Calculated contribution of localised LO phonon modes to the valley current of a double-barrier diode

We have calculated the form factor and the current density assisted by bulk and localised LO phonon emission in an ideal case of a double-barrier diode (DBD). The transmission rate from emitter to collector is given by the transfer Hamiltonian approximation. We extend the formalism developped by Chevoir and Vinter by calculating the matrix elements using the appropriate electron-optical interaction Hamiltonians. We compute the relevant form factors and valley currents versus the applied voltage in the GaAs/Ga_0.6Al_0.4As system. We discuss the coupling dependence upon the phonon emission parameters and notably show the importance of zone center emission to explain the emergence and sharpening of the replica peaks in the current. Finally, evidence is given for a strong dependence of the amplitude of the second AlAs phonon satellite as a function of the emitter barrier width.