Photo-induced electron transfer from a surface attached dye molecule to the band levels of a semiconductor is modeled via an electronic-vibronic quasicontinuum. The description enables one to obtain a fairly accurate expression for the decay of the excited molecular state, including initial vibronic coherences. The model accounts for (a) the effect of a finite band width, (b) variations in reorganization energy and electronic coupling, (c) various energetic positions for the injecting level, (d) different initial vibrational wave packets in the excited state, and (e) two vibrational modes participating in the electron transfer process. Most cases are studied numerically and can be reasonably well understood from the obtained decay expression.