The generation of terahertz (THz) transients in photoconductive emitters has been studied by varying the spatial extent and density of the optically excited photocarriers in asymmetrically excited, biased low-temperature-grown GaAs antenna structures. We find a pronounced dependence of the THz pulse intensity and broadband (>6.0 THz) spectral distribution on the pump excitation density and simulate this with a three-dimensional carrier dynamics model. We attribute the observed variation in THz emission to changes in the strength of the screening field.