Semiconductor Materials: Conductors, Semiconductors & Insulators

What a semiconductor is and why it changed the world. Compare conductors, semiconductors and insulators by resistivity and bandgap; meet elemental (Si, Ge) and compound semiconductors (III-V such as GaAs, InP, GaN; II-VI such as CdTe, ZnSe; IV-IV SiC), wide-bandgap materials, direct vs indirect bandgaps and why that decides whether a material can emit light, and the families of semiconductor devices — integrated circuits, discrete, power, optoelectronic, RF and sensor devices — across computing, automotive, power, communication, medical, aerospace and renewable energy. Python compares resistivities, bandgaps and optical cut-off wavelengths.

A semiconductor is a material whose conductivity sits between metals and insulators — and, crucially, can be changed by millions of times through tiny amounts of impurities (doping), by electric fields, by light and by temperature. That controllability is what makes transistors, diodes, LEDs, solar cells and sensors possible.

This course follows the path from atoms and energy bands to real devices, how they are manufactured, measured, modelled, selected and how they fail.

An analogy

A metal is a motorway with traffic always flowing; an insulator is a road with a locked gate; a semiconductor is a road with a gate you can open a little or a lot — by adding the right 'keys' (dopants), shining light, or applying a voltage.

Conductors, semiconductors, insulators

The difference is how easily electrons can reach states where they move freely:

Why semiconductors are useful

Their conductivity can be set by doping (n-type or p-type), switched by an electric field (transistors), modulated by light (photodetectors, solar cells), and they can emit light (LEDs, lasers). Joining regions of different doping creates junctions that rectify, amplify and store charge — the basis of every device in this course.

Direct vs indirect bandgap

In a direct-gap material (GaAs, GaN, InP) the conduction-band minimum and valence-band maximum occur at the same crystal momentum, so an electron can drop across the gap by emitting a photon — efficient LEDs and lasers. In indirect-gap materials (Si, Ge, SiC) a phonon must also participate, making light emission very inefficient; silicon is excellent for electronics and detectors but poor for emitters.

Device families and applications

Integrated circuits (CPUs, memories, analog/mixed-signal), discrete devices (diodes, transistors), power devices (MOSFETs, IGBTs, thyristors, SiC/GaN), optoelectronics (LEDs, lasers, photodiodes, solar cells), RF devices (HEMTs, HBTs, varactors) and sensors (Hall, temperature, pressure, image). They serve computing, automotive and EVs, power conversion, communications, consumer, industrial, medical, aerospace and renewable energy.

Formulas

Worked example: Photon energy

Given: Green LED, 530 nm

Find: Photon energy.

Answer: ≈ 2.34 eV

Worked example: Cut-off wavelength

Given: Ge, E_g 0.66 eV

Find: λ_c.

Answer: ≈ 1880 nm

Worked example: Doping ratio

Given: Si atoms 5 × 10²² cm⁻³, doping 10¹⁷ cm⁻³

Find: Atoms per dopant.

Answer: 1 dopant per 500 000 atoms

Material families

  Elemental (group IV):   Si (1.12 eV, indirect), Ge (0.66 eV, indirect), C-diamond (5.5 eV)
  IV-IV:                  SiC (4H: 3.26 eV, indirect), SiGe alloys
  III-V:                  GaAs (1.42, direct), InP (1.34, direct), GaN (3.4, direct), InGaAs, AlGaN
  II-VI:                  CdTe (1.5, direct), ZnSe, HgCdTe (IR detectors)
  Oxides / 2-D:           Ga2O3 (~4.8 eV), MoS2, graphene (zero-gap semimetal)

Silicon dominates electronics because of its excellent native oxide (SiO₂), abundance, cheap large wafers and mature processing. Compound semiconductors win where silicon can't: light emission (direct gaps), very high speed (high mobility) and high voltage/temperature (wide gaps).

Resistivity, bandgap and cut-off wavelength

# Conductor vs semiconductor vs insulator: resistivity, bandgap and optical cut-off wavelength
materials = {                      # resistivity (ohm*cm) at 300 K, bandgap (eV), gap type
    "copper":            (1.7e-6, 0.0,  "metal"),
    "Si (intrinsic)":    (2.3e5,  1.12, "indirect"),
    "Si (1e16 P doped)": (0.50,   1.12, "indirect"),
    "GaAs (intrinsic)":  (3.3e8,  1.42, "direct"),
    "GaN":               (1e10,   3.4,  "direct"),
    "4H-SiC":            (1e10,   3.26, "indirect"),
    "SiO2":              (1e16,   9.0,  "insulator"),
}
for name, (rho, eg, kind) in materials.items():
    cut = f"{1240/eg:6.0f} nm" if eg > 0 else "   n/a"
    print(f"{name:18s} rho = {rho:8.1e} ohm*cm  Eg = {eg:4.2f} eV  cut-off {cut}  ({kind})")
print(f"doping silicon changes its resistivity by a factor of {2.3e5/0.50:.1e} -> the key to devices")
# copper             rho =  1.7e-06 ohm*cm  Eg = 0.00 eV  cut-off    n/a  (metal)
# Si (intrinsic)     rho =  2.3e+05 ohm*cm  Eg = 1.12 eV  cut-off   1107 nm  (indirect)
# Si (1e16 P doped)  rho =  5.0e-01 ohm*cm  Eg = 1.12 eV  cut-off   1107 nm  (indirect)
# GaAs (intrinsic)   rho =  3.3e+08 ohm*cm  Eg = 1.42 eV  cut-off    873 nm  (direct)
# GaN                rho =  1.0e+10 ohm*cm  Eg = 3.40 eV  cut-off    365 nm  (direct)
# 4H-SiC             rho =  1.0e+10 ohm*cm  Eg = 3.26 eV  cut-off    380 nm  (indirect)
# SiO2               rho =  1.0e+16 ohm*cm  Eg = 9.00 eV  cut-off    138 nm  (insulator)
# doping silicon changes its resistivity by a factor of 4.6e+05 -> the key to devices

Doping silicon with just one phosphorus atom per five million silicon atoms (10¹⁶ cm⁻³) lowers its resistivity almost half a million times. The bandgap also sets which light a material absorbs or emits: silicon absorbs below ~1.1 µm, GaN works in the ultraviolet.

Common mistakes

Applications

Key takeaways

Going further