Simulation of the Impact of Ionized Impurity Scattering on the Total Mobility in Si Nanowire Transistors

Abstract

Nanowire transistors (NWTs) are being considered as possible candidates for replacing FinFETs, especially for CMOS scaling beyond the 5-nm node, due to their better electrostatic integrity. Hence, there is an urgent need to develop reliable simulation methods to provide deeper insight into NWTs’ physics and operation, and unlock the devices’ technological potential. One simulation approach that delivers reliable mobility values at low-field near-equilibrium conditions is the combination of the quantum confinement effects with the semi-classical Boltzmann transport equation, solved within the relaxation time approximation adopting the Kubo–Greenwood (KG) formalism, as implemented in this work. We consider the most relevant scattering mechanisms governing intraband and multi-subband transitions in NWTs, including phonon, surface roughness and ionized impurity scattering, whose rates have been calculated directly from the Fermi’s Golden rule. In this paper, we couple multi-slice Poisson–Schrödinger solutions to the KG method to analyze the impact of various scattering mechanisms on the mobility of small diameter nanowire transistors. As demonstrated here, phonon and surface roughness scattering are strong mobility-limiting mechanisms in NWTs. However, scattering from ionized impurities has proved to be another important mobility-limiting mechanism, being mandatory for inclusion when simulating realistic and doped nanostructures, due to the short range Coulomb interaction with the carriers. We also illustrate the impact of the nanowire geometry, highlighting the advantage of using circular over square cross section shapes.

Comprehensive Study of Cross-Section Dependent Effective Masses for Silicon Based Gate-All-Around Transistors

“…First, we utilize the potential distribution, the corresponding wavefunctions, and the relevant subband levels calculated in the ballistic NEGF module to compute the scattering rates for the dominant mechanisms in silicon nanowires [11]: acoustic phonon (Ac Ph) scattering, optical phonon (Op Ph) scattering, and surface roughness (SR) scattering. The scattering rates have been directly calculated from the Fermi golden rule accounting for the quantization in the confinement plane [12]. Second, the Kubo-Greenwood formalism is adopted to calculate the scattering-limited mobility solving the semi-classical Boltzmann transport equation (BTE) within the relaxation time approximation.…”

“…More information about the mobility calculation as well as the specific equations for the different scattering mechanisms can be found in Ref. [12]. A detailed discussion on NESS can be found in [10].…”

“…. In general, as the transport effective masses were introduced in the scattering rate equations [12], their modification directly altered the mobility. Due to the relaxation time approach, the mobility for a particular scattering mechanism was inversely proportional to its rate and thus to the transport effective mass.…”

Electron transport through nanosystems driven by pseudo-Gaussian well scattering

“…Particle scattering is of great interest in disruptive technologies, as it critically depends on the dissipationless transport of electrons. It is of great interests about electron mobility calculation as well as the specific equations for the different scattering mechanisms [1]. This allows the evaluation of properties at the macro level, as well as the evaluation of measure at the nanoscale voltage drop caused by the scattering was previously reported [2].…”

Special Issue: Nanowire Field-Effect Transistor (FET)

“…Sano et al [4] focused their work on the physics associated with localized impurities inside the device, describing a systematic methodology on how to treat Coulomb interaction in many body-systems when using drift-diffusion simulations. Sady et al [5], on the other hand, studied the effect of various scattering mechanisms and nanowire cross-section shapes on electron mobility in nanoscale Si NW-FETs.…”