Electrical transport in nanoscale systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2008
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XVI, 476 S. Ill., graph. Darst. |
| ISBN: | 9780521896344 |
Internformat
MARC
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| 100 | 1 | |a Di Ventra, Massimiliano |e Verfasser |0 (DE-588)139775382 |4 aut | |
| 245 | 1 | 0 | |a Electrical transport in nanoscale systems |c Massimiliano Di Ventra |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2008 | |
| 300 | |a XVI, 476 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Electric conductivity | |
| 650 | 4 | |a Electron transport | |
| 650 | 4 | |a Nanoelectromechanical systems | |
| 650 | 4 | |a Nanoelectronics | |
| 650 | 0 | 7 | |a Nanostrukturiertes Material |0 (DE-588)4342626-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Transportprozess |0 (DE-588)4185932-7 |2 gnd |9 rswk-swf |
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| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016747816&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
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Datensatz im Suchindex
| _version_ | 1804138031154724864 |
|---|---|
| adam_text | Contents
A primer on electron transport page
1
1.1
Nanoscale systems
1
1.2
Generating currents
3
1.2.1
Finite versus infinite systems
8
1.2.2
Electron sources
9
1.2.3
Intrinsic nature of the transport problem
10
1.3
Measuring currents
11
1.3.1
Microscopic states
12
1.3.2
The current operator
13
1.3.3
The measurement process
16
1.3.4
Complete measurement and pure states
17
1.4
The statistical operator and macro-states
19
1.4.1
Pure and mixed states
21
1.4.2
Quantum correlations
22
1.4.3
Time evolution of the statistical operator
23
1.4.4
Random or partially specified Hamiltonians
24
1.4.5
Open quantum systems
25
1.4.6
Equilibrium statistical operators
29
1.5
Current measurement and statistical operator truncation
32
1.6
One current, different viewpoints
34
Summary and open questions
36
Exercises
36
Drude
model,
Kubo
formalism and Boltzmann equation
39
2.1
Drude
model
39
2.2
Resistance, coherent and incoherent transport
42
2.2.1
Relaxation vs. dephasing
44
vn
viii Contents
2.2.2
Mean-free path
48
2.2.3
The meaning of momentum relaxation time
49
2.3
Kubo
formalism
50
2.3.1
The current-current response function
55
2.3.2
The use of Density-Functional Theory in the
Kubo
approach
57
2.3.3
The fluctuation-dissipation theorem
60
2.3.4
Ohmic vs. ballistic regimes
66
2.4
Chemical, electrochemical and electrostatic potentials
68
2.5
Drift-diffusion equations
72
2.5.1
Diffusion coefficient of an ideal electron gas in the
non-degenerate limit
73
2.5.2
Generalization to spin-dependent transport
75
2.6
Distribution functions
77
2.7
Boltzmann equation
79
2.7.1
Approach to local equilibrium
82
2.8
Entropy, loss of information, and macroscopic irreversibility
83
2.8.1
The classical statistical entropy
85
2.8.2
Quantum statistical entropy
86
2.8.3
Information content of the N- and one-particle
statistical operators
89
2.8.4
Entropy of open quantum systems
90
2.8.5
Loss of information in the
Kubo
formalism
91
2.8.6
Loss of information with stochastic Hamiltonians
