BJT and MOS Device Physics

This lesson explains how transistors work inside. Their circuit use (amplifiers and biasing) is covered in BJT and MOSFET amplifiers.

Bipolar junction transistor

In active mode (BE forward, BC reverse biased), the emitter injects carriers that diffuse across a thin base and are swept into the collector.

• α = I_C/I_E = γ × α_T (emitter injection efficiency × base transport factor).
• β = α/(1 − α); α = β/(1 + β).
• High β needs a heavily doped emitter, a lightly doped and thin base.
• Early effect (base-width modulation): a higher V_CE narrows the effective base, raising I_C: output resistance r_o = V_A/I_C.
• Punch-through: at very high V_CB, the depletion region crosses the whole base.
• Ebers–Moll model covers all regions.

MOS capacitor

Applying gate voltage to a p-type substrate:

• Oxide capacitance per area C_ox = ε_ox/t_ox (ε_ox = 3.9 ε₀ ≈ 3.45 × 10⁻¹³ F/cm).
• Threshold voltage V_T = V_FB + 2φ_F + Q_dep/C_ox. It increases with substrate doping and oxide thickness.
• Body effect: a reverse source–body voltage V_SB raises V_T: V_T = V_T0 + γ(√(2φ_F + V_SB) − √(2φ_F)).
• C–V curve: high capacitance in accumulation, falling in depletion, and (at low frequency) rising again in inversion.

MOSFET characteristics

• Linear (triode): I_D = μ_n C_ox (W/L)[(V_GS − V_T)V_DS − V_DS²/2].
• Saturation (V_DS ≥ V_GS − V_T): I_D = ½ μ_n C_ox (W/L)(V_GS − V_T)².
• Channel-length modulation: I_D(1 + λV_DS), r_o ≈ 1/(λI_D).
• Short-channel effects: velocity saturation, drain-induced barrier lowering.

IC fabrication (overview)

Oxidation, photolithography, diffusion and ion implantation, deposition, etching and metallisation. CMOS uses n- and p-channel MOSFETs in wells.

Worked example

A MOSFET has t_ox = 10 nm, μ_nC_ox = 200 µA/V², W/L = 10, V_GS − V_T = 0.5 V.

• C_ox = 3.45 × 10⁻¹³/10⁻⁶ = 0.345 µF/cm².
• I_D = ½ × 200 × 10 × 0.25 = 250 µA.

Practice