We have investigated power scaling for the efficient generation of the broadband terahertz (THz) pulses. These THz short pulses are converted from ultrafast laser pulses propagating in a class of semiconductor electrooptic materials. By measuring the dependence of the THz output on the pump beam in terms of incident angle, polarization, azimuthal angle, and pump intensity, we have precisely determined the contributions made by optical rectification, drift of carriers under a surface or external field, and photo-Dember effect. When a second-order nonlinear material is pumped below its bandgap, optical rectification is always the mechanism for the THz generation. Above the bandgap, however, the three mechanisms mentioned earlier often compete with one another, depending on the material characteristics and pump intensity. At a sufficiently high pump intensity, optical rectification usually becomes the dominant mechanism for a second-order nonlinear material. Our analysis indicates that second-order nonlinear coefficients can be resonantly enhanced when a material is pumped above its bandgap. In such a case, the THz output power and normalized conversion efficiency can be dramatically increased. We have also analyzed how the THz generation is affected by some competing processes such as two-photon absorption.