In this paper, the impact of the substrate resistivity on surface waves (SW) is studied for antenna on-chip applications on metal-backed thick substrates. Three silicon (Si) substrates are studied: standard bulk (Std), high-resistivity (HR) and trap-rich (TR) HR. First, a substrate parameter extraction is conducted based on CPW lines and matched with simulations to obtain an electromagnetic model of the material stack. From this, the effect of the parasitic surface conduction (PSC) on the SW attenuation and the high efficiency achieved by the SW propagating through TR are demonstrated by analytically extracting the SW attenuation constant for each substrate. Finally, a dipole-slot antenna is analyzed. It is characterized for several die dimensions. This demonstrates the impact of the resistivity on the excited SW through the radiation pattern (RP) and the S11 variation with die dimension due to SW diffraction and reflection at the die edges. Among the studied Sibased substrates, antennas on TR demonstrate the highest RP and return loss dependency on the chip dimension, due to the low attenuation of the excited SW. This study highlights the promising use of TR substrates as a solution to support highefficiency mm-wave on-chip antennas, under the condition that the excited SW are properly dealt with during the antenna/chip co-design process.