Structure and lattice dynamics of GaN and AlN: ab-initio investigations of strained polytypes and superlattices [Elektronische Ressource] / von Jan-Martin Wagner

Sujets

• Physik

Informations

• Publié par: friedrich-schiller-universitat_jena
• Publié le: 01 janvier 2008
• Nombre de lectures: 15
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Structure and Lattice Dynamics of GaN and AlN:
Ab-Initio Investigations of Strained Polytypes
and Superlattices
D i s s e r t a t i o n
zur Erlangung des akademischen Grades
doctor rerum naturalium (Dr. rer. nat.)
vorgelegt dem Rat der Physikalisch-Astronomischen Fakultät
der Friedrich-Schiller-Universität Jena
von Dipl.-Phys. Jan-Martin Wagner
geboren am 24. Juli 1967 in BerlinGutachter:
1. Prof. Dr. F. Bechstedt, Jena
2. Prof. Dr. D. Strauch, Regensburg
3. Priv.-Doz. Dr. habil. A. Hoffmann, Berlin
Tag der letzten Rigorosumsprüfung: 16. Juli 2004
Tag der öffentlichen Verteidigung: 14. Oktober 2004Rien n’est plus dangereux qu’une idée,
quand on n’a qu’une idée.
(Émile Chartier, dit Alain)
Woher
soll ich wissen,
was ich denke,
bevor ich höre,
was ich sage?
(N. N.)Contents
1 Introduction and Outline 1
2 Fundamentals and Objectives 5
2.1 Preliminaries and Basic Approximations . . . . . . . . . . . . . . . . . . . . . 5
2.2 Density-Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Hohenberg–Kohn Theorem and Variational Principle . . . . . . . . . . 9
2.2.2 Kohn–Sham Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.3 Local-Density Approximation . . . . . . . . . . . . . . . . . . . . . . 12
2.2.4 Frozen-Core and Nonlinear Core Correction . . . . . . 13
2.2.5 Pseudopotentials and Plane-Wave Expansion . . . . . . . . . . . . . . 14
2.2.6 Total-Energy Calculation and Brillouin-Zone Summation . . . . . . . . 16
2.3 Lattice Dynamics in the Harmonic Approximation . . . . . . . . . . . . . . . . 17
2.3.1 Potential Energy Expansion and Equation of Motion . . . . . . . . . . 17
2.3.2 Dynamical Matrix and Phonons . . . . . . . . . . . . . . . . . . . . . 18
2.3.3 Long-Wavelength Limit in Polar Crystals . . . . . . . . . . . . . . . . 20
2.3.3.1 Determination of the Dynamical Matrix . . . . . . . . . . . 20
2.3.3.2 LO–TO Splitting and Static Dielectric Constant . . . . . . . 22
2.4 Density-Functional Perturbation Theory . . . . . . . . . . . . . . . . . . . . . 24
2.5 Frozen-Phonon Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6 Modeling of Strains and Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.6.1 Strained Bulk Crystal Structures . . . . . . . . . . . . . . . . . . . . . 27
2.6.2 Pyroelectricity, Piezoelectricity and Macroscopic Elasticity . . . . . . . 28
2.6.2.1 Wurtzite Symmetry . . . . . . . . . . . . . . . . . . . . . . 29
2.6.2.2 Cubic . . . . . . . . . . . . . . . . . . . . . . . . 31
2.6.3 Elastic Energy of a Strained Hexagonal Superlattice . . . . . . . . . . 33
2.7 Strain- and Stress-Related Phonon Frequency Shifts . . . . . . . . . . . . . . . 34
3 Ground-State Determination and Properties of Unstrained Polytypes 35
3.1 Relaxation Procedure for the 3C and 2H Structures . . . . . . . . . . . . . . . 35
3.2 Convergency Tests and Discussion of Results . . . . . . . . . . . . . . . . . . 37
3.2.1 Structural Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.1.1 Zinc-Blende Phase . . . . . . . . . . . . . . . . . . . . . . . 37
3.2.1.2 Wurtzite Phase . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.1.3 Relative Phase Stability . . . . . . . . . . . . . . . . . . . . 40
3.2.2 Electronic Dielectric Constant and Born Effective Charge . . . . . . . 41
3.2.3 Phonons and Static Dielectric Constant . . . . . . . . . . . . . . . . . 42
3.2.3.1 Zinc-Blende Phase . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.3.2 Wurtzite Phase . . . . . . . . . . . . . . . . . . . . . . . . . 43
iiContents iii
4 Influence of Strain on Bulk GaN and AlN 47
4.1 Relaxation Procedure for the Strained Structures . . . . . . . . . . . . . . . . . 47
4.2 Structural Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.1 Hydrostatic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2.2 Uniaxial and Biaxial Strain . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Elastic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.1 Zinc-Blende Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.2 Wurtzite Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.4 Dielectric Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4.1 Hydrostatic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.4.2 Uni- and Biaxial Strain . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.5 Zone-Center Phonon Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5.1 Hydrostatic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5.2 Uni- and Biaxial Strain . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.6 Phonon Mode Coefficients and Deformation Potentials . . . . . . . . . . . . . 69
