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This work describes a novel simulation approach that combines machine learning and device modelling simulations. The device simulations are based on the quantum mechanical non-equilibrium Greens function (NEGF) approach and the machine learning method is an extension to a convolutional generative network. We have named our new simulation approach ML-NEGF and we have implemented it in our in-house simulator called NESS (nano-electronics simulations software). The reported results demonstrate the improved convergence speed of the ML-NEGF method in comparison to the standard NEGF approach. The trained ML model effectively learns the underlying physics of nano-sheet transistor behaviour, resulting in faster convergence of the coupled Poisson-NEGF simulations. Quantitatively, our ML- NEGF approach achieves an average convergence acceleration of 60%, substantially reducing the computational time while maintaining the same accuracy.

In this paper, we investigate various aspects of the polysilicon gate influence on the random dopant induced threshold voltage fluctuations in sub-100 nm MOSFET's with ultrathin gate oxides. The study is done by using an efficient statistical three-dimensional (3-D) "atomistic" simulation technique described else-where. MOSFET's with uniform channel doping and with low doped epitaxial channels have been investigated. The simulations reveal that even in devices with a single crystal gate the gate depletion and the random dopants in it are responsible for a substantial fraction of the threshold voltage fluctuations when the gate oxide is scaled-in the range of 1-2 nm. Simulation experiments have been used in order to separate the enhancement in the threshold voltage fluctuations due to an effective increase in the oxide thickness associated with the gate depletion from the direct influence of the random dopants in the gate depletion layer. The results of the experiments show that the both factors contribute to the enhancement of the threshold voltage fluctuations, but the effective increase in the oxide-thickness has a dominant effect in the investigated range of devices. Simulations illustrating the effect or the polysilicon grain boundaries on the threshold voltage variation are also presented.

We use the density gradient (DG) simulation approach to study, in 3D, the effect of local oxide thickness fluctuations on the threshold voltage of decanano MOSFETs in a statistical manner. A description of the reconstruction procedure for the random 2D surfaces representing the 'atomistic' Si-SiO2 interface variations is presented. The procedure is based on power spectrum synthesis in the Fourier domain and can include either Gaussian or exponential spectra. The simulations show that threshold voltage variations induced by oxide thickness fluctuation become significant when the gate length of the devices become comparable to the correlation length of the fluctuations. The extent of quantum corrections in the simulations with respect to the classical case and the dependence of threshold variations on the oxide thickness are examined.

In this paper for the first time we study the influence of the polysilicon gate on the random dopant induced threshold voltage fluctuations in sub 100 nm MOSFETs with tunnelling gate oxides. This is done by using an efficient 3D 'atomistic' simulation technique described elsewhere. Devices with uniform channel doping and with low doped epitaxial channels have been investigated. The simulations reveale that the polysilicon gate is responsible for a substantial fraction of the threshold voltage fluctuations in both devices when the gate oxide is scaled to tunnelling thickness in the range of 1 - 2 nm.

When the devices are scaled to decanano dimensions the discreteness of charge and matter introduces significant 'intrinsic' parameter fluctuations. Atomic level 3D process and device modelling on statistical scale is required to understand the effects, the scale of the fluctuations and to design fluctuation resistant devices.

In this paper we use the Density Gradient (DG) simulation approach to study, in 3-D, the effect of local oxide thickness fluctuations on the threshold voltage of decanano MOSFETs on a statistical scale. The random 2-D surfaces used to represent the interface are constructed using the standard assumptions for the auto-correlation function of the interface. The importance of the Quantum Mechanical effects when studying oxide thickness fluctuations are illustrated in several simulation examples.

In this paper we use 3D simulations to study the amplitudes of random telegraph signals (RTS) associated with the trapping of a single carrier in interface states in the channel of sub 100 nm (decanano) MOSFETs. Both simulations using continuous doping charge and random discrete dopants in the active region of the MOSFETs are presented. We have studied the dependence of the RTS amplitudes on the position of the trapped charge in the channel and on the device design parameters. We have observed a significant increase in the maximum RTS amplitude when discrete random dopants are employed in the simulations.

A 3D 'atomistic' simulation technique to study random impurity induced threshold voltage lowering and fluctuations in sub 0. 1 micron MOSFETs is presented. It allows statistical analysis of random impurity effects down to the individual impurity level-Efficient algorithms based on a single solution of Poisson's equation, followed by the solution of a simplified current continuity equation are used in the simulations.

In this paper we present a detailed simulation study of the influence of quantum mechanical effects in the inversion layer on random dopant induced threshold voltage fluctuations and lowering in sub 100 nm MOSFETs. The simulations have been performed using a 3-D implementation of the density gradient (DG) formalism incorporated in our established 3-D atomistic simulation approach. This results in a self-consistent 3-D quantum mechanical picture, which implies not only the vertical inversion layer quantisation but also the lateral confinement effects related to current filamentation in the 'valleys' of the random potential fluctuations. We have shown that the net result of including quantum mechanical effects, while considering statistical dopant fluctuations, is an increase in both threshold voltage fluctuations and lowering. At the same time, the random dopant induced threshold voltage lowering partially compensates for the quantum mechanical threshold voltage shift in aggressively scaled MOSFETs with ultrathin gate oxides.

