Advances in Mathematical Semiconductor Modelling: Devices and Circuits (Beijing, China) 02.03.2004 – 07.03.2004 Organizers: A. Arnold, L. Hsiao, A. Jüngel, S. Tang
Accomodation: CATIC Hotel No. 18, Beichen East Road Chaoyang District, Beijing, China Hotel-address in Chinese:
Tel: +86-10-84970829 (Mr Lei ZHOU, in charge of Sinogerman center affairs) +86-10-84971188 Fax: +86-10-84971288
Venue: Sino-German Center for Science Promotion Shuangqing Lu 83 Beijing 100085 Address of Sino-German Center für Science Promotion in Chinese:
Telephon +86 (10) 6232 0088 + extension (after message) main office (German): -2314 main office (Chinese): -2304 FAX
+86 (10) 8238 0042 or +86 (10) 6234 2637
The SGC is located close to the East Gate of Tsinghua University
Program March 2 (Tuesday)： Registration in CATIC Hotel (17:00 - 19:00) Date
March 3 （Wednesday）
Time 9:00—9:30 9:30—10:10 10:10— 10:30 10:30— 11:10
11:10— 11:50 12:00—2:00
2:40—3:20 3:20—3:40 3:40—4:20 4:20—5:00
Title Opening How to cope with increasing complexity in circuit simulation Break Mixed-mode circuit and device simulation for a CMOS monolithic photoreceiver Multiscale modelling and simulation in chip design Lunch
Coupled device, circuit and interconnect simulations Tischendorf Numerical analysis of coupled circuit and device models Break Alí Modeling and analysis of coupled circuits and devices Zhai Curvature and velocity of magnetic domain walls of garnet
March 4 （Thursday）
Quantum hydrodynamics and diffusion models for semiconductors derived from the entropy principle Asymptotics of fluiddynamic models for semiconductors and plasmas: quasineutral limit of Euler-Poisson system with and without viscosity Break Numerical approximation of the viscous quantum hydrodynamic model for semiconductors A non-equilibrium statistical mechanics without the assumption of molecular chaos Lunch Density matrix theory for ultrafast carrier dynamics in semiconductors: relaxation, transport, and capture processes
March 5 (Friday)
Hybrid models for semiconductors (individual visits)
Semiconductor device simulation in nano scale Numerical simulations for transient problems of semiconductor devices: theory and application Break Finite difference time domain analysis of a two dimensional photonic crystal laser Transparent boundary conditions for quantum-waveguide simulations Lunch The two-dimensional van Roosbroeck system has solutions in Lp Analysis of the generalized drift-diffusion model in semiconductor science Break Time-dependent solutions of semiconductor equations modeling avalanche generation On the Boltzmann equation for Fermi-Dirac particles with angular-cutoff Coulomb potential Quantum-Corrected Drift-Diffusion Models for Transport in Semiconductor Devices Discussion of future projects Workshop Banquet
March 6 （Saturday）
11:55-12:00 12:00—2:00 2:00— March 7 (Sunday)：
Energy method for the Boltzmann equation Control of nonlinear spatio-temporal dynamics in semiconductor nanostructures Break Optimal control of some semiconductor devices A variant of the Gummel iteration for optimal semiconductor design Closing Lunch Visits (Great Wall)
日程安排 3月2日（星期二）： 报到 日期 时间 姓名 9:00—9:30 9:30—10:10 Feldmann
题目 开幕 How to cope with increasing complexity in circuit simulation 休息 Mixed-mode circuit and device simulation for a CMOS monolithic photoreceiver Multiscale modelling and simulation in chip design 午餐 Coupled device, circuit and interconnect simulations Numerical analysis of coupled circuit and device models 休息 Modeling and analysis of coupled circuits and devices Curvature and velocity of magnetic domain walls of garnet Quantum hydrodynamics and diffusion models for semiconductors derived from the entropy principle Asymptotics of fluiddynamic models for semiconductors and plasmas: quasineutral limit of Euler-Poisson system with and without viscosity 休息 Numerical approximation of the viscous quantum hydrodynamic model for semiconductors A non-equilibrium statistical mechanics without the assumption of molecular chaos 午餐 Density matrix theory for ultrafast carrier dynamics in semiconductors: relaxation, transport, and capture processes
