Electrical current density expressions for electrons and holes for materials with position-dependent band structure are presented. This includes materials with nonuniform composition and devices with highly doped regions. Changes in the energy-band edges due to spatial variations in electron affinity and band gap, and spatial variations in the local kinetic energy produce terms in the current-density equations in addition to those for the homogeneous case. These new terms are derived and discussed. The development proceeds from the Boltzmann transport equation. The focus will be on the conceptual framework and the limitations in the underlying theory. Errors in the literature are noted where appropriate. The results are relevant to semiconductor device physics and analysis. ©1997 American Institute of Physics.