3-D Nonequilibrium Green´s Function Simulation of Nonperturbative Scattering From Discrete Dopants in the Source and Drain of a Silicon Nanowire Transistor

As these As transistors are scaled to nanometer dimensions, the discreteness of the dopants becomes increasingly important. Transistors of 3 times 3 nm² cross section contain, on average, approximately one dopant atom per nanometer of length, making any self-averaging impossible. The individual random dopants act as localized scatterers whose distribution, and therefore, impact on the electron transport, varies from device to device. This is complemented by electrostatic variation in the potential that controls the threshold voltage and the dominant current paths. The current density is greatly influenced by resonances associated with the attractive potential of the donors and screening effects. In this paper, for the first time, a full 3-D nonequilibrium Green´s function (NEGF) simulation in the effective mass approximation has been used to study the influence of individual discrete donors in the source/drain on the I-V characteristics of a narrow n-channel Si nanowire transistor. We have compared devices with microscopically different configuration of dopants. The simulated variations in the I-V curves are analyzed with reference to the behavior of the transmission coefficients. We have highlighted the importance of resonance states when solving the NEGF and Poisson equations self-consistently.