The amplitudes of terahertz radiation are measured for a series of GaAs surface intrinsic-n+ (SIN+) structures with various built-in surface electric fields as the bias. As the surface field is lower than the so-called "critical electric field" related with the energy difference between the Γ to L valley of the semiconductor, the amplitude is proportional to the product of the surface field and the number of photo-excited carriers. As the intensity of surface field exceeds the critical field, the THz amplitude is independent of the surface field but proportional the number of the photo-excited carriers. Our study proposed two optimal conditions for an SIN+ structure to serve as a THz emitter: the width of its intrinsic layer is nearly equal to the penetration depth of the pump beam, and the intensity of built-in electric field is nearly equal to the critical electric field. Notably, the critical field determined from the THz amplitude under various electric fields provides one way to estimate the Γ to L valley splitting in semiconductors.