Hybrid models for semiconductors 自由活动
Semiconductor device simulation in nano scale Numerical simulations for transient problems of semiconductor devices: theory and application 休息 Finite difference time domain analysis of a two dimensional photonic crystal laser Transparent boundary conditions for quantum-waveguide simulations 午餐 The two-deminsional van Roosbroeck system has solutions in Lp Analysis of the generalized drift-diffusion model in semiconductor science 休息 Time-dependent solutions of semiconductor equations modeling avalanche generation On the Boltzmann equation for Fermi-Dirac particles with angular-cutoff Coulomb potential Quantum-Corrected Drift-Diffusion Models for Transport in Semiconductor Devices 圆桌讨论 晚宴
11:55-12:00 12:00—2:00 2:00— 3月7日（星期六）：
Energy method for the Boltzmann equation Control of nonlinear spatio-temporal dynamics in semiconductor nanostructures 休息 Optimal control of some semiconductor devices A variant of the Gummel iteration for optimal semiconductor design 闭幕 午餐 参访 离开
Participants: Anton ARNOLD, Mathematics, Münster University, Dept. of Numerical Mathematics, University of Münster, Einsteinstr. 62, 48149 Münster Giuseppe ALI, Applied Mathematics, CNR, Naples, Italy CNR, Via P. Castellino 111, I-80131 Naples Hongda CHEN, Inst of Semiconductor, CAS, Beijing Chinese Academy of Science (CAS), 100083 Beijing Li CHEN, Appl Math, Tsinghua Univ, Beijing Dept of Mathematical Sciences, Tsinghua University, 100084 Beijing Tianquan CHEN, Appl Math, Tsinghua Univ, Beijing Dept of Mathematical Sciences, Tsinghua University, 100084 Beijing Pierre DEGOND, Mathematics, University Toulouse III, France Universite Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse Carlo de FALCO, Dipartimento di Matematica "F.Enriques" Università degli Studi di Milano, Via Saldini 50, 20100 Milano, ITALY Uwe FELDMANN, Infineon, Munich Infineon Technologies, Balanstr. 73, D-81541 Munich Ping GUAN, Mathematics, South-East Univ, Nanjing Dept. of Mathematics, South-East University, 2 Si Pai Lou, 210096 Nanjing Michael GÜNTHER, Mathematics, Wuppertal University Dept of Mathematics, University of Wuppertal, Gaußstr. 20, D-42119 Wuppertal Ling HSIAO, Mathematics, CAS, Beijing Chinese Academy of Sciences (CAS), 100083 Beijing Tilman KUHN, Theoretical Physics, Münster University Dept. of Theoretical Physics, University of Münster, Wilhelm-Klemm-Str.10, D-48149 Münster Hailiang LI, Inst of Math, CAS, Beijing (*) Chinese Academy of Sciences (CAS), 100083 Beijing Xiaoyan LIU, Micro-elctronics, Peking Univ, Beijing Xuguang LU, Appl Math, Tsinghua Univ, Beijing Dept of Mathematical Sciences, Tsinghua University, 100084 Beijing
Luhong MAO, Electronics, Tianjin Univ, Tianjin Tianjin University, 92 Weijin Rd., Nankai District, 300072 Tianjin Helmut MAURER, Mathematics, Münster University Dept. of Numerical Mathematics, University of Münster, Einsteinstr. 62, D-48149 Münster Hagen NEIDHARDT, Mathematics, WIAS-Berlin WIAS Berlin, Mohrenstr. 39, D-10117 Berlin Rene PINNAU, Mathematics, Technical University Darmstadt Dept. of Mathematics, TU Darmstadt, Schlossgartenstr. 7, D-64289 Darmstadt Joachim REHBERG, Mathematics, WIAS-Berlin WIAS Berlin, Mohrenstr. 39, D-10117 Berlin Wil SCHILDERS, Philips, Eindhoven, Netherlands Philips Research,Building Way, Room 4.77, Prof. Holstlaan 4, NL-5656 AA Eindhoven Eckehard SCHÖLL, Theoretical Physics, Technical University Berlin Theoretical Physics, Technical University of Berlin, Hardenbergstr. 