In this paper, we investigate the influence of the carbon content on the Cu-Te phase formation and on the resistive switching behavior in carbon alloyed Cu0.6Te0.4 based conductive bridge random access memory (CBRAM) cells. Carbon alloying of copper-tellurium inhibits the crystallization, while attractive switching behavior is preserved when using the material as Cu-supply layer in CBRAM cells. The phase formation is first investigated in a combinatorial way. With increasing carbon content, an enlargement of the temperature window in which the material stays amorphous was observed. Moreover, if crystalline phases are formed, subsequent phase transformations are inhibited. The electrical switching behavior of memory cells with different carbon contents is then investigated by implementing them in 580 μm diameter dot TiN/Cu0.6Te0.4-C/Al2O3/Si memory cells. Reliable switching behavior is observed for carbon contents up to 40 at. %, with a resistive window of more than 2 orders of magnitude, whereas for 50 at. % carbon, a higher current in the off state and only a small resistive window are present after repeated cycling. This degradation can be ascribed to the higher thermal and lower drift contribution to the reset operation due to a lower Cu affinity towards the supply layer, leading cycle-after-cycle to an increasing amount of Cu in the switching layer, which contributes to the current. The thermal diffusion of Cu into Al2O3 under annealing also gives an indication of the Cu affinity of the source layer. Time of flight secondary ion mass spectroscopy was used to investigate this migration depth in Al2O3 before and after annealing, showing a higher Cu, Te, and C migration for high carbon contents.