Shockley diode equation — Hinglish notes

2.2.10 · Hardware › Doping & PN Junctions

Ye kya hai?

Isko first principles se derive karna (Derivation-from-scratch)

HUM KYA BANATE HAIN: current = charge jo depletion edge ke across per second diffuse karta hai.

Step 1 — Barrier aur Boltzmann statistics. Equilibrium mein junction ka ek built-in potential $V_{bi}$ hota hai. Majority carriers ki wo sankhya jinke paas barrier chadne ke liye kaafi energy hai, Boltzmann factor $e^{- q V_{bi} / k T}$ follow karti hai. Ye step kyun? Carriers ko thermally electrostatic hill hop karni padti hai; jo fraction kar sakta hai wo barrier height mein exponential hota hai — ek universal statistical-mechanics result.

Step 2 — Bias lagao. Forward bias $V$ barrier ko $V_{bi} - V$ tak giraa deta hai. To jo population cross kar sakti hai wo scale karti hai: $e^{- q (V_{bi} - V) / k T} = e^{- q V_{bi} / k T} \cdot e^{q V / k T}$ Ye step kyun? Applied voltage directly electrostatic hill ko shift karta hai; choti hill exponentially zyada carriers ko upar jaane deti hai.

Step 3 — Injected minority-carrier concentration. Equilibrium minority concentration $n_{p 0}$ mein pehle se $e^{- q V_{bi} / k T}$ factor hai. To bias ke under depletion edge par injected excess hai: $n_{p} (0) = n_{p 0} e^{q V / k T}$ Equilibrium se upar excess: $Δ n = n_{p 0} (e^{q V / k T} - 1)$ Ye step kyun? Current un carriers se drive hoti hai jo equilibrium se zyada hain — hum equilibrium wala $1$ subtract karte hain.

Step 4 — Gradient se diffusion current. Ye injected carriers diffuse hote hain aur ek diffusion length $L_{n}$ par recombine karte hain. Diffusion current density (Fick's law) hai: $J_{n} = q D_{n} \frac{Δ n}{L _{n}} = \frac{q D _{n} n _{p 0}}{L _{n}} (e^{q V / k T} - 1)$ Symmetric hole term add karke: $J = J_{S} (\frac{q D _{n} n _{p 0}}{L _{n}} + \frac{q D _{p} p _{n 0}}{L _{p}}) (e^{q V / k T} - 1)$ Ye step kyun? Concentration gradient hamesha diffusion drive karta hai; injected excess $L$ ke upar decay karta hai, slope $Δ n / L$ deta hai.

Step 5 — Constants bundle karo. Area $A$ se multiply karo aur $n$ aur $V_{T} = k T / q$ insert karo: $I = I_{S} (e^{V / (n V_{T})} - 1)$

Equation padhna (teen regimes)

Worked examples

Common mistakes (Steel-man then fix)

Recall Feynman: ek 12-saal ke bachche ko explain karo

Ek pahadi socho jisme ek taraf ke bachche doosri taraf slide karna chahte hain. Pahadi unchi hai, to sirf kuch hi upar se jaate hain — wahi kuch "leakage" hain. Ab tum poori slide ko thoda neeche dhakka do (yahi voltage hai). Har chota dhakka sirf kuch aur bachcho ki madad nahi karta — har chote dhakke se das guna zyada bachche upar se jaate hain! Yahi wajah hai ki ek diode "almost no current" se "bahut current" par ek chote se voltage range mein pahunch jaati hai. Aur agar tum pahadi galat taraf tilted karo, phir bhi sirf wahi chota sa group trickle karta hai — chahe kitna bhi hard tilted karo.

Active-recall flashcards

Shockley diode equation likho.

I = I_{S} (e^{V / (n V_{T})} - 1)

V_{T}

kya hai aur 300 K par iska value kya hai?

Thermal voltage

V_{T} = k T / q \approx 26 mV

at 300 K.

- 1

" term kyun hai?

I = 0

V = 0

par force karta hai aur reverse bias mein constant

- I_{S}

leakage deta hai.

I_{S}

physically kahan se aata hai?

Minority carriers ka diffusion:

I_{S} \propto \frac{q D _{n} n _{p 0}}{L _{n}} + \frac{q D _{p} p _{n 0}}{L _{p}}

(times area).

Strong forward bias mein approximate current?

I \approx I_{S} e^{V / n V_{T}}

(

- 1

chhod do).

Strong reverse bias mein approximate current?

I \approx - I_{S}

(leakage par saturate karta hai).

Current ko 10 se multiply karne ke liye kitna extra voltage chahiye (

n = 1

V_{T} ln 10 \approx 60 mV

I se V get karne ke liye equation invert karo.

V = n V_{T} ln (\frac{I}{I _{S}} + 1)

Ideality factor

n

kya hai aur iska range kya hai?

Recombination ke liye correction;

n = 1

ideal,

1

–

2

real diodes.

Barrier crossing govern karne wala statistical factor?

Boltzmann factor

e^{- q V_{bi} / k T}

; bias barrier ko

V

se giraa deta hai.

Connections

PN Junction — wo device jise ye equation model karti hai
Depletion Region — jahan $I_{S}$ aur injection hoti hai
Built-in Potential — barrier $V_{bi}$ jo Boltzmann factor chadta hai
Diffusion Current — Step 4 mein use ki gayi Fick's law
Minority Carriers — $I_{S}$ ki magnitude set karte hain
Thermal Voltage — $V_{T} = k T / q$
Diode I-V Characteristic — plotted curve
Reverse Breakdown — jahan ideal model fail hota hai