Monte Carlo particle-based simulations of deep-submicron n-MOSFETs with real-space treatment of electron-electron and electron-impurity interactions

In modern deep-submicron devices, for achieving optimum device performance, the doping densities must be quite high. This necessitates a careful treatment of the short- and long-range electron-electron and electron-impurity interactions. We have shown before that by using a corrected Coulomb force, in conjunction with a proper cutoff range, one can properly account for the short-range portion of the force. Our approach naturally incorporates multi-ion contributions, local distortions in the scattering potential due to the movement of the free charges, and carrier-density fluctuations. The doping dependence of the low-field electron mobility obtained from 3D resistor simulations closely followed the experimental results, thus proving the correctness of our approach. Here, we discuss how discrete impurity effects affect the threshold voltage of ultra-small n-channel MOSFETs with gate lengths ranging from 50 to 100 nm. We find that the fluctuations in the threshold voltage increase with increasing the oxide thickness and substrate doping. The averaging effect over the width of the device leads to significantly smaller fluctuations in the threshold voltage for devices with larger gate width. The observed trends are in agreement with the experimental findings.