I am looking for the mathematical relationship (direct or indirect) between the effective density of states in valance band and the external applied field.
Applying a constant electric field E along x-direction means to apply a bias V, where E=-grad V=-dV/dx, hence the change in potential energy for a charge q will be qV=-E ∫dx which will tilt all the bands in the band structure diagram along x direction by an amount proportional to the field.
When electric field is applied coulomb force will be generated in the direction of the E-field, physically the dielectric will be compressed. This will increase the density of the dielectric material.
Electric field will act as an bias voltage on the sample will either retard or accelerate the electrons for photoelectron analysis. It is used to see the whole spectrum in UPS.
How the density of states changes with the process of retardation or acceleration of the electrons for photoelectrons on the application of external field ?