Sung-Min Hong

Deterministic solvers for the Boltzmann transport equation

Introduction. - Electron transport in the 3D k-space: The Boltzmann transport equation and its projection onto spherical harmonics. - Device simulation. - Band structure and scattering mechanisms. - Results. - Transport in a quasi 2D hole gas: Coordinate systems and systems of equation. - Efficient k . p SE solver. - Efficient 2D k-space discretization and non-linear interpolation schemes. - Deterministic solver for the multisubband stationary BTE. - Poisson equation. - Iteration methods. - Results. - References.

A Proposal on an Optimized Device Structure With Experimental Studies on Recent Devices for the DRAM Cell Transistor

We have experimentally analyzed the leakage mechanism and device degradations caused by the Fowler-Nordheim (F-N) and hot carrier stresses for the recently developed dynamic random-access memory cell transistors with deeply recessed channels. We have identified the important differences in the leakage mechanism between saddle fin (S-Fin) and recess channel array transistor (RCAT). These devices have their own respective structural benefits with regard to leakage current. Therefore, we suggest guidelines with respect to the optimal device structures such that they have the advantages of both S-Fin and RCAT structures. With these guidelines, we propose a new recess-FinFET structure that can be realized by feasible manufacturing process steps. The structure has the side-gate form only in the bottom channel region. This enhances the characteristics of the threshold voltage (VTH), ON/OFF currents, and the retention time distributions compared with the S-Fin structure introduced recently.

An Efficient Approach to Include Full-Band Effects in Deterministic Boltzmann Equation Solver Based on High-Order Spherical Harmonics Expansion

We present an efficient method to include full-band-structure effects for the case of a silicon conduction band in a deterministic Boltzmann equation solver based on the high-order spherical harmonics expansion method. This method employs the exact density of states and the group velocity obtained from band structure calculations, and it eliminates the modulus of the wave vector in the formulation such that an explicit invertible dispersion relation is not required. While the present method does not require additional central-processing-unit time and memory, compared with the analytic band model, the simulation results are significantly improved and in excellent agreement with those from the full-band Monte Carlo simulations and from an approach based on an invertible anisotropic band that matches several moments of the group velocity of the full band structure.

Coupled drift-diffusion (DD) and multi-subband Boltzmann transport equation (MSBTE) solver for 3D multi-gate transistors

This paper presents a self-consistent coupled DD/MSBTE solver for the device simulation of realistic 3D multi-gate transistors. The MSBTE for quasi-1D k-space is solved in the channel region while the DD equation is solved in the source/drain regions with an appropriate boundary condition at the DD/MSBTE region interfaces. In the MSBTE region, 2D Schrödinger equation with the two (electrons) or six (holes) band k · p Hamiltonian is solved to obtain the subband structure for arbitrary crystal orientations and stress conditions. Phonon and surface roughness scattering processes are taken into account in the MSBTE where the surface roughness scattering model has been extended to consider arbitrary cross-sections. Silicon nanowire transistors are considered as an application.

A Deterministic Boltzmann Equation Solver Based on a Higher Order Spherical Harmonics Expansion With Full-Band Effects

In this paper, a deterministic Boltzmann equation solver based on a higher order spherical harmonics expansion, including full-band (FB) effects, is presented. An anisotropic band structure for the conduction band with an invertible energy/wave vector relation has been generated by matching several moments of the group velocity of the silicon FB structure. A generalized formulation of the free-streaming operator is presented, which is stabilized according to the maximum entropy dissipation scheme. From the numerical results for various systems such as silicon bulk, an n+-n-n+ structure, and SiGe heterojunction bipolar transistors, it can be concluded that the new model improves significantly the accuracy of the Boltzmann solver compared to previous band models without degrading the numerical stability.

Statistical Noise Analysis of CMOS Image Sensors in Dark Condition

The statistical noise analysis of the CMOS image sensors in the dark condition has been performed with a newly developed 3-D technology computer-aided design framework. The noise histograms of the correlated double sampling output, due to the random distribution of the oxide traps in the source follower MOSFET, have been evaluated. In this framework, the random telegraph signal noise is accurately characterized in the device level, and the numerical efficiency for the statistical analysis is achieved by employing the Greens function method based on the drift-diffusion model. As an application, one million samples of the source follower MOSFET have been simulated, and the effect of the channel width, the channel length, and the oxide trap density on the noise histogram has been investigated.

Statistical analysis of random telegraph noise in CMOS image sensors

We propose a statistical method to predict the dark random readout noise in CMOS image sensors. First, we calculate the dark random noise originated from oxide traps present in the source-follower MOSFET. Statistical variation in the dark noise is associated with the random variation of the oxide defects in the CMOS image sensor cells in both the energy and space domain. Considering the effect of the correlated double sampling, we define the dark random noise as the standard deviation in the time domain and analyze the effect of the MOSFET width and length variations and temperature on its dark random noise.

Solving Boltzmann Transport Equation without Monte-Carlo algorithms - new methods for industrial TCAD applications

The Drift-Diffusion model is still by far the most frequently used numerical device model in industry today. One important reason for this success is the robust numerical implementation of this model providing CPU efficient DC, AC, transient, and noise simulations with high accuracy and high convergence reliability. On the other hand, many of todays design applications vary strain, crystal and channel orientation, material composition, and the carrier confinement. Such applications certainly require the solution of the Boltzmann Transport Equation in order to be predictive. It will be demonstrated in this paper that with new alternative discretization and solution methods avoiding the Monte-Carlo algorithm many of the favorable numerical properties of the traditional Drift-Diffusion model can be transferred to numerical device models that include the solution of the Boltzmann Transport Equation.

Numerical Simulation of Plasma Oscillation in 2-D Electron Gas Using a Periodic Steady-State Solver

The terahertz oscillation due to the plasma instability in the 2-D electron gas is numerically investigated using an in-house developed device simulator, G-Device. In order to overcome practical difficulties in the conventional transient simulation, a periodic steady-state (PSS) solver is implemented. The full Newton-Raphson scheme is applied to a set of discretized equations sampled at various time points during an oscillation period. Numerical results show that there is a threshold value of the injection velocity that allows the PSS oscillation. Moreover, the impact of the drain load resistance on the oscillation amplitude is estimated. It is found that considerable amplitude of the voltage oscillation can be achieved even with finite drain resistances. Although the growth rate of the voltage oscillation exhibits its maximum value with the infinite drain resistance, the maximum output power is obtained at a finite drain resistance.

Inclusion of the Pauli principle in a deterministic Boltzmann equation solver for semiconductor devices

The Pauli principle is included in a deterministic Boltzmann solver for multi-dimensional semiconductor devices. The Newton-Raphson scheme is applied to solve the nonlinear Boltzmann equation, and it is found that the inclusion of the Pauli principle introduces no numerical problems, even for semiconductor devices. The impact of the Pauli principle is numerically investigated for a scaled SiGe HBT.