36, D-10623 Berlin Lixin TIAN, Mathmatics, Jiangsu Univ, Zhenjiang Caren TISCHENDORF, Mathematics, Humboldt University Berlin Dept of Mathematics - Numerical Analysis, Humboldt-University, Rudower-Chaussee 25, D-10099 Berlin Shaoqiang TANG, Mathematics, Beijing University Cinese Academy of Sciences (CAS), 100083 Beijing Shu WANG, Mathematics, Beijing Industrial Univ, Beijing Jiasheng XING, Appl Math, Beihang Univ, Beijing Dept. of Appl. Mathematics, Beihang University, 37 Xueyuan Rd, Haidian District, Beijing Tong YANG, Mathematics, City Univ, Hongkong Dept. of Mathematics, City University of Hong Kong, Tat Chee Ave., Kowloon, Hong Kong Yirang YUAN, Mathematics, Shandong Univ, Jinan Dept of Mathematics, Shandong University, 27 Shanda Nanlu, 250100 Jinan Jian ZHAI, Mathematics, Zhejiang Univ, Hangzhou Dept of Mathematics, Zhejiang University, 310027 Hangzhou Bo ZHANG, Statistics, Renmin Univ, Beijing (*) to be confirmed
Finite Difference Time Domain analysis of a two dimensional photonic crystal laser CHEN Hongda, SUN Zenghui, ZUO Chao State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, The Chinese Academy of Science, Beijing 100083, China
ZHANG Xiaofan Electronic & Information School, Tianjin University, Tianjin 300072, China
Abstract A two dimensional photonic crystal structure is designed and simulated by a Finite Difference Time Domain method. Crystal parameters are analyzed and band diagram is plotted. Photonic band gap width and centre frequency position versus r/a is also analyzed. The centre frequency position moves to a higher value with r/a augment and the width has a peak value near r/a=0.37. A point defect is introduced and defect mode frequency is plotted, which centre at 350THz. Contour picture shows that the resonant mode is efficiently confined in a nanometer cavity.
How to cope with increasing complexity in circuit simulation Dr. Uwe FELDMANN Infineon Technologies, Balanstrasse 73, D-81541 Munich, Germany
Abstract The mathematical models for electronic circuits get more and more complex due to more complex device characteristics, higher relevance of parasitic effects, and the trends to perform ``full chip'' simulation and to integrate systems on chip. This imposes several challenges onto circuit simulation, and requires significant amount of mathematical research. The talk highlights some directions which are pursued at Infineon. It turns out that some activities can and should be performed by industry itself, while on many other fields of research the help of academic partners is strongly needed
Analysis of the Generalized Drift Diffusion Model in Semiconductor Science Li CHEN Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People's Republic of China.
Ansgar JÜNGEL Fachbereich Mathematik und Informatik, Universität Mainz, Staudingerweg 9, 55099 Mainz, Germany
Abstract A generalization of the drift-diffusion model in semiconductor simulation, GDD model, will be analyzed in this paper.
We give a new proof on the existence of the weak solution to mixed Dirichlet-Neumann boundary problem by finite dimensional approximation, which is simultaneously an effective scheme on the numerical simulation.
Multiscale Modelling and Simulation in Chip Design Prof. Dr. Michael GÜNTHER Lehrstuhl für Angewandte Mathematik/Numerische Mathematik, Bergische Universität Wuppertal, Gaußstr. 20, D-42119 Wuppertal, Germany
Abstract In today's chip design, parasitic and second order effects increasingly govern the functionality and operating modes of integrated circuits. Incorporating these effects leads to generalized network models, or mathematically speaking, to mixed systems of differential-algebraic and partial differential equations that are linked by boundary conditions and/or source terms. The numerical simulation of such systems has to be based on a proper model analysis and validation and, for efficiency reasons, must include multiscale effects in both space and time. In this talk, we will derive and discuss this kind of modelling and simulation for generalized networks that include thermal effects and incorporate the spatial dimension of transmission lines and semiconductor devices.
