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Atomistic Simulation Of Quantum Transport In Nanoelectronic Devices (With Cd-rom) [Mīkstie vāki]

(Nanoacademic Technologies Inc, Canada), (Nanoacademic Technologies Inc, Canada), Foreword by (Mcgill Univ & Nanoacademic Technologies Inc, Canada)
  • Formāts: Paperback / softback, 436 pages
  • Izdošanas datums: 14-Jul-2016
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9813141425
  • ISBN-13: 9789813141421
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  • Cena: 75,52 €
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  • Formāts: Paperback / softback, 436 pages
  • Izdošanas datums: 14-Jul-2016
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9813141425
  • ISBN-13: 9789813141421
Citas grāmatas par šo tēmu:
Computational nanoelectronics is an emerging multi-disciplinary field covering condensed matter physics, applied mathematics, computer science, and electronic engineering. In recent decades, a few state-of-the-art software packages have been developed to carry out first-principle atomistic device simulations. Nevertheless those packages are either black boxes (commercial codes) or accessible only to very limited users (private research codes). The purpose of this book is to open one of the commercial black boxes, and to demonstrate the complete procedure from theoretical derivation, to numerical implementation, all the way to device simulation. Meanwhile the affiliated source code constitutes an open platform for new researchers. This is the first book of its kind. We hope the book will make a modest contribution to the field of computational nanoelectronics.
Foreword vii
Preface ix
Acknowledgments xiii
1 Introduction 1(26)
1.1 What is quantum transport?
1(7)
1.2 Every atom counts
8(5)
1.3 Disorder and coherent potential
13(5)
1.4 NECPA-DFT theory and NanoDsim package
18(3)
1.5 A few words about this monograph
21(6)
2 The NECPA theory 27(40)
2.1 Two-probe Hamiltonian
27(3)
2.2 NEGF formalism
30(2)
2.3 Langreth theorem
32(3)
2.4 NEGF in steady-state
35(4)
2.5 Dyson equation
39(4)
2.6 Current formula
43(5)
2.7 Surface Green's function
48(1)
2.8 NECPA equations
49(7)
2.9 Current conservation and dephasing effect
56(5)
2.10 A toy model
61(6)
3 The NECPA-LMTO method 67(46)
3.1 Kohn-Sham equation
67(2)
3.2 Muffin-tin orbital
69(3)
3.3 Structure constant
72(1)
3.4 Tail cancelation
73(1)
3.5 Energy linearization
74(2)
3.6 LMTO Green's function
76(3)
3.7 Screening transform
79(2)
3.8 Physical quantities
81(5)
3.9 Periodicity and Fourier transform
86(2)
3.10 NECPA-LMTO formalism
88(3)
3.11 Self-consistent calculation
91(12)
3.11.1 Flowchart
91(2)
3.11.2 Step-1 calculate structure constant
93(1)
3.11.3 Step-2 calculate self-energy
94(1)
3.11.4 Step-3 make an initial guess
95(1)
3.11.5 Step-4 calculate atomic orbital
96(1)
3.11.6 Step-5 calculate potential parameter
97(1)
3.11.7 Step-6 solve the NECPA equations
98(2)
3.11.8 Step-7 calculate energy moment
100(1)
3.11.9 Step-8 calculate charge density
100(1)
3.11.10 Step-9 calculate charge and dipole
101(1)
3.11.11 Step-10 calculate atomic potential with DFT
102(1)
3.11.12 Step-11 calculate Madelung potential
103(1)
3.11.13 Step-12 calculate total potential
103(1)
3.12 Post-analysis calculation
103(5)
3.12.1 Density of states
103(1)
3.12.2 Transmission coefficient
104(2)
3.12.3 Transmission variation
106(1)
3.12.4 Band structure
107(1)
3.12.5 CPA band structure
107(1)
3.13 Miscellaneous issues
108(5)
3.13.1 Spin degree of freedom
109(1)
3.13.2 Fermi level
109(1)
3.13.3 Linearization center
110(1)
3.13.4 Scalar relativistic equation
111(1)
3.13.5 Wigner-Seitz radius
111(2)
