Semiclassical and quantum transport modeling dragica vasileska, stephen m. The wignerboltzmann equation differs from its classical counterpart principally in that particle transport. The theoretical foundation of nanodsim has been presented in chapter 2 to 3. A fundamental approach to modeling quantum transport of electrons and holes in semiconductor devices is the wignerboltzmann equation, the quantum generalization of the boltzmann equation. Semiclassical and quantum device modeling and simulation provides a comprehensive overview of the essential techniques and methods. Save up to 80% by choosing the etextbook option for isbn. Quantum transport theory has a completely independent origin and is both conceptually and mathematically more complex than the boltzmann type of models 1,2,3,4,5. It clearly explains for what types of devices a particular method is suitable, which is the most critical point that a researcher faces and has to decide upon when modeling semiconductor devices. Modeling of macroscopic electron transport numerically cheaper than kinetic models modeling of quantum transport and quantum di usion e ects numerical approximation of macroscopic models.
Semiclassical expansion semiclassical quantum uid equations l ecture 4. The new feature is that one has to investigate both thermal and quantum e. Pdf ab initio modeling of quantum transport properties of. Ab initio modeling of quantum transport properties of molecular electronic devices jeremy taylor,1 hong guo,1 and jian wang2 1center for the physics of materials and department of physics, mcgill university, montreal, pq, canada h3a 2t8 2department of physics, the university of hong kong, pokfulam road, hong kong, china received 25 october 2000. Modeling of quantum transport in semiconductor devices. A semiclassical transport model for twodimensional thin. This book treats three topics of electronic quantum transport in mesoscopic semiconductor structures.
Ab initio modeling of quantum transport properties of. Electronic quantum transport in mesoscopic semiconductor. It systematically describes theoretical approaches and the numerical solutions that are used in explaining the. This section of the notes provides an understanding of the basic building blocks of semiconductor device structures. Note that the semiclassical device models become invalid in the nanometer. Semiclassical and quantum electronic transport in nanometerscale. Introduction the goa olf numerical semiconductor devic ies simulatio to model. The solutions have roughly firstorder convergence in probability density functions. It systematically explains theoretical approaches and numerical.
Quite a lot of attention has been paid to the quantum mechanical modeling of free collisionless transport. A coherent semiclassical transport model for purestate quantum scattering. Basic quantum transport mechanism can be classified as i dissipative transport ii ballistic transport l device free and iii tunneling transport l device quantum transport mechanism. Novak january 28, 2009 abstract we present a timedependent semiclassical transport model for coherent purestate scattering with quantum barriers. Qfd can be dened as the description of a quantum system in terms of macroscopic uidlike variables, such as density, current, temperature, etc. Nanoscale electronic devices are of great interest for all kinds of applications like switching. This chapter describes quantum transport theory and its application to semiconductor devices. Computational methods for semiclassical and quantum. Semiclassical and quantum device modeling and simulation provides a comprehensive overview of the essential techniques and methods for effectively analyzing transport in. Transport modeling for nanoscale semiconductor devices. Stability and semiclassical limit in a semiconductor full. Computational electronics synthesis lectures on computational. The simulation of nanoscale devices requires, at least rudimentarily, the inclusion of quantum effects.
The approach is based on the solution to the wignerboltzmann equation, which is derived from the schrodinger equation. It is a very hot topic at present time because it is relevant to fundamental principles of quantum mechanics and statistical physics, as well as to. Semiclassical and quantum electronic transport in nanometerscale structures. The real building blocks of the universe with david tong duration.
In quantum transport we have a matrix corresponding to each quantity of interest. Ab initio modeling of quantum transport properties of molecular electronic devices. Semiclassical and quantum device modeling and simulation. The systems representation encodes energetic as well as geometrical information to characterize similarities between disordered. This course is an attempt to provide an overview of basic concepts of quantum transport through modern smallsize structures. A coherent semiclassical transport model for purestate. A new method for accounting for quantum effects in semiclassical device simulation is presented. Chris bowen, and dejan jovanovic corporate research laboratories, texas instruments incorporated, dallas, texas 75243. Modeling electronic quantum transport with machine learning. The wignerboltzmann equation is truncated to order.
