Abstract
We investigate the low temperature acoustic energy relaxation in quantum wells in the presence of disorder incorporating dynamic screening utilising the Keyldysh formalism. Since most of the two-dimensional systems are not exactly two dimensional and there is a strong anisotropy between the responses of the electron gas to an external perturbation along and perpendicular to the growth axis, therefore the finiteness of the electronic wave function must be accounted for in order to correspond with most realistic systems. The two-dimensional electron gas (DEG) formalism for the determination of scattering rate and energy loss rate obtained by Reizer et al has been accordingly tailored for the quantum well (QW) case by invoking a Fang–Howard form factor. We find that consideration of the finiteness of the wave function affects the exponent as well as the pre-factor β from the earlier reported approximate scattering rate βT4 and power law βT6 obtained for a 2DEG under strong static screening and disorder. Further, it is observed that the rates decline in the order 3DEG → 2DEG → QW → 1DEG. The QW relaxation and loss rates lie below that of a 2DEG because of the added weakening of screening due to the inclusion of form factors.
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