These equations are fundamentally particle conservation equations:
Electron continuity equation: ∂n /∂t = (1/q) (∂jN / ∂X) + GN - RN
Hole continuity equation: ∂p /∂t = (1/q) (∂jp / ∂X) + Gp- Rp
Where G and R present carrier generation and recombination rates. Equations will make the basis of most of the device analysis which shall be discussed after. These equations need models for mobility and recombination together with models of contacts and boundaries.