92
2.8.7
Entropy associated with the measurement of currents
93
Summary and open questions
94
Exercises
95
3 Landauer
approach
101
3.1
Formulation of the problem
102
3.2
Local resistivity dipoles and the field response
113
3.3
Conduction from transmission
115
3.3.1
Scattering boundary conditions
115
3.3.2
Transmission and reflection probabilities
119
3.3.3
Total current
123
3.3.4
Two-probe conductance
128
3.4
The
Lippmann—Schwinger
equation
132
3.4.1
Time-dependent
Lippmann—Schwinger
equation
132
3.4.2
Time-independent
Lippmann—Schwinger
equation
140
3.5
Green s functions and self-energy
145
Contents ix
3.5.1 Relation
to scattering theory
154
3.6
The <S matrix
159
3.6.1
Relation between the total Green s function and
the
S
matrix
162
3.7
The transfer matrix
167
3.7.1
Coherent scattering of two resistors in series
169
3.7.2
Incoherent scattering of two resistors in series
171
3.7.3
Relation between the conductance and the transfer
matrix
173
3.7.4
Localization, ohmic and ballistic regimes
174
3.8
Four-probe conductance in the non-invasive limit
178
3.8.1
Single-channel case
179
3.8.2
Geometrical dilution
181
3.8.3
Multi-channel case
182
3.9
Multi-probe conductance in the invasive limit
185
3.9.1
Floating probes and dephasing
187
3.10
Generalization to spin-dependent transport
190
3.10.1
Spin-dependent transmission functions
194
3.10.2
Multi-probe conductance in the presence of a
magnetic field
195
3.10.3
Local resistivity spin dipoles and dynamical effects
196
3.11
The use of Density-Functional Theory in the
Landauer
approach
198
Summary and open questions
202
Exercises
203
Non-equilibrium Green s function formalism
209
4.1
Formulation of the problem
211
4.1.1
Contour ordering
215
4.2
Equilibrium Green s functions
217
4.2.1
Time-ordered Green s functions
218
4.2.2
Dyson s equation for interacting particles
221
4.2.3
More Green s functions
223
4.2.4
The spectral function
225
4.3
Contour-ordered Green s functions
231
4.3.1
Equations of motion for non-equilibrium Green s
functions
233
4.4
Application to steady-state transport
236
4.5
Coulomb blockade
244
4.6
Quantum kinetic equations
250
Contents
Summary and open questions
255
Exercises
257
Noise
258
5.1
The moments of the current
261
5.2
Shot noise
263
5.2.1
The classical
(Poisson)
limit
264
5.2.2
Quantum theory of shot noise
266
5.3
Counting statistics
274
5.4
Thermal noise
275
Summary and open questions
277
Exercises
277
Electron-ion interaction
280
6.1
The many-body electron-ion Hamiltonian
281
6.1.1
The adiabatic approximation for a current-carrying
system
282
6.1.2
The phonon subsystem
284
6.1.3
Electron-phonon coupling in the presence of current
288
6.2
Inelastic current
290
6.2.1
Inelastic current from standard perturbation theory
291
6.2.2
Inelastic current from the NEGF
296
6.3
Local ionic heating
312
6.3.1
Lattice heat conduction
319
6.4
Thermopower
323
6.5
Current-induced forces
328
6.5.1
Elastic vs. inelastic contribution to
electro-migration328
6.5.2
One force, different definitions
330
6.5.3
Local resistivity dipoles and the force sign
333
6.5.4
Forces at equilibrium
333
6.5.5
Forces out of equilibrium
335
6.5.6
Are current-induced forces conservative?
