Oxidation (thermal SiO2 growth) — Hinglish notes

4.3.3 · Hardware › Semiconductor Fabrication

Thermal Oxidation KYA hai?

Growth KAISE hoti hai: Deal–Grove model (derived)

Hum growth law ko teen fluxes se derive karte hain jo steady state mein equal hone chahiye (kuch bhi pile up nahi hota).

Maano $x$ = oxide thickness, $C_{g}, C_{s}, C_{i}$ = oxidant concentrations gas mein, oxide surface par, aur Si interface par hain.

Flux 1 — gas se surface tak (mass transport): $F_{1} = h (C^{*} - C_{s})$ jahan $C^{*}$ oxide mein equilibrium concentration hai, $h$ = gas-phase transfer coefficient.

Flux 2 — existing oxide ke through diffusion (Fick's law, linear gradient): $F_{2} = D \frac{C _{s} - C _{i}}{x}$

Flux 3 — Si surface par reaction (first-order kinetics): $F_{3} = k_{s} C_{i}$ jahan $k_{s}$ = surface reaction rate constant.

Steady state: $F_{1} = F_{2} = F_{3} \equiv F$ . $C_{i}$ ke liye solve karo:

$F = k_{s} C_{i}$ aur $F = D (C_{s} - C_{i}) / x$ aur $F = h (C^{*} - C_{s})$ se, $C_{s}, C_{i}$ ko eliminate karo: $F = \frac{k _{s} C ^{*}}{1 + \frac{k _{s}}{h} + \frac{k _{s} x}{D}}$

Oxide isliye grow hoti hai kyunki flux ki har unit $N_{1}$ oxidant molecules per unit volume of oxide consume karti hai: $\frac{d x}{d t} = \frac{F}{N _{1}} = \frac{k _{s} C ^{*} / N _{1}}{1 + k _{s} / h + k _{s} x / D}$

Do limiting regimes

Figure — Oxidation (thermal SiO2 growth)

WORKED EXAMPLES

COMMON MISTAKES (Steel-manned)

Flashcards

Dry oxidation reaction

Si + O_{2} \to SiO_{2}

Wet oxidation reaction

Si + 2 H_{2} O \to SiO_{2} + 2 H_{2}

Original Si surface ke neeche oxide ka fraction

~46% (ratio 0.46)

Deal–Grove integrated growth law

x^{2} + A x = B (t + τ)

Thin-oxide (early) regime, growth vs time

Linear,

x \approx (B / A) (t + τ)

; reaction-limited

Thick-oxide (late) regime, growth vs time

Parabolic,

x \approx B t

; diffusion-limited

Parabolic constant

B

ka physical meaning

B = 2 D C^{*} / N_{1}

; oxide ke through diffusion control karta hai

Linear constant

B / A

ka physical meaning

Surface reaction + gas transfer limited growth rate

Thickness badhne par growth slow kyun hoti hai

Oxidant ko thicker oxide ke across diffuse karna padta hai → gentle gradient (

1/ x

term)

Thin gate oxides ke liye konsi oxidation aur kyun

Dry — denser, higher quality

Thick field oxides ke liye konsi oxidation aur kyun

Wet — bahut faster growth

B aur B/A ki temperature dependence

Arrhenius

\propto e^{- E_{a} / k T}

; law unchanged, constants badhte hain

Deal–Grove mein teen fluxes

Gas transport

h (C^{*} - C_{s})

; oxide diffusion

D (C_{s} - C_{i}) / x

; interface reaction

k_{s} C_{i}

Recall Feynman: 12-saal ke bacche ko explain karo

Socho tumhare paas ek chocolate bar (silicon) hai aur tum use dhoop mein chhod dete ho taaki upar ek hard sugar crust (oxide) ban jaaye. Shuruaat mein crust fast banta hai. Lekin ek baar thick crust ban jaane ke baad, dhoop ki heat ko neeche aur chocolate pighalane ke liye crust ke through jaana padta hai — toh yeh slow aur slow hota jaata hai. Aur, crust chocolate ke andar khaata hai: uska kuch hissa wahan hai jahan pehle chocolate tha. Bilkul yahi silicon apne aap par glass grow karne mein karta hai: pehle fast, phir slower, aur grow hote hue andar dhansata hai.

Connections

Fick's Law of Diffusion — $D (C_{s} - C_{i}) / x$ flux term ka source
Arrhenius Equation — $B$ aur $B / A$ ki temperature dependence
Photolithography — SiO₂ as mask use hoti hai / oxidation ke baad pattern hoti hai
Ion Implantation — oxide as screen/mask layer
MOSFET Gate Oxide — thin dry oxide ka critical application
LOCOS Isolation — device isolation ke liye thick wet field oxide
Deal-Grove Model — yahan derive kiya gaya parent model