Dynamics of charge transfer from molecule to semiconductor at surface: Numerical method for nonadiabaticity and irreversibility in discrete-continuum transition

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Abstract
The transition probability of an electron from a molecule to a conduction band at an insulator surface is investigated by using the Fano–Anderson model, so as to clarify the effects of nonadiabaticity and irreversibility on this process. The potential for the center‐of‐mass motion of the molecule near the surface is assumed to be harmonic and this motion is solved numerically by using the real time Trotter’s formula, without assuming any a priori trajectories. The transition probability is calculated as a function of the basic three parameters: the conduction band width (≡W), the incident energy of the molecule (≡Ekin), and the resonance transfer integral of electron between the molecule and atoms at the surface (≡Tint). When W is small, the probability is shown to increase as it increases, since W results in the depopulation and the dephasing of surface atomic levels and suppresses the back‐electron transfer. On the other hand, in the case of large W, the transition probability decreases with its increase, since the density of states of the band itself decreases. Thus, the probability is found to become maximum in the intermediate case of W. This probability is also calculated as a function of Ekin and Tint. These results are compared with the Landau–Zener formula for the multilevel crossing, in connection with recent experiments.