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Terahertz (THz) radiation generated by ultrafast laser pulses focused on each monoclinic semiconductor crystal, i.e., GaTe, exhibits unique features. By systemically measuring the dependence of the THz output on the ultrafast pump pulses, in terms of polarization, azimuth angle, incident angle, pump beam size, and pump intensity, we have observed the strong evidence of the unidirectional diffusion of photogenerated carriers within the surface layer of each crystal. Regardless of whether each crystal is pumped above or below its bandgap, the mechanism for THz generation is always attributed to diffusion of the photogenerated carriers. By analyzing data and introducing simplified models, it appears to us that the diffusion of the photogenerated carriers takes place along three different directions.