Verfügbarkeit: Quantum transport in submicron devices

Quantum transport in submicron devices: a theoretical introduction

Gespeichert in:

Bibliographische Detailangaben
Beteiligte Personen:	Magnus, Wim 1954- (VerfasserIn), Schoenmaker, Wim 1954- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 2002
Schriftenreihe:	Springer series in solid state sciences 137
Schlagwörter:	Física do estado sólido Electron transport Holes (Electron deficiencies) Elektronischer Transport Nanostruktur
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009792842&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XVII, 270 S. Ill., graph. Darst.
ISBN:	3540433961

Internformat

MARC


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245	1	0	\|a Quantum transport in submicron devices \|b a theoretical introduction \|c Wim Magnus ; Wim Schoenmaker
264		1	\|a Berlin [u.a.] \|b Springer \|c 2002
300			\|a XVII, 270 S. \|b Ill., graph. Darst.
336			\|b txt \|2 rdacontent
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490	1		\|a Springer series in solid state sciences \|v 137
490	0		\|a Physics and astronomy online library
650		7	\|a Física do estado sólido \|2 larpcal
650		4	\|a Electron transport
650		4	\|a Holes (Electron deficiencies)
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650	0	7	\|a Nanostruktur \|0 (DE-588)4204530-7 \|2 gnd \|9 rswk-swf
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700	1		\|a Schoenmaker, Wim \|d 1954- \|e Verfasser \|0 (DE-588)123650283 \|4 aut
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Datensatz im Suchindex

