We study the electronic density of states (DOS) of a GaAs/GaxAl1-xAs superlattice with impurities arranged according to the Fibonacci sequence. Our theory uses a Green function method based on Dyson's equation within the real-space renormalization-group approach in the framework of the tight-binding Hamiltonian for the Fibonacci quasiperiodic lattice. An exact decimation transformation has been done for the physical parameters characterizing the Fibonacci chain considering the scaling factor, under which the system is self-similar, equal to the golden mean tau=(1+root5)/2. The electronic energy spectrum are then used to determine the electronic specific heat which, due to the localization of the electronic states, exhibits strong Schottky anomalies when the temperature goes to zero together with a log-periodic oscillation. (C) 2004 Elsevier B.V. All rights reserved.