340
6.6
Local ionic heating vs. current-induced forces
343
Summary and open questions
344
Exercises
344
The micro-canonical picture of transport
346
7.1
Formulation of the problem
347
7.1.1
Transport from a finite-system point of view
347
7.1.2
Initial conditions and dynamics
349
7.2
Electrical current theorems within dynamical DFTs
351
7.2.1
Closed and finite quantum systems in a pure state
351
Contents
Xl
7.2.2
Closed quantum systems in a pure state with
arbitrary boundary conditions
353
7.2.3
Current in open quantum systems
354
7.2.4
Closure of the BBGKY hierarchy
356
7.2.5
Functional approximations and loss of information
357
7.3
Transient dynamics
358
7.4
Properties of quasi-steady states
360
7.4.1
Variational definition of quasi-steady states
360
7.4.2
Dependence of quasi-steady states on initial condi¬
tions
364
7.5
A non-equilibrium entropy principle
365
7.6
Approach to steady state in nanoscale systems
369
7.7
Definition of conductance in the micro-canonical picture
374
Summary and open questions
375
8
Hydrodynamics of the electron liquid
376
8.1
The Madelung equations for a single particle
378
8.2
Hydrodynamic form of the
Schrödinger
equation
380
8.2.1
Quantum
Navier—
Stokes equations
382
8.3
Conductance quantization from hydrodynamics
388
8.4
Viscosity from Time-Dependent Current Density-Functional
Theory
391
8.4.1
Functional approximation, loss
ofinformation,
and
dissipative dynamics
394
8.4.2
Effect of viscosity on resistance
395
8.5
Turbulent transport
397
8.6
Local electron heating
403
8.6.1
Electron heat conduction
405
8.6.2
Hydrodynamics of heat transfer
406
8.6.3
Effect of local electron heating on ionic heating
410
Summary and open questions
412
Exercises
413
Appendices
Appendix A A primer on second quantization
415
Appendix
В
The quantum BBGKY hierarchy
420
Appendix
С
The
Lindblad
equation
423
C.I The
Lindblad
theorem
424
C.2 Derivation of the
Lindblad
equation
426
C.3 Steadv-state solutions
430
xii
Contents
Appendix
D
Ground-state Density-Functional Theory
431
D.I The Hohenberg-Kohn theorem
431
D.2 The Kohn-Sham equations
432
D.3 Generalization to grand-canonical equilibrium
434
D.4 The local density approximation and beyond
434
Appendix
E
Time-Dependent DFT
436
E.I The
Runge—
Gross theorem
436
E.2 The time-dependent Kohn—Sham equations
437
E.3 The adiabatic local density approximation
437
Appendix
F
Time-Dependent Current DFT
439
F.I The current density as the main variable
439
F.2 The exchange-correlation electric field
440
F.3 Approximate formulas for the viscosity
442
Appendix
G
Stochastic Time-Dependent Current DFT
444
G.I The stochastic
Schrödinger
equation
444
G.2 Derivation of the quantum master equation
446
G.3 The theorem of Stochastic TD-CDFT
449
Appendix
H
Inelastic corrections to current and shot noise
451
Appendix I Hydrodynamic form of the
Schrödinger equation454
Appendix
J
Equation of motion for the stress tensor
458
Appendix
К
Cut-off of the viscosity divergence
461
Appendix
L
Bernoulli s equation
463
References
464
Index
470
in recent years there has been a huge increase
in the research and development of nanoscaie
science and technology, with electrical transport
playing a central role. This graduate textbook
provides an in-depth description of the transport
phenomena relevantto systems of nanoscaie
dimensions.
in this textbook the different theoretical
approaches are critically discussed, with
emphasis on their basic assumptions and
approximations. The book also covers
information content in the measurement
of currents, the role of initial conditions in
establishing a steady state, and the modem
use of density-functional theory. Topics are
introduced by simple physical arguments, with
particular attention to the non-equilibrium
statistical nature of electrical conduction, and
followed by a detailed formal derivation. This
textbook is ideal for graduate students in physics,
chemistry, and electrical engineering.
