The time-domain waveforms of terahertz (THz) emission spectroscopy (TES) can tell us the ultrafast nature of the material photoresponse, and TES is becoming an essential tool to explore the advanced material functionalities and disclose the dynamics of the photocarriers. However, universal applications can not be reached without understanding physics in more detail over the broad dimensional range in the time-domain. We have applied TES and LTEM to Si-based materials and devices and proven that one can estimate various parameters, such as surface potential, work function, impurity doping density, defects density in passivation layers, surface state density, and so on, semi-quantitatively and non-contactly by just observing the THz radiation. In the present work, we review the TES application to wide bandgap semiconductors.