3D drift diffusion and 3D Monte Carlo simulation of on-current variability due to random dopants

In this work Random Discrete Dopant induced on-current variations have been studied using the Glasgow 3D atomistic drift/diffusion simulator and Monte Carlo simulations. A methodology for incorporating quantum corrections into self-consistent atomistic Monte Carlo simulations via the density gradient effective potential is presented. Quantum corrections based on the density gradient formalism are used to simultaneously capture quantum confinement effects. The quantum corrections not only capture charge confinement effects, but accurately represent the electron impurity interaction used in previous \textit{ab initio} atomistic MC simulations, showing agreement with bulk mobility simulation. The effect of quantum corrected transport variation in statistical atomistic MC simulation is then investigated using a series of realistic scaled devices nMOSFETs transistors with channel lengths 35 nm, 25 nm, 18nm, 13 nm and 9 nm. Such simulations result in an increased drain current variability when compared with drift diffusion simulation. The comprehensive statistical analysis of drain current variations is presented separately for each scaled transistor. The investigation has shown increased current variation compared with quantum corrected drift diffusion simulation and with previous classical MC results. Furthermore, it has been studied consistently the impact of transport variability due to scattering from random discrete dopants on the on-current variability in realistic nano CMOS transistors. For the first time, a hierarchic simulation strategy to accurately transfer the increased on-current variability obtained from the ‘ab initio’ MC simulations to DD simulations is subsequently presented. The MC corrected DD simulations are used to produce target $I_D-V_G$ characteristics from which statistical compact models are extracted for use in preliminary design kits at the early stage of new technology development. The impact of transport variability on the accuracy of delay simulation are investigated in detail. Accurate compact models extraction methodology transferring results from accurate physical variability simulation into statistical compact models suitable for statistical circuit simulation is presented. In order to examine te size of this effect on circuits Monte Carlo SPICE simulations of inverter were carried out for 100 samples

Antenna near-field wave studies in magnetized plasmas as part of the optimization of auxiliary heating in fusion devicesAntenna near-field wave studies in magnetized plasmas as part of the optimization of auxiliary heating in fusion devices

C

Monte Carlo study of current variability in UTB SOI DG MOSFETs

The scaling of conventional silicon based MOSFETs is increasingly difficult into the nanometer regime due to short channel effects, tunneling and subthreshold leakage current. Ultra-thin body silicon-on-insulator based architectures offer a promising alternative, alleviating these problems through their geometry. However, the transport behaviour in these devices is more complex, especially for silicon thicknesses below 10 nm, with enhancement from band splitting and volume inversion competing with scattering from phonons, Coulomb interactions, interface roughness and body thickness fluctuation. Here, the effect of the last scattering mechanism on the drive current is examined as it is considered a significant limitation to device performance for body thicknesses below 5 nm. A simulation technique that properly captures non-equilibrium transport, includes quantum effects and maintains computational efficiency is essential for the study of this scattering mechanism. Therefore, a 3D Monte Carlo simulator has been developed which includes this scattering effect in an ab initio fashion, and quantum corrections using the Density Gradient formalism. Monte Carlo simulations using `frozen field' approximation have been carried out to examine the dependence of mobility on silicon thickness in large, self averaging devices. This approximation is then used to carry out statistical studies of uniquely different devices to examine the variability of on-current. Finally, Monte Carlo simulations self consistent with Poisson's equation have been carried out to further investigate this mechanism

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

AbstractWe present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations

DFT AND RELATED MODELING OF POST-SILICON VALENCE 4 MATERIALS: SiC AND Ge

Though silicon (Si) is in many ways the material of choice for many electronic applications due in part to its mature processing technology, its intrinsic properties are not always suited for every challenge. Specialized high power and high temper- ature devices benefit from using semiconductors with a larger band-gap and higher thermal conductivity such as silicon carbide (SiC). Additionally, the 1.1eV bandgap of Si makes it unable to effectively absorb infrared photons so a material with a smaller bandgap, like germanium (Ge), is more suited to the task. Currently SiC power transistors are commercially available but suffer from poor channel mobility due to interface roughness which limits their performance. To predict the maximum theoretically achievable mobility for different crystallo- graphic interfaces I developed a novel technique for extracting an atomic-roughness scattering rate from an arbitrary atomic surface. The term atomic-roughness here means an interface purely due to the variation of atom species and position without the presence of a crystallographic miscut due to epitaxial growth considerations. I used Density Functional Theory (DFT) to obtain a perturbation potential from which I can calculate a scattering rate. This scattering rate can then be used in a Monte Carlo simulation to predict mobility for a given field configuration. In addition to SiC’s low channel mobility, SiC p-type dopant species also ex- hibit an abnormally large ionization energy compared to its n-type dopants and to the primary dopants in many other semiconductors. This fact can cause is- sues such as unexpectedly high resistance regions at lower operating temperatures - causing the need to dope at significantly higher concentration. To characterize the incomplete ionization fraction p/N A , I first gathered nearly all existing pub- lished data on the ionization energy of aluminum (Al) in 4H-SiC and created an empirical concentration-dependent model of this function. Then I put together a physics-based model of the entire acceptor and valence band system and used my concentration-dependent ionization energy as an input to predict p/N A . I verify my physics-based model result against a separate experimental dataset derived from nearly-exhaustive literature measurements of Hall mobility and resistivity. Finally, I transform fully temperature-dependent result of p/N A from a complex numerical computation to a more easily implementable parameterized function with the use of a genetic algorithm. The remaining part of my work was performed on Germanium which has interesting application in short-wave infrared imaging due its 0.66eV indirect and 0.85 eV direct bandgaps, which corresponds closely to the peak illumination of the “night glow” at 0.75 eV. Optical devices greatly benefit from direct gap band structures to increase photon absorption and emission efficiency. Though Ge is an indirect gap material, it can be alloyed with a direct gap material, namely tin (Sn), to transition it to a direct gap material at a certain molar fraction. Through DFT calculations I investigate the nature of this transition and determine theoretically the minimum molar fraction needed to achieve a direct bandgap