SN · Solid-state, nuclear and particle models

A semiconductor’s conductivity depends on available states and carriers, not merely on the number of electrons in the material.

Prerequisites: 25, 45, 46.

• Use band and carrier descriptions
• Apply radioactive decay and binding-energy ideas
• Check conservation laws in particle reactions

Filled bands cannot carry ordinary current without accessible nearby states. Metals have partially filled or overlapping bands; semiconductors have a small band gap 带隙. Donor and acceptor doping change carrier populations.

Fermi–Dirac occupancy is 1/[exp((E−μ)/(kT))+1]. At zero temperature it becomes a step at the Fermi energy; thermal broadening does not make every state half occupied.

Radioactive populations obey N=N0e^(−λt), activity λN and half-life 半衰期 ln2/λ. Binding energy 结合能 comes from a mass deficit multiplied by c²; compare binding energy per nucleon when discussing stability.

Nuclear and particle processes must conserve charge, energy, momentum and the applicable quantum numbers. Beta decay includes a neutrino or antineutrino; a two-body electron-only story cannot explain its continuous energy spectrum.

Binding energy is the positive energy required to separate a nucleus into free nucleons. For a reaction use total initial and final rest masses, with a consistent mass convention.

A mass decrease of 0.0040 atomic mass units gives Positive Q means energy release. Charge, nucleon number, energy and momentum must still balance; Q alone does not establish a reaction rate.

Activity and surviving population both decay, but their units differ: activity is transitions per second.

band gap: An energy interval with no allowed bulk electronic states in the band model.

half-life: Time for a radioactive population to halve.