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adam_text	CONTENTS PART I. GENERAL FORMALISM 1. THE MANY FACES OF TRANSPORT ............................. 3 2. CLASSICAL MECHANICS ....................................... 7 2.1 GENERALIZED COORDINATES AND CONSTRAINTS . . . . . . . . . . . . . . . . . . 7 2.2 DALEMBERTS PRINCIPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 REDUCTION OF DYNAMICS TO STATICS. . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 THE LAGRANGIAN AND EULERLAGRANGE EQUATIONS . . . . . . . . . . . . 11 2.5 MAUPERTUIS AND MASERATI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.6 FROM LAGRANGIAN TO HAMILTONIAN . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.7 PHASE SPACE AND CONFIGURATION SPACE . . . . . . . . . . . . . . . . . . . . . 14 2.8 THE LIOUVILLE EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.9 THE MICRO-CANONICAL ENSEMBLE. . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.10 THE BOLTZMANN EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.11 DRUDES MODEL OF CARRIER TRANSPORT . . . . . . . . . . . . . . . . . . . . . . . 21 2.12 CURRENTS IN SEMICONDUCTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3. MATHEMATICAL INTERLUDE ................................... 27 3.1 GENERALIZED FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1.1 THE STEP FUNCTION * ( X ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1.2 THE DELTA FUNCTION * ( X ) . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.1.3 SOME USEFUL RELATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2 FUNCTIONS OF FUNCTIONS * FUNCTIONALS . . . . . . . . . . . . . . . . . . . . . . 29 3.3 FUNCTIONAL INTEGRATION * PATH INTEGRALS . . . . . . . . . . . . . . . . . . . . 30 3.4 VECTOR IDENTITIES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.5 A FEW THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4. QUANTUM MECHANICS ...................................... 35 4.1 RULES OF THE GAME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.1.1 STATES IN FOCK SPACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.1.2 THE SUPERPOSITION PRINCIPLE . . . . . . . . . . . . . . . . . . . . . . . 36 4.1.3 SCALAR PRODUCTS AND PROBABILITY AMPLITUDES . . . . . . . . . 36 4.1.4 OBSERVABLE QUANTITIES AND OPERATORS . . . . . . . . . . . . . . . 36 XIV CONTENTS 4.1.5 MEASUREMENTS AND EXPECTATION VALUES . . . . . . . . . . . . . . 37 4.1.6 DYNAMICS * THE SCHR¨ ODINGER EQUATION . . . . . . . . . . . . . . 38 4.2 THE BOOK OF RECIPES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.2.1 FIRST RECIPE * CORRESPONDENCE PRINCIPLE . . . . . . . . . . . . 40 4.2.2 SECOND RECIPE * CANONICAL COMMUTATION RULES . . . . . . 40 4.2.3 THIRD RECIPE * USE YOUR IMAGINATION . . . . . . . . . . . . . . . 40 4.2.4 FOURTH RECIPE * CHOOSE AN APPROPRIATE BASIS. . . . . . . . 40 4.3 THE POSITION AND MOMENTUM REPRESENTATION . . . . . . . . . . . . . . 43 4.3.1 POSITION REPRESENTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.3.2 MOMENTUM REPRESENTATION . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3.3 STATIONARY SCHR¨ ODINGER EQUATION . . . . . . . . . . . . . . . . . . . 44 4.4 COMMUTING OPERATORS,GOOD QUANTUM NUMBERS . . . . . . . . . . 44 4.5 PATH INTEGRALS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5. SINGLE-PARTICLE QUANTUM MECHANICS ...................... 53 5.1 CHARGE DENSITY,CURRENT AND SINGLE PARTICLE WAVE FUNCTIONS . 53 5.2 CONSTANT POTENTIAL,ENERGY BANDS AND ENERGY SUBBANDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.3 POTENTIAL WELLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.4 POTENTIAL BARRIERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.5 ELECTROMAGNETIC FIELDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.6 SPIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6. SECOND QUANTIZATION ...................................... 79 6.1 IDENTICAL PARTICLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 6.2 FIELD OPERATORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 6.2.1 DEFINITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 6.2.2 FIELD OPERATORS,WAVE FUNCTIONS AND TOPOLOGY . . . . . . 84 6.2.3 FIELD OPERATORS IN FOCK SPACE . . . . . . . . . . . . . . . . . . . . . 85 6.2.4 THE CONNECTION TO FIRST QUANTIZATION. . . . . . . . . . . . . . . 88 6.2.5 HOW TO CONSTRUCT THE OPERATORS . . . . . . . . . . . . . . . . . . . 90 6.3 MORE CREATION AND ANNIHILATION OPERATORS . . . . . . . . . . . . . . . . 94 6.3.1 THE ELECTRON HAMILTONIAN . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.3.2 THE NUMBER OPERATOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.3.3 CHARGE AND CURRENT DENSITY . . . . . . . . . . . . . . . . . . . . . . . 96 6.3.4 MANY-PARTICLE GROUND STATE OF A NON-INTERACTING SYSTEM . . . . . . . . . . . . . . . . . . . . . . . 96 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 EXERCISE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 CONTENTS XV 7. EQUILIBRIUM STATISTICAL MECHANICS ......................... 99 7.1 THE ENTROPY PRINCIPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 7.2 THE CANONICAL AND GRAND-CANONICAL ENSEMBLES . . . . . . . . . . . . 101 7.3 QUANTUM STATISTICAL PHYSICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 7.4 QUANTUM ENSEMBLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 7.5 PHOTONS AND PHONONS * SOME PARTITION FUNCTIONS . . . . . . . . . . 107 7.6 PREVIEW OF NON-EQUILIBRIUM THEORY . . . . . . . . . . . . . . . . . . . . . . . 111 EXERCISES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 8. NON-EQUILIBRIUM STATISTICAL MECHANICS .................... 115 8.1 DEFINITION OF THE PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 8.2 HYDRODYNAMICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 8.2.1 A FIRST GLANCE AT ENTROPY . . . . . . . . . . . . . . . . . . . . . . . . . 119 8.2.2 DERIVING FOURIERS LAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 8.2.3 A SECOND GLANCE AT ENTROPY . . . . . . . . . . . . . . . . . . . . . . . 126 8.3 MATSUBARA FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 EXERCISE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 9. WIGNER DISTRIBUTION FUNCTIONS ............................ 131 10. BALANCE EQUATIONS ........................................ 137 10.1 BASIC ASSUMPTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 10.2 CHARGE AND CURRENT DENSITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 10.3 TOTAL HAMILTONIAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 10.4 BASIC EQUATIONS OF MOTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 10.5 CONTINUITY EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 10.6 ENERGY BALANCE EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 10.7 LINEAR AND ANGULAR MOMENTUM BALANCE EQUATION . . . . . . . . . . 