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In this paper, we show that periodic arrays of rectangular slots with subwavelength width provide for local electromagnetic field enhancements due to edge effects in low-frequency range, 10-25 cm-1. Periodic structures of Au, doped Si, and InSb with subwavelength thickness were studied. The half power enhancement width is ~500 nm and less around the slot edges in all cases, thereby possibly bringing terahertz (THz) sensing to the nanoscale. InSb is confirmed to offer the best results with the local power enhancements on the order of 1100 at frequency 14 cm-1. InSb and Si have large skin depths in the frequency range of interest and so the analysis of their structures was done through the Fourier expansion method of field diffracted from gratings. Au, however, has small skin depths at these frequencies compared with the thickness. Surface impedance boundary conditions were employed to model the Au structure, for which the Fourier expansion method was unsuitable owing to the huge magnitude of Au permittivity at these frequencies. The applications possibly include development of novel biosensors, with the strongly enhanced local electromagnetic fields leading to increased detection sensitivity, and monitoring biophysical processes such as DNA denaturation.