A 3D statistical 'atomistic' simulation technique has been developed to study the effect of the random dopant induced parameter fluctuations in aggressively scaled MOSFETs. Efficient implementation of the 'atomistic' simulation approach has been used to investigate the threshold voltage standard deviation and lowering in the case of uniformly doped MOSFETs, and in fluctuation-resistant architectures utilising epitaxial-layers and delta-doping. The effect of the random doping in the polysilicon gate on the threshold voltage fluctuations has also been thoroughly investigated. The influence of a single-charge trapping on the channel conductivity in decanano MOSFETs is studied in the 'atomistic' framework as well. Quantum effects are taken into consideration in our 'atomistic' simulations using the density gradient formalism.

When MOSFETs are scaled to deep submicron dimensions the discreteness and randomness of the dopant charges in the channel region introduces significant fluctuations in the device characteristics. This effect, predicted 20 year ago, has been confirmed experimentally and in simulation studies. The impact of the fluctuations on the functionality, yield, and reliability of the corresponding systems shifts the paradigm of the numerical device simulation. It becomes insufficient to simulate only one device representing one macroscopical design in a continuous charge approximation. An ensemble of macroscopically identical but microscopically different devices has to be characterized by simulation of statistically significant samples. The aims of the numerical simulations shift from predicting the characteristics of a single device with continuous doping towards estimating the mean values and the standard deviations of basic design parameters such as threshold voltage, subthreshold slope, transconductance, drive current, etc. for the whole ensemble of 'atomistically' different devices in the system. It has to be pointed out that even the mean values obtained from 'atomistic' simulations are not identical to the values obtained from continuous doping simulations. In this paper we present a hierarchical approach to the 'atomistic' simulation of aggressively scaled decanano MOSFETs. A full scale 3D drift-diffusion'atomostic' simulation approach is first described and used for verification of the more economical, but also more restricted, options. To reduce the processor time and memory requirements at high drain voltage we have developed a self-consistent option based on a thin slab solution of the current continuity equation only in the channel region. This is coupled to the Poisson's equation solution in the whole simulation domain in the Gummel iteration cycles. The accuracy of this approach is investigated in comparison with the full self-consistent solution. At low drain voltage only single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. A pilot version of a hydrodynamic 'atomistic' simulator has been developed in order to study the effect of the nonequilibrium, non local transport in decanano MOSFETs on the random dopant induced current fluctuations. For the first time we have also applied the density gradient approach in 3D to investigate the effect of the quantum confinement on the threshold voltage fluctuations. The developed 'atomistic' simulation techniques have been applied to study various fluctuation resistant MOSFET architectures including epitaxial and delta doped devices.

3D 'atomistic' simulations are used to study random dopant related threshold voltage fluctuations in 50 nm MOSFETs. Comparisons are made between conventionally doped transistors and transistors with thin epitaxial silicon layers on heavily doped silicon. Issues related to both the optimum threshold voltage control and the suppression of the threshold voltage dispersion are addressed.

We study the effect of trapping/detrapping of a single-electron in interface states in the channel of n-type MOSFETs with decanano dimensions using 3D atomistic simulation techniques. In order to highlight the basic dependencies, the simulations are carried out initially assuming continuous doping charge, and discrete localized charge only for the trapped electron. The dependence of the random telegraph signal (RTS) amplitudes on the device dimensions and on the position of the trapped charge in the channel are studied in detail. Later, in full-scale, atomistic simulations assuming discrete charge for both randomly placed dopants and the trapped electron, we highlight the importance of current percolation and of traps with strategic position where the trapped electron blocks a dominant current path.

We have introduced in a simple and efficient manner quantum mechanical corrections in our 3D 'atomistic' MOSFET simulator using the density gradient formalism. We have studied in comparison with classical simulations the effect of the quantum mechanical corrections on the simulation of random dopant induced threshold voltage fluctuations, the effect of the single charge trapping on interface states and the effect of the oxide thickness fluctuations in decanano MOSFETs with ultrathin gate oxides. The introduction of quantum corrections enhances the threshold voltage fluctuations but does not affect significantly the amplitude of the random telegraph noise associated with single carrier trapping. The importance of the quantum corrections for proper simulation of oxide thickness fluctuation effects has also been demonstrated.

