II. EXPERIMENTAL AND THEORETICAL DETAILS

A series of nominally undoped InN films were epitaxied on a 1.5-μm-thick wurtzite GaN underlayer with (0001) sapphire substrate by MOVPE. During the growth of GaN underlayer, trimethylgallium (TMGa) and ammonia (NH₃) were used as the source precursors, with high purity N₂ as the carrier gas. Then, InN film was epitaxied for about 1 h on the top of GaN underlayer using trimethylindium (TMIn) instead of TMGa. Three sets of wafers of about 250-nm-thick InN films were chosen to examine the effects of growth condition. The growth conditions of the three sets of films are summarized in Table I. For the first set (T₁P₂R₃, T₂P₂R₃, T₃P₂R₃, T₄P₂R₃), the growth temperatures varied from 450 °C to 650 °C under a pressure of 300 Torr with a V/III molar ratio of 15,000. For the second set (T₂P₁R₃, T₂P₂R₃, T₂P₃R₃), the pressures of chamber increased from 150 to 450 Torr with a step of 150 Torr, while the V/III ratio were kept on 15,000 at the growth temperature of 550 °C. Finally, for the third set (T₂P₂R₁, T₂P₂R₂, T₂P₂R₃, T₂P₂R₄), the V/III ratio varied from 7000 to 25,000 with a constant NH₃ flow of 5500 sccm, while the temperature and the pressure were fixed at 550 °C and 300 Torr.

TABLE I.

Growth conditions of various wafers.

The crystalline structures of the as-grown wafers were characterized by an XRD system (Panalytical X’pert PRO, PANalytical B.V., Holland) and a confocal microprobe Raman system equipped with a CCD detector and a Leica DMLM microscope (Renishaw UV–vis 1000, Renishaw, UK). Raman spectra were recorded at room temperature in backscattering geometry, where z is perpendicular to the InN film surface. The excitation light source was the 514 nm line of Ar-ion laser.

To identify the Raman scattering results, phonon dispersions were calculated within the framework of LDA,Reference Hohenberg and Kohn^6, Reference Kohn and Sham⁷ using ABINIT package.Reference Gonze, Rignanese, Verstraete, Beuken, Pouillon, Caracas, Jollet, Torrent, Zerah, Mikami, Ghosez, Veithen, Raty, Olevano, Bruneval, Reining, Godby, Onida, Hamann and Allan^8–10 The interaction between the ions and valence electrons was described by the Hatwigsen, Goedecker, and Hutter (HGH) pseudopotentials.Reference Hartwigsen, Goedecker and Hutter¹¹ The Brillouin zones were sampled by an 8 × 8 × 8 Monkhorst-Pack mesh of k points. The convergence for the ground-state total energy was attained at a plane-wave cut off of 90 Ry. For linear response functions, the density functional perturbation theoryReference Baroni, Giannozzi and Testa^12, Reference Giannozzi, de Gironcoli, Pavone and Baroni¹³ was implemented to calculate the interatomic force matrices, from which phonon band structures in the Brillouin zone were obtained, with the LO–TO splitting being taken into account.Reference Gonze, Rignanese, Verstraete, Beuken, Pouillon, Caracas, Jollet, Torrent, Zerah, Mikami, Ghosez, Veithen, Raty, Olevano, Bruneval, Reining, Godby, Onida, Hamann and Allan^8, Reference Saib, Bouarissa, Rodríguez-Hernández and Muñoz¹⁴

III. RESULTS AND DISCUSSION

XRD is an effective experimental method of revealing general crystal properties of the films. A θ-2θ scan was carried out for all samples in the range from 25° to 80°. The XRD patterns ranging from 25° to 34° are shown in Fig. 1 for the four InN thin films grown at different temperatures. For comparison, the spectrum of the sample without InN film on the GaN underlayer is also displayed. All the samples with InN films exhibit diffraction peaks only in the range of 30°–34°, except for the background spectrum from GaN underlayer and sapphire substrate. It is apparent that these peaks all come from the InN films.¹⁵ The dominant peak of the InN films grown at low temperature is narrower and centered at about 31.8°, which was assigned to the InN (002) plane of wurtzite (WZ) structure after comparing it with the Powder Diffraction File (PDF). The width of the dominant peak becomes broader and weaker when the growth temperature increases. As the temperature is raised up to 600 °C, another diffraction pattern appears in lower angle side and emerges as a diffraction peak in the sample grown at 650 °C. The peak position is centered at about 31.3° according to the fitting results as cyan short dotted line shown in Fig. 1. On both sides of the dominant peak, there are two weak shoulders in all the films. By fitting the diffraction patterns, the shoulders in upper and lower angle sides are determined to be at 33.0° and 30.9° and are assigned to the WZ InN (101) and ZB InN (111), respectively, according to the PDF. Besides, the structural phase related to the fitted diffraction peak centered at 2θ = 31.3° could not be determined from the current data for the sample T₃P₂R₃ and T₄P₂R₃. Lattice constants were found to be c = 5.60–5.63 Å and a = 3.56–3.59 Å for WZ structure and a = 5.01 Å for ZB structure, with a slight deviation from previous reports.Reference Kim, Lambrecht and Segall¹⁶ As the films are about 250-nm-thick, the deviation is probably due to the internal or thermal stress. In addition, XRD profiles in the range from 34° to 80° of the InN film only show similar patterns of InN WZ (004), (202), and ZB (222) [not shown here]. Although there are different phase diffractions, XRD diffraction intensity of the films is dominated by WZ structure peaks, especially for the films grown at lower temperatures.

