  High energy single- to few-cycle terahertz pulses enable the exploration of
the frontier of science, such as electron acceleration, strong-field physics,
and spectroscopy. One important method of generating such terahertz pulses is
to use the tilted-pulse-front (TPF) technique. However, due to the
non-collinear phase-matching, the large angular dispersion leads to a spatial
and temporal break-up of the optical pump, limiting the terahertz generation
efficiency and reducing the few-cycle character of the generated terahertz
fields. To reduce the effects caused by angular dispersion, multiple schemes
with discrete pulse-front-tilt have been suggested. We propose a terahertz
generation scheme, where a spatio-temporally chirped (STC) pump pulse is
utilized. With our 2D+1 numerical model, we perform a systematic comparative
study of the conventional TPF scheme, three discrete TPF schemes, and the STC
scheme. This model predicts smaller optimal interaction length and
significantly smaller conversion efficiency compared to simple 1D models. We
conclude that the STC scheme delivers spatially homogeneous few-cycle terahertz
pulses with the highest conversion efficiency. Additionally, given a short
interaction length, the discrete TPF schemes cannot outperform the continuous
ones. In general, this work gives guidance to choose the most appropriate setup
for a given terahertz experiment
