Query: Electrostatic Potential Profile Generator for Two-Dimensional Semiconductor Devices

Candidate papers:

abstract: As efficiency is one of the bottlenecks of device simulation, we propose to employ deep neural networks to generate two dimensional electrostatic potential profiles for efficiency. Supervising with previously obtained simulation results for various BJT devices, we train deep neural networks to generate an electrostatic potential profile as an initial guess for a non equilibrium condition with estimating carrier densities by the frozen field simulation. With the generated potential profiles, we significantly reduce the number of Newton iterations without loss of accuracy.
author_names: Seung-Cheol Han

Jonghyun Choi

Sung-Min Hong
title: Electrostatic Potential Profile Generator for Two Dimensional Semiconductor Devices
venue: 2020 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD)
year: 2020

abstract: Numerical iterative methods of solution of the one dimensional basic two carrier transport equations describing the behavior of semiconductor junctions under both steady state and transient conditions are presented. The methods are of a very general character: none of the conventional assumptions and restrictions are introduced, and freedom is available in the choice of the doping profile, generation recombination law, mobility dependencies, injection level. and boundary conditions applied solely at the external contacts. For a specified arbitrary input signal of either current or voltage (as a function of time) the solution yields terminal properties and all the quantities of interest in the interior of the device, such as carrier densities, electric field, electrostatic potential, particle and displacement currents, as functions of position (and time) The work is divided into two parts. In Part I a numerical method of solution of the steady state problem, already available in the literature, is improved and extended, and is applied to a two contact and a three contact device. The analytical formulation of the original method is shown to be unsuitable for generating a sound numerical algorithm sufficiently accurate and valid for high reverse bias conditions. Difficulties and limitations are exposed and overcome by an improved formulation extended to any bias condition. As a simple application of the improved formulation, "exact" and first order theory results for an idealized N P structure are presented and compared. The poorness of some of the basic assumptions of the conventional first order theory is exposed, in spite of a satisfactory agreement between the exact and first order results of the terminal properties for particular bias conditions. Results for an N P N transistor are also reported and the inadequacy of the one dimensional model discussed. The time dependent analysis of the problem is presented in Part II. The fundamental equations are rearranged to an equivalent set of three non linear partial differential equations more suitable for numerical methods. A highly non uniform two dimensional mesh, subject to maintenance of constant truncation errors in both spatial and time domains of certain pointwise operations, is chosen for the discretization of the problem, in view of the variation of most quantities over extreme ranges within short regions. Consequently an implicit discretization scheme is selected for the second order partial differential equations of the parabolic type in order to avoid restrictions on the mesh size, without endangering numerical stability. An iterative procedure is necessary at each instant of time to cope with the several non linearities of the problem and to achieve consistency between the internal distributions and the generating equations. This procedure is easily generalized to incorporate equations pertinent to networks of passive elements and ideal generators connected to the semiconductor device. Results for a particular single junction structure under typical time dependent excitations of external current and terminal voltage, and for an N P diode interacting with an external resistor under switching conditions. are reported and discussed in detail. Considerable attention is focused on the numerical analysis of the steady state and transient problems in order to achieve a numerical algorithm sufficiently sound and efficient to cope with the several difficulties of the problem, such as the small differences between nearly equal numbers, the variation of most quantities over extremely wide ranges in short regions, and the stability conditions related to the discretization of partial differential equations of the parabolic type.
author_names: A De Mari
title: Accurate Numerical Steady State and Transient One Dimensional Solutions of Semiconductor Devices
year: 1968

abstract: Exact solution of two dimensional (2D) Poisson's equation for fully depleted double gate silicon on insulator metal oxide semiconductor field effect transistor is derived using three zone Green's function solution technique. Framework consists of consideration of source drain junction curvature. 2D potential profile obtained forms the basis for estimation of threshold voltage. Temperature dependence of front surface potential distribution, back surface potential distribution and front gate threshold voltage are modeled using temperature sensitive parameters. Applying newly developed model, surface potential and threshold voltage sensitivities to gate oxide thickness have been comprehensively investigated. Device simulation is performed using ATLAS 2D (SILVACO, 4701 Patrick Henry Drive, Bldg. Santa Clara, CA 95054 USA) device simulator, and the results obtained are compared with the proposed 2D model. The model results are found to be in good agreement with the simulated data. Copyright (c) 2013 John Wiley Sons, Ltd.
author_names: Rajiv Sharma

