2.3.5 · Hardware › Diodes & Applications
Intuition Ek-sentence ki picture
Ek photodiode aur ek solar cell same reverse-biased-friendly PN junction hain, lekin same I–V curve ke opposite corners mein kaam karte hain: photodiode light ko measure karta hai (hume current signal ki parwah hai), jabki solar cell light ko harvest karta hai (hume V × I ki power ki parwah hai jo woh deliver karta hai). Dono isliye kaam karte hain kyunki enough energy wala ek photon ek bond todta hai aur ek free electron–hole pair create karta hai , aur junction ka built-in field us pair ko recombine hone se pehle alag kar deta hai.
Definition Core physical event
Jab photon energy E p h = h ν ki light semiconductor material pe padti hai, toh woh ek electron ko valence band se conduction band mein promote karne ke liye absorb ho sakti hai sirf tab jab E p h ≥ E g (bandgap) ho. Isse ek free electron–hole pair (EHP) create hota hai. Yahi photovoltaic / photoconductive effect hai.
Bandgap threshold KYUN? Ek electron jo valence band mein baitha hai woh "bonded" hai. Usse free karne ke liye tumhe kam se kam energy gap E g supply karni padegi. Ek photon exactly h ν energy ka ek packet hai; agar woh packet bahut chhota hai, toh woh gap bridge nahi kar sakta aur bas guzar jaata hai (material uske liye transparent hai).
E p h = h ν = λ h c ≥ E g ⇒ λ ≤ λ ma x = E g h c
Intuition Depletion region ek one-way conveyor belt hai
Depletion region ke andar n → p direction mein point karta ek built-in electric field hota hai. Jab ek photon wahan (ya paas mein, taaki carriers diffuse in kar sakein) ek EHP create karta hai, toh field electron ko n-side ki taraf aur hole ko p-side ki taraf dhakelta hai. Yeh directed flow ==photocurrent I L == hai (isse I p h ya I sc -source bhi kehte hain). Importantly, yeh diode ki reverse direction mein flow karta hai.
Toh total diode current ordinary diode equation minus ek light-generated term ban jaati hai:
I = normal diode I 0 ( e V / n V T − 1 ) − light I L
Minus sign KYUN? Photocurrent ek reverse (n→p external) current hai, forward diode current ke sign ke opposite. Zyada light ⇒ bada I L ⇒ poori I–V curve neeche shift ho jaati hai.
Definition Photodiode operation
Reverse bias mein operate hota hai (V < 0 ). Exponential diode term chhoti hoti hai (≈ − I 0 ), toh:
I ≈ − ( I 0 + I L )
Measured reverse current ==dark current I 0 plus ek photocurrent I L hai jo light intensity ke proportional hai==. Hum current se intensity padhte hain.
Reverse bias KYUN?
Depletion region ko wider karta hai ⇒ bada collection volume ⇒ zyada EHPs catch hote hain.
Wider ⇒ lower junction capacitance ⇒ faster response (high-speed optical comms).
Linear relation I L ∝ optical power ⇒ ek clean measurement.
Intuition Same curve, fourth quadrant
Koi battery connected nahi hai. Light I L ko flow karne ke liye force karti hai; woh current load ke across junction ko forward-bias karta hai, toh cell positive voltage develop karta hai jabki current bahar push karta hai — yeh power deliver karta hai. Hum us region mein operate karte hain jahan V > 0 aur I < 0 (+ terminal se current bahar): diode I–V ka fourth quadrant , yaani power-generating quadrant.
Do key operating points, dono I = I 0 ( e V / n V T − 1 ) − I L se derived:
Definition Fill factor & efficiency
Real max power P ma x = V m p I m p ek interior "knee" par hoti hai. ==Fill factor F F = V oc I sc V m p I m p == measure karta hai ki curve kitna "square" hai (typical Si ≈ 0.7–0.8). Efficiency η ce l l = P in , o pt i c a l P ma x = P in F F V oc I sc .
Worked example 1 — Silicon cut-off wavelength
Q: Si (E g = 1.12 eV) ki sabse lambi wavelength jo detect ho sake?
Use karo λ ma x = 1.24/ E g = 1.24/1.12 = 1.107 μ m .
Yeh step kyun? Humne h c / E g ke liye engineer's shortcut use kiya taaki SI constants ke saath juggle na karna pade. Answer: ≈ 1.1 μm (near-IR) — Si visible + near-IR ke liye kaam karta hai, fiber-optic 850 nm systems se match karta hai.
Worked example 2 — Photodiode ki responsivity
Q: η = 0.8 at λ = 850 nm. R find karo.
R = h c η q λ = 6.63 × 1 0 − 34 × 3 × 1 0 8 0.8 × 1.6 × 1 0 − 19 × 850 × 1 0 − 9
= 1.989 × 1 0 − 25 1.088 × 1 0 − 25 ≈ 0.55 A/W .
Yeh step kyun? Numerator = charge liberated per second per watt; denominator = energy per photon. Unka ratio current per watt hai. Toh 850 nm light ka 1 mW ≈ 0.55 mA deta hai.
Worked example 3 — Solar cell ka open-circuit voltage
Q: I L = 35 mA, I 0 = 1 nA, n = 1 , V T = 25.9 mV. V oc find karo.
V oc = 0.0259 ln ( 1 × 1 0 − 9 35 × 1 0 − 3 ) = 0.0259 ln ( 3.5 × 1 0 7 )
= 0.0259 × 17.37 ≈ 0.45 V .