We present a hierarchical approach to the 'atomistic' simulation of aggressively scaled sub-0.1 micron MOSFET's. These devices are so small that their characteristics depend on the precise location of dopant atoms within them, not just on their average density. A full-scale three-dimensional drift-diffusion atomistic simulation approach is first described and used to verify more economical, but restricted, options. To reduce processor time and memory requirements at high drain voltage, we have developed a self-consistent option based on a solution of the current continuity equation restricted to a thin slab of the channel. This is coupled to the solution of the Poisson equation in the whole simulation domain in the Gummel iteration cycles. The accuracy of this approach is investigated in comparison to the full self-consistent solution. At low drain voltage, a single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. In this case, the current is calculated by solving the current continuity equation in a drift approximation only, also in a thin slab containing the MOSFET channel. The regions of applicability for the different components of this hierarchical approach are illustrated in example simulations covering the random dopant-induced threshold voltage fluctuations, threshold voltage lowering, threshold voltage asymmetry, and drain current fluctuations.

A detailed three-dimensional (3-D) statistical 'atomistic' simulation study of fluctuation-resistant sub-0.1-(micron)meter MOSFET architectures with epitaxial channels and delta doping is presented. The need for enhancing the fluctuation resistance of the sub-0.1-(micron)meter generation transistors is highlighted by presenting summarized results from atomistic simulations of a wide range of conventional devices with uniformly doped channel. According to our atomistic results, the doping concentration dependence of the random dopant-induced threshold voltage fluctuations in conventional devices is stronger than the analytically predicted fourth-root dependence. As a result of this, the scaling of such devices will be restricted by the "intrinsic" random dopant-induced fluctuations earlier than anticipated. Our atomistic simulations confirm that the introduction of a thin epitaxial layer in the MOSFET's channel can efficiently suppress the random dopant-induced threshold voltage fluctuations in sub-0.1-(micron)meter devices. For the first time, we observe an "anomalous" reduction in the threshold voltage fluctuations with an increase in the doping concentration behind the epitaxial channel, which we attribute to screening effects. Also, for the first time we study the effect of a delta-doping, positioned behind the epitaxial layer, on the intrinsic threshold voltage fluctuations. Above a certain thickness of epitaxial layer, we observe a pronounced anomalous decrease in the threshold voltage fluctuation with the increase of the delta doping. This phenomenon, which is also associated with screening, enhances the importance of the delta doping in the design of properly scaled fluctuation-resistant sub-0.1-(micron)meter MOSFET's. Index Terms-Doping, fluctuations, MOSFET, semiconductor device simulation, silicon devices, threshold.

A detailed study of the influence of quantum effects in the inversion layer on the random dopant induced threshold voltage fluctuations and lowering in sub 0.1 micron MOSFETs has been performed. This has been achieved using a full 3D implementation of the density gradient (DG) formalism incorporated in our previously published 3D 'atomistic' simulation approach. This results in a consistent, fully 3D, quantum mechanical picture which implies not only the vertical inversion layer quantisation but also the lateral confinement effects manifested by current filamentation in the 'valleys' of the random potential fluctuations. We have shown that the net result of including quantum mechanical effects, while considering statistical fluctuations, is an increase in both threshold voltage fluctuations and lowering.

A 3D 'atomistic' simulation study of random dopant induced threshold voltage fluctuations and lowering in sub 50 nm MOSFETs is presented. The attention is focused mainly on devices with 30 nm effective channel length which represent the expected level of scaling at the end of the Silicon Roadmap. An efficient algorithm, based on a single 3D ap solution of the Poisson equation and a simplified current continuity equation, is used in the simulations. Large samples of microscopically different devices (typically 200) arc used in order to obtain statistically reliable results. The influence of different aspects of the conventional MOSFET design on the threshold voltage fluctuations and lowering are investigated. Results for fluctuation resistant device architectures based on low-doped epitaxial channel MOSFETs are also presented.

A three-dimensional (3-D) "atomistic" simulation study of random dopant induced threshold voltage lowering and fluctuations in sub-0.1 microns MOSFET's is presented. For the first time a systematic analysis of random dopant effects down to an individual dopant level was carried out in 3-D on a scale sufficient to provide quantitative statistical predictions. Efficient algorithms based on a single multigrid solution of the Poisson equation followed by the solution of a simplified current continuity equation are used in the simulations. The effects of various MOSFET design parameters, including the channel length and width, oxide thickness and channel doping, on the threshold voltage lowering and fluctuations are studied using typical samples of 200 atomistically different MOSFET's. The atomistic results for the threshold voltage fluctuations were compared with two analytical models based on dopant number fluctuations. Although the analytical models predict the general trends in the threshold voltage fluctuations, they fail to describe quantitatively the magnitude of the fluctuations. The distribution of the atomistically calculated threshold voltage and its correlation with the number of dopants in the channel of the MOSFET's was analyzed based on a sample of 2500 microscopically different devices. The detailed analysis shows that the threshold voltage fluctuations are determined not only by the fluctuation in the dopant number, but also in the dopant position.

A 3D 'atomistic' simulation technique to study random dopant induced threshold voltage lowering and fluctuations in sub 0.1 micron MOSFETs is presented. It allows statistical analysis of random impurity effects down to the individual impurity level. Efficient algorithms based on a single solution of Poisson's equation, followed by the solution of a simplified current continuity equation are used in the simulations.