Multi-subband Boltzmann Transport Equation Research Articles

Study of β-Ga2O3-Based Thin-Channel MODFET Devices Using a Coupled Drift-Diffusion/Multisubband BTE Solver

Gallium-oxide-based modulation-doped field-effect transistors (MODFETs) are theoretically investigated. In order to properly consider the electrical characteristics of the two-dimensional electron gases (2DEGs) in thin-channel devices, a coupled drift-diffusion (DD)/multisubband Boltzmann transport equation (MS-BTE) solver is implemented. Parameters adopted in the simulation are determined by referring to the experimental results of existing long-channel devices. The impact of the channel length, the channel thickness, the ungated region length, and contact resistance on the cutoff frequency is rigorously calculated. It is found that the cutoff frequency can have about 90 GHz with a contact resistance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.4~\Omega ~\cdot $ </tex-math></inline-formula> mm and a channel whose length and thickness are 30 and 5 nm, respectively.

Theoretical Study of Electron Transport Properties in GaN-Based HEMTs Using a Deterministic Multi-Subband Boltzmann Transport Equation Solver

A high-electron mobility transistor (HEMT) with a GaN channel is simulated using a deterministic multi-subband Boltzmann transport equation solver. A structure that includes an InGaN back barrier is considered. The electron mobility is calculated for the 1-D heterostructure to identify the contribution of each scattering mechanism to the electron mobility. For GaN-based HEMTs, electron transport in a non-equilibrium state is determined by solving the multi-subband Boltzmann equation expanded with Fourier harmonics. The polar optical phonon and the deformation potential phonon are considered to explain the scattering of the device while considering the Pauli principle. The results of a simulation conducted to assess the mobility and ${I}$ – ${V}$ characteristics are compared with experimental results from the AlInN/AlN/GaN/InGaN HEMT structure. The cutoff frequency of the HEMT is also estimated under the quasi-static approximation.

Systematic calibration of drift diffusion model for InGaAs MOSFETs in quasi-ballistic regime

This paper proposes a systematic procedure to calibrate the parameters of the drift-diffusion (DD) model for a performance evaluation of InGaAs MOSFETs in the quasi-ballistic regime. The simulation results of a deterministic multi-subband Boltzmann transport equation (BTE) solver serve as the standard. The DD model is calibrated both under low and high electric fields. The electrostatic characteristics, low field mobility model, and high field saturation model are calibrated in proper sequence, and a good agreement among the drive current, carrier distribution, and velocity distribution are achieved between the results of the calibrated DD model and the BTE solver. The proposed calibration procedure can also be employed in devices made of other materials.

Physical Insights on Quantum Confinement and Carrier Mobility in Si, Si0.45Ge0.55, Ge Gate-All-Around NSFET for 5 nm Technology Node

We present a comprehensive theoretical investigation of the quantum confinement limited mobility in the Si1− x Ge x -channel gate-all-around nanosheet field effect transistor for 5-nm node. The study encompasses physics-based quantum mechanical models both for P and NMOS with specified channel/wafer orientations and channel thicknesses: 1) k.p model with Poisson solver for band structures, bandgap variations, and confined charge distributions; 2) Kubo-greenwood model for low field mobility with considering surface roughness and stress; 3) multisub-band Boltzmann transport equation based on a state-of-the-art phase space approach is employed to evaluate device IV characteristics; and 4) the threshold voltage ( V T ) variations with different channel/wafer orientations are also evaluated. Our simulation study shows that {110} wafer Ge channel can be an attractive option for 5-nm node pMOS, and Si is still promising for nMOS due to strong quantum confinement in Ge channel.

Resistivity scaling in metallic thin films and nanowires due to grain boundary and surface roughness scattering

A modeling approach, based on an analytical solution of the semiclassical multi-subband Boltzmann transport equation, is presented to study resistivity scaling in metallic thin films and nanowires due to grain boundary and surface roughness scattering. While taking into account the detailed statistical properties of grains, roughness and barrier material as well as the metallic band structure and quantum mechanical aspects of scattering and confinement, the model does not rely on phenomenological fitting parameters.

Investigation of transient responses of nanoscale transistors by deterministic solution of the time-dependent BTE

In this work, the transient characteristics of nanoscale field-effect transistors (FETs) have been investigated using a deterministic solver based on the time-dependent multi-subband Boltzmann transport equation (BTE). The response to a step signal superimposed on the gate or drain electrode is simulated. The transient process can be understood as a combination of electrostatic and transport relaxation. The extracted transient relaxation time for the drain current, which is unrelated to the direct-current (DC) shift, is important for transient device modeling.

