The flashover across semiconducting materials disables many high power semiconductor devices from their further application under high electric field. Up to now, the physical mechanism of the flashover was still not understood clearly. Surface flashover experiments of silicon and gallium arsenide were performed under pulsed high voltage. The filament current channels on their surface were observed in the infrared photographs, and the infrared radiation bright spot was found in the central region between the electrodes. On the surface of different samples undergone flashover events for several times, the filament damage phenomena were observed, and for the n100 silicon sample, some circular pits were found around the filament channel, with a conical jut in the center of each pit. According to the damage phenomena at the edge of electrodes, the thermal injection and relaxation characteristics of majority carriers were discussed. An injection model induced by minority carriers was proposed, which emphasizes the surface field enhancement by non-equilibrium carrier channel, which possibly leads to the ionization of the ambient gas above the filament channel. The model was consistent with the observed experimental results.