The effect of a finite barrier on the electron-phonon scattering rates in a quantum well

Full text: Recently, many publications have appeared where the main aim of theoretical investigations into optical phonon confinement has been to reduce the scattering rate with electrons in a quantum well. It is mainly optical phonon scattering that limits the electron mobility at room temperature and hence any structure that can change the form of the phonon potential to give a reduced rate is advantageous. One of the main suggestions to produce this reduction is the inclusion one or more monolayers of a different material inside the quantum well. Neglecting the effect to the electron wavefunctions, two models of optical phonon confinement have been used to suggest that the phonon modes are changed considerably and hence a reduction should be expected. The model most employed for phonon confinement is the dielectric continuum (DC) model. This model neglects the mechanical nature connecting the phonons of the different materials across the interface and can be expressed with just the electrostatic potential in the non-retarded limit. The boundary conditions used are those of electromagnetic theory, i.e. normal D and tangential E fields continuous. The DC model has been used by to obtain a reduction in the ground state intra subband scattering rate by including a monolayer in the quantum well. This reduction is quite significant and is against a sum rule which states that the results should be between the scattering rates via the bulk phonons of each material. Another model, the hybrid model, takes into account the mechanical nature of the phonons at the interfaces and includes a condition on the phonon displacement as well as the electromagnetic boundary conditions. The hybrid model was used to suggest that a reduction in the inter subband scattering rate should occur for a quantum well with a monolayer. This is because the antisymmetric modes of the quantum well are changed drastically when imposing the additional mechanical boundary conditions at the interfaces between the monolayer and the well material. In this report we have extended the calculation for a barrier of finite thickness in the centre of the well. We have obtained the intra subband and inter subband scattering rates and have shown that the effect on the total scattering rates is not marginal. (author)