A method for manufacturing a thin film resistor (TFR) module in an integrated circuit (IC) structure may include forming a trench in a dielectric region; forming a TFR element in the trench, the TFR element including a laterally-extending TFR region and a TFR ridge extending upwardly from a laterally-extending TFR region; depositing at least one metal layer over the TFR element; and patterning the at least one metal layer and etching the at least one metal layer using a metal etch to define a pair of metal TFR heads over the TFR element, wherein the metal etch also removes at least a portion of the upwardly-extending TFR ridge. The method may also include forming at least one conductive TFR contact extending through the TFR element and in contact with a respective TFR head to thereby increase a conductive path between the respective TFR head and the TFR element.