HRXRD analysis

Figure 2 shows ω/2θ scanning curves and strain distribution analysis of the GaN(0002) lattice plane irradiated with 5.3-MeV Kr¹⁹⁺ and 2.3-MeV Ne⁸⁺ at different fluences. The measured lattice constant c of the original specimen was 0.5188 nm, which is slightly larger than the standard value of 0.5185 nm. This difference is attributed to the biaxial stress between the epitaxial GaN films and sapphire substrates [36, 37].

Fig. 2Full-screen View

(Color online) ω~2θ scanning profiles and strain-distribution analysis of GaN (0002) lattice plane irradiated with (a) 5.3-MeV Kr¹⁹⁺ ions and (b) 2.3-MeV Ne⁸⁺ ions at different fluences

The ω/2θ scanning results for GaN irradiated with the two types of ions exhibited the same trend. The diffraction peak shifted regularly to smaller angles as the ion fluence increased, and increasing broadening of the diffraction peak was observed with increasing ion fluence. Moreover, a split in the main peak occurred and several satellite peaks beside the main peak appeared at relatively higher fluences (Figs. 2a and b). The appearance of these small peaks at lower angles was due to the expansion of the original lattices and the generation of new crystal planes, and the extinction of some small peaks was due to the distortion of new crystal planes or the occurrence of partial amorphization for higher-fluence irradiation. Similar phenomena were observed in Ar-ion-irradiated GaN specimens [37]. These were also ascribed to defect creations in the crystal structure, which led to lattice expansion and variation in the interplanar distance. The lattice expansion can be calculated using Bragg’s law, 2dsinθ=jλ (λ=0.15406 nm and θ is the diffraction angle of the HRXRD curves). Furthermore, these were also attributed to the build-up of lattice compression and lattice strain in GaN films by the energy deposition of incident ions [37-39]. In addition, the broadening of the diffraction peaks indicated that the introduced stress was not uniformly distributed and that a depth distribution with a continuously varying damage level was formed.

To determine the weight of the two types of energy deposition via electronic excitation/ionization or nuclear collision processes in the production of damage in GaN, the ω/2θ scanning curves between the two different types of ions were compared. In the SRIM 2013 estimates (Fig. 1), we can observe that along the entire range of incident ions, at the same ion fluence, the electronic energy deposition of a Kr ion is approximately 1.5 times that of a Ne ion, whereas the nuclear energy deposition of a Kr ion is approximately 5 times that of a Ne ion. The diffraction peak corresponding to the smallest diffraction angle shown in Fig. 2 is from the region of the damage peak induced by the displacement damage owing to nuclear energy deposition.

In addition to the lattice expansion and interplanar spacing changes, lattice strain can be deduced from the HRXRD curves. Based on Hooke’s law, the value of Δd/d characterizes lattice strain. This is obtained from the differential form of Bragg’s equation [40, 41].(1)where Δθ is the difference between the diffraction angle and Bragg angle. The smallest diffraction angle was selected for calculating Δθ and Δd in the HRXRD curves. After 5.3-MeV Kr¹⁹⁺ ion irradiation, significant lattice strains with values of 0.00005, 0.0006, and 0.0032 were generated for 1.0×10¹¹, 1.0×10¹², and 1.0×10¹³ Kr ions/cm² irradiation, respectively (Fig. 2a). Meanwhile, 2.3-MeV Ne⁸⁺ ion irradiation at fluences of 1.0×10¹¹, 1.0×10¹², 1.0×10¹³, 1.0×10¹⁴, and 1.0×10¹⁵ Ne ions/cm², the corresponding strain values were 0, 0.00008, 0.0006, 0.0044, and 0.0068, respectively (Fig. 2b).

To investigate the dependence of lattice strains on ion fluences in the GaN specimens, we also determined the relationship between the lattice strain (Δd/d) and dpa levels in Fig. 3 after the GaN specimens were irradiated with Kr¹⁹⁺ and Ne⁸⁺ ions with different fluences. Moreover, data for GaN irradiated with 100 keV Si ions at different fluences from the work of Qadri et al. [42] are also included in Fig. 3. The dpa level is a measure of atomic displacement due to nuclear collision processes. For the diffraction patterns with more than one peak in the HRXRD curves, the peak with the smallest diffraction angle was selected to calculate Δd. The curve for 2.3 MeV Ne⁸⁺ ion-irradiated GaN was coincident with that of 5.3 MeV Kr¹⁹⁺ ion-irradiated GaN and was in good agreement with that of 100 keV Si⁺ ion-irradiated GaN (Fig. 3). In other words, the strains in GaN induced by the three ions (Kr¹⁹⁺, Ne⁸⁺, and Si⁺) displayed the same trend (Fig. 3). The lattice strain (Δd/d) in the GaN specimens increases with the dpa levels generally (Fig. 3). This further verifies that nuclear energy loss is the main reason for damage production in the peak dpa region in GaN in the present cases of ion irradiation. The electronic energy loss (below 3 keV/nm/ion can be ignored in this experiment).

