A physically based mobility model for numerical simulation of nonplanar devices
01 Nov 1988-IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (IEEE)-Vol. 7, Iss: 11, pp 1164-1171
TL;DR: A local mobility function, set up in terms of a simple Mattiessen's rule, provides a careful description of MOSFET operation in a wide range of normal (or gate) electric fields.
Abstract: A semiempirical model for carrier mobility in silicon inversion layers is presented. The model, strongly oriented to CAD (computer-aided design) applications, is suitable for two-dimensional numerical simulations of nonplanar devices. A local mobility function, set up in terms of a simple Mattiessen's rule, provides a careful description of MOSFET operation in a wide range of normal (or gate) electric fields, channel impurity concentrations of between 5*10/sup 14/ cm/sup -3/ and 10/sup 17/ cm/sup -3/ for the acceptor density of states and 6*10/sup 14/ cm/sup -3/ and 3*10/sup 17/ cm/sup -3/ for the donor density of states; and temperatures between 200 K and 460 K. Best-fit model parameters are extracted by comparing the calculated drain conductance with a very large set of experimental data points. >
Citations
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TL;DR: In this paper, the impact of statistical dopant fluctuations on the threshold voltage and device performance of silicon MOSFET's is investigated by means of analytical and numerical modeling, and it is found that the average V/sub T/-shift is positive for long, narrow devices, and negative for short, wide devices.
Abstract: The impact of statistical dopant fluctuations on the threshold voltage V/sub T/ and device performance of silicon MOSFET's is investigated by means of analytical and numerical modeling. A new analytical model describing dopant fluctuations in the active device area enables the derivation of the standard deviation, /spl sigma/V/sub T/, of the threshold voltage distribution for arbitrary channel doping profiles. Using the MINIMOS device simulator to extend the analytical approach, it is found that /spl sigma/V/sub T/, can be properly derived from two-dimensional (2-D) or three-dimensional (3-D) simulations using a relatively coarse simulation grid. Evaluating the threshold voltage shift arising from dopant fluctuations, on the other hand, calls for full 3-D simulations with a numerical grid that is sufficiently refined to represent the discrete nature of the dopant distribution. The average V/sub T/-shift is found to be positive for long, narrow devices, and negative for short, wide devices. The fast 2-D MINIMOS modeling of dopant fluctuations enables an extensive statistical analysis of the intrinsic spreading in a large set of compact model parameters for state-of-the-art CMOS technology. It is predicted that V/sub T/-variations due to dopant fluctuations become unacceptably large in CMOS generations of 0.18 /spl mu/m and beyond when the present scaling scenarios are pursued. Parameter variations can be drastically reduced by using alternative device designs with ground-plane channel profiles.
442 citations
Additional excerpts
...Different device simulators use different models for the field-dependent mobility of the channel inversion layer [ 15 ], [16]....
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TL;DR: In this article, the authors quantify the influence of the roughness of the dielectric on the mobility of pentacene transistors and discuss the cause of the effect of roughness on the performance of organic thin-film transistors.
Abstract: The properties of the dielectric strongly influence the performance of organic thin-film transistors. In this letter, we show experimental results that quantify the influence of the roughness of the dielectric on the mobility of pentacene transistors and discuss the cause of it. We consider the movement of charge carriers out of the “roughness valleys” or across those valleys at the dielectric–semiconductor interface as the limiting step for the roughness-dependent mobility in the transistor channel.
367 citations
TL;DR: In this article, the analog performance as well as some new RF figures of merit are reported for the first time of a gate stack double gate (GS-DG) metal oxide semiconductor field effect transistor (MOSFET) with various gates and channel engineering.
324 citations
TL;DR: In this paper, a physically-based, semi-empirical, local model for transverse-field dependent electron and hole mobility in MOS transistors is presented to accurately predict the measured relationship between the effective mobility and effective electric field over a wide range of substrate doping and bias.
