The quantum theory of intraband magneto-optical transition in semiconductors introduced previously in terms of continued-fraction-based power-series-expansion technique is reviewed in connection with examination of temperature- and dimensional-dependence of the width in GaAs and US in which piezoelectric scattering is dominant. With the same values of the piezoelectric coupling constant K and the expansion parameter e the width in two-dimensions increases with temperature as in three-dimensions. Furthermore, the width becomes smaller uniformly as the dimension is reduced in the direction of static magnetic field in the quantum limit, which is physical. Therefore, the continued-fraction-based theory gives quite good interpretation of the acoustic phonon scattering in the quantum limit. (C) 2003 Elsevier B.V. All rights reserved.