Fig. 3Full-screen View

(Color online) Strain as a function of displacement per atom (dpa) level for GaN films irradiated with Kr¹⁹⁺, Ne⁸⁺, and Si⁺ ions at different fluences, where the solid red line is a fitting curve of experimental data points from three ions (Kr¹⁹⁺, Ne⁸⁺, and Si⁺). The purple, black, and blue dashed with open symbols lines denote variations of strain versus fluence (dpa), corresponding to the Kr¹⁹⁺, Ne⁸⁺, and Si⁺ irradiated specimens, respectively. The vertical dashed red line points to the value of ~0.055 dpa

Meanwhile, it is noticeable that the strain value (Δd/d) increases in an approximately linear proportion with the value of dpa when the dpa value is less than ~0.055, whereas it increases more slowly as the value of dpa increases above ~0.055, as shown in Fig. 3. This turning point at approximately 0.055 dpa is regarded as a transfer between the two stages of defect accumulation in GaN. When the damage accumulation via nuclear energy loss is lower than a certain level, defects in GaN are almost point-type, and there is no overlap of the individual damage zones produced by each incident ion. In the case of a low damage level, the dpa value, concentration of point defects, and stress and strain built up in GaN are linearly correlated with each other. Here, ~0.055 dpa is assumed to be the threshold value above which point defects become saturated and begin to combine with each other to form more complex types. The evolution of defects was responsible for the behavior of the strain (Δd/d) at dpa levels above 0.055. Moreover, the fitting curve of strain versus fluence (dpa) was obtained by fitting the strain data of the three ions (Kr¹⁹⁺, Ne⁸⁺, and Si⁺) in GaN materials at different fluences in Fig. 3. The fitting curve equation was also used to characterize the dependence of strains in GaN films on the dpa level. The fitting equation is as follows:(2)where ε is the strain and ϕ is the ion fluence (dpa). As can be observed from Eq. (2), the strain in GaN films is primarily composed of two parts after irradiation at different fluences. Based on the displacement damage and ion concentration distributions after irradiation, we conclude that the strains, as expressed in Eq. (2), are mainly defect-induced and incident-ion-induced strains, respectively. Defect-induced strains arise from displacement damage regions owing to the accumulation of various defects. Incident-ion-induced strains originate from ion implantation regions at the end of the ion range. As the ion fluence successively increased to a relatively higher value, defect evolution and stress release occurred, leading to a slow increase in strain. The first term in Eq.(2) can be attributed to defect-related strains caused by displacement damage owing to nuclear energy deposition. The second term in Eq. (2) can be ascribed to lattice deformation-induced strains owing to the addition of incident ions. The coefficient of ϕ is considered as the damage cross section in Eq. (2). Comparing the fitted data in Eq. (2), we found that the damage cross-section of the first term (-39.53) is much larger than that of the second term (-3.573) in Eq. (2). Therefore, we can conclude that the defect characteristics caused by nuclear energy loss play a significant role in the changes in strain.