Density matrix theory for ultrafast carrier dynamics in semiconductors: Relaxation, transport, and capture processes Tilmann KUHN Institut für Festkörpertheorie, Universität Münster, Wilhelm-Klemm-Strasse 10, 48149 Münster, Germany
Abstract On ultrashort time- and length scales the semiclassical picture of transport in semiconductors based on sequences of free flights interrupted by scattering events as described by the Boltzmann equation is no more valid. Instead, a quantum kinetic theory is required. In the talk the density matrix approach for the description of the ultrafast carrier dynamics in semiconductor materials and nanostructures is presented. The derivation of quantum kinetic scattering terms for electronphonon, electron-electron, and electron-light interaction is discussed. The theory is applied to the study of relaxation, transport, and capture processes. The results show typical quantum phenomena like energy-time uncertainty and coherent superpositions of states giving rise to quantum beats.
Optimal control of some semiconductor devices Prof. Helmut MAURER, Jang-Ho Robert Kim Westfälische Wilhelms-Universität Münster, Institut für Numerische Mathematik, Einsteinstr. 62, D-48161 Münster, Germany
Abstract Many applications, e.g., pulse lasers in technology and optical communication require a stable and controllable operation of devices. In this talk, we discuss the optimal control of some semiconductor devices. First example we consider a semiconductor gas discharge image converter which has been designed for the conversion of infrared images to visible light. The control function is the feeding voltage. We show that the optimal control decreases the transient time substantially and suppresses an overshooting in the output signal. A similar picture arises in the control of a semiconductor laser where the injected current fronts are taken as control functions. The optimal control that minimizes the transition time is a bang-bang control which dramatically reduces the relaxation oscillations. Finally, we speculate about the application of optimal control techniques to the design of semiconductors modelled by a drift-diffusion system.
A Variant of the Gummel Iteration for Optimal Semiconductor Design Prof. Dr. Rene PINNAU TU Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
Abstract We present a new approach to the design of semiconductor devices, which leads to fast optimization methods whose numerical effort is of the same order as a single forward simulation of the underlying stationary drift diffusion model. The investigated design objective is to increase the outflow current on a contact for fixed applied voltages and the natural design variable is the doping profile. Interpreting the electrostatic potential as a new design variable, we obtain a simpler optimization problem, whose Karush-Kuhn-Tucker conditions partially decouple. We construct an efficient iterative algorithm in the spirit of the well-known Gummel iteration, which gives the desired fast convergence. The efficiency and success of the new approach is demonstrated in several numerical examples.
The two-dimensional Van Roosbroeck system has solutions p in L Dr. Joachim REHBERG Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, 10117 Berlin
Abstract In mathematical semiconductor device modelling Van Roosbroeck's system seems the most frequently used simulation tool up to now. The natural formulation of the continuity equations is
Ξ being any suitable subdomain of the whole domain under consideration. In the talk the following question is addressed: Is there a solution of Van Roosbroeck's system which satisfies the continuity equations (0.1)? We will show that the two dimensional Van Roosbroeck system can be treated adequately in an L p context - what automatically ensures that the divergence of the species currents indeed are functions and Gauss' theorem is applicable.
Energy Method for Boltzmann Equation Tong YANG Department of Mathematics, City University of Hong Kong
Abstract A basic, simple energy method for the Boltzmann equation is presented here. It is based on a new macro-micro decomposition of the Boltzmann equation as well as the H-theorem. This allows us to make uses of the ideas from hyperbolic conservation laws and viscous conservation laws to yield the direct energy method. As an illustration, we apply the method for the study of the timeasymptotic, nonlinear stability of the global Maxwellian states and rarefaction waves. Previous energy method, starting with Grad and finished with Ukai, involves the spectral analysis and regularity of collision operator through sophisticated weighted norms.
Numerical Analysis of Coupled Circuit and Device Models Caren TISCHENDORF Humboldt University of Berlin, Rudower Chaussee 25, 10099 Berlin, Germany
Abstract The increase of performance of high-frequency circuits bases on higher complexity of integrated systems, increasing frequencies and smaller geometries of circuit elements. The behavior of highfrequency elements is more and more influenced by the surrounding circuit. Furthermore, a high modeling precision is important for a reliable evaluation of the circuit function. Therefore, we are interested in circuit simulation including distributed semiconductor device models. Using the instationary drift-diffusion model, the device equations represent a system of elliptic and parabolic differential equations. The network is described by a differential-algebraic system. Both systems are mutually coupled via boundary conditions. The arising coupled system can be analyzed as an abstract differential algebraic system in proper Hilbert spaces. From the theory of DAEs we know that the sensitivity of circuits with respect to perturbations depends mainly on the DAE-index. We will introduce an index concept that extends the DAE-index to abstract differential-algebraic systems. Finally, we will present network topological criteria for the index of the coupled systems.
