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 conduction band continuum of semiconductor states, is obtained via a qualitative theoretical model. The density matrix formalism is utilized to obtain an expression for the sequential pump-probe signal in terms of the nonlinear third-order polarization of the molecular system. Electron transfer slower than 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 consequence. Decay of the excited state into a continuum of electronic states is examined for various energy positions of the injecting state and for different bandwidths of the continuum. The decay can be fitted by exponential functions for the majority of the cases considering different dimensionalities of the semiconductor continuum. Model calculations are performed for the snapshot limit of the pump-probe signal. Under the assumed conditions one obtains oscillations due to vibronic coherences that are superimposed on temperature-independent irreversible charge transfer decays, as is reported in recent experiments.