Effective mass (solid-state physics) from both sides gives where is the th element of , is the th element of , and are the th and th elements of , respectively, and is the total energy of the particle according to the Planck–Einstein relation. The index is contracted by the use of Einstein notation (there is an implicit summation over ). Since Newton's second law uses the inertial mass (not the gravitational mass), we can identify the inverse of this mass in the equation above as the tensor This tensor expresses the change in group velocity due to a change in crystal momentum. Its
Law of mass action formula. The law of mass action also has implications in semiconductor physics. Regardless of doping, the product of electron and hole densities is a constant at equilibrium. This constant depends on the thermal energy of the system (i.e. the product of the Boltzmann constant, formula_20, and temperature, formula_21), as well as the band gap (the energy separation between conduction and valence bands, formula_22) and effective density of states in the valence formula_23 and conduction formula_24 bands. When the equilibrium electron formula_25 and hole formula_26 densities are equal, their density is called the "intrinsic" carrier density formula_27 as this would be