Pump-probe spectroscopy of ultrafast electron injection from the excited state of an anchored chromophore to a semiconductor surface in UHV: A theoretical model

Decay of excited state absorption, owing to charge injection into the condu ction band continuum of semiconductor states, is obtained via a qualitative theoretical model. The density matrix formalism is utilized to obtain an e xpression for the sequential pump-probe signal in terms of the nonlinear th ird-order polarization of the molecular system. Electron transfer slower th an the pump and probe pulses is assumed and reorganization of the molecule upon charge injection is ignored while obtaining the final expressions. The lifetime of the excited state decouples from nuclear motion as a consequen ce. Decay of the excited state into a continuum of electronic states is exa mined for various energy positions of the injecting state and for different bandwidths of the continuum. The decay can be fitted by exponential functi ons for the majority of the cases considering different dimensionalities of the semiconductor continuum. Model calculations are performed for the snap shot limit of the pump-probe signal. Under the assumed conditions one obtai ns oscillations due to vibronic coherences that are superimposed on tempera ture-independent irreversible charge transfer decays, as is reported in rec ent experiments.