ABSTRACT
In this chapter, the authors derive the basic theory of the chemical capacitance. The central result is that the chemical capacitance provides a direct measurement of the density of states, although the relationship is not satisfied in some situations. This feature finds many applications in the analysis of materials that show a broad density of states, especially in amorphous or disordered materials that contain localized states in the bandgap. The authors also review the features of voltage-charge curves in intercalation materials, and the quantum capacitance of graphene. This type of capacitance is ubiquitous at interfaces with space charge such as the surface depletion layer in a semiconductor and the Helmholtz layer at the solid/solution interface. In semiconductor devices that include very narrow layers, showing strong quantization effects, the capacitance associated with adding carriers to the band structure of the semiconductor, is called the quantum capacitance.
