Exciting imperfection [Elektronische Ressource] : real-structure effects in magnesium-, cadmium-, and zinc-oxide / von André Schleife

André Schleife

Sujets

• Physik

Informations

• Publié par: friedrich-schiller-universitat_jena
• Publié le: 01 janvier 2010
• Nombre de lectures: 22
• Langue: Deutsch
• Poids de l'ouvrage: 12 Mo

Extrait

Exciting Imperfection
Real-structure effectsin
magnesium-, cadmium-,and zinc-oxide
DISSERTATION
zur ErlangungdesakademischenGrades
doctor rerum naturalium (Dr. rer. nat.)
FRIEDRICH-SCHILLER-UNIVERSITÄT JENA
vorgelegt dem Rat der Physikalisch-AstronomischenFakultät
der Friedrich-Schiller-Universität Jena
von Dipl.-Phys.André Schleife
geboren am 04.12.1981 in MeeraneGutachter:
1. Prof. Dr. sc. nat.Friedhelm Bechstedt, Friedrich-Schiller-Universität Jena
2. Prof. Dr. rer. nat. Wolf Gero Schmidt, Universität Paderborn
3. Prof. Dr. Walter R. L. Lambrecht, Case Western Reserve University, Cleveland
Tag der Disputation: 1.Juli 2010Für meine Familie,
Für Oma Ruth.
Für Yvonne.
We’ve stuck to our own beliefs,
we haven’t cheated anyone,
and we’ve done what we wanted.
Lars UlrichContents
1 Introduction 1
2 Fundamentals 4
2.1 Settingthe stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 Interactingelectrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.3 Quantum-fieldtheoretical description . . . . . . . . . . . . . . . . . . . 6
2.2 Groundstate: Density functional theory . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Hohenberg-Kohntheorem I . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Hohenberg-Kohntheorem II . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.3 Kohn-Shamequations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.4 Exchangeand correlation . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.5 Non-collinearspins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 One-particleexcitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Green’sfunction and equation of motion . . . . . . . . . . . . . . . . . . 15
2.3.2 The electronicself-energy . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Two-particle excitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.1 Bethe-Salpeterequation . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.2 Excitonic Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4.3 Macroscopicdielectric function . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.4 Screeningin heavily doped materials . . . . . . . . . . . . . . . . . . . . 21
2.4.5 SemiconductorBloch equations . . . . . . . . . . . . . . . . . . . . . . . 23
2.5 Alloystatistics and thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5.1 Cluster expansion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5.2 Generalizedquasi-chemical approximation . . . . . . . . . . . . . . . . . 26
2.5.3 Strict-regularsolution and microscopicdecomposition limit . . . . . . . 27
3 Practical issues 29
3.1 Electronicproperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.1 Hybrid functional and quasiparticle corrections . . . . . . . . . . . . . . 29
3.1.2 Mappingto an affordable approach . . . . . . . . . . . . . . . . . . . . . 30
3.1.3 Inclusionof spin-orbit coupling . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Optical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1 Adapted sampling of the Brillouinzone. . . . . . . . . . . . . . . . . . . 32
3.2.2 Inclusionof spin-orbit coupling . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.3 Screeningof the electron-holeinteraction . . . . . . . . . . . . . . . . . 33
4 Ideal MgO, ZnO, and CdO 34
4.1 One-particleexcitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.1 Band structures and densities of states . . . . . . . . . . . . . . . . . . . 35
4.1.2 Inclusionof spin-orbit coupling . . . . . . . . . . . . . . . . . . . . . . . 40
4.1.3 Application: Band alignmentat interfaces . . . . . . . . . . . . . . . . . 44
I4.2 Two-particle excitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2.1 Impact of many-body effects on the optical properties. . . . . . . . . . . 47
4.2.2 Complexfrequency-dependentdielectric function . . . . . . . . . . . . . 48
4.2.3 Excitons and spin-orbit coupling . . . . . . . . . . . . . . . . . . . . . . 53
4.2.4 Application: Electron-energyloss function . . . . . . . . . . . . . . . . . 54
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5 Latticedistortions: Strain and non-equilibriumpolymorphs 57
