Semiconductor Cheatsheet

ece-1109 ECE-1109 Introduction to ECE

📘 Semiconductor Physics & Diode Fundamentals – Cheat Sheet

1. Band Theory & Classification

Energy Band: Closely spaced energy levels from overlapping atomic orbitals.
Valence Band (VB): Occupied by valence electrons.
Conduction Band (CB): Empty, higher-energy band where electrons move freely.
Forbidden Band (Eg): Energy gap between VB and CB.

Material	Band Relation	Eg (eV)	Behavior
Conductor	VB & CB overlap	0	High conductivity
Insulator	Wide gap	~15	No conduction
Semiconductor	Narrow gap	< 2	Conductivity ↑ with T

2. Carrier Generation & Transport

At T=0 K: All electrons bound.
With ↑T: Electrons jump VB → CB, leaving holes.
Drift Current: Due to applied field $E$ .
- Electrons: $J_{n} = e n μ_{n} E$
- Holes: $J_{p} = e p μ_{p} E$
- Total: $J = e (n μ_{n} + p μ_{p}) E$
Diffusion Current: Due to concentration gradient.
- Electrons: $J_{n} = e D_{n} \frac{d n}{d x}$
- Holes: $J_{p} = e D_{p} \frac{d p}{d x}$

3. Extrinsic Semiconductors

N-type: Pentavalent dopants (P, As, Sb) → extra electrons.
P-type: Trivalent dopants (B, Al, Ga) → holes.
Fermi Level (EF):
- Intrinsic: Mid-gap.
- N-type: Near CB.
- P-type: Near VB.

Carrier balance: $n_{0} p_{0} = n_{i}^{2}$

N-type: $n_{0} \approx N_{D}, p_{0} = n_{i}^{2} / N_{D}$
P-type: $p_{0} \approx N_{A}, n_{0} = n_{i}^{2} / N_{A}$

4. p–n Junction

Formation: Electrons diffuse N→P, holes P→N → leaves fixed ions → depletion region.
Built-in Potential (V0): Electric field barrier balances diffusion & drift.
Depletion Width (W): Inversely proportional to doping.

Biasing:

Forward: (+P, –N) → Barrier ↓, diffusion dominates → large current.
Reverse: (+N, –P) → Barrier ↑, drift dominates → small leakage.

5. Diode Characteristics

Diode Equation: [ I_D = I_s \left(e^{V_D / (\eta V_T)} - 1 \right) ]
Forward: Exponential growth.
Reverse: $I_{D} \approx - I_{s}$ (small leakage).
Temperature:
- Forward voltage ↓ with T.
- Reverse current doubles per ~10°C.

6. Breakdown Mechanisms

Avalanche: Low doping, high Vr. Carriers collide → impact ionization.
Zener: High doping, thin depletion → tunneling.

7. Diode Resistances & Capacitances

Static Resistance: $R_{D C} = V_{D} / I_{D}$
Dynamic Resistance: $r_{d} = η V_{T} / I_{D}$
Transition Capacitance (CT): Reverse bias, decreases with Vr.
Diffusion Capacitance (CD): Forward bias, increases with Vf.
Reverse Recovery Time (trr): Switching delay.

8. Direct vs Indirect Semiconductors

Direct bandgap: VB max & CB min at same k → efficient light emission (LED, Laser).
Indirect bandgap: Require phonon for transition → poor emitters (e.g., Si).

📌 Key Values:

Si: Eg ≈ 1.1 eV, Vf ≈ 0.7 V
Ge: Eg ≈ 0.66 eV, Vf ≈ 0.3 V
Thermal Voltage (VT): ≈ 26 mV at 300K