Random Dopant Induced Threshold Voltage Research Articles

Sensitivity of trigate MOSFETs to random dopant induced threshold voltage fluctuations

In this paper, we investigate random doping fluctuation effects in trigate SOI MOSFETs by solving the three-dimensional (3D) Poisson, drift-diffusion and continuity equations numerically. A single doping impurity atom is introduced in the undoped channel region of the device and the resulting shift of threshold voltage is measured from the simulated I– V characteristics. This enables the derivation of the threshold voltage shift (Δ V TH) for any arbitrary location of the doping atom in the transistor. Based on an analysis of a sub-20 nm trigate MOSFET device, we find that the typical variation of V TH per doping atom is a few tens of mV. Inversion-mode (IM) trigate devices are more sensitive to the doping fluctuation effects than accumulation-mode (AM) devices. The threshold voltage shift arising from doping fluctuations is maximum when the doping atom is near the center of the channel region, which means the original SOI film doping, the random contamination effects or any other impurity doping in the channel region is more important than atoms introduced in the channel by the S/D implantation process for sub-20 nm transistors.

Statistical simulation of random dopant induced threshold voltage fluctuations for 35 nm channel length MOSFET

Intrinsic parameter fluctuations have become a very important problem for the scaling and integration of future generations of nano-CMOS transistors impacting on circuit and systems yield and reliability. In this paper random discrete dopant (RDD) induced threshold voltage variations have been studied using the Glasgow 3D atomistic drift/diffusion simulator. For the first time, we have carried out statistical simulation based on groundbreaking sample of 100,000 transistors which may assess more than 4 σ of the statistical distribution. In order to correctly access the accuracy and the confidence level of the statistical parameters, we have carried out comprehensive statistical analysis using state-of-art statistical tools amenable to our problem. We use the first four moments to fit distribution of RDD induced fluctuations in the threshold voltage by means of several statistical approaches.

Accurate Statistical Description of Random Dopant-Induced Threshold Voltage Variability

We have studied the detailed threshold voltage distribution in a state-of-the-art n-channel MOSFET in the presence of random discrete dopants. A ground-breaking sample of 100 000 transistors with statistically unique random dopant distributions were simulated using the Glasgow 3-D device simulator and advanced grid computing technologies. The results indicate that the threshold voltage distribution deviates substantially from a Gaussian distribution, which may have significant implications for the margins used in circuit design, particularly in SRAM cells.

A new method to simulate random dopant induced threshold voltage fluctuations in sub-50 nm MOSFET’s with non-uniform channel doping

In this paper, based on a precise and efficient analytical function of relatively realistic dopant fluctuations, a new method is proposed to simulate the threshold voltage variation of MOSFET’s with non-uniform channel doping due to random dopant fluctuations. Both the number and position fluctuations of dopants are taken into account. Using this method, 2500 microscopically different devices under certain process conditions that cover the range of channel length L from 35nm to 90nm, oxide thickness Tox from 1nm to 4nm and channel surface doping concentration NA from 1×1018 to 5×1018cm−3 are simulated to show how our method works.

Increase in the random dopant induced threshold fluctuations and lowering in sub-100 nm MOSFETs due to quantum effects: a 3-D density-gradient simulation study

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 mn MOSFETs. The simulations have been performed using a three-dimensional (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 quantization 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.

Quantum Corrections to the ‘Atomistic’ MOSFET Simulations

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.

Polysilicon gate enhancement of the random dopant induced threshold voltage fluctuations in sub-100 nm MOSFETs with ultrathin gate oxide

In this paper, we investigate various aspects of the polysilicon gate influence on the random dopant induced threshold voltage fluctuations in sub-100 nm MOSFETs with ultrathin gate oxides. The study is done by using an efficient statistical three-dimensional (3D) atomistic simulation technique. MOSFETs 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 to thickness 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 of the polysilicon grain boundaries on the threshold voltage variation are also presented.

Random dopant induced threshold voltage lowering and fluctuations in sub 50 nm MOSFETs: a statistical 3D `atomistic' simulation study

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 solution of the Poisson equation and a simplified current continuity equation, is used in the simulations. Large samples of microscopically different devices (typically 200) are 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.

Suppression of random dopant-induced threshold voltage fluctuations in sub-0.1-μm MOSFET's with epitaxial and δ-doped channels

A detailed three-dimensional (3-D) statistical simulation study of fluctuation-resistant sub 0.1-/spl mu/m MOSFET architectures with epitaxial channels and delta doping is presented. The need for enhancing the fluctuation resistance of the sub-0.1-/spl mu/m generation transistors is highlighted by presenting summarized results from atomistic simulations of a wide range of conventional devices with uniformly doped channels. 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 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-/spl mu/m devices. For the first time, we observe an 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-/spl mu/m MOSFET's.

Hierarchical approach to "atomistic" 3-D MOSFET simulation

We present a hierarchical approach to the simulation of aggressively scaled sub-0.1-/spl mu/m MOSFETs. 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.

Random dopant induced threshold voltage lowering and fluctuations in sub-0.1 μm MOSFET's: A 3-D "atomistic" simulation study

A three-dimensional (3-D) simulation study of random dopant induced threshold voltage lowering and fluctuations in sub-0.1 /spl mu/m MOSFETs 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 MOSFETs. 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 MOSFETs 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.