4.6.1 Hydrostatic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.6.2 Uni- and Biaxial Strain . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5 Short-Period GaN/AlN Superlattices 75
5.1 Structural Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1.1 Symmetry and Relaxation . . . . . . . . . . . . . . . . . . . . . . . . 75
5.1.2 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2 Phonon Modes of Short-Period SLs . . . . . . . . . . . . . . . . . . . . . . . 78
5.2.1 General Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.2.2 Phonons of 1 1 Superlattices . . . . . . . . . . . . . . . . . . . . . . 80
5.2.3 Folded Acoustic Phonons . . . . . . . . . . . . . . . . . . . . . . . . 84
5.2.4 TO Phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2.5 LO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6 Summary and Outlook 91
Bibliography 95
Publications 103
Zusammenfassung 105iv ContentsChapter 1
Introduction and Outline
Modern semiconductor technology has lead to a variety of beneficial and useful devices play-
ing an important role in every-day life. For most applications, silicon is still the predominant
material. However, since the demands regarding functionality are ever growing, different mate-
rials are introduced in areas where silicon is ill-suited. These are, e. g., optical communication
as well as high-frequency, high-power, high-voltage, and high-temperature electronics. Here,
substances like gallium arsenide (GaAs) or silicon carbide (SiC) are used [Mor94].
A specific goal of the last decade was to obtain a high-brightness blue light–emitting diode
(LED) and its further development towards a laser diode (LD). For these devices, there are
many possible applications in solid-state lighting and as versatile tools, e. g., in medicine, for
ordinary and effect lighting, traffic lights etc. Most important, since standard compact disc
and DVD players are based on long-wavelength infrared LDs, optical discs with much higher
storage capacity would be possible if blue-light emitting LDs would be used to read the data
tracks (which, in fact, will appear on the market in the near future [CSN04]). Due to the shorter
wavelength, the blue light can be focused on a smaller area, allowing a higher storage density.
SiC-based blue emitters, existing already for many years, have an output power far too low
even to be used in a large-area full-colour display consisting of LEDs. This is because SiC
is an indirect-gap material and therefore ill-suited for highly effective light emission; its blue
luminescence comes from donor-acceptor pair recombinations as well as free and impurity-
bound excitons.
First attempts to achieve blue luminescence from p–n junctions of direct-gap semiconduc-
tors were based on the wide-gap II–VI compounds zinc sulfide (ZnS) and zinc selenide (ZnSe)
[Rob75, Yam77]. However, the lifetime of high-brightness ZnSe-based LEDs and LDs [Haa91]
was severely limited by degradation, even if grown on homoepitaxial substrates [Bon96]. There-
fore, as an alternative material system, among the III–V semiconductors the nitride compounds
were taken into consideration [Nak97]. Due to its room-temperature band-gap energy of about
3.4 eV [Mon74], gallium nitride (GaN) is well-suited for light emission in the blue spectral
region. Moreover, by alloying with aluminium and/or indium, an energetical range even wider
than the whole visible spectrum can be covered, since InN has a (low-temperature) band gap of
about 0.7 eV [Dav02], and AlN of about 6.1 eV [Li03], respectively. In contrast to other III–V
compounds crystallizing in cubic zinc-blende (3C) structure, under ambient conditions, group-
III nitrides crystallize in the hexagonal wurtzite (2H) structure. In epitaxial growth, however,
also thin films of the metastable cubic phase can be obtained. Cubic AlN (c-AlN) is an indirect-
12 Chapter 1. Introduction and Outline
gap material with a minimum gap of about 5.3 eV [Tho01]. The room-temperature band gap of
c-GaN (also known as -GaN; -GaN refers to the wurtzite polytype) is about 3.2 eV [Ram94],
i. e., it is slightly lower than that of the hexagonal polytype. It can be expected that the same
holds for the band gap of c-InN [Bec02a].
Due to the wurtzite structure and the high electronegativity of nitrogen, the 2H polytypes
of the group-III nitrides are pyroelectric.