P. B. Griffin, EE 212 class handout 10, chapter 6 ‘Thermal Oxidation’ (Stanford, 1999), hosted on the University of Washington EE 528 site (fetch-tool summary); C. Henkel and M. Ostling, IH2655 Lecture 5, ‘Thermal Oxidation of Silicon’, KTH Royal Institute of Technology (2012) (fetch-tool summary).

References

1. City University of Hong Kong, AP6120, chapter 4, “Thermal Oxidation,” course notes. Available: https://www.cityu.edu.hk/phy/appkchu/AP6120/4.PDF
2. L. Filipovic, “Topography Simulation of Novel Processing Techniques,” PhD thesis, Institute for Microelectronics, TU Wien, section on the Deal-Grove model. Available: https://www.iue.tuwien.ac.at/phd/filipovic/node31.html
3. J. D. Plummer, M. D. Deal and P. B. Griffin, EE 212 Handout 10, “Chapter 6: Thermal Oxidation,” Stanford University, 1999. Available: https://dunham.ece.uw.edu/ee528/notes/Chapter6.pdf
4. C. Henkel and M. Ostling, “Thermal Oxidation of Silicon,” IH2655 Lecture 5, KTH, 2012. Available: https://www.kth.se/social/upload/51029fc0f276540764a5c298/Lecture%205.pdf
5. “Method of oxidation of semiconductor wafers in a rapid thermal processing (RTP) system,” US Patent 5,935,650. Available: https://image-ppubs.uspto.gov/dirsearch-public/print/downloadPdf/5935650

Related pages in this vault: Physical Constants, MOS Capacitor, Long Channel MOSFET, Spectroscopic Ellipsometer, Spectral Reflectometer, Corona-Kelvin Metrology, Temperature Acceleration Models (Arrhenius and Eyring), Rapid Thermal Oxidation System, Plasma and Radical Oxidation Tool, CMP Polisher, Beamline Ion Implanter, Diffusion Furnace, Furnace Anneal System, RCA Wet Bench, LPCVD Furnace.