Rectennas are widely used for energy harvesting purposes. For THz rectennas, traditional semiconductor-based diodes cannot be used as they are not fast enough. As an alternate, fast metal-insulator-metal (MIM) diodes have been considered in the recent past, however, they suffer from limited cut-off frequency due to high RC constant (especially high capacitance). Geometric diode, on the other hand, can solve the issue of high capacitance due to its planar structure. The neck width of the geometric diode affects its responsivity, so smaller the neck width, better is the responsivity. Previously, the lowest reported neck width for a funnel-shaped graphene geometric diode is 50 nm with a zero-bias responsivity of 0.06 A/W. In this work, we propose a better design with the lowest reported neck width of 28 nm, which shows a higher zero-bias responsivity of 0.17 A/W experimentally.