|
| adam_txt |
Contents
A primer on electron transport page
1
1.1
Nanoscale systems
1
1.2
Generating currents
3
1.2.1
Finite versus infinite systems
8
1.2.2
Electron sources
9
1.2.3
Intrinsic nature of the transport problem
10
1.3
Measuring currents
11
1.3.1
Microscopic states
12
1.3.2
The current operator
13
1.3.3
The measurement process
16
1.3.4
Complete measurement and pure states
17
1.4
The statistical operator and macro-states
19
1.4.1
Pure and mixed states
21
1.4.2
Quantum correlations
22
1.4.3
Time evolution of the statistical operator
23
1.4.4
Random or partially specified Hamiltonians
24
1.4.5
Open quantum systems
25
1.4.6
Equilibrium statistical operators
29
1.5
Current measurement and statistical operator truncation
32
1.6
One current, different viewpoints
34
Summary and open questions
36
Exercises
36
Drude
model,
Kubo
formalism and Boltzmann equation
39
2.1
Drude
model
39
2.2
Resistance, coherent and incoherent transport
42
2.2.1
Relaxation vs. dephasing
44
vn
viii Contents
2.2.2
Mean-free path
48
2.2.3
The meaning of momentum relaxation time
49
2.3
Kubo
formalism
50
2.3.1
The current-current response function
55
2.3.2
The use of Density-Functional Theory in the
Kubo
approach
57
2.3.3
The fluctuation-dissipation theorem
60
2.3.4
Ohmic vs. ballistic regimes
66
2.4
Chemical, electrochemical and electrostatic potentials
68
2.5
Drift-diffusion equations
72
2.5.1
Diffusion coefficient of an ideal electron gas in the
non-degenerate limit
73
2.5.2
Generalization to spin-dependent transport
75
2.6
Distribution functions
77
2.7
Boltzmann equation
79
2.7.1
Approach to local equilibrium
82
2.8
Entropy, loss of information, and macroscopic irreversibility
83
2.8.1
The classical statistical entropy
85
2.8.2
Quantum statistical entropy
86
2.8.3
Information content of the N- and one-particle
statistical operators
89
2.8.4
Entropy of open quantum systems
90
2.8.5
Loss of information in the
Kubo
formalism
91
2.8.6
Loss of information with stochastic Hamiltonians
92
2.8.7
Entropy associated with the measurement of currents
93
Summary and open questions
94
Exercises
95
3 Landauer
approach
101
3.1
Formulation of the problem
102
3.2
Local resistivity dipoles and the "field response"
113
3.3
Conduction from transmission
115
3.3.1
Scattering boundary conditions
115
3.3.2
Transmission and reflection probabilities
119
3.3.3
Total current
123
3.3.4
Two-probe conductance
128
3.4
The
Lippmann—Schwinger
equation
132
3.4.1
Time-dependent
Lippmann—Schwinger
equation
132
3.4.2
Time-independent
Lippmann—Schwinger
equation
140
3.5
Green's functions and self-energy
145
Contents ix
3.5.1 Relation
to scattering theory
154
3.6
The <S matrix
159
3.6.1
Relation between the total Green's function and
the
S
matrix
162
3.7
The transfer matrix
167
3.7.1
Coherent scattering of two resistors in series
169
3.7.2
Incoherent scattering of two resistors in series
171
3.7.3
Relation between the conductance and the transfer
matrix
173
3.7.4
Localization, ohmic and ballistic regimes
174
3.8
Four-probe conductance in the non-invasive limit
178
3.8.1
Single-channel case
179
3.8.2
Geometrical "dilution"
181
3.8.3
Multi-channel case
182
3.9
Multi-probe conductance in the invasive limit
185
3.9.1
Floating probes and dephasing
187
3.10
Generalization to spin-dependent transport
190
3.10.1
Spin-dependent transmission functions
194
3.10.2
Multi-probe conductance in the presence of a
magnetic field
195
3.10.3
Local resistivity spin dipoles and dynamical effects
196
3.11
The use of Density-Functional Theory in the
Landauer
approach
198
Summary and open questions
202
Exercises
203
Non-equilibrium Green's function formalism
209
4.1
Formulation of the problem
211
4.1.1
Contour ordering
215
4.2
Equilibrium Green's functions
217
4.2.1
Time-ordered Green's functions
218
4.2.2
Dyson's equation for interacting particles
221
4.2.3
More Green's functions
223
4.2.4
The spectral function
225
4.3
Contour-ordered Green's functions
231
4.3.1
Equations of motion for non-equilibrium Green's
functions
233
4.4
Application to steady-state transport
236
4.5
Coulomb blockade
244
4.6
Quantum kinetic equations
250
Contents
Summary and open questions
255
Exercises
257
Noise
258
5.1
The moments of the current
261
5.2
Shot noise
263
5.2.1
The classical
(Poisson)
limit
264
5.2.2
Quantum theory of shot noise
266
5.3
Counting statistics
274
5.4
Thermal noise
275
Summary and open questions
277
Exercises
277
Electron-ion interaction
280
6.1
The many-body electron-ion Hamiltonian
281
6.1.1
The adiabatic approximation for a current-carrying
system
282
6.1.2
The phonon subsystem
284
6.1.3
Electron-phonon coupling in the presence of current
288
6.2
Inelastic current
290
6.2.1
Inelastic current from standard perturbation theory
291
6.2.2
Inelastic current from the NEGF
296
6.3
Local ionic heating
312
6.3.1
Lattice heat conduction
319
6.4
Thermopower
323
6.5
Current-induced forces
328
6.5.1
Elastic vs. inelastic contribution to
electro-migration328
6.5.2
One force, different definitions
330
6.5.3
Local resistivity dipoles and the force sign
333
6.5.4
Forces at equilibrium
333
6.5.5
Forces out of equilibrium
335
6.5.6
Are current-induced forces conservative?