FIG. 1.

X-ray diffraction (XRD) patterns of InN thin films at different growth temperatures, with the pressures of chamber at 300 Torr and the V/III molar ratio at 15,000. The temperatures are labeled above each curve. The peaks labeled with short dotted line are the fit peaks.

We then closely examine the intensity dependence of diffraction peaks on the growth temperature for an optimization. As the temperature changes from 450 °C to 550 °C, there is a slight increase in the WZ InN (002) peak intensity and a slight decrease in both ZB (111) and WZ (101) peaks. When the temperature further increases to 600 °C and to 650 °C, the peak intensity of WZ InN (002) decreases while that of the WZ InN (101) increases; the intensity ratio of ZB (111) to WZ (002) also increases, and both their full-width at half-maximum (FWHM) increases. The FWHM of InN (002) peak decreases from 0.31° to 0.28° when the growth temperature changes from 450 °C to 550 °C and significantly increases to 0.36° and 0.46° when the temperature further increases to 600 °C and 650 °C, respectively. This suggests that 550 °C is closest to the optimal growth temperature for a single-phase and high quality WZ InN film, in which the thermal decomposition or thermal etching of InN is smallest.

While XRD patterns reveal the general crystal properties in the long-range order crystal, Raman spectra are very sensitive to local crystallinity and microstructures near the film surface. Figure 2 displays the room-temperature Raman spectrum for InN films grown at different temperatures. All four spectra display a strong peak at 568 cm⁻¹, which is the characteristic E₂ phonon frequency of the GaN underlayer. Additionally, the spectra show a few other weak bands at 141, 415, 732, and 745 cm⁻¹, which can be assigned to the phonons of GaN underlayers and sapphire substrates.Reference Azuhata, Sota, Suzuki and Nakamura^17, Reference Kladko, Kolomys, Slobodian, Strelchuk, Raycheva, Belyaev, Bukalov, Hardtdegen, Sydoruk, Klein and Vitusevich¹⁸ Except for above scattering peaks, three prominent modes typical for InN films appear at 86, 490–495, and 592–603 cm⁻¹. There is also a new phonon band centered at about 700 cm⁻¹ when the growth temperature is 600 and 650 °C. The mode centered at 86 cm⁻¹ is sharp and is intuitively attributed to the E₂ low phonon mode of WZ InN structure according to the previous reports.Reference Yu Davydov, Emtsev, Goncharuk, Smirnov, Petrikov, Mamutin, Vek-shin, Ivanov, Smirnov and Inushima^19, Reference Ranjan, Bin-Omran, Sichuga, Nichols and Bellaiche²⁰ In comparison with the E₂ low phonon peak, the latter three bands exhibit broader line width and more asymmetric line shape, labeled as A, B, and C, which means that they may not simply come from WZ InN structure, and this will be studied on later.

FIG. 2.

Raman spectra of InN thin films at different growth temperatures, with the pressures of chamber at 300 Torr and the V/III molar ratio at 15,000. The temperatures are labeled above each curve. The peaks labeled with short dotted line are the fit peaks.

