An improved scheme of optical pump terahertz probe (OPTP) technique is proposed using ultrashort broadband terahertz (THz) radiated from air-plasma as the probe pulse of OPTP. The photo-excited dynamics in silicon is characterized with the improved OPTP, and the capability of the OPTP system based on the improved scheme of this paper is verified through a characterization process. The pump depth of sample increases with higher pump power, and the pump depth of 400nm pump pulse is greater than that of 800nm pump pulse. The pump depth of p-doped silicon is the largest, followed by intrinsic silicon, and the smallest for n-doped silicon while using 400nm pump pulse. However, the pump depth of p-doped silicon is the largest, followed by n-doped silicon, and the smallest for intrinsic silicon while using 800nm pump pulse. Furthermore, due to the ultrashort pulse duration and broad bandwidth of the probe pulse, the sub-picosecond phonon wavepacket oscillation in excited state has been observed.