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An electron hole is an unoccupied Electron quantum state in an otherwise nearly full energy band, often the valence band. “Filled” refers to occupation of the allowed quantum states, not to filling all space with a continuous fluid of Electrons. Each state, including its spin label, can hold at most one Electron by the Pauli exclusion principle. The almost full energy band and its few missing occupants are therefore simpler to describe as a background plus a few electron holes. The electron hole is a quasiparticle, not a Positron inserted into the crystal.

Removing an Electron of electric charge $-e$ changes the background's electric charge by $+e$. Thus an electron hole carries positive electric charge relative to that background. Promoting an Electron into the conduction band creates an electron hole without changing the whole crystal's electric charge: $(-e)+(+e)=0$. An unbound pair still consists of two separate charge carriers; only a bound state of their relative motion is an exciton.

The local cartoon explains why a vacancy can move: when a neighboring Electron fills it, another vacancy appears where that Electron was. The vacancy has moved opposite to that particular transfer of an Electron. In an extended Bloch state, use crystal momentum instead of imagining a permanently empty atomic site. For a completely filled energy band the summed electric current vanishes. Omitting one Electron with group velocity ${\mathbf{v}}_v$ removes its contribution $-e{\mathbf{v}}_v$, leaving a contribution $+e{\mathbf{v}}_v$. This fixes both the positive electric charge and the velocity convention of the electron hole.

More precisely, near a parabolic valence band maximum, set its energy $E_v(0)$ as reference and define the electron hole wave vector by ${\mathbf{k}}_h=-{\mathbf{k}}_v$. ThenThe occupied Electron branch has negative curvature there, while the electron hole branch has positive effective mass $m_h^{\ast }$. The velocity equality compares the electron hole with the missing Bloch state's group velocity; it does not contradict the opposite vacancy motion in a local transfer cartoon. The sign conventions are listed in Phys 460 Lecture 17.