Curvature and Velocity of Magnetic Domain Walls of garnet Jian ZHAI Department of Mathematics, Zhejiang University, Hangzhou, 310027, P.R.China
We give the velocity of domain wall motions of garnet with demagnetizing field and external field. In this paper, we consider the effect of the polygonal curvature on the velocity of the domain wall motion.
Numerical Simulations for Transient Problems of Semiconductor Devices: Theory and Application Yi Yang YUAN Institute of Mathematics, Shandong University, Jinan,Shandong, 250100, China
Abstract The mathematical model of the three-dimensional semiconductor device of heat conduction is described by initial boundary value problem made up of a system of four quasilinear partial differential equations. One equation of the elliptic type for electric potential, two of convectiondominated diffusion type for the conservation of electron and hole concentrations, and the last one for the heat conduction.
The unknown functions are the electrostatic potential ψand the electron and hole concentrations p e, and temperature T. In modern numerical simulation of semiconductor devices，the problems met are often three-dimensional, large-scale and large-scope. The node number is as large as tens of thousands, which calls for the new technology of fractional steps to solve the problem. First , characteristic finite difference fractional steps methods is put forward. Thick and thin grids are used to form a complete set of techniques, such as piecewise product threefold-quadratic interpolation, calculus of variations,multiplicative commutation rule of difference operators ,and decomposition of high order difference operators. The prior estimates and techniques are adopted. Optimal order estimates in L2 norm are derived to determine the errors in the approximate solution. Next, we put forward a kind of upwind finite difference fractional steps methods，optimal order estimates in L2 norm are derived for the errors in the approximate solution. These methods are successfully used in the transient state problem of semiconductor.
Transparent Boundary Conditions for Quantum-Waveguide Simulations Anton ARNOLD Institute for Numerical Mathematics, Münster University, Germany
Abstract The electron transport through a quantum-waveguide can be modeled in good approximation by a 2D Schrödinger equation on an unbounded domain. For numerical simulations, however, it is necessary to restrict this problem to a finite domain. This is possible without changing the solution by introducing “transparent boundary conditions” (TBC), which are non-local in time (convolution type). The numerical discretizations of these artificial boundary conditions is a main challenge, as it may easily render the initial-boundary value problem unstable. Based on a Crank-Nicolson-finitedifference discretization of the Schrödinger equation, we shall discuss a dicrete TBC, which makes the overall scheme unconditionally stable. Further, we derive approximations of the involved discrete convolutions by exponential sums, and analyze the stability of the resulting numerical scheme. The derived boundary conditions are illustrated by simulations of a wavequide with a resonating stab.
On the Boltzmann equation for Fermi-Dirac particles with angular-cutoff Coulomb potential Xuguang LU Tsinghua University, Beijing
Abstract We prove the existence of global (in time) weak solutions of the spatially homogeneous Boltzmann equation for Fermi-Dirac particles for very soft potentials with angular-cutoff. In particular, an angular-cutoff Coulomb potential is included. The method is based on a new regularizing property of the Boltzmann collision operators relative to the collisional difference of smooth test functions. One of the points is to represent the collisional difference through the inverse Fourier transform of the test functions. This provides a nice structure for the Fourier transform of the relative collision operators.
Quantum hydrodynamics and diffusion models for semiconductors derived from the entropy principle. Pierre DEGOND, Florian MEHATS Mathématiques pour l'Industrie et la Physique, CNRS, Universite Paul Sabatier, INSA Toulouse et Université Toulouse 1, France
Christian RINGHOFER Mathematics, Arizona State University, Phoenix, USA
Abstract In this work, we give an overview of recently derived quantum hydrodynamic and diffusion models. A quantum local equilibrium is defined as a minimizer of the quantum entropy subject to local moment constraints (such as given local mass, momentum and energy densities). These equilibria relate the thermodynamic parameters (such as the temperature or chemical potential) to the densities in a non-local way. Quantum hydrodynamic models are obtained through moment expansions of the quantum kinetic equations closed by quantum equilibria. We also derive collision operators for quantum kinetic models which decrease the quantum entropy and relax towards quantum equilibria. Then, through diffusion limits of the quantum kinetic equation, we establish various classes of models which are quantum extensions of the classical energy-transport and drift-diffusion models.
