📘 ELECTRONIC DEVICES - GATE NUMERICAL CHEATSHEET
🎯 QUESTION → FORMULA MAPPING
1️⃣ MASS ACTION LAW ⭐⭐⭐
Formula
np = n2i
When to Use
"Find minority carrier concentration"
"Given n-type/p-type doping"
"At thermal equilibrium"
Example Trigger
"An n-type silicon has donor concentration 10¹⁶ cm⁻³. Find hole concentration."
n2
i
Action: p = ND
2️⃣ DOPING APPROXIMATION ⭐⭐⭐
Formulas
2
N-type: n ≈ ND , p = NnD
i
2
P-type: p ≈ NA , n = NnA
i
When to Use
Doping ≫ nᵢ
Room temperature (300 K)
"Assume complete ionization"
, 3️⃣ FERMI LEVEL SHIFT ⭐⭐⭐
Formulas
N-type: Ef − Ei = kT ln ( NnD
i
)
P-type: Ei − Ef = kT ln ( NnA
i
)
When to Use
"Position of Fermi level"
"How far Ef shifts from Ei"
"Energy difference in eV"
Shortcut at 300 K
kT
= 0.026 V
q
Sign interpretation:
Positive → n-type
Negative → p-type
4️⃣ DRIFT CURRENT ⭐⭐⭐⭐
Formulas
Drift velocity: vd = μE
Current density: J = q(nμn + pμp )E
Conductivity: σ = q(nμn + pμp )
Resistivity: ρ = σ1
When to Use
"Electric field of X V/cm is applied"
Current density/conductivity asked
Uniform semiconductor
Trick
If n-type → ignore hole term, use only majority carriers
🎯 QUESTION → FORMULA MAPPING
1️⃣ MASS ACTION LAW ⭐⭐⭐
Formula
np = n2i
When to Use
"Find minority carrier concentration"
"Given n-type/p-type doping"
"At thermal equilibrium"
Example Trigger
"An n-type silicon has donor concentration 10¹⁶ cm⁻³. Find hole concentration."
n2
i
Action: p = ND
2️⃣ DOPING APPROXIMATION ⭐⭐⭐
Formulas
2
N-type: n ≈ ND , p = NnD
i
2
P-type: p ≈ NA , n = NnA
i
When to Use
Doping ≫ nᵢ
Room temperature (300 K)
"Assume complete ionization"
, 3️⃣ FERMI LEVEL SHIFT ⭐⭐⭐
Formulas
N-type: Ef − Ei = kT ln ( NnD
i
)
P-type: Ei − Ef = kT ln ( NnA
i
)
When to Use
"Position of Fermi level"
"How far Ef shifts from Ei"
"Energy difference in eV"
Shortcut at 300 K
kT
= 0.026 V
q
Sign interpretation:
Positive → n-type
Negative → p-type
4️⃣ DRIFT CURRENT ⭐⭐⭐⭐
Formulas
Drift velocity: vd = μE
Current density: J = q(nμn + pμp )E
Conductivity: σ = q(nμn + pμp )
Resistivity: ρ = σ1
When to Use
"Electric field of X V/cm is applied"
Current density/conductivity asked
Uniform semiconductor
Trick
If n-type → ignore hole term, use only majority carriers
