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As devices shrink, the current density through interconnects increases proportionally making new materials a necessity for industry growth. Carbon nanofiber (CNF) and carbon nanotube's (CNT) potential for high current density make them a possible replacement for metal contacts. Learning the limitations of CNFs and CNTs is important if they are to be used in next- generation electronics. As current density increases, heat is generated throughout the CNF structure. This heating eventually leads to breakdown as the temperature reaches the bonding energy of the Carbon-Carbon (C-C) bond, the bond between two carbon atoms. The resultant reaction is the vaporization of the carbon, eliminating electromigration problems common with metal interconnects. The physics of breakdown of CNFs is poorly understood. The CNF interconnects' heating under a voltage sweep between two electrodes is modeled in this thesis. A working model was created with Silvaco ATLAS using experimental data provided by Santa Clara University (SCU). An analytical solution was found for the heat generation occurring within the device. The simulation does not show the breakdown occurring; instead, it accurately predicts the temperature and electrical characteristics of the device. This model will aid in the analysis of CNFs' reliability and potential future integration into the next generation electronics.