A simple quantum mechanical treatment of scattering in nanoscale transistors

Abstract

We present a computationally efficient, two-dimensional quantum mechanical simulation scheme for modeling dissipative electron transport in thin body, fully depleted, n-channel, silicon-on-insulator transistors. The simulation scheme, which solves the nonequilibrium Green's function equations self consistently with Poisson's equation, treats the effect of scattering using a simple approximation inspired by the ''Büttiker probes,'' often used in mesoscopic physics. It is based on an expansion of the active device Hamiltonian in decoupled mode space. Simulation results are used to highlight quantum effects, discuss the physics of scattering and to relate the quantum mechanical quantities used in our model to experimentally measured low field mobilities. Additionally, quantum boundary conditions are rigorously derived and the effects of strong off-equilibrium transport are examined. This paper shows that our approximate treatment of scattering, is an efficient and useful simulation method for modeling electron transport in nanoscale, silicon-on-insulator transistors.

The fundamental downscaling limit of field effect transistors

“…13,16 Surface and interface roughness are included with the real-space treatment, 17 inelastic scattering processes are emulated with an analog of relaxation time approximation or "Buttiker probes." 18 We note, however, that in this study the emulation of inelastic scattering only affected the on-current values (about 10% reduction compared with the case of elastic scattering only) and practically did not affect the capacitance and the switching energy values. The CBR3D simulator shows a linear scaling with the number of grid points (i.e., problem size) and a nearly linear speed-up with the number of CPUs as shown in Fig.…”

Analysis of a Quantum Subband Model for the Transport of Partially Confined Charged Particles

“…In many nanoscale semiconductor devices like ultrashort channel doublegate MOSFETs, electrons might be extremely confined in one direction transverse to the transport directions. The mode-space approach, also referred to as subband decomposition method [30,31,9,10,32], was recently introduced by several authors in order to take advantage of this reduction of dimensionality and design efficient numerical codes. This method consists of a "block diagonalisation" of the electron Hamiltonian thanks to a separation of the confinement and transport directions.…”

Effect of intravalley acoustic phonon scattering on quantum transport in multigate silicon nanowire metal-oxide-semiconductor field-effect transistors

“…However, the current magnitude decreases compared to the ballistic case because scattered electrons lose momentum as a result of scattering. 13,17 To get a better understanding of the contributions of tunneling and diffusion to the current spectrum, we have plotted the LDOS of the channel region. Figure 5͑a͒ clearly shows that there is some available DOS under the barrier in the case of ballistic transport, which causes tunneling current, the dominant transport mechanism in subthreshold operation.…”

“…One can observe that the LDOS for ballistic transport exhibits strong oscillations which are due to quantum interference whereas in the case of AP scattering LDOS has been broaden to adjacent energy levels because scattering inside the nanowire randomizes the phase of the electrons and hence destroys the quantum coherence in the device. 12,17,22 In Fig. 6 we have plotted the energy-resolved electron density for L g = 30 nm and V DS = 0.4 V. In the presence of elastic AP scattering, the carriers will change direction in the channel without losing energy which leads to increase in carrier back scattering and charge reduction in channel.…”

“…The Büttiker probe technique is known to sometimes predict unphysically high tunneling leakage in the off-state. 17 A rigorous treatment of scattering within the NEGF formalism and its application to multigate silicon nanowire transistors was first presented by Jin et al 12 where they studied the effect of electron-phonon scattering on the low-field mobility in the long channel limit. However in their study they neither considered the self-consistent coupling of scattering self-energies and density of states ͑DOS͒ nor the current reduction mechanisms.…”