Injection from metallic electrodes serves as a main channel of charge generation in organic semiconducting devices and the quantum effect is normally regarded to be essential. We develop a dynamic approach based upon the surface hopping (SH) algorithm and classical device modeling, by which both quantum tunneling and thermionic emission of charge carrier injection at metal/organic interfaces are concurrently investigated. The injected charges from metallic electrode are observed to quickly spread onto the organic molecules following by an accumulation close to the interface induced by the built-in electric field, exhibiting a transition from delocalization to localization. We compare the Ehrenfest dynamics on mean-field level and the SH algorithm by simulating the temperature dependence of charge injection dynamics, and it is found that the former one leads to an improper result that the injection efficiency decreases with increasing temperature at room-temperature regime while SH results are credible. The relationship between injected charges and the applied bias voltage suggests it is the quantum tunneling that dominates the low-threshold injection characteristics in molecular crystals, which is further supported by the calculation results of small entropy change during the injection processes. An optimum interfacial width for charge injection efficiency at the interface is also quantified and can be utilized to understand the role of interfacial buffer layer in practical devices.
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