Size effects on polar optical phonon scattering of 1-D and 2-D electron gas in synthetic semiconductors

The total scattering rate and the transition probability for electron-phonon interaction in 1-D and 2-D semiconductor materials are calculated in taking into account the finite dimensions of the structure. Although noticeable, size effects on the scattering rate are generally small, with more pronounced features for 1-D structures than for 2-D structures. For 2-D layers, our theory agrees with recent experimental results whereas it contradicts the previous theory predicting large size effects and mass-independent electron-phonon scattering rates. In 1-D structures singularities in the phonon emission rate appear as a natural consequence of the 1-D density of states. However, for high energy the 1-D emission rate is found smaller than the corresponding 3-D rate. An additional consequence of the confinement is the quenching of the phonon absorption rate.