Yeh step kyun? Bada ratio I L / I 0 ek ln ke andar baitha hai, toh 3.5 × 1 0 7 bhi sirf ~0.45 V deta hai — yahi reason hai ki ek single Si cell sirf ~0.5–0.6 V hoti hai aur panels mein bahut saari cells series mein chahiye hoti hain.
Common mistake "Zyada intense light matlab photodiode ka zyada voltage/current, aur voltage ke liye bhi simple linear ramp hai."
Kyun sahi lagta hai: intensity clearly output control karti hai, aur current is linear hai (I L ∝ intensity), toh voltage bhi hona chahiye. Fix: current linear hai lekin V oc ∝ ln ( I L ) — logarithmic. Voltage saturate hota hai; intensity mostly current dilati hai, voltage nahi.
Common mistake "Photodiode aur solar cell alag devices hain."
Kyun sahi lagta hai: ek detect karta hai, ek generate karta hai; alag packages. Fix: yeh same PN junction hain, same equation I = I 0 ( e V / n V T − 1 ) − I L se describe hote hain. Sirf operating quadrant differ karta hai (reverse-bias 3rd quadrant vs. power-generating 4th quadrant).
Common mistake "Koi bhi color ka light, agar bright enough ho, electrons free kar dega."
Kyun sahi lagta hai: zyada brightness = surface pe zyada energy. Fix: absorption per-photon energy h ν par depend karta hai, total brightness par nahi. Agar h ν < E g hai, toh us wavelength ki andhi kar dene wali beam bhi kuch free nahi karegi — woh bas guzar jaayegi. (Yeh solid state mein photoelectric-effect ka lesson hai.)
Common mistake "Photocurrent forward diode current ki same direction mein flow karta hai."
Kyun sahi lagta hai: yeh "diode se current" hai, toh surely same direction. Fix: built-in field electrons ko n ki taraf aur holes ko p ki taraf sweep karta hai — yeh reverse direction hai, isliye − I L sign hai. Sign galat karo toh I sc = − I L explain nahi kar sakte.
Ek photon ko electron–hole pair create karne ke liye kya condition satisfy karni chahiye? E p h = h ν ≥ E g (photon energy ≥ bandgap).
Cut-off wavelength ka formula aur engineer's shortcut? λ ma x = h c / E g ≈ 1.24/ E g ( eV ) μ m .
Reverse bias ek photodiode ki help KYUN karta hai? Depletion region wider hoti hai (zyada collection, faster) aur junction capacitance kam hoti hai (faster response).
Dono devices ko cover karne wali full I–V equation? I = I 0 ( e V / n V T − 1 ) − I L .
Solar cell ka short-circuit current? I sc = I L (V = 0 set karo, diode term vanish ho jaata hai).
Solar cell ka open-circuit voltage? V oc = n V T ln ( I L / I 0 + 1 ) ; light ke saath sirf logarithmically badhta hai.
Responsivity ki definition? R = I L / P o pt = η q λ / ( h c ) ; light ke watt per current.
Ek Si cell ka V oc sirf ~0.5 V KYUN hota hai? Kyunki yeh n V T ln ( I L / I 0 ) hai — ek bade ratio ka log phir bhi chhota number deta hai.
Fill factor kya hai? F F = V m p I m p / ( V oc I sc ) ; I–V curve kitna square/ideal hai.
Solar cell kis quadrant mein operate karta hai? Fourth quadrant (V>0, I<0): power-deliver karne wala region.
Recall Feynman: 12-saal ke bachche ko explain karo
Ek chhoti pahadi par ek tiny gate imagine karo. Sunlight chhoti energy-bullets jaisi hai. Agar ek bullet strong enough ho, toh woh ek marble knock loose kar deti hai. Pahadi (built-in field) loose marbles ko hamesha ek side neeche roll karti hai, toh woh pile up ho jaate hain aur ek toy car (electricity!) push kar sakte hain. Agar tumhe sirf bullets count karni hain, toh pahadi ko hard tilt karo (reverse bias) aur dekho marbles kitni tez roll karte hain — yahi photodiode hai. Agar tumhe marbles se apni toy car power karni hai, toh unhe pile up hone do aur ek wheel ghoomne do — yahi solar cell hai. Same pahadi, do kaam. Aur ek weak, wimpy bullet (bahut red light) koi marble knock loose nahi kar sakti, chahe kitni bhi throw karo.
Mnemonic Dono modes yaad karo
"DVoc, harvests; Detect, reverse."
S olar cell = S ame junction, S hort-circuit deta hai I sc = I L , aur V oc ek V ery-slow log hai. PhotoD iode = D etect, D riven in reverse. Sign rule: light current I = I 0 ( e ... − 1 ) − I L mein L oser (minus) hai.
PN Junction Diode — same device physics, built-in field & depletion region.
Diode I-V Characteristic Equation — parent equation jisme se humne I L subtract ki.
Reverse Bias and Depletion Width — kyun reverse bias detection speed up karta hai.
Bandgap and Semiconductor Materials — λ ma x set karta hai; kyun Si vs GaAs vs Ge differ karte hain.
LEDs — inverse device (current → light instead of light → current).
Photoelectric Effect — E p h ≥ E g threshold ki quantum root.
absorbed only if hv >= Eg
gives lambda_max approx 1.1 um
Cut-off wavelength lambda_max = hc/Eg
Built-in field in depletion region
Photocurrent I_L reverse direction
Diode eqn I = I0 exp - 1 minus I_L
Silicon Eg approx 1.12 eV