Diode I-V characteristic curve — Hinglish notes

2.2.9 · Hardware › Doping & PN Junctions

I-V curve KYA hai?

Poori curve Shockley diode equation mein capture hoti hai:

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

$I_{S}$ = reverse saturation current (bahut chota, Si ke liye ~ $1 0^{- 12}$ A)
$n$ = ideality factor (1–2, ≈1 ideal)
$V_{T} = k T / q$ = thermal voltage (≈ 25.85 mV at 300 K)

Yeh aisa kyun dikhta hai? (Scratch se Derivation)

PN junction mein ek built-in depletion region hoti hai jisme ek potential barrier hota hai. Carriers ko cross karne ke liye is barrier ko climb karna padta hai. Jinke paas kisi energy barrier $Δ E$ ko climb karne ke liye kaafi thermal energy hai, unki sankhya Boltzmann statistics follow karti hai:

$n (can cross) \propto e^{- Δ E / k T}$

Step 1 — equilibrium par barrier. Kisi bias ke bina, diffusion current (carriers ka climb karna) drift current (carriers ka roll back karna) ko exactly cancel karta hai. Balanced drift current ko $I_{S}$ kaho.

Yeh step kyun? Equilibrium par net current zero hona chahiye, isliye dono flows equal aur opposite hain — yeh reference current ko $I_{S}$ par pin kar deta hai.

Step 2 — forward voltage $V$ apply karo. Forward bias barrier ko energy $q V$ se lower karta hai. Naya diffusion current:

$I_{diff} = I_{S} e^{q V / k T}$

Yeh step kyun? Barrier energy ko $q V$ se lower karna Boltzmann factor ko $e^{q V / k T}$ se multiply karta hai, isliye exponentially zyada carriers cross karte hain.

Step 3 — drift current unchanged rehta hai. Drift minority carriers par depend karta hai jo field se sweep hote hain, jinki supply limited hai, barrier height par nahi. Isliye yeh $I_{S}$ par rehta hai (doosri taraf flow karte hue):

$I = I_{diff} - I_{drift} = I_{S} e^{q V / k T} - I_{S} = I_{S} (e^{q V / k T} - 1)$

Step 4 — $V_{T} = k T / q$ define karo aur real (non-ideal) recombination ke liye ideality $n$ insert karo:

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

Knee (turn-on) voltage

Koi ek sach-much threshold nahi hai — exponential smooth hai — lekin practically current $\approx$ "noticeable" ho jaati hai:

Silicon: $V_{γ} \approx 0.7$ V
Germanium: $\approx 0.3$ V
LED (varies): 1.8–3.3 V

Worked Examples

Common Mistakes

Flashcards

Shockley diode equation

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

What is

V_{T}

and its value at 300 K?

Thermal voltage

k T / q \approx 25.85

Why is the forward I-V exponential?

Barrier-crossing carriers follow Boltzmann

e^{q V / k T}

; voltage lowers the barrier exponentially

Reverse-bias current value

\approx - I_{S}

(reverse saturation / leakage), tiny aur roughly constant

What does

n

(ideality factor) represent?

Non-ideality from recombination; 1 (ideal) to 2

Voltage change per decade of current (60 mV rule)

V_{T} ln 10 \approx 59.6

Invert Shockley for V

V = n V_{T} ln (I / I_{S} + 1)

Why can we drop the "−1" in forward bias?

Kyunki

e^{V / n V_{T}} ≫ 1

jab

V ≫ n V_{T}

hota hai

Silicon vs Germanium knee voltage

Si ≈ 0.7 V, Ge ≈ 0.3 V

What happens beyond reverse breakdown

V_{B R}

Large reverse current flows (avalanche/Zener); diode backwards conduct karta hai

Effect of temperature on

I_{S}

Badhta hai (roughly har ~10 °C mein double ho jaata hai), leakage badhata hai

Recall Feynman: ek 12-year-old ko explain karo

Ek pahaad ke upar ek gate imagine karo aur bachon ki ek bheed cross karne ki koshish kar rahi hai. Normally pahaad bahut uncha hota hai — sirf kuch super-energetic bachhe hi cross kar paate hain (woh tiny leakage hai). Agar tum gate ko push karo taaki pahaad chota ho jaaye (forward voltage), toh suddenly BAHUT ZYADA bachhe climb kar sakte hain — aur jitna thoda aur chota karo, das guna zyada rush kar ke aate hain. Galat direction mein push karo aur tum pahaad ko uncha kar dete ho, isliye almost koi cross nahi karta. Woh "almost nobody, phir suddenly ek flood" exactly diode curve hai.

Connections

PN Junction — woh barrier jiska lowering hi exponential hai
Depletion Region — jahan potential barrier rehta hai
Boltzmann Distribution — $e^{q V / k T}$ term ka source
Thermal Voltage — $V_{T} = k T / q$
Zener Diode — engineered breakdown region
Doping — $I_{S}$ aur barrier height set karta hai
Diode Circuit Models — is curve ka 0.7 V approximation