Band structure momentum. The band structure describes the states of energy in the crystal momentum space that electrons and holes are allowed to have. It also tells the the group velocity of that wavefunction, which is needed in integrals of electrical and thermal conductivity. It presents the electronic dispersion relation under the influence of the potential of the solid. In this chapter, we will focus on understanding how the energy of an electron depends on its momentum when it moves in a lattice environment. . The usual formula for kinetic energy, E = 1 2mv2 = p2/2m, is one of the first things we learn in theoretical physics as children. Note that the bands fold back on themselves so that high energy does not imply high momentum; this is an effect of the potential, and happens in more realistic models of materials. Nov 17, 2023 · With the band index, k vector, and spin orientation, you have uniquely identified an electron wave function (in the independent electron approximation). Therefore we can assign an average value to the momentum of a Bloch state, which is simply: Away from the band edges the electron has a finite and nonzero group velocity as the band edge is approached the group velocity decreases until it is equal to zero. This model highlights the intricacies of band structure calculations as both the orbital phases and the relative orbital overlap in each direction must be considered in order to calculate an energy for a discrete k vector. Because a band diagram shows the changes in the band structure from place to place, the resolution of a band diagram is limited by the Heisenberg uncertainty principle: the band structure relies on momentum, which is only precisely defined for large length scales. bmnjrwt yzi ghoyu lynfobo xpupn zyvt mrwsb yhszro auiytka arrnfss