Sapphire lattice parameters

Figure 12. Reconstructed exit wave function (phase) of a GaN/Sapphire interface. The lattice parameters next to the interface were determined with very high accuracy. (C. Kisielowski et...

The mechanical properties of materials involve various concepts such as hardness, shear and bulk modulus. The group III nitrides are now mostly used as fihns or layers grown by metal organic vapour phase epitaxy (MOVPE) or molecular beam epitaxy (MBE) on sapphire, GaAs or SiC. The lattice parameters of the substrate do not generally match those of the deposited layer, and therefore, stresses appear at the interface and in the layer and modify its physical properties. Hence, it is necessary to have a good knowledge of these properties. 

The shift of the A line in the epilayers has been connected with the variation of the lattice parameters of GaN [1,11,12], The shift of this line was also measured in samples subjected to hydrostatic pressure (see Datareview A3.1). Combination of all these data permits one to obtain the whole series of excitonic deformation potentials [6,16], Two sets of data are available which are consistent with each other and are given in TABLE 1. The discrepancies between them are linked to the differences in the values of the stiflhess coefficients of GaN used by the authors. Gil and Alemu [6] in their work subsequent to the work of Shan et al [16] used data not available when Shan et al calculated their values. The notations are the same and are linked to the relationship with the quasi cubic model of Pikus and Bir [17], Deformation potentials as and a6 have been obtained by Alemu et al [8] who studied the anisotropy of the optical response in the growth plane of GaN epilayers orthorhombically distorted by growth on A-plane sapphire. For a detailed presentation of the theoretical values of deformation potentials of GaN we refer the reader to Suzuki and Uenoyama [20] who took the old values of the stiflhess coefficients of GaN [21]. 

In general, the ternary nitride layers on sapphire exhibit much broader X-ray diffraction peaks than the GaN layers. For example, Akasaki et al [23] reported 400 arc sec for the 00.2 FWHM for an Alo.1Gao.9N layer (90 arc sec for a GaN layer). The peak broadening was caused by the lattice-parameter gradients and larger mosaicity. 

The compositions of the ternary layers were evaluated from the lattice parameters measured using X-ray diffraction (see Datareview A1.2) and from the positions of the photoluminescence peaks. Both methods gave the same results, if the bowing parameters of 3.2 eV and 0.1 eV, for InGaN and AlGaN, respectively, were used (as proposed by Takeuchi et al [25] for strained layers on relaxed GaN on sapphire). 

Bulk sapphire has rhombohedral symmetry, which is usually treated as hexagonal (space group R3c), with 30 atoms (six AI2O3 units) per primitive unit cell. The lattice parameters (a=fe=4.7570 A, c=12.9877 A) and the internal coordinates (x=0.3063, z=0.3522) are taken from ref. [56]. The bulk unit cell consists of an alternated stacking, along the c-axis, of two Al planes (twelve in the unit cell) with one atom per plane, and one oxygen plane (six in the unit cell) with three O ions arranged with a threefold symmetry. 

The growth on foreign substrates typically leads to the presence of built-in strain in heteroepitaxial GaN layers owing to the difference in lattice parameters and thermal expansion coefficients between layers and substrates [19, 25-27]. Sapphire and SiC are among the most often used substrates, and typically growth is realized on the basal (0001) c-plane of sapphire and SiC. In such instances, nitride films grow along the polar [0001] direction. The sixfold symmetry of the basal planes of the wurtzite (nitrides, SiC) and rhombohedral (sapphire) crystal structures dictates their isotropy in the basal plane and hence, the thermal expansion coefficients, piezoelectric and elastic properties... 

The lattice parameters and thermal expansion coefficients at room temperature of GaN and sapphire are shown in Table 11.1 (on the basis of data given in Refs. 11 and 12). For the case of a-plane GaN grown on r-plane sapphire, the translational periods of the respective lattice planes [10] in [llOOjcaN direction is given by AjijoojGaN = V acaN for GaN and by A[oooi]a1203 = aAi.o, for the sapphire, and in the [0001]caN direction A[oooi]GaN = CcaN for GaN and... 

Table 11.1 Lattice parameters and thermal expansion coefficients at room temperature (perpendicular and parallel to the c-plane) for GaN and sapphire [11,12].

Inserting the lattice parameter values given in Table 11.1 into Equations 1 and 2 results in i ioo] = 16.1% and oooi] = 1.1%. It can be expected that the strong difference in the relative lattice mismatch between a-plane GaN and r-plane sapphire plays a significant role in the defect formation process during film growth. 

Experiments on N ion implantation in ZrN thin films were performed in order to investigate the process of N atom incorporation in this material and its influence on the structure, electrical resistivity, and superconductivity. Polycrystalline stoichiometric thin films of ZrN with thicknesses of about 250 nm deposited on single-crystal sapphire substrates by RF sputtering using Ar and Nj gas were used for the implantation samples. The partial pressure was 2 X 10 torr for Ar gas and in the range 1.7 to 8 X 10" torr for Nj gas, and the substrate temperature was maintained at 1000°C during the deposition. Samples had a well-developed polycrystalline structure and had values of the lattice parameter (Co) around 4.572 A, around 9.5 K, and residual resistivity (at UK) around 30 pQ cm. 

To reduce the strains and dislocation density in epitaxial ZnO and related films, closely lattice-matched substrates are favored for growth. Sapphire substrates are commonly used for ZnO heteroepitaxial growth, primarily on the (0001) orientation (basal or c-plane), and also on the (11 20) o-plane. In addition, ZnO and related oxides have been grown on Si [20], SiC [39], GaAs [21, 22], Cap2 [19], and ScAlMg04 [23]. Lattice parameters of several substrate materials frequently used for ZnO growth and their mismatch to ZnO are listed in Table 2.3. 

To eliminate the orientational domains often observed in ZnO thin films grown on (0001) sapphire, (11 20) sapphire substrates have been used for ZnO epitaxy. The lattice parameter a = 0.3250 nm of ZnO and parameter c = 1.299 nm of sapphire are related almost exactly by a factor of 4, with a mismatch less than 0.08% at room temperature. On the basis of this fact and coining the term uniaxial locked epitaxy, ... 

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