SEMICLASSICAL SIMULATIONS OF HOT ELECTRONS IN GATE-ALL-AROUND SILICON MOSFETS

Abstract

The Monte Carlo technique is employed for self-consistently solving the Boltzmann-Poisson transport equations with full electronic and phonon energy bands to simulate the non-equilibrium carrier transport in materials and devices. Simulations of hot-carrier energy loss to the lattice and cold carriers show that the impact ionization and phonon interactions at or below ~5 eV primarily contribute to the experimentally derived radiation-ionization energies (3.69 eV/electron-hole pair in Si and 2.62 eV/ehp in Ge) of the semiconducting materials. In addition to an energy loss equal to the band gap energy via impact ionization, acoustic-phonon emission, which has been omitted in prior work, contributes 30% of the remaining carrier-energy loss, while optical-phonon emission contributes the other 70%. Next, the energy distributions of electrons in gate-all-around (GAA) Si MOSFETs are analyzed, including additional considerations for elastic interactions, which become important at reduced dimensions and high-carrier densities. Excellent agreement is obtained with experimental current–voltage characteristics. For these 24-nm gate length devices, the electron distribution features a smeared energy peak with an extended tail due to scattering. A fraction of electrons that enter the drain retains their energy, resulting in an out-of-equilibrium distribution in the drain region. The simulated density and average energy of the hot electrons correlate well with experimentally observed device degradation. The results imply that the interaction of high-energy electrons with hydrogen-passivated phosphorus dopant complexes within the drain may provide an additional pathway for interface-trap formation in these devices. Simulated momentum transfer events in the Si NW MOSFETs channel show that the Coulomb processes (often ignored as a higher-order phenomenon) significantly reduce mobility at low-field conditions ⸻ a phenomenon that already redefined Moore’s scaling law as we know it.