Intrinsic vs extrinsic semiconductors — Hinglish notes

1.3.5 · Hardware › Materials & Atomic Structure

HUM KIS BAARE MEIN BAAT KAR RAHE HAIN?

EK PURE CRYSTAL CONDUCT KYU KARTA HAI?

Silicon (group IV) ke 4 valence electrons hain, sab $T = 0$ K par covalent bonds mein locked hain. Ek locked electron move nahi kar sakta → absolute zero par insulator jaisa behaviour.

$T > 0$ par, thermal vibration itni energy $E_{g}$ supply kar sakti hai (band gap, Si ke liye ≈ 1.12 eV) ki ek bond toot jaye. Yeh ek saath do kaam karta hai:

Conduction band mein ek free electron aa jaata hai.
Khaali hua bond ek hole hai jo positive mobile charge ki tarah behave karta hai.

Kyunki ek bond todne par hamesha ek-ek banta hai, pure crystal mein: $n = p = n_{i}$

INTRINSIC CONCENTRATION $n_{i}$ KAISE NIKALTE HAIN? (scratch se derivation)

Derive kyun karein: Taaki aap kabhi formula blindly yaad na karein.

Conduction band mein electrons ki sankhya hai (promote hone ke liye available electrons) × (promotion ki probability). Statistical mechanics ek energy gap cross karne ki promotion probability ko Boltzmann-jaisi factor ke roop mein deta hai. Puri density-of-states integral (jise hum yahan dobara nahi karenge) karne par milta hai:

$n = N_{c} e^{- (E_{c} - E_{F}) / k T}, p = N_{v} e^{- (E_{F} - E_{v}) / k T}$

jahan $N_{c}, N_{v}$ har band mein "effective density of states" hain.

Inhe multiply karein — kyun multiply? kyunki product anjaan Fermi level $E_{F}$ ko khatam kar deta hai:

$n p = N_{c} N_{v} e^{- (E_{c} - E_{v}) / k T} = N_{c} N_{v} e^{- E_{g} / k T}$

Intrinsic material mein $n = p$ , isliye: $n_{i} = N_{c} N_{v} e^{- E_{g} /2 k T}$

DOPING KAISE KAAM KARTI HAI?

n-type (donors)

Si atom ko group-V atom (P, As, Sb) se replace karein. Woh 4 bonds banata hai aur 1 electron bach jaata hai, jo bahut hi weakly (≈ 0.05 eV) bound hota hai. Room temperature par woh electron essentially free hota hai.

Har donor ek electron deta hai bina hole banaye → $n ≫ p$ .
$n \approx N_{D}$ (donor concentration).

p-type (acceptors)

Si ko group-III atom (B, Al, Ga) se replace karein. Uske paas sirf 3 electrons hain → ek bond missing hai → ek hole jo electron accept karne ke liye taiyar hai.

Har acceptor ek hole deta hai → $p ≫ n$ .
$p \approx N_{A}$ .

Figure — Intrinsic vs extrinsic semiconductors

Worked Examples

Common Mistakes

Recall Feynman: ek 12-saal ke bachche ko samjhao

Socho ek classroom jahan har bachcha haath pakad ke baith hai (bonds) — koi idhar-udhar nahi ja sakta, toh koi "current" nahi. Kamre ko garam karo aur kuch bachche haath chhodkar ghoomne lagte hain (free electrons), khaali haath-wali jagahein bhi chalti dikhai deti hain (holes). Yeh hai pure semiconductor: kamzor, bahut kam ghoomne waale. Ab ek bachche ko extra haath wala ghusao jo kisi se haath nahi mila sakta — woh spare haath wala bachcha aasaani se ghoomne lagta hai (n-type donor). Ya ek bachche ko ek haath nahi wala ghusao, ek permanent khaali jagah banao jisme doosre daudkar aate hain (p-type acceptor). Kaun se special bachche add karne hain yeh chunkar, hum design karte hain exactly ki class kaise flow karti hai.

Flashcards

n_{i}

kya hai?

Intrinsic carrier concentration — pure semiconductor mein ek diye gaye temperature par electrons aur holes ki barabar sankhya.

Ek intrinsic semiconductor mein

n

aur

p

kaise compare karte hain?

Dono barabar hote hain:

n = p = n_{i}

Law of Mass Action kya hai?

n p = n_{i}^{2} = N_{c} N_{v} e^{- E_{g} / k T}

, jo equilibrium mein kisi bhi doping ke liye valid hai.

n_{i}

temperature ke saath kyun badhta hai?

Zyada thermal energy zyada bonds todti hai, zyada electron–hole pairs generate karte hain;

n_{i} \propto e^{- E_{g} /2 k T}

Donor dopants kis group se aate hain aur kaunsa type banate hain?

Group V, n-type banate hain (extra electron).

Acceptor dopants kis group se aate hain aur kaunsa type banate hain?

Group III, p-type banate hain (extra hole).

n-type Si mein

N_{D} ≫ n_{i}

ke saath hole concentration kya hai?

p = n_{i}^{2} / N_{D}

Kya doping crystal ko electrically charged banati hai?

Nahi — dopant ka nucleus uske extra carrier ko balance karta hai; crystal neutral rehta hai.

Bada band gap

E_{g}

insulating behaviour se kyun associated hai?

n_{i}

E_{g}

ke saath exponentially girta hai, isliye thermally bahut kam carriers generate hote hain.

Ek extrinsic device kab "intrinsic ho jaata hai"?

Jab temperature itna badh jaaye ki

n_{i} (T)

doping concentration ke comparable ho jaaye.

Hum holes ko particles ki tarah track kyun kar sakte hain?

Khaali bond tab move karta hai jab neighbouring electrons hop karte hain, ek mobile positive charge

+ e

ki tarah behave karta hai.

Connections

Band gap and energy bands
Fermi level and Fermi-Dirac statistics
Silicon crystal structure and covalent bonding
PN junction diode — n aur p dono regions chahiye
Carrier mobility and drift current
Temperature dependence of resistance in semiconductors