Indium nitride, like other group-III nitride members, crystalizes in the stable forms of wurtzite and zinc blende and exists in a pseudomorphic-stable rocksalt form [13–18]. Various growth techniques discussed in detail in Chapter 4 are utilized for the growth of different crystalline forms. The transitions of the wurtzite phase to the rocksalt were observed at high hydrostatic pressures [13–16]. For instance, group-III nitrides transform to the semiconducting rocksalt phase under the pressure of 21.6, 51.8, 16.6, and 850 GPa for InN, GaN, AlN, and BN, respectively [15].
Here, stable forms of zinc blende and wurtzite InN crystal structures are investigated and physical properties of InN material are listed in Table 2.1. The zinc blende, or rarely defined as a sphalerite form, InN crystal structure has cubic lattice symmetry, illustrated in Fig. 2.1a. The wurtzite InN crystal structure possesses hexagonal lattice symmetry, illustrated in Fig. 2.1b. A substance that can occur in more than one crystal form is said to be polymorphic (or phase separation) [19]. Conventional InN growth techniques often lead to single crystalline phase due to the great difference in the growth conditions [20].
The indium element has two valence electrons in an s orbital, one valance electron in a p orbital, for a total of three valence electrons. InN is a covalent network compound and indium to nitrogen bond is a co-ordinate covalent (or dative) bond [21]. In dative bond, the bond is formed by sharing of electron pair, but shared pair is contributed by one atom (nitrogen in this case);
therefore, co-ordinate covalent bond is semi polar bond. The interesting characteristic of covalent network compounds has four dative bonds available to form tetrahedral configuration regardless of hybridization [21]. Thus, each indium atom is surrounded by four nitrogen neighbors forming a tetrahedron or vice versa.
Figure 2.1 Ball and stick representation of a (a) zinc blende and (b) wurtzite unit cells [22].
In the case of wurtzite structure, a hexagonal primitive cell (basis) contains two indium atoms and two nitrogen atoms with two lattice parameters, a and c. Ideal wurtzite structure belongs to the space group of C6v4 in the Schoenflies notation and P63mc in the Hermann-
Mauguin notation [23]. The ideal hexagonal structure has a c/a = (8/3)1/2 = 1.633 lattice parameter ratios and a distortion parameter of u = 3/8 = 0.375 [23]. In generally, c/a lattice ratio is related to the spontaneous polarization and u parameter is related to the isotropicity of the structure. Since ideal wurtzite structure has two isotropic planes, isotropicity measurements are important in the wurtzite structure.
In the case of zinc blende, a cubic primitive cell contains one indium atom and one nitrogen atom with cubic lattice parameters of a. Ideal zinc blende structure belongs to the space group of T2d in the Schoenflies notation and F4¯3m in the Hermann-Mauguin notation. The
difference of the primitive cells of zinc blende and wurtzite structures are shown in the insets of Figs. 2.2a and 2.2b.
The wurtzite and zinc blende primitive cells differ in terms of both number of atoms and bond angle of the second nearest neighbors. In other words, stacking order of the basal planes are different [23]. The bond angle of second nearest neighbor is 0° in a wurtzite structure; whereas, it is 60° in a zinc blende structure shown in the insets of Figs. 2.2a and 2.2b, respectively. Due to tetrahedral bonding, in the wurtzite and zinc blende structures, there exist four nearest neighbors and 12 second nearest neighbors. However, stacking orders of wurtzite and zinc blende differ due to different second nearest neighboring angle [23]. The wurtzite structure consists of triangularly ordered alternating diatomic planes along the [001] direction; for instance, the stacking sequence of wurtzite InN material is In1, N1, In2, and N2, shown in Fig. 2.2b. The zinc
blende structure, however, consists of triangularly ordered diatomic planes along the (111) plane [23]. Thus, the stacking sequence of zinc blende InN material is In1, N1, In2, N2, In3, and N3,
shown in Fig. 2.2a. Therefore, the stacking of order of wurtzite and zinc blende structure can be summarized as ABABAB… and ABCABC…, respectively.
a b
Figure 2.2 Ball and stick representation of atomic arrangements for (a) cubic zinc blende lattice structure along the [111] direction and (b) hexagonal wurtzite lattice structure along the [001] direction, respectively. Insets show corresponding bonding configurations.
InN, like other group-III nitrides, has lower c/a ratio than the ideal value of 1.633; thus, wurtzite InN structure is slightly (1.31%) compressed along the c-axis (or 0001 direction) [24]. In other words, the intrinsic asymmetry of the tetrahedral bonding in the wurtzite group-III nitride materials leads to a negative spontaneous polarization. Spontaneous polarization increases from GaN over InN to AlN [25]. If polarization results from mechanical stress, it is called
piezoelectric polarization. Piezoelectric polarization is generally expressed negative for tensile and positive for compressive stress [26].
i. If the mechanical stress is tensile strain, the orientation of the spontaneous and piezoelectric polarization is parallel.
ii. If the mechanical stress is compressive strain, the orientation of the spontaneous and piezoelectric polarization is antiparallel.
Total polarization of the wurtzite structure is given by the following relation:
PTotal = PPiezzolectric + PSpontaneous. (2.1)
However, mechanical strain associated with the dislocations may also be expected to have a pronounced influence on the piezoelectric effect, which is known to be strong in the nitride materials [27]. The force needed to enlarge of all the atoms along the c-axis in a wurtzite structure is very large; however, movements of the dislocations allow atoms in a crystal plane to slip by one another at a much lower force [28]. Because a low energy is required to move along the densest planes of atoms, dislocations enforce lowest energy direction of alignment within a grain of the material. This results in slip that occurs along parallel planes within the grain and that are known as slip bands, discussed in detail for the structural impurities. These parallel slip planes were observed in GaN epilayers grown on sapphire substrate [29]. Therefore, slip planes have a huge impact on the piezoelectric polarizations.