The authors propose an equivalent transfer-matrix theory using the formal structure factors to study the critical plasmons in a Fibonacci HgTe/CdTe superlattice. In such a system, the bulk- and the surface-plasmon spectra will exhibit many different features when the surface layer of the semi-infinite superlattice is selected at different positions. It provides useful information about the surface-plasmon branch the authors are interested in for surface-wave device applications.