Carrier Transport
In lightly doped semiconductors, lattice scattering dominates, and the carrier mobility decreases with temperature. In general, the trend is decrease in mobility with higher temperature and with higher doping.
Intrinsic Carrier Concentration
A key nuance in the derivation of intrinsic carrier concentration is that it assumes thermal equilibrium—meaning the carrier concentration remains constant over time. But how does this make sense? We’ve established that electrons are continually being thermally excited from the valence band to the conduction band due to random thermal processes. If this generation kept happening unchecked, electrons would accumulate in the conduction band and holes in the valence band, driving the system out of equilibrium.
Energy Bands
Intuitively, if two atoms were close enough and their electrons remained at the same energy level, it would violate the Pauli Exclusion Principle, which states that no two electrons can occupy the same quantum state. Therefore, the energy levels split, ensuring each electron has a unique quantum state.
Quantum Physics
The uncertainty principle serves as a fundamental safeguard of quantum mechanics. Heisenberg realized that if it were possible to measure both the position and momentum of a particle with perfect accuracy, the entire framework of quantum mechanics would fail.