Crystal lattice structure of silicon — Hinglish notes

1.3.4 · Hardware › Materials & Atomic Structure

Silicon lattice KYA hai?

Diamond cubic KYO? Silicon periodic table ke group IV mein hai → iske paas 4 valence electrons hain. Har atom apne outer shell mein 8 electrons chahta hai. 4 neighbours mein se har ek ke saath ek electron share karke (4 shared pairs = har atom ke around 8 electrons), har atom satisfied ho jaata hai. Chaar neighbours jo equally door-door push karte hain woh khud ko ek tetrahedron mein arrange kar lete hain — yahi geometry, space mein tile hoke, hai diamond cubic lattice.

Bonding HOW geometry force karti hai

Tetrahedral bond angle scratch se derive karna:

Ek tetrahedron ke 4 vertices ko ek cube ke alternate corners par rakhein: $a = (1, 1, 1), b = (1, - 1, - 1), c = (- 1, 1, - 1), d = (- 1, - 1, 1)$

Central atom origin par hai. Do bonds ke beech ka angle (maano $a$ aur $b$ ki taraf) dot product se aata hai: $cos θ = \frac{a \cdot b}{∣ a ∣∣ b ∣}$

Yeh step kyun? Vectors ke beech ka angle define hota hai dot product se; yahi ek tool chahiye.

$a \cdot b = (1) (1) + (1) (- 1) + (1) (- 1) = - 1, ∣ a ∣ = ∣ b ∣ = 3$ $cos θ = \frac{- 1}{3} \Rightarrow θ = arccos (- \frac{1}{3}) \approx 109.4 7^{\circ}$

Yeh step kyun? Numbers plug in karo. Negative cosine humein batata hai ki angle obtuse hai — bonds ek doosre se door point kar rahe hain, jo maximum spread confirm karta hai.

Unit cell mein actually kitne atoms hain?

8 aur 2 se kyun divide karte hain? Ek corner atom ek "communal" shared atom hai — iska sirf 1/8 hissa is cube ka hai; ek face atom 2 cubes ke beech split hota hai. 4 tetrahedral interior atoms poori tarah is cell ke hain.

Figure — Crystal lattice structure of silicon

Chips ke liye yeh KYO matter karta hai

Common mistakes

Recall Feynman: 12-saal ke bachche ko samjhao

Socho ek giant, perfectly neat 3D jungle-gym jahan har ball exactly 4 doosri balls se rods se connected hai, ek pyramid tent ki tarah phaili hui. Silicon atoms khud ko is exactly repeating cage mein banate hain. Kyunki har atom 4 dosto ke saath haath thamta hai, unme se koi bhi freely ghoomna nahi chahta — isliye silicon electricity barely conduct karta hai. Lekin agar hum isse thoda garam karein, ya ek alag tarah ka atom sneakily daal dein, toh kuch "haath" choot jaate hain aur electricity flow kar sakti hai. Wahi controllable in-between-ness hai jiske liye hum iske se computer chips banate hain!

Flashcards

Silicon kaun si crystal structure form karta hai?

Diamond cubic — do aapas mein ghuse hue FCC lattices jo body diagonal ke 1/4 se offset hain.

Har Si atom ke kitne nearest neighbours hain, aur kis geometry mein?

4 neighbours ek tetrahedron mein arranged hain.

Tetrahedral bond angle kya hai aur yeh derive kaise hota hai?

109.4 7^{\circ} = arccos (- 1/3)

, alternate cube corners tak vectors ke dot product se.

Silicon ke diamond-cubic unit cell mein kitne atoms hain?

8 (= 8×1/8 corners + 6×1/2 faces + 4 interior).

Silicon ki lattice constant kya hai?

a \approx 5.43 \overset{˚}{A}

(0.543 nm).

Silicon ki atomic density kya hai?

\approx 5.0 \times 1 0^{22} atoms/cm^{3}

Silicon 4 bonds kyun banata hai?

Yeh group IV mein hai jisme 4 valence electrons hain; 4 neighbours mein se har ek ke saath ek share karne se har atom ko full octet (8 electrons) milta hai.

Silicon ki bond length

a

ke terms mein kya hai?

\frac{3}{4} a \approx 2.35 \overset{˚}{A}

(body diagonal ka quarter).

Semiconductors ke liye periodic lattice kyun matter karta hai?

Periodicity energy band gap (

E_{g} \approx 1.12

eV) create karti hai; ordered lattice ke bina, band structure aur device behaviour degrade ho jaata hai.

0 K par, kya pure silicon conductor hai ya insulator, aur kyun?

Insulator — saare electrons bonds mein locked hain, koi move karne ke liye free nahi.

Connections

Face-centred cubic (FCC) lattice
Diamond cubic structure
Valence electrons and the octet rule
Energy band gap in semiconductors
Holes and electrons as charge carriers
Doping of silicon
Single-crystal silicon wafer manufacturing
Miller indices and crystal planes