Hadis Morkoç received his Ph.D. degree in Electrical Engineering from Cornell University. From 1978 to 1997 he was with the University of Illinois, then joined the newly established School of Engineering at the Virginia Commonwealth University in Richmond. He and his group have been responsible for a number of advancements in GaN and devices based on them. Professor Morkoç has authored several books and numerous book chapters and articles. He serves or has served as a consultant to some 20 major industrial laboratories. Professor Morkoç is, among others, a Fellow of the American Physical Society, the Material Research Society, and of the Optical Society of America.

Ümit Özgür is a research scientist in the Electrical Engineering Department at Virginia
Commonwealth University. He has received BS degrees in EE and physics from Bogazici
University, Turkey, and,in 2003, his Ph.D. degree from Duke University, where he has made many contributions to the understanding of ultrafast carrier dynamics in nitride heterostructures. Dr. Özgür has authored over 50 scientific publications and several book chapters on growth, fabrication, and characterization of wide bandgap semiconductor materials and nanostructures based on group III-nitrides and ZnO. He is a member of the Institute of Electrical and Electronics Engineers and the American Physical Society.

Zinc Oxide

Fundamentals, Materials and Device TechnologyBy Hadis Morkoç Ümit Özgür

John Wiley & Sons

Copyright © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
All right reserved.
ISBN: 978-3-527-40813-9

Chapter One

General Properties of ZnO

In this chapter, crystal structure of ZnO encompassing lattice parameters, electronic band structure, mechanical properties, including elastic constants and piezoelectric constants, lattice dynamics, and vibrational processes, thermal properties, electrical properties, and low-field and high-field carrier transport is treated.

1.1 Crystal Structure

Most of the group II–VI binary compound semiconductors crystallize in either cubic zinc blende or hexagonal wurtzite (Wz) structure where each anion is surrounded by four cations at the corners of a tetrahedron, and vice versa. This tetrahedral coordination is typical of sp covalent bonding nature, but these materials also have a substantial ionic character that tends to increase the bandgap beyond the one expected from the covalent bonding. ZnO is a II–VI compound semiconductor whose ionicity resides at the borderline between the covalent and ionic semiconductors. The crystal structures shared by ZnO are wurtzite (B4), zinc blende)(B3), and rocksalt (or Rochelle salt)) (B1) as schematically shown in Figure 1.1. B1, B3, and B4 denote the Strukturbericht) designations for the three phases. Under ambient conditions, the thermodynamically stable phase is that of wurtzite symmetry. The zinc blende ZnO structure can be stabilized only by growth on cubic substrates, and the rocksalt or Rochelle salt (NaCl) structure may be obtained at relatively high pressures, as in the case of GaN.

The wurtzite structure has a hexagonal unit cell with two lattice parameters a and c in the ratio of c/a = &radius;8/3 = 1:633 (in an ideal wurtzite structure) and belongs to the space group C⁴_6v in the Schoenflies notation and P6₃mc in the Hermann–Mauguin notation. A schematic representation of the wurtzitic ZnO structure is shown in Figure 1.2. The structure is composed of two interpenetrating hexagonal close-packed (hcp) sublattices, each of which consists of one type of atom displaced with respect to each other along the threefold c-axis by the amount of u = 3/8 = 0.375 (in an ideal wurtzite structure)in fractional coordinates. The internal parameter u is defined as the length of the bond parallel to the c-axis (anion–cation bond length or the nearest-neighbor distance) divided by the c lattice parameter. The basal plane lattice parameter (the edge length of the basal plane hexagon) is universally depicted by a; the axial lattice parameter (unit cell height), perpendicular to the basal plane, is universally described by c. Each sublattice includes four atoms per unit cell, and every atom of one kind (group II atom) is surrounded by four atoms of the other kind (group VI), or vice versa, which are coordinated at the edges of a tetrahedron. The crystallographic vectors of wurtzite are a = a(1/2, &radius;3/22, 0), b = a(1/2, -&radius;3/2, 0), and c = a(0,0, c/a). In Cartesian coordinates, the basis atoms are (0, 0, 0), (0, 0, uc), a(1/2, &radius;3/6, c/2a), and a(1/2, &radius;3/6, [u + 1/2]c/a).

