Schottky diodes and metal-semiconductor junctions

2.3.6 · Hardware › Diodes & Applications

YEH HAI KYA? (Definition)

BARRIER KYUN BANTA HAI? (First principles se derivation)

Step 1 — Metal mein electron jo barrier dekhta hai (the Schottky barrier). Ek electron jo metal → semiconductor jaane ki koshish karta hai, use metal Fermi level se $E_{C}$ tak climb karna padta hai. Uski height hai

$ϕ_{B} = ϕ_{M} - χ$

Yeh step kyun? Metal ka electron vacuum se $ϕ_{M}$ neeche baitha hai; semiconductor ka conduction band vacuum se $χ$ neeche hai. Difference exactly wall ki height hai. Importantly $ϕ_{B}$ applied voltage par depend nahi karta — barrier ka yeh side fixed hai.

Step 2 — Semiconductor ki taraf se barrier (the built-in potential). Contact se pehle, semiconductor ka $E_{C}$ apne $E_{F}$ se $(ϕ_{S} - χ)$ neeche hota hai. Contact ke baad $E_{F}$ , $(ϕ_{M} - ϕ_{S})$ se drop hota hai metal se match karne ke liye, isliye band upar ki taraf bend hota hai

$q V_{bi} = ϕ_{M} - ϕ_{S}$

Yeh step kyun? $V_{bi}$ woh energy hai jitni bands ko dono Fermi levels ko ek saath laane ke liye bend karna padta hai. Yeh woh barrier hai jo ek semiconductor electron dekhta hai, aur yeh forward bias se ghatta hai.

Step 3 — Dono barriers unequal hain, aur yahi poora point hai. Kyunki $ϕ_{B} = ϕ_{M} - χ$ aur $q V_{bi} = ϕ_{M} - ϕ_{S}$ , aur $ϕ_{S} = χ + (E_{C} - E_{F})_{bulk}$ : $ϕ_{B} = q V_{bi} + (E_{C} - E_{F})_{bulk}$ Isliye metal-side barrier $ϕ_{B}$ semiconductor-side barrier $q V_{bi}$ se thoda zyada uncha hai.

Figure — Schottky diodes and metal-semiconductor junctions

YEH RECTIFY KAISE KARTA HAI? (Bias behaviour)

Worked examples

Common mistakes (Steel-man → fix)

Flashcards

Schottky diode physically kya define karta hai?

Ek metal aur ek lightly-doped (usually n-type) semiconductor ke beech ek rectifying junction, jo sirf majority carriers use karta hai.

Metal / n-type semiconductor contact ke liye rectifying condition

ϕ_{M} > ϕ_{S}

Metal / p-type contact ke liye rectifying condition

ϕ_{M} < ϕ_{S}

Schottky barrier height

ϕ_{B}

(n-type) ka formula

ϕ_{B} = ϕ_{M} - χ

(metal work function minus electron affinity).

Built-in potential ka formula

q V_{bi} = ϕ_{M} - ϕ_{S}

Kya applied bias

ϕ_{B}

ko change karta hai?

Nahi — metal-side barrier fixed hota hai; sirf semiconductor-side barrier

q (V_{bi} - V)

change hota hai.

Schottky diode p–n diode se faster kyun switch karta hai?

Majority-carrier device hai → koi minority-charge storage nahi → near-zero reverse-recovery time.

Schottky vs Si p–n diode ka typical forward turn-on voltage

~0.2–0.4 V vs ~0.7 V.

Turn-on voltage lower kyun hota hai?

Lower barrier ⇒ bahut bada saturation current

I_{S} = A A^{*} T^{2} e^{- ϕ_{B} / k T}

⇒ same current chhote

V

par hi.

Depletion width ka formula

W = 2 ε_{s} (V_{bi} - V) / (q N_{D})

Agar metal ke paas semiconductor ko bahut heavily dope karo to kya hoga?

Barrier patla ho jaata hai, electrons tunnel karte hain → ohmic contact (koi rectification nahi).

Schottky diode mein current-transport mechanism kya hai?

Barrier ke upar majority electrons ki thermionic emission, jo

I = I_{S} (e^{q V / nk T} - 1)

deta hai.

ϕ_{B}

aur

q V_{bi}

ke beech relation

ϕ_{B} = q V_{bi} + (E_{C} - E_{F})_{b u l k}

Recall Feynman: 12-saal ke bachche ko explain karo

Socho ek metal aur ek special sand (semiconductor) touch kar rahe hain. Sand mein tiny electric marbles (electrons) metal ke comparison mein ek unchi shelf par baithte hain, isliye woh metal mein roll down ho jaate hain — lekin woh peeche ek "wall" of static chhod jaate hain jo aur ko aane se rokti hai. Ab: bijli ko ek taraf push karo to sand ki side ki wall neeche aa jaati hai aur marbles across flood ho jaate hain → light bahut chhoti push se jal jaati hai. Doosri taraf push karo aur metal ki wall unchi rehti hai, isliye almost kuch nahi guzarta. Aur kyunki sirf yeh fast marbles move karte hain (koi slow "hole" partners clean up karne ke liye nahi hote), switch super quickly on aur off flick karta hai.

Connections

PN Junction Diode — contrast: minority carriers, 0.7 V, reverse recovery.
Work Function and Electron Affinity — energies $ϕ_{M}, ϕ_{S}, χ$ yahan se aati hain.
Depletion Region and Poisson's Equation — $W$ formula ka source.
Thermionic Emission and Richardson's Law — $I_{S} = A A^{*} T^{2} e^{- ϕ_{B} / k T}$ ka origin.
Ohmic Contacts — heavy doping se bana non-rectifying cousin.
Rectifiers and Switching Power Supplies — jahan Schottky ki speed exploit ki jaati hai.