A Finite Volume Method for the Multi Subband Boltzmann Equation with Realistic 2D Scattering in Double Gate MOSFETs

AbstractWe propose a deterministic solver for the time-dependent multi-subband Boltzmann transport equation (MSBTE) for the two dimensional (2D) electron gas in double gate metal oxide semiconductor field effect transistors (MOSFETs) with flared out source/drain contacts. A realistic model with six-valleys of the conduction band of silicon and both intra-valley and inter-valley phonon-electron scattering is solved. We propose a second order finite volume method based on the positive and flux conservative (PFC) method to discretize the Boltzmann transport equations (BTEs). The transport part of the BTEs is split into two problems. One is a 1D transport problem in the position space, and the other is a 2D transport problem in the wavevector space. In order to reduce the splitting error, the 2D transport problem in the wavevector space is solved directly by using the PFC method instead of splitting into two 1D problems. The solver is applied to a nanoscale double gate MOSFET and the current-voltage characteristic is investigated. Comparison of the numerical results with ballistic solutions show that the scattering influence is not ignorable even when the size of a nanoscale semiconductor device goes to the scale of the electron mean free path.

Comparison of strained SiGe heterostructure-on-insulator (0 0 1) and (1 1 0) PMOSFETs: C–V characteristics, mobility, and ON current

Strained SiGe heterostructure-on-insulator (001) and (110) PMOSFETs are investigated including important aspects like C–V characteristics, mobility, and ON current. The simulations are based on the self-consistent solution of 6×6 k·p Schrödinger Equation, multi subband Boltzmann Transport Equation and Poisson Equation, and capture size quantization, strain, crystallographic orientation, and SiGe alloy effects on a solid physical basis. The simulation results are validated by comparison with different experimental data sources. The simulation results show that the strained SiGe HOI PMOSFET with (110) surface orientation has a higher gate capacitance and a much higher mobility and ON current compared to a similar device with the traditional (001) surface orientation.

On the numerical aspects of deterministic multisubband device simulations for strained double gate PMOSFETs

In this paper numerical aspects of deterministic multisubband device simulations are presented for strained double gate PMOSFETs including magnetotransport. The simulations are based on a self-consistent solution of the multisubband Boltzmann transport equation (BTE), 6×6 k⋅p Schrodinger equation (SE) and Poisson equation (PE). For accurate and efficient calculation of the subband structure, an efficient discretization of the 2D k-space combined with a monotonic cubic spline interpolation is employed. The multisubband BTE is solved with a deterministic method based on a Fourier expansion of the distribution function. The Fourier series is found to converge rapidly for nanoscale double gate PMOSFETs. A convergence enhancement method for the Gummel type SE-PE-BTE loop by solving the BTE-PE simultaneously is proposed.

Theoretical Study of Carrier Transport in Silicon Nanowire Transistors Based on the Multisubband Boltzmann Transport Equation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We study electronic transport in silicon nanowire transistors at room temperature based on the self-consistent numerical solution of the multisubband Boltzmann transport equation and Poisson equation. The SchrÖdinger equation with nonparabolic corrections is solved in order to obtain the multisubband structure. Relevant microscopic scattering mechanisms due to acoustic and intervalley phonons, surface roughness, and ionized impurities are included in the simulation. A flux-conserving discretization scheme based on the uniform total energy grid is employed to avoid excessive numerical diffusion originating from the conventional kinetic-energy-based upwind scheme. We report an interesting kink behavior in the output characteristics and study the electron energy distribution inside the transistor as a function of bias conditions and scattering mechanisms. </para>

Differential conductance fluctuations in silicon nanowire transistors caused by quasiballistic transport and scattering induced intersubband transitions

Calculations based on the multisubband Boltzmann transport equation with relevant microscopic scattering mechanisms predict abrupt differential conductance fluctuations (kinks) in the drain current versus drain voltage curves of silicon nanowire transistors at room temperature. The kink originates from the change of series resistance at the drain extension related to the interplay between quasiballistic transport and intersubband transitions of electrons caused by elastic interactions with acoustic phonons, surface roughness, and ionized impurities. The kink occurs when the energy of the second subband in the drain extension is aligned with the peak of the net electron flux distribution in the first subband. This bias condition yields a large series resistance in the drain extension because those quasiballistic electrons in the first subband which reach the drain can scatter isotropically into the second subband.

Simulation of Silicon Nanowire Transistors Using Boltzmann Transport Equation Under Relaxation Time Approximation

An efficient approach for the simulation of electronic transport in nanoscale transistors is presented based on the multi-subband Boltzmann transport equation under the relaxation time approximation, which takes into account the effects of quantum confinement and quasi-ballistic transport. This approach is applied to the study of electronic transport in circular gate-all-around silicon nanowire transistors. Comparison with the nonequilibrium Green's function method shows that the new method gives reasonably accurate terminal characteristics. We study the influence of silicon body diameter and gate length on the terminal current and subthreshold slope (SS). We have found that the calculated ON current is inversely proportional to the gate length to the power 1/2, and that the silicon body diameter should be smaller than roughly 2/3 of the channel length in order to maintain the SS within 80 mV/dec.