Formula Reference, Comparison Tables & Glossary

Everything in one place. Formula cards for semiconductor physics (np = n_i², σ, ρ, J_drift, L = √(Dτ)), PN junctions (V_bi, W, diode equation), BJTs (I_E = I_C + I_B, β, α, g_m), MOSFETs (region-specific equations), thermal (T_J = T_A + Pθ_JA), CMOS (P = αCV²f) and optoelectronics (photon energy, responsivity, QE, solar efficiency) — each with symbols, units, assumptions and validity; engineering comparison tables (conductor/semiconductor/insulator, intrinsic/extrinsic, N/P, drift/diffusion, PN/Schottky, Zener/avalanche, BJT/JFET/MOSFET, NPN/PNP, enhancement/depletion, NMOS/PMOS, planar/FinFET/GAA, Si/SiC/GaN, MOSFET/IGBT, SCR/TRIAC/GTO/IGCT, LED/laser, PN/PIN/APD, solar cell/photodiode, SRAM/DRAM/flash, bulk/SOI, wire bond/flip-chip, conventional/advanced packaging); a searchable glossary; and a Python formula self-check.

Use this lesson as a quick reference while working through the course or designing. Every formula here is explained in its lesson — this page collects them with their assumptions so they are not misused.

Try the self-check: compute each value by hand, then compare with the verified Python output.

An analogy

This lesson is the course's toolbox lid with every tool outlined: find the formula quickly, but remember which job each tool is designed for (its assumptions and validity range).

Glossary A–D

Key terms:

Glossary E–M

More terms:

Glossary O–W

And the rest:

Comparison tables in the course

Conductor/semiconductor/insulator (Materials), intrinsic/extrinsic and N/P (Doping), drift/diffusion (Transport), PN/Schottky (Metal–semiconductor), Zener/avalanche (Breakdown), signal/power diodes (Diode families, Power fundamentals), BJT/JFET/MOSFET and NPN/PNP (below), enhancement/depletion and NMOS/PMOS (MOSFET operation), planar/FinFET/GAA and bulk/SOI (FinFET lesson), Si/SiC/GaN (Wide bandgap), MOSFET/IGBT (Power MOSFETs & IGBTs), SCR/TRIAC/GTO/IGCT (Thyristors), LED/laser (LEDs & lasers), PN/PIN/APD and solar/photodiode (Photodetectors), SRAM/DRAM/flash (Memory), wire bond/flip-chip and conventional/advanced packaging (Packaging). Values depend on device and process — tables give typical ranges.

Formulas

Worked example: Minority holes

Given: N_D 10¹⁶, n_i 9.65 × 10⁹

Find: p₀.

Answer: ≈ 9.3 × 10³ cm⁻³

Worked example: Photon energy

Given: λ 1310 nm

Find: E.

Answer: 0.947 eV

Worked example: α from β

Given: β 99

Find: α.

Answer: 0.99

Formula-card format

  ┌──────────────────────────────────────────────────────────────┐
  │ Formula:   V_bi = V_T ln(N_A N_D / n_i²)                       │
  │ Symbols:   V_T = kT/q, N_A/N_D doping (cm⁻³), n_i intrinsic    │
  │ Units:     volts                                              │
  │ Assumes:   abrupt junction, non-degenerate doping, equilibrium│
  │ Example:   N_A = N_D = 10¹⁶ → 0.716 V (n_i 9.65e9)             │
  │ Validity:  fails for degenerate doping (> ~10¹⁹ cm⁻³)          │
  └──────────────────────────────────────────────────────────────┘

Every formula in the course should be read with its symbols, units, assumptions, an example and its limits. Misapplying a formula outside its validity (e.g. square law in short channels, Boltzmann statistics in degenerate material) is the most common source of wrong answers.

Formula self-check

import math
# Formula self-check: core semiconductor-device values
q, k, T = 1.602e-19, 1.380649e-23, 300.0
VT = k * T / q
checks = {
    "thermal voltage VT (mV)": VT * 1e3,
    "n-type Si 1e16: p0 (cm^-3)": (9.65e9) ** 2 / 1e16,
    "Vbi for Na=Nd=1e16 (V)": VT * math.log(1e32 / 9.65e9 ** 2),
    "resistivity n=1e16, mu=1180 (ohm*cm)": 1 / (q * 1e16 * 1180),
    "diffusion length D=12, tau=10us (um)": math.sqrt(12 * 10e-6) * 1e4,
    "BJT gm at 1 mA (mA/V)": 1e-3 / VT * 1e3,
    "Cox for 2 nm SiO2 (uF/cm^2)": 3.9 * 8.854e-14 / 2e-7 * 1e6,
    "photon energy at 850 nm (eV)": 1240 / 850,
    "Tj: 50 C + 3 W x 20 C/W": 50 + 3 * 20,
    "CMOS power 0.1*1nF*1V^2*1GHz (W)": 0.1 * 1e-9 * 1 * 1e9,
}
for kname, v in checks.items():
    print(f"{kname:40s} {v:12.4g}")
# thermal voltage VT (mV)                         25.85
# n-type Si 1e16: p0 (cm^-3)                       9312
# Vbi for Na=Nd=1e16 (V)                         0.7162
# resistivity n=1e16, mu=1180 (ohm*cm)            0.529
# diffusion length D=12, tau=10us (um)            109.5
# BJT gm at 1 mA (mA/V)                           38.68
# Cox for 2 nm SiO2 (uF/cm^2)                     1.727
# photon energy at 850 nm (eV)                    1.459
# Tj: 50 C + 3 W x 20 C/W                           110
# CMOS power 0.1*1nF*1V^2*1GHz (W)                  0.1

Work each value out by hand first: V_T 25.85 mV, p₀ ≈ 9300 cm⁻³, V_bi 0.716 V, ρ 0.53 Ω·cm, L 110 µm, g_m 38.7 mA/V, C_ox 1.73 µF/cm², 1.46 eV at 850 nm, T_J 110 °C, 0.1 W. Differences point to the lesson to revisit.

Common mistakes

Applications

Key takeaways

Going further