Sujata Pandey

Shail Bala Jain
title: Green's function approach for modeling of electrostatic effects in nanoscale fully depleted double gate silicon on insulator metal oxide semiconductor field effect transistors
year: 2014

abstract: A two dimensional mathematical model is developed to predict the internal behavior of power transistors operating under steady state conditions. This model includes the internal self heating effects in power transistors and is applicable to predict the transistor behavior under high current and high voltage operating conditions. The complete set of partial differential equations governing the bipolar semiconductor device behavior under nonisothermal conditions is solved by numerical techniques without assuming internal junctions and other conventional approximations. Input parameters for this model are the dimension of the device, doping profile, mobility expressions, generation recombination model, and the boundary conditions for external contacts. Computer results of the analysis of a typical power transistor design are presented for specified operating conditions. The current density, electrostatic potential, carrier charge density, and temperature distribution plots within the transistor structure illustrate the combined effect of the electrothermal interaction, base conductivity modulation, current crowding, base pushout, space charge layer widening, and current spreading phenomena in power transistors.
author_names: Santosh P Gaur

D H Navon
title: Two dimensional carrier flow in a transistor structure under nonisothermal conditions
venue: IEEE Transactions on Electron Devices
year: 1976

abstract: Summary form only given, as follows. A two dimensional mathematical model is developed to predict the internal behavior of power transistors operating under steady state conditions. This model includes the internal self heating effects in power transistors and is applicable to predict the transistor behavior under high current and high voltage operating conditions. The complete set of partial differential equations governing the bipolar semiconductor device behavior under non isothermal conditions is solved by numerical techniques without assuming internal junctions and other conventional approximations. No restrictions are made on the choice of the doping profile, mobility dependence, boundary conditions for external contacts, generation recombination model and the injection level. Computed results of the analysis of a typical power transistor design are presented for various operating conditions. The current density, electrostatic potential, carrier charge density and temperature distribution plots within the transistor structure illustrate the combined effect of the electro thermal interaction, base conductivity modulation, current crowding, base push out, space charge layer widening and current spreading phenomena in power transistors.
author_names: Santosh P Gaur

D H Navon
title: Two dimensional carrier flow in a transistor structure under non isothermal conditions
year: 1974

abstract: A two dimensional numerical solution of electrostatic potential and electric field profiles are presented for lightly doped nano scale Double Gate Metal Oxide Semiconductor Field Effect Transistor (DG MOSFET) We have developed quasi static (QS) model for evaluating bulk and inversion charges based on symmetric linearization model. We have also shown the non quasi static (NQS) effect on the charge due to a time varying gate voltage. It is seen that various symmetries of DG MOSFET characteristics with respect to source/drain interchange is maintained in quasi static as well as non quasi static version of the symmetrically linearized model. The variation of the threshold voltage with the varying width of the device is evaluated and presented. The results have been compared and contrasted with reported analytical model for QS condition for the purpose of verification of the model. The variation of threshold voltage along the width of the device is also predicted. This numerical model can be extended to analyze the transport phenomenon in sub 30 nm channel length DG MOSFETs.
author_names: Deepanjan Datta

