Foundations — Yield, defect density, and binning

4.3.21 · D1 · Hardware › Semiconductor Fabrication › Yield, defect density, and binning

Yeh Yield, defect density, and binning ka ground-floor page hai. Agar wahan koi symbol confuse kar gaya, toh woh yahan zero se define kiya gaya hai. Upar se neeche padho — har item mein sirf wahi cheezein use hoti hain jo uske upar define ho chuki hain.

1. Wafer — ek round disk

Ek round pizza imagine karo. Radius centre-to-crust hai; diameter crust-to-crust seedha beech se hai. Fabs wafers ko diameter se quote karte hain ("a 300 mm wafer"), isliye tum constantly convert karte ho: agar $d=300$ mm toh $r=150$ mm $=15$ cm.

2. Area — flat jagah ki miqdar

Square (woh chota ${}^2$) kyun? Area do directions mein rehta hai — width aur height — isliye iski units length times length hoti hain, jaise centimetres times centimetres, likha jaata hai ${\text{cm}}^2$ ("square centimetres"). Ek akela direction (ek line) kisi surface ko cover nahi kar sakti.

Hum ek ko doosre se divide karenge thodi der mein — yahi "kitne chips fit hote hain" ka poora idea hai.

3. Die aur gross dies-per-wafer (DPW)

Sabse pehla estimate bas "bada area ÷ chhota area" hai:

$\text{ideal count}=\frac{\pi r^2}{A}=\frac{\text{poore wafer par jagah}}{\text{ek chip ko jo jagah chahiye}}.$

4. Defect density $D_0$ — process kitna dirty hai

Picture yeh hai: poore wafer par namak chidko. $D_0$ yeh nahi ki daane kahan gire — yeh hai ki tum ne kitna chidka, average mein, per square centimetre.

5. $\lambda$ — ek die par expected defects

Units cancel hokar ek pure count dete hain: $\frac{\text{defects}}{{\text{cm}}^2}\times {\text{cm}}^2=\text{defects}$. Agar tum $0.5$ defects/cm² chidkte ho aur ek die $2$ cm² hai, toh tum us par $1$ defect expect karte ho — hamesha exactly ek nahi, lekin average mein ek.

6. $e$ aur exponential — survival curve

Figure se shape padho: $\lambda =0$ par (ek spotless process) survival $e^0=1=100\%$ hai. Jaise $\lambda$ badhta hai, survival fast girta hai lekin kabhi zero nahi chhoota — hamesha ek slim chance hoti hai ki ek bada die lucky raha.

Poora reason kyun exactly yahi curve (aur koi dusri nahi) defects govern karti hai woh Poisson distribution hai — D2 page usse derive karta hai; yahan tumhe sirf shape par trust karna hai.

7. Yield $Y$ — punchline fraction

Aage ka sab kuch — wafer per good dies, cost — bas yeh $Y$ section 3 ke counts se multiply ya divide hai. Chips banne ke baad $Y$ actually kaise measure kiya jaata hai uske liye Wafer testing and probe dekho.

8. Clustering knob $\alpha$

9. Cost per good die — counts aur fraction ko saath laana

Picture yeh hai: tum poori pizza ke paisa dete ho chahe har slice edible ho ya na ho, isliye tum price sirf achhi slices mein divide karte ho. Yeh Chip economics and cost per transistor ka bridge hai aur isliye bhi ki giant dies ko Chiplets and MCM mein kyun kaat diya jaata hai.

10. Binning — survivors ko sort karna

Picture yeh hai: achhi cookies taste karne ke baad, jo sabse crunchy hain woh "premium" box mein jaate hain aur jo softer hain woh "budget" box mein. Koi naya recipe nahi — wahi die alag prices par.

Prerequisite map

Equipment checklist