As with the XRD pattern, the bands A and B likely came from WZ and ZB structures because they appear in all the samples. The WZ structure has six Raman-active phonons of A₁ (TO), A₁ (LO), E₁ (TO), E₁ (LO), and a doubly degenerate E₂, while the ZB structure has only two Raman-active phonons F₂ (TO) and F₂ (LO).Reference Harima²¹ For WZ InN grown along c direction, the backscattering geometry allowed the observation of the E₂ and A₁ (LO) phonon modes, while for ZB InN with [111] orientation, both F₂ (TO) and F₂ (LO) modes should be allowed in this geometry. To further analyze the structural properties from the bands A and B, the phonon dispersions for both the WZ and ZB InN were calculated. The calculated results are shown in Fig. 3. There are twelve phonon modes, including nine optical and three acoustic branches, in the WZ InN structure, whereas the ZB InN gives only six phonon modes, three of which are acoustical and the others are optical branches. The calculated dispersion curves for the WZ and ZB phase are in agreement with the results given in literatures.Reference Ranjan, Bin-Omran, Sichuga, Nichols and Bellaiche^20, Reference Tütüncü, Srivastava and Duman²² For the WZ InN structure, the allowed E₂ low, E₂ high, and A₁ (LO) modes are located at 85, 489, and 600 cm⁻¹ at Γ point, respectively. The allowed TO and LO phonon modes of ZB InN appear at 478 and 588 cm⁻¹, respectively, which is in the same regions of band A and B. Taking into account the appearance of WZ InN (101) in XRD patterns, the Raman selection rule would probably be broken so that the other phonon peaks such as E₁ (TO), A₁ (TO), and E₁ (LO) might show up. Nevertheless, Raman spectra do not show any visible peak at about 448 cm⁻¹, where the A₁ (TO) mode should appear. This fact means that the Raman selection rule is almost complied with even if the crystal orientation is not perfect. For this reason, we speculate that the contribution of E₁ (TO) at about 474 cm⁻¹ and E₁ (LO) at about 583 cm⁻¹ to the bands A and B is negligible for WZ InN. Thus, in view of the co-existence of WZ and ZB phase, Raman bands of both A and B can be fitted with two individual peaks. The former is fitted with F₂ (TO) of ZB InN and E₂ high phonon of WZ InN and the latter is synthesized by F₂ (LO) of ZB InN and A₁ (LO) mode of WZ InN structure, as represented by the dashed lines in Fig. 2. The experimental fitted values of F₂ (TO) and F₂ (LO) of ZB InN and E₂ high and A₁ (LO) of WZ InN are compared with our calculated results of the zone-center and the values reported previously in Table II.Reference Yu Davydov, Emtsev, Goncharuk, Smirnov, Petrikov, Mamutin, Vek-shin, Ivanov, Smirnov and Inushima^19, Reference Ranjan, Bin-Omran, Sichuga, Nichols and Bellaiche^20, Reference Kwon, Lee, Miki, Yamano and Yoshida^23–Reference Kaczmarczyk, Kaschner, Reich, Hoffmann, Thomsen, As, Lima, Schikora, Lischka, Averbeck and Riechert²⁵ The fitted values of four phonon modes are close to the calculated values, although they shifted slightly in different samples. Moreover, both our theoretical and experimental results are in good agreement with the comparison data despite a little higher value for A₁ (LO) mode. Accordingly, these data further confirm the presence of the ZB structure in InN films deduced from the XRD measurement.

FIG. 3.

Phonon dispersion curves of InN for both WZ and ZB in the structure.

TABLE II.

Summary of the experimentally observed and theoretically calculated phonons of InN (WZ and ZB modifications).

Close comparison reveals that the bands A and B shift slightly to higher wave number as the temperature changes from 450 °C to 550 °C and shift back when the temperature further increases to 650 °C. It is known that the phonon frequency is closely related to the misfit stress between InN film and GaN underlayer, which is generally accommodated by lattice strain and defects. On the basis of Raman scattering data along with XRD measurements, we can deduce that the higher the Raman phonon frequency of bands A and B are, the narrower the FWHM of the InN XRD (002) peak is, which indicates higher crystalline quality with fewer defects. The shift in phonon frequency is likely due to the lattice strain rather than defects as the sample grown at 550 °C has the narrowest FWHM. In light of this, we simulated phonon dispersions of WZ structure under different biaxial compressive strains. As expected, the phonon frequency at Brillouin center increases with increase in the compressive strain. On the basis of above analysis, the growth temperature of 550 °C is more appropriate for the InN film epitaxy.