Numerical approximation of the viscous quantum hydrodynamic model for semiconductors Ansgar JÜNGEL, Shaoqiang TANG
Abstract The viscous quantum hydrodynamic equations for semiconductors with constant temperature are numerically studied. They consist of the one-dimensional Euler equations for the electron density and current density, including a quantum correction and viscous terms, coupled to the Poisson equation for the electrostatic potential. The equations can be derived formally from a WignerFokker-Planck model by a moment method. Two different numerical techniques are used: a hyperbolic relaxation scheme and a central finite-difference method. By simulating a ballistic diode and a resonant tunneling diode, it is shown that numerical or physical viscosity changes significantly the behavior of the solutions. Moreover, the current-voltage characteristics show negative differential resistance and hysteresis effects.
Asymptotics of Fluiddynamic Models for Semiconductors and Plasmas Quasineutral Limit of Euler-Poisson System with and without Viscosity Shu WANG College of Science, Beijing University of Technology, PingLeYuan100, ChaoyangDistrict, Beijing100022, P. R. China
Peter A. MARKOWICH Institut für Mathematik, Universität Wien, Boltzmanngasse 9, 1090 Wien, Austria
Abstract In this talk we survey asymptotics of fluiddynamic models for semiconductors and plasmas. The models involved here contain Euler-Maxwell system, Euler-Poisson system, e-MHD system, Navier-Stokes-Poisson system and drift-diffusion system etc. The asymptotics concern large time behaviors and scaling asymptotic limits, such as non-relativistic limit, zero singular relaxation limit and quasineutral limit etc. We will give recent results in this field, such as the convergence of Euler-Maxwell system to the incompressible Euler system, the zero relaxation limit of EulerPoisson system to drift-diffusion model and quasineutral limit of drift-diffusion model, and also review some methods or new ideas involved.
Mixed-Mode Circuit and Device Simulation for a CMOS monolithic Photoreceiver L.H. Mao Tianjin University
Abstract By using mixed-mode simulator in ATLAS, a commercial simulator produced by Silvaco International, we designed a CMOS-process-compatible OEIC receiver which has an Photodetector and a transimpedance amplifier. The optic wavelength response, optic frequency response and optic pulse response of the OEIC um CMOS process. um and 0.6 receiver are simulated in 0.35 The sensitivity of the OEIC receiver is optimized in giving detector area and receiver bandwidth. The feedback resistor in transimpedance amplifier is simulated both for bandwidth and for sensitivity.
Hybrid Models for Semiconductors H. NEIDHARDT Weierstrass-Institute for Applied Analysis and Stochastics, Mohrenstr. 39, D-10117 Berlin,Germany
Abstract The paper analyzes an one dimensional current coupled hybrid model for semiconductors consisting of a drift-diffusion model without generation and recombination in which is embedded a quantum transmitting Schrödinger-Poisson system (QTSP-system). With respect to a further numerical treatment the embedded QTSP-system is replaced by a discretized system which leads to a dissipative hybrid model. It is shown that the dissipative hybrid model admits always a solution with constant current densities. All solutions are uniformly bounded where the bound depends only on the data of the hybrid model. The current densities are different from zero if the boundary values of the electro-chemical potentials are different.
A Non-Equilibrium Statistical Mechanics without the Assumption of Molecular Chaos Tianquan CHEN
In recent years the author is endeavoring to derive the functional equations governing the evolutions of fluid flows, including both the so called laminar and turbulent flows, from the first principle of non-equilibrium statistical mechanics. The results are described in the book .  T.-Q. Chen, (2003), A Non-equilibrium Statistical Mechanics without the Assumption of Molecular Chaos, World Scientific Publishing Co., Singapore.
