We show that carbon nanotube sensors with gold particles on the single-walled carbon nanotube (SWNT) network operate as Schottky barrier transistors, in which transistor action occurs primarily by varying the resistance of Au-SWNT junction rather than the channel conductance modulation. Transistor characteristics are calculated for the statistically simplified geometries, and the sensing mechanisms are analyzed by comparing the simulation results of the MOSFET model and Schottky junction model with the experimental data. We demonstrated that the semiconductor MOSFET effect cannot explain the experimental phenomena such as the very low limit of detection (LOD) and the logarithmic dependence of sensitivity to the DNA concentration. By building an asymmetric concentric-electrode model which consists of serially-connected segments of CNTFETs and Schottky diodes, we found that for a proper explanation of the experimental data, the work function shifts should be ~ 0.1 eV for 100 pM DNA concentration and ~ 0.4 eV for $100{mu}M$.