Abstract: A new, comprehensive, physically-based, semiempirical, local model for transverse-field dependent electron and hole mobility in MOS transistors is presented. In order to accurately predict the measured relationship between the effective mobility and effective electric field over a wide range of substrate doping and bias, we account for the dependence of surface roughness limited mobility on the inversion charge density, in addition to including the effect of coulomb screening of impurities by charge carriers in the bulk mobility term. The result is a single mobility model applicable throughout a generalized device structure that gives good agreement with measured mobility data and measured MOS I-V characteristics over a wide range of substrate doping, channel length, transverse electric field, substrate bias, and temperature.
179 citations
Cites background or methods from "A physically based mobility model f..."
...What is needed is a mobility model that depends only on local quantities, and is applicable throughout a general device structure [5], [6]....
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...This is taken into account here by adopting a similar formulation to that of Lombardi [5], which follows the approximation suggested by Schwarz and Russek [12]....
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...To evaluate the carrier mobility we use the Mathiessen rule that approximates the local mobility, , at low longitudinal field as the sum of three terms [5]...
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...In previously published local mobility models [2], [5], [6], [8] the dependence on the transverse field has the form...
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..., where is the temperature dependence of the probability of surface phonon scattering, as discussed in [12], and is an empirical parameter fit to measurements [5]....
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TL;DR: In this article, a comprehensive physical model for the analysis, characterization, and design of 4H-silicon carbide (SiC) MOSFETs has been developed.
Abstract: A comprehensive physical model for the analysis, characterization, and design of 4H-silicon carbide (SiC) MOSFETs has been developed. The model has been verified for an extensive range of bias conditions and temperatures. It incorporates details of interface trap densities, Coulombic interface trap scattering, surface roughness scattering, phonon scattering, velocity saturation, and their dependences on bias and temperature. The physics-based models were implemented into our device simulator that is tailored for 4H-SiC MOSFET analysis. By using a methodology of numerical modeling, simulation, and close correlation with experimental data, values for various physical parameters governing the operation of 4H-SiC MOSFETs, including the temperature-dependent interface trap density of states, the root-mean-square height and correlation length of the surface roughness, and the electron saturation velocity in the channel and its dependence on temperature, have been extracted. Coulomb scattering and surface roughness scattering limit surface mobility for a wide range of temperatures in the subthreshold and linear regions of device operation, whereas the saturation velocity and the high-field mobility limit current in the saturation region.
158 citations
References
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Book•
01 Jan 1984
TL;DR: The history of numerical device modeling can be traced back to the early 1970s as mentioned in this paper, when the basic Semiconductor Equations were defined and the goal of modeling was to identify the most fundamental properties of numerical devices.
Abstract: 1. Introduction.- 1.1 The Goal of Modeling.- 1.2 The History of Numerical Device Modeling.- 1.3 References.- 2. Some Fundamental Properties.- 2.1 Poisson's Equation.- 2.2 Continuity Equations.- 2.3 Carrier Transport Equations.- 2.4 Carrier Concentrations.- 2.5 Heat Flow Equation.- 2.6 The Basic Semiconductor Equations.- 2.7 References.- 3. Proeess Modeling.- 3.1 Ion Implantation.- 3.2 Diffusion.- 3.3 Oxidation.- 3.4 References.- 4. The Physical Parameters.- 4.1 Carrier Mobility Modeling.- 4.2 Carrier Generation-Recombination Modeling.- 4.3 Thermal Conductivity Modeling.- 4.4 Thermal Generation Modeling.- 4.5 References.- 5. Analytical Investigations About the Basic Semiconductor Equations.- 5.1 Domain and Boundary Conditions.- 5.2 Dependent Variables.- 5.3 The Existence of Solutions.- 5.4 Uniqueness or Non-Uniqueness of Solutions.- 5.5 Sealing.- 5.6 The Singular Perturbation Approach.- 5.7 Referenees.- 6. The Diseretization of the Basic Semiconductor Equations.- 6.1 Finite Differences.- 6.2 Finite Boxes.- 6.3 Finite Elements.- 6.4 The Transient Problem.- 6.5 Designing a Mesh.- 6.6 Referenees.- 7. The Solution of Systems of Nonlinear Algebraic Equations.- 7.1 Newton's Method and Extensions.- 7.2 Iterative Methods.- 7.3 Referenees.- 8. The Solution of Sparse Systems of Linear Equations.- 8.1 Direct Methods.- 8.2 Ordering Methods.- 8.3 Relaxation Methods.- 8.4 Alternating Direction Methods.- 8.5 Strongly Implicit Methods.- 8.6 Convergence Acceleration of Iterative Methods.- 8.7 Referenees.- 9. A Glimpse on Results.- 9.1 Breakdown Phenomena in MOSFET's.- 9.2 The Rate Effect in Thyristors.- 9.3 Referenees.- Author Index.- Table Index.