To confirm the strain changes induced by defect evolution further, we estimated the dislocation density (δ) parameter from the HRXRD curves using an equation that describes the relationship between the shape and broadening of the diffraction peaks and the density of dislocations within a crystal lattice [43]. This analysis provides insight into the strain changes induced by defect evolution within the crystal structure. The equation form is as follows [43]:(3)where D is the thickness of the diffraction layer in the GaN(0002) plane. Fitting the HR-XRD curves (Fig. 2), the full width at half maximum (FWHM) and Bragg angle of the diffraction peak of the GaN(0002) lattice plane were determined. The value of D was obtained using an empirical Scherrer equation. D was calculated from the HRXRD curves in a previous study [44]. For the un-irradiated GaN specimen, its value is approximately (178.6558±7.146) nm. After Kr¹⁹⁺ ion irradiation at fluences of 1.0×10¹¹, 1.0×10¹², and 1.0×10¹³ Kr ions/cm², the corresponding thicknesses of the diffraction layer (D) were approximately (135.3325±6.7666), (115.1562±4.6062), and (59.3774±2.9688) nm, respectively. Meanwhile, for Ne⁸⁺ ion irradiation at fluences of 1.0×10¹¹, 1.0×10¹², 1.0×10¹³, 1.0×10¹⁴, and 1.0×10¹⁵ Ne ions/cm², the corresponding thicknesses of the diffraction layer (D) were approximately (171.2225±6.489), (168.0248±8.4012), (112.5115±4.5004), (23.9323±1.1966), and (22.8045±1.1402) nm, respectively. The dislocation density parameter (δ) was also calculated at different fluences for the two types of ion irradiation. For the un-irradiated GaN specimen, the value of the dislocation density parameter (δ) was approximately (3.1330±0.1253)×10^-5 lines/nm². After Kr¹⁹⁺ ion irradiation, dislocation density parameters (δ) with values of approximately (5.4600±0.2184)×10^-5, (7.5409±0.3770)×10^-5, and (28.363±1.134)×10^-5 lines/nm² were calculated, corresponding to 1.0×10¹¹, 1.0×10¹², and 1.0×10¹³ Kr ions/cm² irradiation, respectively. Clearly, as the irradiation fluence successively increased to 1.0×10¹² Kr¹⁹⁺/cm², the average dislocation density slowly increased from (3.1330±0.1253)×10^-5 to (7.5409±0.3770)×10^-5 lines/nm². Above this fluence, the average dislocation density rapidly increased to (28.363±1.134)×10^-5 lines/nm². After Ne⁸⁺ ion irradiation at fluences of 1.0×10¹¹, 1.0×10¹², 1.0×10¹³, 1.0×10¹⁴, and 1.0×10¹⁵ Ne ions/cm², the corresponding values of the average dislocation density were approximately (3.4109±0.1705)×10^-5, (3.5420±0.1416)×10^-5, (7.8996±0.3949)×10^-5, (175.2±7.031)×10^-5, and (192.3±9.011)×10^-5 lines/nm². When the irradiation fluence was successively increased to 1.0×10¹³ Ne⁸⁺/cm², the average dislocation density slowly increased from (3.1330±0.1253)×10^-5 to (7.8996±0.3949)×10^-5 lines/nm². When the ion fluence increased to 1.0×10¹⁴ Ne⁸⁺/cm², the average dislocation density sharply increased to (1.752±0.07031)×10^-3 lines/nm². As the irradiation fluence was further increased to 1.0×10¹⁵ Ne⁸⁺/cm², the average dislocation density gradually increased to (1.923±0.09011)×10^-3 lines/nm ². Generally, as the ion fluence increased successively, similar changes in the dislocation density were observed for the two types of ion-irradiated GaN films. These results indicated that the disordered regions and distorted lattice planes increased with increasing ion fluences in the irradiated GaN films owing to defect accumulation. Consequently, the amorphous rate of the GaN films was enhanced. It should be noted that a conflicting trend appeared between the lattice strains and the dislocation density with ion fluences (Fig. 3). Based on the data presented in Fig. 3 and the abovementioned dislocation density, we can conclude that the dislocation density increases sharply during the process of strain release.

Additionally, to provide further insight into the structural changes induced by MeV energy ion irradiation and to understand the overall strain behavior of the GaN films under different conditions, the distortion parameters (g) of all the specimens, including the unirradiated and irradiated GaN films, were calculated from the HRXRD curves based on the following specific formula [45]:(4)where β is the FWHM of GaN (0002) diffraction peak and θ describes the Bragg diffraction angle of the GaN(0002) main peak. For the un-irradiated GaN specimen, the calculated value of the distortion parameter was approximately (3.216±0.128)%. After Kr¹⁹⁺ ion irradiation with fluences of 1.0×10¹¹, 1.0×10¹², and 1.0×10¹³ Kr ions/cm², the corresponding values of the distortion parameter were approximately (4.046±0.202)%, (4.648±0.185)%, and (9.007±0.450)%, respectively. Meanwhile, for Ne⁸⁺ irradiation, distortion parameters with approximate values of (3.319±0.165)%, (3.373±0.168)%, (3.493±0.139)%, (13.11±0.655)%, and (13.15±0.526)% were estimated, corresponding to 1.0×10¹¹, 1.0×10¹², 1.0×10¹³, 1.0×10¹⁴, and 1.0×10¹⁵ Ne ions/cm² irradiation, respectively. It is evident that the distortion parameters increase with increasing ion fluences. This confirms the formation of disordered structures in the irradiated GaN films. Furthermore, the dislocation density (δ) and distortion parameters (g) exhibit the same trend with respect to the ion fluences for both ion irradiations. As the irradiation fluence successively increased to 1.0×10¹² Kr¹⁹⁺/cm², the average distortion parameters slowly increased from (3.216±0.128)% to (4.648±0.185)%. Above this fluence, the average distortion parameter rapidly increased to (9.007±0.450)%. For Ne⁸⁺ ion irradiation, when the irradiation fluence successively increased to 1.0×10¹³ Ne⁸⁺/cm², the average distortion parameters slowly increased from (3.216±0.128)% to (3.493±0.139)%. When the ion fluence increased to 1.0×10¹⁴ Ne⁸⁺/cm², the average distortion parameters sharply increased to (13.11±0.655)%. As the irradiation fluence further rose up to 1.0×10¹⁵ Ne⁸⁺/cm², the average distortion parameters gently increased to (13.15±0.526)%. It is worth mentioning that during the distortion process, the parameters increased remarkably, and as stated above, the lattice strains underwent a transition from a rapid increase to a mild increase (Fig. 3). This can be attributed to the release of lattice stress via the migration and rearrangement of dislocations and stacking faults, as a result of which the strain energy is consumed by material deformation, cracks, and fractures.