Time-dependent solutions of semiconductor equations modeling avalanche generation Ping GUAN Dept. of Math., Southeast Univ., Nanjing 210096, P.R.China
Modelling and analysis of coupled circuits and devices Giuseppe ALI Istituto per le Applicazioni del Calcolo "Mauro Picone", CNR, Via P. Castellino 111, I-80131 Naples, Italy
Abstract In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multiphysics approach. For linear RLC networks containing diodes as distributed devices, a class of mathematical models is constructed that combine the differentialalgebraic network equations of the circuit with elliptic and parabolic-elliptic boundary value problems modelling the diodes. For these mixed initial-boundary value problems of partial differential-algebraic equations, existence and uniqueness results are discussed.
Control of nonlinear spatio-temporal dynamics in semiconductor nanostructures E. SCHÖLL Theoretical Physics, Technical University Berlin
Abstract Nonlinear transport in semiconductor nanostructure devices can be modelled on the basis of the spatio-temporal dynamics of charge carriers in combination with the electric field and circuit equations. Negative differential conductivity, current instabilities and self-organized pattern formation may arise in the regime of strong nonlinearities far from thermodynamic equilibrium. It is the aim of this talk to show that complex and chaotic behavior can be controlled by simple time-delayed feedback methods (Time delay autosynchronization). In particular, we study two models of semiconductor nanostructures which are of current interest : (i) Charge accumulation in the quantum-well of a double-barrier resonant-tunneling diode (DBRT) may result in lateral spatio-temporal patterns of the current density. Various oscillatory instabilities in form of periodic or chaotic breathing and spiking modes may occur. We demonstrate that unstable current density patterns can be stabilized in a wide parameter range by means of a delayed feedback loop. (ii) Electron transport in semiconductor super lattices (SL) exhibits complex scenarios including chaotic motion of charge accumulation and depletion fronts under time-independent bias conditions. We show that self-stabilization of current oscillations corresponding to travelling field domain modes is possible by a novel low-pass filtered time delayed feedback control.  E. Schöll, Nonlinear spatio-temporal dynamics and chaos in semiconductors (Cambridge University Press, Cambridge, 2001)
Coupled device, circuit and interconnect simulations Wil SCHILDERS Philips, Eindhoven, Netherlands
Abstract Until recently, simulations of devices and circuits were performed in separate programmes. With shrinking dimensions and increasing frequencies, there is a growing need for coupled simulations. In this talk, we will discuss various issues that are related to this coupling.
Quantum-Corrected Drift-Diffusion Models for Transport in Semiconductor Devices Carlo de Falco Dipartimento di Matematica “F.Enrique”, Università degli Studi di Milano,Via Saldini 50, 20133 Milano, Italy
Abstract In this lecture, we propose a unified framework for Quantum-Corrected Drift-Diffusion (QCDD) models in nanoscale semiconductor device simulation. QCDD models are presented as a suitable generalization of the classical Drift-Diffusion (DD) system, each particular model being identified by the constitutive relation for the quantum-correction to the electric potential. We examine two special, and relevant, examples of QCDD models; the first one is the modified DD model (named Schrödinger-Poisson-Drift-Diffusion, SPDD) proposed in , and the second one is the Quantum-Drift-Diffusion (QDD) model proposed in . For the decoupled solution of the two models, we introduce a functional iteration technique that extends the classical Gummel algorithm widely used in the iterative solution of the DD system. We discuss the finite element discretization of the various differential subsystems, with special emphasis on their stability properties, and illustrate the performance of the proposed algorithms and models on the numerical simulation of nano-scale devices in two spatial dimensions. Acknowledgments This is a joint work with Prof. Riccardo Sacco, MOX, Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Via Bonardi 9, 20133 Milano, Italy; Prof. E. Gatti and Prof. A. L. Lacaita, DEI-Dipartimento di Elettronica e Informazione, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano, Italy.  A. Pirovano, A.L. Lacaita, A.S. Spinelli, Two-Dimensional Quantum Effects in Nanoscale MOSFETs, IEEE Trans. Electron Devices, 1 (47), 25-31 (2002).  M.G. Ancona, G.J. Iafrate, Quantum Correction to the Equation of State of an Electron Gas in a Semiconductor, Phys. Rev. B, 39, 95369540 (1989).
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