Electronic Devices and Semiconductor Physics
Electronic Devices and Semiconductor Physics tests the physics behind the terminal equations - carrier statistics, drift and diffusion, junction electrostatics, and the non-ideal behaviour of diodes, BJTs and MOSFETs.
Semiconductors
- Mass action: n·p = n_i². Intrinsic concentration rises steeply with temperature, roughly doubling every 8–10 K for silicon near 300 K.
- Drift current density J = qnμ_nE + qpμ_pE; diffusion current follows the gradient qD dn/dx. The Einstein relation gives D/μ = V_T ≈ 25.85 mV at 300 K.
- Doping moves the Fermi level toward a band edge. Depletion width scales as √(2ε(V_bi − V)(1/N_A + 1/N_D)/q), so heavier doping narrows the junction.
Junctions and devices
- Shockley diode: I = I_s(e^(V/(nV_T)) − 1). Forward drop is about 0.7 V for silicon, with a temperature coefficient near −2 mV/°C.
- BJT forward-active requires V_BE > 0 and V_BC < 0, with β = I_C/I_B. Base-width modulation (the Early effect) slopes the output characteristics.
- MOSFET regions: cutoff; linear when V_DS < V_GS − V_th; saturation above. The body effect raises V_th. Subthreshold conduction is exponential and sets the leakage floor.
Worked example
A silicon diode with I_s = 10⁻¹⁴ A and n = 1 at 300 K, where V_T = 25.85 mV. At 0.6 V the exponent is 0.6/0.02585 = 23.2, so e^23.2 ≈ 1.2 × 10¹⁰ and I ≈ 10⁻¹⁴ × 1.2 × 10¹⁰ = 1.2 × 10⁻⁴ A = 0.12 mA. Raising the bias to about 0.66 V multiplies the exponent by roughly 2.3 and the current by a decade - the classic 60 mV per decade rule that makes the diode clamp so sharply.
Traps
Using 0.7 V as a fixed drop at every current; forgetting that n > 1 flattens the exponential; assuming resistance scales like depletion width when it has the opposite doping dependence; declaring MOSFET saturation without checking V_DS; treating channel-length modulation as a small-signal parameter rather than a large-signal effect.