340
6.6
Local ionic heating vs. current-induced forces
343
Summary and open questions
344
Exercises
344
The micro-canonical picture of transport
346
7.1
Formulation of the problem
347
7.1.1
Transport from a finite-system point of view
347
7.1.2
Initial conditions and dynamics
349
7.2
Electrical current theorems within dynamical DFTs
351
7.2.1
Closed and finite quantum systems in a pure state
351
Contents
Xl
7.2.2
Closed quantum systems in a pure state with
arbitrary boundary conditions
353
7.2.3
Current in open quantum systems
354
7.2.4
Closure of the BBGKY hierarchy
356
7.2.5
Functional approximations and loss of information
357
7.3
Transient dynamics
358
7.4
Properties of quasi-steady states
360
7.4.1
Variational definition of quasi-steady states
360
7.4.2
Dependence of quasi-steady states on initial condi¬
tions
364
7.5
A non-equilibrium entropy principle
365
7.6
Approach to steady state in nanoscale systems
369
7.7
Definition of conductance in the micro-canonical picture
374
Summary and open questions
375
8
Hydrodynamics of the electron liquid
376
8.1
The Madelung equations for a single particle
378
8.2
Hydrodynamic form of the
Schrödinger
equation
380
8.2.1
Quantum
Navier—
Stokes equations
382
8.3
Conductance quantization from hydrodynamics
388
8.4
Viscosity from Time-Dependent Current Density-Functional
Theory
391
8.4.1
Functional approximation, loss
ofinformation,
and
dissipative dynamics
394
8.4.2
Effect of viscosity on resistance
395
8.5
Turbulent transport
397
8.6
Local electron heating
403
8.6.1
Electron heat conduction
405
8.6.2
Hydrodynamics of heat transfer
406
8.6.3
Effect of local electron heating on ionic heating
410
Summary and open questions
412
Exercises
413
Appendices
Appendix A A primer on second quantization
415
Appendix
В
The quantum BBGKY hierarchy
420
Appendix
С
The
Lindblad
equation
423
C.I The
Lindblad
theorem
424
C.2 Derivation of the
Lindblad
equation
426
C.3 Steadv-state solutions
430
xii
Contents
Appendix
D
Ground-state Density-Functional Theory
431
D.I The Hohenberg-Kohn theorem
431
D.2 The Kohn-Sham equations
432
D.3 Generalization to grand-canonical equilibrium
434
D.4 The local density approximation and beyond
434
Appendix
E
Time-Dependent DFT
436
E.I The
Runge—
Gross theorem
436
E.2 The time-dependent Kohn—Sham equations
437
E.3 The adiabatic local density approximation
437
Appendix
F
Time-Dependent Current DFT
439
F.I The current density as the main variable
439
F.2 The exchange-correlation electric field
440
F.3 Approximate formulas for the viscosity
442
Appendix
G
Stochastic Time-Dependent Current DFT
444
G.I The stochastic
Schrödinger
equation
444
G.2 Derivation of the quantum master equation
446
G.3 The theorem of Stochastic TD-CDFT
449
Appendix
H
Inelastic corrections to current and shot noise
451
Appendix I Hydrodynamic form of the
Schrödinger equation454
Appendix
J
Equation of motion for the stress tensor
458
Appendix
К
Cut-off of the viscosity divergence
461
Appendix
L
Bernoulli's equation
463
References
464
Index
470
in recent years there has been a huge increase
in the research and development of nanoscaie
science and technology, with electrical transport
playing a central role. This graduate textbook
provides an in-depth description of the transport
phenomena relevantto systems of nanoscaie
dimensions.