2,550 citations
TL;DR: In this article, the present knowledge of charge transport properties in silicon, with special emphasis on their application in the design of solid-state devices, is reviewed, and most attention is devoted to experimental findings in the temperature range around 300 K and to high-field properties.
Abstract: This paper reviews the present knowledge of charge transport properties in silicon, with special emphasis on their application in the design of solid-state devices. Therefore, most attention is devoted to experimental findings in the temperature range around 300 K and to high-field properties. Phenomenological expressions are given, when possible, for the most important transport quantities as functions of temperature, field or impurity concentration. The discussion is limited to bulk properties, with only a few comments on surface transport.
1,067 citations
"A physically based mobility model f..." refers background in this paper
...The temperature dependence of U, is assumed to be the same as in bulk silicon [ 17 ]....
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...Accordingly, we assumed Tinit = 2.42 as an initial estimate for y [ 17 ]....
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IBM1
TL;DR: In this article, self-consistent results for energy levels, populations, and charge distributions are given for $n$-type inversion layers on $p$ -type silicon.
Abstract: Self-consistent results for energy levels, populations, and charge distributions are given for $n$-type inversion layers on $p$-type silicon. Quantum effects are taken into account in the effective-mass approximation, and the envelope wave function is assumed to vanish at the surface. Approximate analytic results are given for some special cases. Numerical results are given for representative surface orientations, bulk acceptor concentrations, inversion-layer electron concentrations, and temperatures.
987 citations
TL;DR: In this article, the electron mobility data for both arsenic-and boron-doped silicon are presented in the high doping range, and it is shown that electron mobility is significantly lower in As-and Boron-Doped silicon for carrier concentrations higher than 1019cm-3.
Abstract: New carrier mobility data for both arsenic- and boron-doped silicon are presented in the high doping range. The data definitely show that the electron mobility in As-doped silicon is significantly lower than in P-doped silicon for carrier concentrations higher than 1019cm-3. By integrating these data with those previously published, empirical relationships able to model the carrier mobility against carrier concentration in the whole experimental range examined to date (about eight decades in concentration) for As-, P-, and B-doped silicon are derived. Different parameters in the expression for the n-type dopants provide differentiation between the electron mobility in As-and in P-doped silicon. Finally, it is shown that these new expressions, once implemented in the SUPREM II process simulator, lead to reduced errors in the simulation of the sheet resistance values.
908 citations
TL;DR: In this paper, an extensive set of experimental results on the behavior of electron surface mobility in thermally oxidized silicon structures are presented, which allow the calculation of electron mobility under a wide variety of substrate, process, and electrical conditions.
Abstract: Accurate modeling of MOS devices requires quantitative knowledge of carrier mobilities in surface inversion and accumulation layers. Optimization of device structures and accurate circuit simulation, particulary as technologies push toward fundamental limits, necessitate an understanding of how impurity doping levels, oxide charge densities, process techniques, and applied electric fields affect carrier surface mobilities. It is the purpose of this paper to present an extensive set experimental results on the behavior of electron surface mobility in thermally oxidized silicon structures. Empirical equations are developed which allow the calculation of electron mobility under a wide variety of substrate, process, and electrical conditions. The experimental results are interpreted in terms of the dominant physical mechanisms responsible for mobility degradation at the Si/SiO 2 interface. From the observed effects of process parameters on mobility roll-off under high vertical fields, conclusions are drawn about optimum process conditions for maximizing mobility. The implications of this work for performance limits of several types of MOS devices are described.
610 citations