The transmission coefficients of disordered systems were computed to provide training and test datasets to the machine. Barker 1980a, b has described a quantum mechanical model for very smallscale devices quantum transport theory will play an essential role is in. Connects concepts of transport in nanoscale semiconductor devices to correlated transport in superconductors, metalinsulator transitions, and emerging novel materials in which transport exhibits. This book compiles different approaches to the problem of transport in mesoscopic semiconductor systems, ranging from semiclassical to fully quantum. Semiclassical and quantum device modeling and simulation provides a comprehensive overview of the essential techniques and methods for effectively analyzing. The hierarchy of semiclassical and quantum transport models. We present a machine learning approach to solve electronic quantum transport equations of onedimensional nanostructures. Quantum transport in electron devices and novel materials. Introduction to nanoelectronics 5 contents introduction 6 part 1. Quantum transport is an essential and challenging part of nanoscience, and understanding its concepts and methods is vital to the successful fabrication of devices at the. The goal of chapter 4 to 7 is to convert the formalism of section 3. A semiclassical transport model for twodimensional thin quantum barriers shi jina,1 and kyle a. This book describes the state of the art in transport modeling, relevant for the simulation of nanoscale semiconductor.
Semiclassical and quantum macroscopic semiconductor. In particular, since quantum effect are more easy to see in lowerdimensional systems, it concentrates on the essential physics necessary to understand semiconductor devices containing. Nanoelectronic devices 9781441988393, 9781441988409. Incorporation of quantum corrections to semiclassical two. Nanoelectronic devices semiclassical and quantum transport modeling by dragica vasileska and publisher springer. This book surveys the advanced simulation methods needed for proper modeling of stateoftheart nanoscale devices. Another quantum energy transport model has been studied by chen and liu 7. This book describes the state of the art in transport modeling, relevant for the simulation of nanoscale semiconductor devices. In some situations one can use the singleparticle pauli master equation pme 12, which, by its ability to model dissipation of. Chris bowen, and dejan jovanovic corporate research laboratories, texas instruments incorporated, dallas, texas 75243 received november 1996. The model is based on a complexvalued liouville equation, with interface conditions at quantum. Semiclassical and quantum transport modeling this book describes the state of the art in transport modeling, relevant for the simulation of nanoscale. Computational electronics semiclassical and quantum. Computational methods for semiclassical and quantum transport in semiconductor devices volume 6 christian ringhofer.
Semiclassical and quantum transport, particlebased device simulations, boltzmann transport equation, electronelectron and. Semiclassical and quantum device modeling and simulation provides a comprehensive overview of the essential techniques and methods for effectively. The coupling of the fundamentally quantum mechanical nanoelectronic transport simulation through resonant tunneling diodes to semiclassical drift diffusion in the contacts is demonstrated. Quantum transport is a diverse field, sometimes combining seemingly contradicting concepts quantum and classical, conduction and insulating within a single nanodevice. The coupling between the nonequilibrium green function formalism used in nemo to the drift diffusion equation is established by the use of spatially dependent quasi fermi levels in the. Mixed initialboundary value problem in particle modeling of microelectronic devices. Nanodsim, short for nanoelectronic device simulator, is a modeling package for atomistic simulation of quantum transport and electronic properties of nanostructures. Single and multiband modeling of quantum electron transport through layered semiconductor devices roger lake,a gerhard klimeck, r. Quantum transport simulation of experimentally fabricated nanofinfet hr khan, d mamaluy, d vasileska ieee transactions on electron devices 54 4, 784796, 2007. The model is based on a complexvalued liouville equation, with interface condition at quantum.
In the o4 approximation where is the reduced planck constant, the equations become local, but their mathematical structure is still unclear. It is important to distinguish between quantum transport theory which completely describes a quantum view of a system and the application of quantum mechanics to the semiclassical. Novak december 27, 2008 abstract we present a timedependent semiclassical transport model for coherent purestate scattering with quantum barriers. C quantum transport effects in nanoscale devices 1. This book surveys the advanced simulation methods needed for proper modeling. Quantum states are con ned, localized in each individual quantum well, and do not participate in transport. Starting with the simplest semiclassical approaches and ending with the description of complex fully quantum mechanical methods for quantum transport analysis of stateoftheart devices, computational electronics. Chapter 4 quantum master equations in electronic transport. To date, there are about 60 major devices, with over 100 device variations related to them. This equation can be understood in semiclassical terms if we. Abstract computational electronics is devoted to state of the art numerical.
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