Constant Total Energy for A Given Mass and At A Given Temperature Is the Source of The Universal Mass-Energy Equivalence Relation in Semiconductor and Insulator Materials Having A Bandgap

Abstract

In this research article it is shown that the motion of an electron or hole in semiconductor and insulator materials having a bandgap is similar to the falling object on the surface of the earth at constant acceleration due to gravity g of 9.8 meters/sec². The constant total energy for a given mass and at a given temperature is the source of the universal mass-energy equivalence relation in materials having a bandgap.  This relation is given as dE/E = dm/m.  In materials, dE is the differential potential energy from the intrinsic Fermi energy level E_i to the conduction band of the materials, and E is the semiconductor bandgap as the total potential energy of the electrons.  These energies are also the total mechanical energies of the electrons at the cathode of the materials where the velocity of the electron in the material is zero at zero electric field, and so it possesses only potential energy as the total mechanical energy.  The dm is the differential mass as the longitudinal electron effective mass and m is the free electron mass.