M. Karner

Interface traps density-of-states as a vital component for hot-carrier degradation modeling

We refine our approach for hot-carrier degradation modeling based on a thorough evaluation of the carrier energy distribution by means of a full-band Monte–Carlo simulator. The model is extended to describe the linear current degradation over a wide range of operation conditions. For this purpose we employ two types of interface states, either created by single- or by multiple-electron processes. These traps apparently have different densities of states which is important to consider when calculating the charges stored in these traps. By calibrating the model to represent the degradation of the transfer characteristics, we extract the number of particles trapped by both types of interface traps. We find that traps created by the single- and multiple-electron mechanisms are differently distributed over energy with the latter shifted toward higher energies. This concept allows for an accurate representation of the degradation of the transistor transfer characteristics.

Hot-carrier degradation modeling using full-band Monte-Carlo simulations

We propose and verify a model for hot carrier degradation based on the exhaustive evaluation of the energy distribution function for charge carriers in the channel by means of a full-band Monte-Carlo device simulator. This approach allows us to capture the interplay between “hot” and “colder” electrons and their contribution to the damage build-up. In fact, particles characterized by higher energy are able to produce interface traps by a single-carrier process while colder ones trigger multivibrational mode excitation of a Si-H bond. For the model validation we use long-channel MOSFETs and represent the degradation of the linear drain current. The single-carrier component dominates degradation (this is the usual tendency for long devices), however, the multiple-carrier process is still considerable being less and less pronounced as the source-drain stress voltage increases

Physical modeling of NB TI: From individual defects to devices

Given the rapid recovery of the degradation induced by bias-temperature stress, the understanding and modeling of NBTI has been a challenge for nearly half a century. With the introduction of the time-dependent defect spectroscopy (TDDS), NBTI could be studied at the single defect level, confirming that it is dominated by a collection of first-order reactions rather then the previously invoked reaction-diffusion mechanism. The most intriguing feature of these first-order processes is the wide distribution of their time constants, which can be visualized in capture/emission time (CET) maps. In the following we clarify the microscopic link between individual defects seen in TDDS studies and the response of a large ensemble visible in the CET maps. In particular, we show how the distribution of the individual defect parameters can be extracted from measurements on large-area devices.

Exploring the design space of non-planar channels: Shape, orientation, and strain

We conduct a comprehensive simulation study of non-planar n-type channels based on consistent, physical models containing measurable quantities rather than fit-parameters. This contrasts empirical thin-body models used in classical/quantum-corrected TCAD. The method involves the self-consistent solution of the two-dimensional Schrödinger-Poisson system, combined with linearized Boltzmann transport in the third dimension. We advance the art of simulation by (i) introducing quantum simulation on unstructured meshes for arbitrary geometries, (ii) providing an efficient framework for rapid evaluation of device designs, and (iii) contributing a surface roughness scattering model for arbitrarily shaped surfaces. Consistent modeling allows us to make reliable assertions with respect to device performance.

A Model for Switching Traps in Amorphous Oxides

Negative Bias Temperature Instability (NBTI) is frequently suspected to arise from a delicate interplay between some sort of hole trapping and an interface generation mechanism. In a recently suggested model the E′ center along with its second form as an Si−Si dimer are supposed to play a key role. Despite of its successful application to a large amount of experimental data, this model relies on a classical determination of the bandedge energy diagram and the carrier concentrations. The occurrence of subbands in the inversion layer shifts the initial energy level for charge trapping and may thus strongly impact the trapping dynamics. We evaluate the new model against measurement data in order to investigate the impact of quantization effects on the model parameters.

Modeling of high-k-Metal-Gate-stacks using the non-equilibrium Green’s function formalism

A high-k-metal-gate stack has been investigated using an open boundary model based on the non-equilibrium Greenpsilas function formalism. The numerical energy integration, which is crucial because of the very narrow resonant states, is pointed out in detail. The model has been benchmarked against the established classical and closed boundary Schrodinger-Poisson model. In contrast to the established models, the solution covers distinct resonant states with a realistic broadening and results in a major difference in the current density spectrum.

On the validity of momentum relaxation time in low-dimensional carrier gases

The momentum relaxation time (MRT) is widely used to simplify low-field mobility calculations including anisotropic scattering processes. Although not always fully justified, it has been very practical in simulating transport in bulk and in low-dimensional carrier gases alike. We review the assumptions behind the MRT, quantify the error introduced by its usage for low-dimensional carrier gases, and point out its weakness in accounting for inter-subband interaction, occurring specifically at low inversion densities.

Physical modeling — A new paradigm in device simulation

We go far beyond classical TCAD in and create a simulation framework that is ready for devices based on contemporary and future technology nodes. We do so by extending the common drift-diffusion-type device simulation framework with additional tools: (i) a k p-based subband structure tool, (ii) a deterministic subband Boltzmann transport solver, and (iii) a TCAD-compatible quantum transport solver, to capture every important aspect of device operation at the nano-scale. An atomistic ab-initio tool suite complements the framework providing material properties that would be hard to obtain otherwise. The capabilities of the approach are demonstrated on two different devices featuring non-planar geometry and alternative channel materials.

Coupling of non-equilibrium Green’s function and Wigner function approaches

We propose a coupling scheme, where the advantages of the coherent Greenpsilas function formalism are combined with the ability of the Wigner formalism to account for phase-breaking processes of interaction with phonons and other lattice imperfections. The Greenpsilas function formalism is used to calculate the coherent Wigner function which provides the initial condition in an equation, from which corrections due to phonon interactions can be calculated. A variety of possible approaches to the obtained equation are considered, and the case where the initial condition is small is investigated numerically.

Vertically stacked nanowire MOSFETs for sub-10nm nodes: Advanced topography, device, variability, and reliability simulations

Using an advanced simulation framework we analyze a recent sub-10 nm technology demonstration based on stacked nanowire transistors (NW-FETs). The study encompasses (i) topography simulation which realistically reproduces the fabricated device, (ii) device simulation based on the subband Boltzmann transport equation (iii) a comprehensive set of scattering models for the gate stack, (iv) physical models for time-zero variability and BTI device degradation. We find that (i) the fabrication process introduces parasitic capacitances not present in a comparable FinFET, (ii) the device performance is significantly affected by interface-charge-induced Coulomb scattering resulting in up to 50% reduction in drain current compared to an ideal device, (iii) device time-zero variability is increased due to a lower amount of dopant atoms per device, (iv) the device is more affected by BTI than a comparable FinFET. Using physics-based TCAD for technology path-finding and device optimization, we are able to point out critical improvements required for the stacked NW-FET to surpass current FinFET technology.