Points to Ponder

The conduction band minimum $E_C$ and valence band maximum $E_V$ are delocalised across the entire crystal — they are not pinned to any single atom or location. When textbooks draw $E_C$ and $E_V$ as flat horizontal lines, those lines represent the average energy of the band edges, not a fixed energy at a specific point in space.

In elemental semiconductors like Si or Ge, you create n-type or p-type material by intentionally adding impurity atoms (dopants) as point defects. In compound semiconductors such as GaAs, you can also change the carrier type simply by altering the stoichiometry — making the crystal slightly rich in one element. For example, ideal GaAs has a 1:1 ratio of Ga to As, but Ga-rich Ga$_{1.1}$As$_{0.9}$ or As-rich Ga$_{0.9}$As$_{1.1}$ will behave differently. In gen …