Part 3: Electronic Materials
Electronic materials lie at the heart of modern technology. In this part, we explore how the electronic structure of solids determines their electrical, optical, and thermal properties. From the free electron model of metals to the band theory of semiconductors, these concepts explain why materials conduct, insulate, or semiconduct.
What You Will Learn
- βBand theory: valence bands, conduction bands, and band gaps
- βIntrinsic and extrinsic semiconductors, n-type and p-type doping
- βThe p-n junction and its role in electronic devices
- βFree electron model and density of states in metals
- βFermi-Dirac distribution and electronic heat capacity
- βDrude model of electrical conductivity
Key Equations
Intrinsic carrier concentration
$$n_i = \sqrt{N_c N_v}\,\exp\!\left(-\frac{E_g}{2k_BT}\right)$$
Fermi-Dirac distribution
$$f(E) = \frac{1}{\exp\!\left(\frac{E - E_F}{k_BT}\right) + 1}$$
Fermi energy (free electron)
$$E_F = \frac{\hbar^2}{2m}\left(3\pi^2 n\right)^{2/3}$$
Drude conductivity
$$\sigma = \frac{ne^2\tau}{m}$$
Topics
3.1 Semiconductors & Doping
Band theory, intrinsic and extrinsic semiconductors, carrier concentration, p-n junctions, and conductivity in semiconducting materials.
3.2 Metallic Bonding & Free Electron Model
Free electron model, density of states, Fermi energy, Fermi-Dirac statistics, Drude model, and electronic heat capacity.