In a real ZnO crystal, the wurtzite structure deviates from the ideal arrangement, by changing the c/a ratio or the u value. The experimentally observed c/a ratios are smaller than ideal, as in the case of GaN, where it has been postulated that not being so would lead to zinc blende phase. It should be pointed out that a strong correlation exists between the c/a ratio and the u parameter in that when the c/a ratio decreases, the u parameter increases in such a way that those four tetrahedral distances remain nearly constant through a distortion of tetrahedral angles due to long-range polar interactions. These two slightly different bond lengths will be equal if the following relation holds:

u = (1/3)(a²/c²) + 1/4. (1.1)

The nearest-neighbor bond lengths along the c-direction (expressed as b) and off c-axis (expressed as b₁) can be calculated as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1.2)

In addition to the nearest neighbors, there are three types of second-nearest neighbors designated as b’₁ (one along the c-direction), b’₂ (six of them), and b’₃ (three of them) with the bond lengths

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1.3)

The bond angles, α and β, are given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1.4)

The lattice parameters are commonly measured at room temperature by X-ray diffraction (XRD), which happens to be the most accurate one, using the Bragg law. In ternary compounds, the technique is also used for determining the composition; however, strain and relevant issues must be taken into consideration as the samples are in the form of epitaxial layers on foreign substrates. The accuracy of the X-ray diffraction and less than accurate knowledge of elastic parameters together allow determination of the composition to only within about 1% molar fraction. In addition to composition, the lattice parameter can be affected by free charge, impurities, stress, and temperature. Because the c/a ratio also correlates with the difference of the electronegativities of the two constituents, components with the greatest differences show largest departure from the ideal c/a ratio.

The nomenclature for various commonly used planes of hexagonal semiconductors in two- and three-dimensional versions is presented in Figures 1.3 and 1.4. The Wz ZnO lacks an inversion plane perpendicular to the c-axis; thus, surfaces have either a group II element (Zn, Cd, or Mg) polarity (referred to as Zn polarity) with a designation of (0 0 0 1) or (0 0 0 1)A plane or an O polarity with a designation of (0 0 0 1) or (0 0 0 1)B plane. The distinction between these two directions is essential due to polarization charge. Three surfaces and directions are of special importance, which are (0 0 0 1), (1 1 2 0), and (1 1 0 0) planes and the directions associated with them, <0 0 0 1>, <1 1 2 0>, and <1 1 0 0>, as shown in Figure 1.5. The (0 0 0 1), or the basal plane, is the most commonly used surface for growth. The other two are important in that they represent the primary directions employed in reflection high-energy electron diffraction (RHEED) observations in MBE growth, apart from being perpendicular to one another.

The zinc blende ZnO structure is metastable and can be stabilized only by heteroepitaxial growth on cubic substrates, such as ZnS, GaAs/ZnS, and Pt/Ti/SiO₂/Si, reflecting topological compatibility to overcome the intrinsic tendency of forming wurtzite phase. In the case of highly mismatched substrates, there is usually a certain amount of zinc blende phase of ZnO separated by crystallographic defects from the wurtzite phase. The symmetry of the zinc blende structure is given by space group F 43m in the Hermann–Mauguin notation and T²_d in the Schoenflies notation and is composed of two interpenetrating face-centered cubic (fcc) sublattices shifted along the body diagonal by one-quarter of the length of the body diagonal. There are four atoms per unit cell and every atom of one type (group II) is tetrahedrally coordinated with four atoms of other type (group VI), and vice versa.

