The effect of varying the n-layer on the propensity of guiding surface-plasmon-polariton (SPP) waves by the back-contact of a p-i-n solar cell was studied theoretically. The i-layer was assumed to consist of an a-SiGex:H homogeneous layer of bandgap energy 1.3 eV. To determine the SPP waves that can propagate at the metal/multilayer material interface, a canonical boundary-value problem comprising periodically repeated p-i-n semiconductor layers partnering a homogeneous metal was solved for four different n-layers. The canonical problem was formulated to predict both of the TM- and TE-polarized SPP waves that can be guided by the interface. It was found that the configurations that have an amorphous silicon layer partnering the metal have equivalent propensity for guiding TM- and TE-polarized SPP waves by the planar metal/multilayer material interface, although their phase speeds, e-folding distances, and localization are slightly altered. On the other hand, the configuration that has an aluminum zinc oxide partnering the metal has significantly reduced propensity for guiding TE-polarized SPP waves. To examine the excitability of the SPP waves predicted from the canonical problem, one of the considered configurations is incorporated in a practical grating-coupled configuration. Oblique incidence was assumed, and multiple SPP waves were successfully excited. The total absorptance of the p-i-n solar cell shows enhancement at the SPP wave excitation wavelengths.