Picosecond dynamics of transient velocity overshoot in Si observed using terahertz radiation technique

Hot-electron effects such as ballistic transport and transient velocity overshoot have been utilized in recent years in the conceptualization of numerous high-speed semiconductor devices. Therefore, substantive physical information on the behavior of velocity overshoot is of great importance in the design of ultra-small, high-speed transistors. In the last year, transient velocity overshoot in GaAs has been successfully studied using a terahertz radiation technique. We have now applied the same technique to investigate time-domain velocity overshoot in Si. A reverse-biased lateral p-i-n structure has been used to provide a uniform electric field in the undoped region of a Si wafer. The i-region was photoexcited with 80-fs optical pulses from a self-mode-locked Ti:sapphire laser to generate carriers in the lowest conduction band. The dynamics of the photogenerated carriers were then measured using photoconductive detection of the terahertz (THz) radiation which emanated from the Si. The THz radiation in the far-field is proportional to the time derivative of the photocurrent. This broadband radiation has been measured over a wind range of electric fields up to 80 kV/ cm. The THz waveform from the Si sample is observed to be unipolar at a low electric field of 5 kV/cm, while at 70 kV/cm it is bipolar (Fig. 1), implying that the photocurrent displays an overshoot only at high fields. We have defined a quantity to describe the degree of overshoot as the ratio of the magnitudes of the negative and positive peaks. The field dependence of the degree of overshoot is plotted in Fig. 2. The degree of overshoot increases as the electric field increases, showing saturation behavior at electric fields above 50 kV/cm. This is different from GaAs case which shows the maximum degree of overshoot at around 40-50 kV/cm and the decrease of overshoot at higher fields. It is possible to have screening of the applied electric field due to the long lifetime of photogenerated carriers in Si. Therefore, a small optical power, less than 2 mW, has been used to prevent the screening effect. To prove that the electric field in the gap was the same as the field externally applied, we have measured the waveforms at many different optical fluences. The amplitude change is linear with the optical power change when the optical power is below 4 mW (Fig. 3). For the first time, we have directly observed the transient velocity overshoot in Si experimentally. This has not been possible in other optical experiments because Si is not a direct bandgap material. We have also studied the electric field dependence of the degree of overshoot. The transient velocity overshoot in Si increases as the electric field increases.