A Ananda Prasad Sarab

Sudeb Dasgupta
title: Two dimensional numerical modeling of lightly doped nano scale double gate MOSFET
venue: Microelectron. J.
year: 2006

abstract: The control of coherent electrons is becoming relevant in emerging devices as (semi )ballistic transport is observed within nanometer semiconductor structures at room temperature. The evolution of a wave packet representing an electron in a semiconductor can be manipulated using specially shaped potential profiles with convex or concave features, similar to refractive lenses used in optics. Such electrostatic lenses offer the possibility, for instance, to concentrate a single wave packet which has been invoked by a laser pulse, or split it up into several wave packets. Moreover, the shape of the potential profile can be dynamically changed by an externally applied potential, depending on the desired behaviour. The evolution of a wave packet under the influence of a two dimensional potential the electrostatic lens is investigated by computing the physical densities using the Wigner function. The latter is obtained by using the signed particle Wigner Monte Carlo method.
author_names: Paul Ellinghaus

Mihail Nedjalkov

Siegfried Selberherr
title: The Influence of Electrostatic Lenses on Wave Packet Dynamics
venue: LSSC
year: 2015

abstract: The measurement of potentials associated with dopant atoms in semiconductors at nanometer spatial resolution using off axis electron holography is known to be affected by the presence of the surfaces of thin specimens. In particular, the potential across a p n junction is often found to be lower than would be expected from predicted properties of bulk devices. Here we present simulations of two dimensional potential profiles within a thin p n junction. We find that the potential across the p n junction is always smaller, when projected through the specimen, than would be expected from the properties of the bulk material. Crucially, the step in potential across the junction is independent of the value of the potential on the surface of the specimen for high dopant concentrations >10 17 cm 3 The simulations are compared with experimental data. Although they can account for some of the reduction in the observed potential, they do not fully explain the experimental results.
author_names: Philippa K Somodi

Rafal E Dunin-Borkowski

A C Twitchett

Crispin H W Barnes

Paul A Midgley
title: Simulations of the electrostatic potential in a thin silicon specimen containing a p n junction
year: 2004

abstract: We study the unitary propagation of a two particle one dimensional Schrodinger equation by means of the Split Step Fourier method, to study the coherent evolution of a spatially indirect exciton (IX) in semiconductor heterostructures. The mutual Coulomb interaction of the electron hole pair and the electrostatic potentials generated by external gates and acting on the two particles separately are taken into account exactly in the two particle dynamics. As relevant examples, step/downhill and barrier/well potential profiles are considered. The space and time dependent evolutions during the scattering event as well as the asymptotic time behavior are analyzed. For typical parameters of GaAs based devices, the transmission or reflection of the pair turns out to be a complex two particle process, due to comparable and competing Coulomb, electrostatic, and kinetic energy scales. Depending on the intensity and anisotropy of the scattering potentials, the quantum evolution may result in excitation of the IX internal degrees of freedom, dissociation of the pair, or transmission in small periodic IX wavepackets due to dwelling of one particle in the barrier region. We discuss the occurrence of each process in the full parameter space of the scattering potentials and the relevance of our results for current excitronic technologies.
author_names: Federico Grasselli

Andrea Bertoni

Guido Goldoni
title: Space and time dependent quantum dynamics of spatially indirect excitons in semiconductor heterostructures.
venue: The Journal of chemical physics
year: 2015

abstract: Electron holography (EH) based on transmission electron microscope (TEM) is widely recognized as a powerful interferometric technique to image and quantify electric and magnetic fields for a variety of physical and chemical applications [1] Off axis EH has been successfully applied for accurate quantitative two dimensional (2D) mapping of intrinsic electrostatic potentials arising from material dependent mean inner potentials or semiconductor s dopant profiles, where the target objects are in the stationary state and isolated from external electric bias [2] But for measuring exotic properties of an electrically biased material or an operando device, a global electric field has to be inevitably involved, which is typically nonuniform and also nonlinear to applied voltages. In these scenarios, reference background approximation was often used but sometimes tended to cause nonnegligible artifacts. Thus, it is critical to develop a new strategy to overcome these drawbacks and achieve more accurate measurements.
author_names: Kaizhou He

John Cumings
title: A New Design for Measuring Potentials in Operando Nanoelectronic Devices by Electron Holography
year: 2014