Connection 1: Semiconductors ↔ Atomic Physics (Bohr Model)

Energy levels in atoms → energy bands in solids. When atoms are brought together, discrete atomic levels split into continuous bands (Pauli exclusion principle at work). The valence shell electrons form the valence band; the next available energy range forms the conduction band. The band gap is the quantum mechanical "forbidden zone" — a direct consequence of wave function overlap and electron-electron repulsion in the lattice.

NEET link: Questions may provide E_g and ask which type; OR provide n_i at given temperature (connects to thermal physics — Boltzmann distribution governs excited electron population).

Connection 2: Semiconductors ↔ Photoelectric Effect (Modern Physics)

LEDs and solar cells are "reverse photoelectric effects":

• Photoelectric effect: Photon in → electron out (light to electricity)
• LED: Electron recombination → photon out (electricity to light)
• Solar cell: Photon in → voltage/current out (photovoltaic = internal photoelectric)
• Photodiode: Photon in → current out (reverse-biased photovoltaic)

The threshold energy condition $E_{photon} \geq E_g$ mirrors the photoelectric threshold $E_{photon} \geq \phi$ (work function).

Connection 3: Logic Gates ↔ Mathematics (Boolean Algebra)

De Morgan's theorems are Boolean algebra identities directly used in gate circuit simplification. The same theorems appear in set theory: $\overline{A \cup B} = \overline{A} \cap \overline{B}$ parallels $\overline{A + B} = \overline{A} \cdot \overline{B}$.

Connection 4: Temperature Coefficient ↔ Thermal Physics

Semiconductors have negative temperature coefficient (NTC): $\sigma \propto e^{-E_g/2kT}$ (Arrhenius-type relation). As T increases, more carriers are thermally excited, increasing conductivity. Metals have positive temperature coefficient (PTC): increased lattice vibrations scatter electrons, increasing resistivity. This connection explains thermistor behavior — NTC thermistors are semiconductors; PTC thermistors are certain doped ceramics.