4 NanoDsim: the package design 113(34)
4.1 Do you speak MATLAB?
113(5)
4.2 MATLAB: vectorization technique
118(2)
4.3 MATLAB: hybrid programming
120(5)
4.4 MATLAB: object oriented programming
125(7)
4.5 NanoDsim: overall design
132(2)
4.6 NanoDsim: dsim-solvers
134(4)
4.7 NanoDsim: dsim-calculators
138(1)
4.8 NanoDsim: dsim-classes
139(2)
4.9 NanoDsim: supporting libraries
141(2)
4.10 NanoDsim: implementation and debugging
143(4)
5 NanoDsim: bulk systems 147(42)
5.1 Bulk classes
148(6)
5.1.1 Oclass_cpaBulk
148(2)
5.1.2 Oclass_cpaAtom
150(1)
5.1.3 Oclass_lmtoAtom
151(2)
5.1.4 ©class-lmtoOrbital
153(1)
5.2 Bulk solver
154(2)
5.3 Structure constant
156(3)
5.4 Ewald sum technique
159(6)
5.5 Radial equation
165(6)
5.6 Complex contour integral
171(5)
5.7 CPA equations
176(5)
5.8 Fermi level
181(2)
5.9 Bulk calculator: band structure
183(2)
5.10 Bulk calculator: density of states
185(4)
6 NanoDsim: two-probe systems 189(58)
6.1 Two-probe classes
189(4)
6.1.1 @class_necpaTwoProbe
190(2)
6.1.2 @class_necpaAtom
192(1)
6.2 Two-probe solver
193(2)
6.3 Ewald sum technique
195(11)
6.3.1 2d Madelung potential
195(5)
6.3.2 Surface Madelung potential
200(4)
6.3.3 Boundary condition
204(2)
6.4 Surface Green's function
206(10)
6.4.1 Analytically solvable case
206(3)
6.4.2 Recursive method
209(3)
6.4.3 Eigenvalue method
212(2)
6.4.4 A few comments
214(2)
6.5 Real axis integral
216(3)
6.6 k-integral in the Brillouin zone
219(13)
6.6.1 Uniform k-sampling
220(1)
6.6.2 Symmetric k-sampling
221(5)
6.6.3 Time-reversal symmetry
226(6)
6.7 NECPA equations
232(5)
6.8 Fermi level alignment
237(2)
6.9 Two-probe calculator: transmission coefficient
239(2)
6.10 Verification of the implementation
241(6)
7 NanoDsim: optimization and parallelization 247(36)
7.1 Performance analysis
247(3)
7.2 Memory issues
250(3)
7.3 Speed issues
253(8)
7.3.1 Order-N methods
253(1)
7.3.2 Iterative methods
254(3)
7.3.3 Direct methods
257(3)
7.3.4 Summary
260(1)
7.4 Principal layer algorithm
261(8)
7.4.1 Retarded Green's function
261(4)
7.4.2 Lesser Green's function
265(1)
7.4.3 Transmission coefficient
266(1)
7.4.4 Cost estimate
267(2)
7.4.5 Implementation details
269(1)
7.5 MATLAB interface to MPI
269(3)
7.6 Parallelization
272(2)
7.7 Benchmark
274(2)
7.8 Convergence issues
276(2)
7.9 Error analysis
278(5)
8 Kaleidoscope of the physics in disordered systems 283(36)
8.1 Simple examples: bulk Cu, Fe, Co, Ni
283(3)
8.2 CPA vs supercell: Cu/Co alloy
286(2)
8.3 Si with uniaxial strain
288(4)
8.4 Band offset of GaAs/Al Ga1-x As heterojunctions
292(2)
8.5 NECPA vs supercell: Cu/Co interface
294(4)
8.6 Si transistors with localized doping
298(4)
8.7 Graphene transistors with disorder scattering
302(5)
8.8 Fe/MgO/Fe tunnel junctions
307(4)
8.9 Cu films with surface scattering
311(4)
8.10 Concluding remarks
315(4)
Appendix 319
A.1 Atomic units
319(1)
A.2 Phase diagram of the toy model
320(4)
A.3 Classical transport vs quantum transport
324(10)
A.3.1 Drift-Diffusion model
325(2)
A.3.2 Effective-Mass model
327(6)
A.3.3 Numerical results
333(1)
A.4 Lehmann spectrum of NEGF
334(5)
A.5 Low concentration approximation
339(6)
A.5.1 Multiple scattering theory
339(3)
A.5.2 Transmission coefficient and transmission variation
342(3)
A.6 Scattering states approach
345(10)
A.6.1 Bulk states
345(2)
A.6.2 Wave scattering
347(3)
A.6.3 Transmission coefficient
350(2)
A.6.4 Further discussion: group velocity
352(1)
A.6.5 Further discussion: number of modes
352(1)
A.6.6 Further discussion: numerical issues
353(2)
A.6.7 Summary
355(1)
A.7 Density matrix in clean bulk systems
355(2)
A.8 Connection to the CPA-NVC theory
357(1)
A.9 Explicit expressions of XC-functionals
358(5)
A.9.1 LDA: Perdew and Zunger (1981)
359(1)
A.9.2 GGA: Perdew, Burke, and Ernzerhof (1996)
360(1)
A.9.3 MBJ: Tran and Blaha (2009)
361(2)
A.9.4 A few comments
363(1)
A.10 Complex-valued and real-valued spherical harmonics
363(2)
A.11 Gaunt coefficients
365(1)
A.12 Eigensolutions of TST and TSC matrices
366(2)
A.13 Proof of the Wronskian identity
368(1)
A.14 Numerical proof
369(1)
A.15 Transmission coefficient in the LMTO method
370(3)
A.16 Specular scattering vs diffusive scattering
373(3)
A.17 Fill the space with atomic spheres
376(4)
A.17.1 Regular structures
376(2)
A.17.2 Irregular structures
378(2)
A.18 Symmetric k-sampling
380(5)
A.19 Unfolding algorithm
385(1)
A.20 Mixing algorithms
386(3)
A.21 Modified Fermi pole summation technique
389(2)
A.22 Field effect transistor with gate terminals
391(2)
A.23 Algorithms for solving the Poisson equation
393(9)
A.23.1 Numerical discretization
393(2)
A.23.2 Algorithms in 1d case
395(3)
A.23.3 Algorithms in 2d and 3d cases
398(1)
A.23.4 Nonorthogonal Poisson box
399(1)
A.23.5 Nonlinear Poisson equation
400(2)
A.24 Locality in nonequilibrium
402(1)
A.25 Lanczos algorithm
403(4)
A.26 Preconditioner designed for quantum transport
407(4)
A.27 Content of the affiliated CD
411
A.27.1 NanoDsim package
411(1)
A.27.2 ResearchCode package
411