From Table II, it is observed that neither WZ nor ZB InN structure would have the phonon mode at around 700 cm⁻¹, which appears in sample T₃P₂R₃ and T₄P₂R₃. Generally, the excited states of free electrons, either single-particle excitation or collective excitation (plasmons), can also contribute to Raman scattering by coupling with lattice vibration. Since almost all the InN thin films obtained so far are of n type with high electron concentration, the formation of plasmon will be easier and the coupling between plasmon and LO phonon (PLP) will be enhanced.Reference Harima^21, Reference Qian, Shen, Ogawa and Guo²⁶ With increasing electron concentration, the upper branch PLP⁺ mode increases from the LO frequency to higher value, while the lower branch PLP⁻ mode goes to the TO frequency range. From this point of view, 700 cm⁻¹ should be related to the PLP⁺ if the band C could be attributed to PLP. However, most observed PLP modes in previous reports are PLP⁻.Reference Yu Davydov, Emtsev, Goncharuk, Smirnov, Petrikov, Mamutin, Vek-shin, Ivanov, Smirnov and Inushima^19, Reference Aderhold, Davydov, Fedler, Klausing, Mistele, Rotter, Semchinova, Stemmer and Graul^27, Reference Inushima, Mamutin, Vekshin, Ivanov, Sakon, Motokawa and Ohoya²⁸ Simultaneously, the XRD patterns of those two samples with band C show an undefined peak at about 2θ = 31.3°. In the light of this, we would ascribe the band C to another new structure phase rather than PLP coupling mode. In addition to WZ and ZB structure, InN has rocksalt (RS) phase that usually appear in the sample under high pressure.Reference Pinquier, Demangeot, Frandon, Chervin, Polian, Couzinet, Munsch, Briot, Ruffenach, Gil and Maleyre^29, Reference Ueno, Yoshida, Onodera, Shimomura and Takemura³⁰ It has been found that an intrinsic compressive stress (i.e., Laplace pressure) induced by the surface tension exists in many isolated 3D islands in Volmer–Weber growth.Reference Wang, Kushvaha, Yan and Xiao^31–Reference Pao and Srolovitz³³ For this reason, small structures are subjected to a stressed state even without any external force. To further identify this additional Raman peak, we calculated the phonon dispersion curves for the RS structure (not displayed here). The phonon dispersion curves eliminate the possible contribution of RS phase because there is no phonon mode in the region higher than 600 cm⁻¹. Therefore, the band C in Raman spectrum and the undefined peak in XRD pattern are believed to come from a new structural phase, which needs further investigations.

Since the growth pressures and V/III molar ratios are other critical components to obtain high-quality InN films, another five samples were epitaxially grown under different conditions at the optimized temperature of 550 °C, as listed in Table I. Figure 4 shows XRD patterns and Raman spectra of InN films growth at 15,000 V/III ratio under different reactor pressures. As seen in Fig. 4(a), no diffraction peak of the unspecified structure appears at 31.3°. Furthermore, neither noticeable intensity nor position variation is observed as the reactor pressure changed in the region of 150–450 Torr, except for slightly narrower FWHM of WZ (002) under higher pressure. This tendency is in agreement with the previous report in the region of 150–450 Torr.Reference Kadir, Ganguli, Gokhale, Shaha, Chandvankar, Aroraa and Bhattacharya³⁴ Similarly, the unspecified phonon band is also invisible at about 700 cm⁻¹, as shown in Fig. 4(b), which confirms that there is no unspecified structural phase in the InN films grown under different pressures. Besides, the line width and the intensity of all InN Raman phonon modes are rarely affected by reactor pressure as compared to the growth temperature. The relatively higher quality could be attributed to the enhancement of ammonia decomposition as a result of reduced flow velocity of the reactant gases and the suppression of re-evaporation of nitrogen from the InN layer under higher pressure. However, as the effective In supply at the growth surface is influenced by the reactor pressure,Reference Kadir, Ganguli, Gokhale, Shaha, Chandvankar, Aroraa and Bhattacharya³⁴ the structural quality will probably be degraded under the reactor pressure higher than 450 Torr. For these reasons, we further examined the influence of V/III ratio with a compromised reactor pressure of 300 Torr.

FIG. 4.

(a) XRD patterns and (b) Raman scattering spectra of InN thin films under different reactor pressure, with the V/III ratio kept at 15,000 and the growth temperature kept at 550 °C.

The effect of V/III ratio on the structural properties of InN films is illustrated in Fig. 5. Neither XRD patterns nor Raman spectra show the unspecified peak or any obvious change in different samples. Close examination shows that the line width of XRD patterns weakly broaden as V/III ratio increased in a given range of 7000–25,000. According to the InN phase diagram calculated by Jones et al.,Reference Jones and Rose³⁵ the boundary line as a function of N full composition between solid phase and liquid phase at the temperature of 550 °C is about 97%. Because the ammonia decomposition rate at this temperature is less than 0.1%,Reference Piner, Behbehani and El-Masry³⁶ all V/III ratios in our case appear in the solid and liquid coexistent region. The V/III ratio of 7000 is located closer to the solid line. Several studies in literature pointed out that a high V/III ratio is required to achieve In droplet-free InN filmsReference Nanishi, Saito and Yamaguchi^1, Reference Koukitu, Takahashi and Seki^37, Reference Matsuoka and Pearton³⁸ although some achieved good quality films with a low V/III ratio.Reference Briot, Maleyre, Clur-Ruffenach, Gil, Pinquier, Demangeot and Frandon³⁹ Nevertheless, the In-droplet growth regime is tentatively precluded because no obvious In diffraction peak is observed in all our samples. On the basis of above analysis, we believe that a relatively lower V/III ratio of precursor is more conducive to obtain high quality InN films, although it has modest effect on the InN microstructures.

FIG. 5.

(a) XRD patterns and (b) Raman scattering spectra of InN thin films as a function of V/III ratio with the temperature and the pressure fixed at 550 °C and 300 Torr, respectively.