Because of the tetrahedral coordination of wurtzite and zinc blende structures, the 4 nearest neighbors and 12 next-nearest neighbors have the same bond distance in both structures. Stick-and-ball stacking models for 2H wurtzitic and 3C zinc blende polytypes of ZnO crystals are shown in Figure 1.6. The wurtzite and zinc blende structures differ only in the bond angle of the second-nearest neighbors and, therefore, in the stacking sequence of close-packed diatomic planes. The wurtzite structure consists of triangularly arranged alternating biatomic close-packed (0 0 0 1) planes, for example, Zn and O pairs; thus, the stacking sequence of the (0 0 0 1) plane is AaBbAaBb … in the <0 0 0 1> direction, meaning a mirror image but no in-plane rotation with the bond angles. In contrast, the zinc blende structure along the [1 1 1] direction exhibits a 60° rotation and, therefore, consists of triangularly arranged atoms in the close-packed (1 1 1) planes along the <1 1 1> direction that causes a stacking order of AaBbCcAaBbCc…. The point with regard to rotation is very well illustrated in Figure 1.6b. Upper and lower case letters in the stacking sequences stand for the two different kinds of constituents.

Like other II–VI semiconductors, wurtzite ZnO can be transformed to the rocksalt (NaCl) structure at relatively modest external hydrostatic pressures. The reason for this is that the reduction of the lattice dimensions causes the interionic Coulomb interaction to favor the ionicity more over the covalent nature. The space group symmetry of the rocksalt type of structure is Fm3m in the Hermann–Mauguin notation and O⁵_h in the Schoenflies notation, and the structure is sixfold coordinated. However, the rocksalt structure cannot be stabilized by the epitaxial growth. In ZnO, the pressure-induced phase transition from the wurtzite (B4) to the rocksalt (B1) phase occurs in the range of 10 GPa associated with a large decrease in volume of about 17%. High-pressure cubic phase has been found to be metastable for long periods of time even at ambient pressure and above 100 °C. Energy-dispersive X-ray diffraction (EDXD) measurements using synchrotron radiation have shown that the hexagonal wurtzite structure of ZnO undergoes a structural phase transformation with a transition pressure p_T = 10 GPa and completed at about 15 GPa. The measured lattice-plane spacings as a function of pressure for the B1 phase are shown in Figure 1.7. Accordingly, a large fraction of the B1 phase is retained when the pressure is released indicating the metastable state of the rocksalt phase of ZnO even at zero pressure.

In contrast, using in situ X-ray diffraction, and later EDXD, this transition was reported to be reversible at room temperature. EDXD spectra recorded at pressures ranging from 0.1 MPa to 56 [+ or -] 1 GPa at room temperature with increasing and decreasing pressures show a clear wurtzite-to-rocksalt transition starting at 9.1 [+ or -] 0.2 GPa with increasing pressure. The two phases coexist over a pressure range of 9.1–9.6 GPa, as shown in Figure 1.8. The structural transition is complete at 9.6 GPa resulting in a 16.7% change in the unit cell volume. Upon decompression, it was observed that ZnO reverts to the wurtzite structure beginning at 1.9 [+ or -] 0.2 GPa, below which only a single wurtzite phase is present. Consequently, the phase hysteresis is substantial. Similar hysteresis was also reported for this transition using X-ray diffraction and Zn Mõssbauer spectroscopy. The transition pressure was measured to be 8.7 GPa for increasing pressure whereas it was 2.0 GPa for decreasing pressure.

On the theoretical side, there have been several first-principles studies of compressive parameters of dense ZnO, such as the linear combination of Gaussian-type orbitals (LCGTO), the Hartree–Fock (HF) method, the full-potential linear muffin-tin orbital (FP-LMTO) approach to density functional theory (DFT) within the local density approximation (LDA) and generalized gradient approximation (GGA), linear augmented plane wave (LAPW) LDA, HF, correlated HF perturbed ion (HF-PI) models, LCGTO-LDA and GGA methods, and the extended ionic model. A critical comparison between experimental and theoretical results can be made for ZnO as the structural and compressive parameters are measured because the dense solid adopts simple structures. These calculations have mostly been limited to the same pressure range as the experiments, and reasonable agreements are realized. Both experimental and theoretical results are summarized in Table 1.1 for comparison.

