Propagation of plasmon-polariton in a metallic nano-chain in a dielectric surroundings is almost undamped and irradiationless and such nano-chains are considered as quasi-perfect wave-guides for plasmon-polaritons. If, however, a chain is deposited on a semiconductor substrate or embedded in a semiconductor surroundings, plasmon-polaritons are strongly quenched due to the energy transfer from plasmon oscillations to band electrons in the semiconductor medium via the nearfield coupling channel. For the reverse direction of this energy transfer the balance of the thermal losses of plasmon-polariton can be achieved. By a control of a dielectric spacing between the metallic nano-chain and the semiconductor substrate (and a type of the deposition), various regimes for coupling of two systems can be organized. We present the exact solution for propagation of strongly damped plasmon-polaritons in metallic nano-chain due to coupling of plasmons with band electrons in the semiconductor substrate.