In this study, the inter-metal dielectric material of FSG was changed by low-k material in $0.13{mu}m$ foundry-compatible technology (FCT) device process based on fluorinated silicate glass (FSG). Black diamond (BD) was used as a low-k material with a dielectric constant of 2.95 for optimization and yield-improvement of the low-k based device process. For yield-improvement in low-k based device process, some problems such as photoresist (PR) poisoning, damage of low-k in etch/ash/cleaning process, and chemical mechanical planarization (CMP) delamination must be solved. The PR poisoning was not observed in BD based device. The pressure in CMP process decreased to 2.8 psi to remove the CMP delamination for Cu-CMP and USG-CMP. $H_2O$ ashing process was selected instead of $O_2$ ashing process due to the lowest condition of low-k damage. NE14 cleaning after ashing process lot the removal of organic residues in vias and trenches was employed for wet process instead of dilute HF (DHF) process. The similar-state of SRAM yield was obtained in Cu/low-k process compared with the conventional $0.13{mu}m$ FCT device by the optimization of these process conditions.