I am trying to understand the meaning of the value E1,E2 in a tunnelling current expression derived in the following paper. http://aip.scitation.org/doi/pdf/10.1063/1.1735965
A more succinct overview is given in Sze, Ng 2nd edition "Physics of Semiconductor Devices", pages 422 to 424. I am unsure of how to interpret the meaning of Es within the integral. In the image, these terms are defined as the value of the classical turning point, when the electron or hole would hit their respective band at the junction:
I would assume this depends on the energy, however if that is the case would it not be a function of the the integration variable E? Furthermore, in the derivation, they say Es defined as the lesser of E1 and E2. In which case is it not a constant value? If so, why does that expression remain within the integral, if there is no explicit E dependence? It seems like the values of E1, E2 must remain between their respective band edge and fermi level on both sides as I integrate from Ec to Ev.
