Formation of a PN junction — Hinglish notes

2.2.4 · Hardware › Doping & PN Junctions

PN junction KYA hai?

Contact se pehle ke key players:

Region	Majority carriers	Minority carriers	Fixed ions (immobile)
p-type	holes ( $p$ )	electrons	negative acceptor ions $N_{A}^{-}$
n-type	electrons ( $n$ )	holes	positive donor ions $N_{D}^{+}$

HOW banta hai — 4 steps mein poori kahani

Step 1 — Diffusion (concentration barabar hona chahti hai). N-side par electrons bahut zyada hain aur p-side par holes bahut zyada hain. Ek concentration gradient exist karta hai.

Step 2 — Fixed ions ka uncover hona (depletion region). Jab ek electron n-side chhodta hai, peeche ek fixed positive donor ion $N_{D}^{+}$ reh jaata hai. Jab ek hole p-side chhodta hai, peeche ek fixed negative acceptor ion $N_{A}^{-}$ reh jaata hai. Junction ke paas mobile carriers bahar nikal jaate hain.

Step 3 — Built-in electric field. Exposed ions ek dipole banate hain: n-side par $+$ ions, p-side par $-$ ions. Yeh ek internal electric field $E$ banata hai jo n→p direction mein point karta hai (+ charge se − charge ki taraf).

Step 4 — Equilibrium (drift, diffusion ko cancel karta hai). Diffusion carriers ko across push karne ki koshish karta rehta hai; badhta hua field unhe wapas push karta hai (drift). Region tab tak badhta hai jab tak: $J_{diffusion} = J_{drift} \Rightarrow J_{net} = 0$ Is balance par ek stable built-in potential $V_{bi}$ depletion region ke across exist karta hai aur koi external current flow nahi karta.

Built-in potential $V_{bi}$ ko first principles se derive karna

Yeh step kyun? Hum $E = - \frac{d V}{d x}$ use karte hain (field, potential ka negative slope hai) taaki field ko potential se replace kar sakein: $0 = - q μ_{n} n \frac{d V}{d x} + q D_{n} \frac{d n}{d x}$

Yeh step kyun? $q n$ se divide karo aur variables alag karne ke liye rearrange karo: $\frac{d V}{d x} = \frac{D _{n}}{μ _{n}} \frac{1}{n} \frac{d n}{d x}$

Yeh step kyun? Einstein relation $\frac{D _{n}}{μ _{n}} = \frac{k T}{q}$ use karo (thermal voltage $V_{T} = k T / q$ ), jo diffusion ko thermal energy se link karta hai: $d V = \frac{k T}{q} \frac{d n}{n}$

Yeh step kyun? p-side ( $V_{p}$ , electron conc. $n_{p}$ ) se n-side ( $V_{n}$ , electron conc. $n_{n}$ ) tak integrate karo: $V_{n} - V_{p} = \frac{k T}{q} ln \frac{n _{n}}{n _{p}}$

Toh:

Depletion width intuition (Forecast-then-Verify)

Flashcards

PN junction physically kya hai?

Single continuous crystal ke andar woh boundary jahan doping p-type se n-type ho jaati hai.

Junction form hone par kaun se carriers diffuse karte hain aur kis direction mein?

Electrons n→p diffuse karte hain aur holes p→n diffuse karte hain (high se low concentration ki taraf).

Depletion region kya hai?

Junction ke paas woh zone jo mobile carriers se khali ho jaata hai, sirf fixed dopant ions contain karta hai.

Har side par exposed ions ke signs kya hain?

P-side par negative acceptor ions, n-side par positive donor ions.

Built-in electric field kis direction mein point karta hai?

N-side se p-side ki taraf (positive ions se negative ions ki taraf).

Junction equilibrium ki condition kya define karti hai?

Drift current, diffusion current ko exactly cancel karta hai, toh net current = 0.

Built-in potential formula batao.

V_{bi} = (k T / q) ln (N_{A} N_{D} / n_{i}^{2})

Room temperature par silicon ka typical

V_{bi}

Lagbhag 0.6–0.7 V.

Derivation mein use ki gayi Einstein relation?

D / μ = k T / q

(thermal voltage).

Depletion region kis side par zyada wide hoti hai?

Zyada lightly doped side par (kyunki

N_{A} x_{p} = N_{D} x_{n}

Ek shorted diode mein

V_{bi}

current kyun drive nahi karta?

Metal contacts par contact potentials use cancel kar dete hain; net loop EMF zero hota hai.

Recall Feynman: ek 12-saal ke bacche ko samjhao

Socho ek bheed bhari room (n-side par electrons) ke saath ek khali room jisme bohot saari khali kursiyan hain (holes on p-side). Log bheed wali room se khali room mein kursi par baithne ke liye bhaagte hain — yahi diffusion hai, aur har baithna ek recombination hai. Lekin jo bhi banda bheed wali room chhodta hai, woh wall par ek "+" sticker chhod jaata hai, aur har bhari hui kursi doosri wall par ek "−" sticker lagaati hai. Jald hi "+" stickers ki ek wall logon ko wapas kheenchti hai aur "−" stickers unhe wapas push karti hain. Aakhirkar pushing, rushing ko balance karta hai, aur sab kuch ruk jaata hai. Stickers ki woh invisible wall depletion region hai, aur jo pull woh banati hai woh built-in voltage hai.

Connections

Doping of Semiconductors — pehle se hi p aur n regions banata hai.
Intrinsic vs Extrinsic Semiconductors — $n_{i}$ aur mass-action law $n p = n_{i}^{2}$ ka source.
Diffusion and Drift Currents — woh do currents jo equilibrium par balance hote hain.
PN Junction under Bias — jab external voltage apply karo tab kya hota hai.
Diode I-V Characteristics — is barrier par built exponential curve.
Einstein Relation — $D / μ = k T / q$ bridge.