in this textbook the different theoretical
approaches are critically discussed, with
emphasis on their basic assumptions and
approximations. The book also covers
information content in the measurement
of currents, the role of initial conditions in
establishing a steady state, and the modem
use of density-functional theory. Topics are
introduced by simple physical arguments, with
particular attention to the non-equilibrium
statistical nature of electrical conduction, and
followed by a detailed formal derivation. This
textbook is ideal for graduate students in physics,
chemistry, and electrical engineering. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Di Ventra, Massimiliano |
| author_GND | (DE-588)139775382 |
| author_facet | Di Ventra, Massimiliano |
| author_role | aut |
| author_sort | Di Ventra, Massimiliano |
| author_variant | v m d vm vmd |
| building | Verbundindex |
| bvnumber | BV035079551 |
| callnumber-first | Q - Science |
| callnumber-label | QC176 |
| callnumber-raw | QC176.8.N35 |
| callnumber-search | QC176.8.N35 |
| callnumber-sort | QC 3176.8 N35 |
| callnumber-subject | QC - Physics |
| classification_rvk | UP 3150 |
| ctrlnum | (OCoLC)227031860 (DE-599)BVBBV035079551 |
| dewey-full | 620.5 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.5 |
| dewey-search | 620.5 |
| dewey-sort | 3620.5 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV035079551 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:06:37Z |
| indexdate | 2024-07-09T21:21:43Z |
| institution | BVB |
| isbn | 9780521896344 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016747816 |
| oclc_num | 227031860 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-20 DE-19 DE-BY-UBM DE-12 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-20 DE-19 DE-BY-UBM DE-12 |
| physical | XVI, 476 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Di Ventra, Massimiliano Verfasser (DE-588)139775382 aut Electrical transport in nanoscale systems Massimiliano Di Ventra 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2008 XVI, 476 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Electric conductivity Electron transport Nanoelectromechanical systems Nanoelectronics Nanostrukturiertes Material (DE-588)4342626-8 gnd rswk-swf Transportprozess (DE-588)4185932-7 gnd rswk-swf Transportprozess (DE-588)4185932-7 s Nanostrukturiertes Material (DE-588)4342626-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016747816&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016747816&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Di Ventra, Massimiliano Electrical transport in nanoscale systems Electric conductivity Electron transport Nanoelectromechanical systems Nanoelectronics Nanostrukturiertes Material (DE-588)4342626-8 gnd Transportprozess (DE-588)4185932-7 gnd |
| subject_GND | (DE-588)4342626-8 (DE-588)4185932-7 |
| title | Electrical transport in nanoscale systems |
| title_auth | Electrical transport in nanoscale systems |
| title_exact_search | Electrical transport in nanoscale systems |
| title_exact_search_txtP | Electrical transport in nanoscale systems |
| title_full | Electrical transport in nanoscale systems Massimiliano Di Ventra |
| title_fullStr | Electrical transport in nanoscale systems Massimiliano Di Ventra |
| title_full_unstemmed | Electrical transport in nanoscale systems Massimiliano Di Ventra |
| title_short | Electrical transport in nanoscale systems |
| title_sort | electrical transport in nanoscale systems |
| topic | Electric conductivity Electron transport Nanoelectromechanical systems Nanoelectronics Nanostrukturiertes Material (DE-588)4342626-8 gnd Transportprozess (DE-588)4185932-7 gnd |
| topic_facet | Electric conductivity Electron transport Nanoelectromechanical systems Nanoelectronics Nanostrukturiertes Material Transportprozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016747816&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016747816&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT diventramassimiliano electricaltransportinnanoscalesystems |