In addition to the commonly observed and calculated phase transition of ZnO from B4 to B1 at moderate pressures (maximum pressure attained in any experiment on ZnO to date is 56 GPa where the B1 phase remained stable), it has been suggested that at sufficiently high pressures ZnO would undergo a phase transformation from the sixfold-coordinated B1 (cubic NaCl) to the eightfold-coordinated B2 (cubic CsCl) structure, in analogy to the alkali halides and alkaline earth oxides. The transition pressure from B1 phase to B2 phase was predicted at p_T2 = 260 and 256 GPa by employing local density approximation and generalized gradient – corrected local density – approximation, respectively, whereas atomistic calculations based on an interatomic pair potential within the shell model approach resulted in a higher value of p_T2 = 352 GPa. However, these theoretical predictions are still awaiting experimental confirmation.

The ground-state total energy of ZnO in wurtzite, zinc blende, and rocksalt structures has been calculated as a function of the unit cell volume using first-principles periodic Hartree–Fock linear combination of atomic orbitals (LCAO) theory. The total energy data versus volume for the three phases are shown in Figure 1.9 along with the fits to the empirical functional form of the third-order Murnaghan equation, which is used to calculate the derived structural properties:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1.5)

where E₀, V₀, and B₀ are the total energy, volume per ZnO formula unit, and bulk modulus at zero pressure (P), respectively, and B’ = dB/dP is assumed to be constant.

In this calculation, although E0 represents the sum of the total energies of isolated neutral Zn and O atoms, the absolute value of the energy at the minimum of each curve was considered as a rough estimate of the equilibrium cohesive energy of the corresponding ZnO phases. The total energy (or roughly the cohesive energy per bond) in wurtzite variety was calculated to be -5.658 eV for wurtzite, -5.606 eV for zinc blende, and -5.416 eV for rocksalt phases. The density functional theory using two different approximations, namely, the local density and the generalized gradient approximations, in the exchange correlation function was also employed to calculate the total energy and electronic structure of ZnO. In these calculations, cohesive energies were obtained by subtracting the total energy per ZnO formula unit of the solid at its equilibrium lattice constant from the energy of the corresponding isolated atoms. The cohesive energies of ZnO obtained by using the LDA are -9.769, -9.754, and -9.611 eV for wurtzite, zinc blende, and rocksalt structures, respectively. The best agreement with the experimental value of -7.52 eV, which is deduced from experimental Zn heat vaporization, ZnO enthalpy of formation, and O₂ binding energy for the wurtzite phase, was achieved using the GGA technique. The GGA gives -7.692, -7.679, and -7.455 eV cohesive energies for wurtzite, zinc blende, and rocksalt phases, respectively. In these two techniques, although the calculated energy difference [increment of E]_W-ZB between wurtzite and zinc blende lattice is small (about -15 and -13 meV atom^-1 for LDA and GGA, respectively), whereas it is relatively large, ~50 meV atom^-1, for Hartree–Fock approximation, the wurtzite form is energetically favorable compared to zinc blende and rocksalt forms.

Because none of the three structures described above possesses inversion symmetry, the crystal exhibits crystallographic polarity, which indicates the direction of the bonds; that is, close-packed (1 1 1) planes in zinc blende and rocksalt (Rochelle salt) structures and corresponding (0 0 0 1) basal planes in the wurtzite structure differ from (1 1 1) and (0 0 0 1) planes, respectively. The convention is that the [0 0 0 1] axis points from the face of the O plane to the Zn plane and is the positive z-direction. In other words, when the bonds along the c-direction are from cation (Zn) to anion (O), the polarity is referred to as Zn polarity. By the same argument, when the bonds along the c-direction are from anion (O) to cation (Zn), the polarity is referred to as O polarity. Many properties of the material depend also on its polarity, for example, growth, etching, defect generation and plasticity, spontaneous polarization, and piezoelectricity. In wurtzite ZnO, besides the primary polar plane (0 0 0 1) and associated direction <0 0 0 1>, which is the most commonly used surface and direction for growth, many other secondary planes and directions exist in the crystal structure.

(Continues…)

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