🔮 Semiconductor Basics

PN junctions, diode characteristics, BJT operating regions, and MOSFET fundamentals — with diagrams.

PN Junction

What is a PN Junction?

A PN junction forms when p-type silicon (doped with boron — extra holes) is joined to n-type silicon (doped with phosphorus — extra electrons).

At the boundary, electrons from the n-side diffuse into the p-side and recombine with holes, creating a depletion region that acts as a barrier to further flow.

Built-in barrier voltage ≈ 0.7 V (silicon) | ≈ 0.3 V (germanium)

Forward vs Reverse Bias

Forward bias: Positive voltage on the p-side shrinks the depletion region. At ≈0.7 V (silicon) current flows freely.

Reverse bias: Positive voltage on the n-side widens the depletion region. Only tiny leakage current flows until breakdown voltage is reached.

BJT Operating Regions

NPN BJT — Four Operating Regions

Three terminals: Base (B), Collector (C), Emitter (E). For NPN: IC = β × IB in the active region.

Region	B-E Junction	B-C Junction	Condition	Use
Cutoff	Reverse	Reverse	IB = 0, IC ≈ 0	Switch OFF
Active (Linear)	Forward	Reverse	IC = β×IB	Amplifier
Saturation	Forward	Forward	VCE ≈ 0.2 V	Switch ON
Reverse Active	Reverse	Forward	IC = βR×IB	Rarely used

IC = β × IB | IE = IC + IB | β (hFE) = IC/IB | VBE ≈ 0.7 V

BJT as Switch

To saturate an NPN (switch fully ON): drive enough base current so IC_desired / β < IB_actual.

IB = (Vin − VBE) / RB
IC = Vcc / RL (saturation)
VBE ≈ 0.7 V, VCE_sat ≈ 0.2 V

BJT as Amplifier

Common-emitter amplifier inverts the signal and provides voltage gain. Gain depends on collector resistor and transconductance.

Av = −gm × RC
gm = IC / VT (VT = 26 mV at 25°C)
Av ≈ −RC × IC / 0.026

MOSFET Fundamentals

Enhancement N-Channel MOSFET

Gate voltage creates an electric field that induces a channel between Drain and Source. No DC gate current flows (oxide insulation). Key parameter: threshold voltage Vth.

ID = k(VGS − Vth)² [saturation]
Gate current ≈ 0 A (DC)
Vth typically 1–4 V (power MOSFETs)

MOSFET Operating Regions

Region	Condition	Use
Cutoff	VGS < Vth	Switch OFF
Linear (Ohmic)	VDS < VGS−Vth	Switch ON
Saturation	VDS ≥ VGS−Vth	Amplifier

P_sw = ID² × RDS(on)

Semiconductor Materials

Material	Bandgap (eV)	Applications	Notes
Silicon (Si)	1.12	Most ICs, transistors, diodes, solar cells	Most widely used; excellent native oxide (SiO₂)
Germanium (Ge)	0.66	Early transistors, low-Vf diodes	Lower threshold; poor high-temp performance
GaAs	1.42	RF/microwave, LEDs, solar cells	High electron mobility; direct bandgap
SiC	2.86–3.26	High-power/high-temp power devices	Very high breakdown voltage
GaN	3.4	Power electronics, blue LEDs, 5G	Very high electron velocity

Key insight: Silicon dominates because it forms a native oxide (SiO₂) that serves as an excellent gate insulator — critical for MOSFET fabrication. No other semiconductor has this property.