Simplified formulas for the generation of terahertz waves from semiconductor surfaces excited with a femtosecond laser

We derive simple formulas to explain terahertz (THz) emission from semiconductor surfaces excited by a femtosecond (fs) laser. Femtosecond optical pulses with energies larger than the bandgap create photocarriers that travel and generate THz radiation, according to the time derivative of the photocurrent. By assuming that only electrons traveling in an ultrafast time scale, less than a few hundred fs, contribute to THz radiation, one can obtain simple expressions for the emission originating from the photocarrier drift accelerated with a built-in field or from the photocarrier diffusion. The emission amplitude of the former is in proportion with the electron mobility, the Schottky-barrier height, and the laser intensity and one of the latter with the laser intensity and diffusion coefficient squared. We also discuss the formula for emission from metal-insulator-semiconductor structures. The derived expressions are useful in understanding the THz emission properties observed by a laser THz emission microscope (LTEM), bringing the LTEM into real applications in the field of semiconductor research and development.