5.1 Uniaxial and biaxial strain in ZnO . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.1.1 Quasiparticle energiesin the proximity of the band gap . . . . . . . . . . 58
5.1.2 Excitons under the influenceof biaxial strain . . . . . . . . . . . . . . . 59
5.2 Non-equilibriumwurtzite structure: MgOand CdO . . . . . . . . . . . . . . . . 61
5.2.1 Quasiparticle energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2.2 Optical properties of the absorption edge. . . . . . . . . . . . . . . . . . 63
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6 Pseudobinary alloys: IsostructuralversusheterostructuralMgZnO and CdZnO 66
6.1 Thermodynamicproperties and lattice structure . . . . . . . . . . . . . . . . . . 66
6.1.1 Mixingfree energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.1.2 Structuralcomposition of heterostructuralalloys . . . . . . . . . . . . . 70
6.2 One-particleexcitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2.1 Quasiparticle band structures . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2.2 Densities of states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.3 Dielectricfunction of wz-Mg Zn O. . . . . . . . . . . . . . . . . . . . . . . . . 76x 1-x
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7 Apoint defect: The oxygen vacancy as F-centerin rs-MgO 78
7.1 Atomic geometries and chargestates . . . . . . . . . . . . . . . . . . . . . . . . 79
7.2 Transition energiesand absorption . . . . . . . . . . . . . . . . . . . . . . . . . 79
7.3 Exciton binding energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
8 Heavy n-doping: Wannier-Mott and Mahan excitons in wz-ZnO 82
8.1 Approachingthe problemvia a two-band model . . . . . . . . . . . . . . . . . . 83
8.1.1 Effects due to a degenerateelectrongas . . . . . . . . . . . . . . . . . . 83
8.1.2 SemiconductorBloch equations . . . . . . . . . . . . . . . . . . . . . . . 84
8.2 Ab-initio calculationsfor wz-ZnO . . . . . . . . . . . . . . . . . . . . . . . . . . 86
8.2.1 Absorption coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.2.2 Binding energiesand oscillator strengths . . . . . . . . . . . . . . . . . . 88
8.2.3 Inter-conduction-bandabsorption . . . . . . . . . . . . . . . . . . . . . . 89
8.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
9 The end... and futureprospects 91
A Appendix A-1
A.1 Cluster expansions for the wurtzite and the rocksalt crystal structure . . . . . . A-1
A.2 Parametersused in the calculations . . . . . . . . . . . . . . . . . . . . . . . . . A-2
Bibliography 93
II1 Introduction
Undaus dem Chaos sprach eine Stimme
zu mir: “Lächle und sei froh,es könnte
schlimmer kommen!” Und ich lachte und
warfroh– denn es kam schlimmer!
OttoWaalkes
Thousands of years ago, in the glowing embersof the dawning Bronzeage, alloyingthe two
metalscopperandtin wasa ground-breakingdiscoverythat started anewera. Centurieslater,
gaining an understanding of matter had becomea central goal of the philosophy of nature and
the application of this knowledge has acted as basis of the progress for mankind since then.
Historically, physics was anempirical field, continuouslyaccompaniedby efforts to achieve re-
liable predictions. In the beginning of the last century, with the advent of quantum theory, the
fundament for an atomistic description of matter was laid. It was clear from the very begin-
ning that the corresponding equations are too complex to be solved exactly for real systems.
Approximations had to be made, and, ironically, are the reason why theory and experiment
startedfromdifferentpointsofview. Availablesamplesofthematerialswerefarfromtheideal
systems that theory was able to describe. Nowadays, generations later, both disciplines have
approached each other. Enhanced experimental techniques provide crystals of high quality,
whilethetheoreticaldescriptionbenefitsfromthecontinuouslyincreasingpowerofcomputers,
which rendersthem capableof solving complicated problemswithout crudeapproximations.
Interestingly,computersarenotjustprovidingsolutionsforexistingproblems. Theirincreas-
ing capabilities triggered the evolution from the industrial towards the information age and
they evenbecamean own driving force for development, e.g., materials research. Initially, the
electronic circuits that allowed the breakthrough of the computer were largely silicon-based.
Nowadays,thenextwaveofthisdevelopmentisabouttorolldown—mobility. Mobiledevices
working with fast wireless networks enable the Internet to become an integrated part