145 10.8 CALCULATION OF THE DC CURRENT . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 10.8.1 GEDANKENEXPERIMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 10.8.2 EQUILIBRIUM CURRENTS AND BROKEN TIME REVERSAL SYMMETRY . . . . . . . . . . . . . . 147 10.8.3 PERTURBATIVE SOLUTION SCHEME . . . . . . . . . . . . . . . . . . . . . . 150 EXERCISE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 PART II. APPLICATIONS 11. VELOCITYFIELD CHARACTERISTICS OF A SILICON MOSFET ...... 157 11.1 MOMENTUM AND ENERGY BALANCE EQUATIONS FOR A MOSFET CHANNEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 11.2 CALCULATION OF THE ELEMENTARY GREEN FUNCTIONS. . . . . . . . . . . . . 162 XVI CONTENTS 12. GATE LEAKAGE CURRENTS ................................... 169 12.1 SUBBAND STATES AND RESONANCES . . . . . . . . . . . . . . . . . . . . . . . . . . 170 12.2 TUNNELING GATE CURRENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 12.3 RESULTS OF THE GATE-LEAKAGE CURRENT CALCULATIONS . . . . . . . . . . 184 13. QUANTUM TRANSPORT IN VERTICAL DEVICES ................... 189 13.1 QUANTUM TRANSPORT IN A CYLINDRICAL MOSFET . . . . . . . . . . . . . 190 13.2 THE HAMILTONIAN OF THE SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . 191 13.3 THE LIOUVILLE EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 13.4 ELECTRON SCATTERING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 13.5 THE NUMERICAL MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 13.6 NUMERICAL RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 14. AN EXACTLY SOLVABLE ELECTRONPHONON SYSTEM ............ 209 14.1 THE TIME DEPENDENT DRIFT VELOCITY FOR THE CL MODEL . . . . . . . 210 14.2 SOLUTION OF THE TRANSPORT EQUATION . . . . . . . . . . . . . . . . . . . . . . 213 14.3 HOW TO INVERT LAPLACE TRANSFORMS . . . . . . . . . . . . . . . . . . . . . . . . 215 14.4 IRREVERSIBILITY AND THE OHMIC CASE . . . . . . . . . . . . . . . . . . . . . . . . 216 14.5 ENTROPY PRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 15. OPEN VERSUS CLOSED SYSTEMS ............................. 221 16. CONDUCTANCE QUANTIZATION ................................ 225 16.1 CIRCUIT TOPOLOGY,NON-CONSERVATIVE FIELDS AND DISSIPATIONLESS TRANSPORT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 16.2 QUANTUM RINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 16.3 HAMILTONIAN AND CURRENT RESPONSE . . . . . . . . . . . . . . . . . . . . . . . 235 16.4 OPEN VERSUS CLOSED CIRCUITS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 16.5 ENERGY DISSIPATION VERSUS CURRENT LIMITATION . . . . . . . . . . . . . . 241 16.6 FLUX QUANTIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 16.7 LOCALIZATION OF THE ELECTRIC FIELD . . . . . . . . . . . . . . . . . . . . . . . . . 243 16.8 A QUANTUM LENZ LAW? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 17. TRANSPORT IN QUANTUM WIRES ............................. 245 17.1 BALANCE EQUATIONS FOR AN IMPERFECT QUANTUM WIRE . . . . . . . . . 245 17.2 CURRENT*VOLTAGE CHARACTERISTICS AND LOCAL ENERGY DISSIPATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 18. FUTURE WORK .............................................. 251 18.1 CONSTRUCTING NON-EQUILIBRIUM ENSEMBLES . . . . . . . . . . . . . . . . . . 251 18.1.1 COVARIANCE IN CLASSICAL PHYSICS . . . . . . . . . . . . . . . . . . . . . 253 18.1.2 CANONICAL QUANTIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 18.1.3 PATH-INTEGRAL QUANTIZATION . . . . . . . . . . . . . . . . . . . . . . . . 255 CONTENTS XVII 18.1.4 GUESSING A DENSITY FUNCTION . . . . . . . . . . . . . . . . . . . . . . . 258 18.2 QUANTUM CIRCUIT THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 REFERENCES .................................................... 261 INDEX ......................................................... 265
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author	Magnus, Wim 1954- Schoenmaker, Wim 1954-
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id	DE-604.BV014279640
illustrated	Illustrated
indexdate	2024-12-20T11:02:28Z
institution	BVB
isbn	3540433961
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-009792842
oclc_num	49493469
open_access_boolean
owner	DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-634 DE-83 DE-11
owner_facet	DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-634 DE-83 DE-11
physical	XVII, 270 S. Ill., graph. Darst.
publishDate	2002
publishDateSearch	2002
publishDateSort	2002
publisher	Springer
record_format	marc
series	Springer series in solid state sciences
series2	Springer series in solid state sciences Physics and astronomy online library
spellingShingle	Magnus, Wim 1954- Schoenmaker, Wim 1954- Quantum transport in submicron devices a theoretical introduction Springer series in solid state sciences Física do estado sólido larpcal Electron transport Holes (Electron deficiencies) Elektronischer Transport (DE-588)4210733-7 gnd Nanostruktur (DE-588)4204530-7 gnd
subject_GND	(DE-588)4210733-7 (DE-588)4204530-7
title	Quantum transport in submicron devices a theoretical introduction
title_auth	Quantum transport in submicron devices a theoretical introduction
title_exact_search	Quantum transport in submicron devices a theoretical introduction
title_full	Quantum transport in submicron devices a theoretical introduction Wim Magnus ; Wim Schoenmaker
title_fullStr	Quantum transport in submicron devices a theoretical introduction Wim Magnus ; Wim Schoenmaker
title_full_unstemmed	Quantum transport in submicron devices a theoretical introduction Wim Magnus ; Wim Schoenmaker
title_short	Quantum transport in submicron devices
title_sort	quantum transport in submicron devices a theoretical introduction
title_sub	a theoretical introduction
topic	Física do estado sólido larpcal Electron transport Holes (Electron deficiencies) Elektronischer Transport (DE-588)4210733-7 gnd Nanostruktur (DE-588)4204530-7 gnd
topic_facet	Física do estado sólido Electron transport Holes (Electron deficiencies) Elektronischer Transport Nanostruktur
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009792842&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000016582
work_keys_str_mv	AT magnuswim quantumtransportinsubmicrondevicesatheoreticalintroduction AT schoenmakerwim quantumtransportinsubmicrondevicesatheoreticalintroduction

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