UV-Vis Spectrum

Bandgap energy is a vital optical parameter for semiconductor materials (GaN). To investigate the effects of lattice strains caused by irradiation on the bandgap energy, we carried out UV-Vis transmittance spectrum analysis on the irradiated GaN films. Figures 4a and b show the UV-Vis transmittance spectrum curves of GaN films irradiated with 5.3-MeV Kr¹⁹⁺ and 2.3-MeV Ne⁸⁺ ions, respectively, at different fluences. From Fig. 4, we can observe that with an increase in ion fluence, the transmissivity of GaN films decreases for the two types of ion irradiation. This is due to the enhancement in the absorption and scattering of defects induced by irradiation. Simultaneously, a wide interference band appears owing to the interface between the GaN film and its substrate (Al₂O₃). Moreover, the shape of the optical absorption edge in the GaN films gradually becomes oblique with respect to the ion fluence. This change is ascribed to the introduction of absorption structures within the bandgap. In particular, this alteration in the band-edge absorption of irradiated GaN films is attributed to the introduction of additional electronic energy states [46]. These states are likely a consequence of the structural changes induced by irradiation, such as the creation of various defects in the material. Overall, these observations highlight the complex interplay between lattice stresses, irradiations, and the optical and electronic properties of GaN films. The mechanisms involved have significant implications for the performance and reliability of GaN-based devices and materials. Tauc’s formula [47] was used to estimate the optical bandgap energy (Eg) as follows:(5)where α is the absorption coefficient, which can be calculated from the UV-Vis transmittance curve. hν is the photon’s energy computed as hν=1240/λ. A is a constant correlated with the refractivity, reduced mass, and absorption brink width. Additionally, n represents the optical transition phase. For direct bandgap semiconductor materials (GaN), the value of n was set to 1/2.

Fig. 4Full-screen View

(Color online) UV-Vis transmittance spectrum curves of GaN films irradiated with (a) 5.3-MeV Kr¹⁹⁺ ions and (b) 2.3-MeV Ne⁸⁺ ions at different fluences

Using this formula [47], the optical bandgap energy (Eg) of GaN films can be deduced from the versus (hν) plots. The bandgap energies of all GaN films, including the unirradiated, Kr¹⁹⁺ ion-irradiated, and Ne⁸⁺ ion-irradiated specimens, were computed based on the above formula [47]. The bandgap energy of the un-irradiated GaN specimen is approximately (3.3562±0.1667) eV. After Kr¹⁹⁺ ion irradiation at a fluence of 1.0×10¹¹, 1.0×10¹², and 1.0×10¹³ Kr ions/cm², the corresponding values of the bandgap energy (Eg) were approximately (3.2645±0.1632), (3.2372±0.1618), and (2.9394±0.1469) eV under approximate lattice strains of 0.005%, 0.06%, and 0.32%, respectively. Meanwhile, for Ne⁸⁺ ion irradiation with fluences of 1.0×10¹¹, 1.0×10¹², 1.0×10¹³, 1.0×10¹⁴, and 1.0×10¹⁵ Ne ions/cm², the corresponding bandgap energy (Eg) values of GaN films were approximately (3.3513±0.1675), (3.3245±0.1662), (3.2916±0.1645), (2.9258±0.1629), and (2.8645±0.1617) eV under approximate lattice strains of 0, 0.008%, 0.06%, 0.44%, and 0.68%, respectively. When the ion fluence was enhanced, the bandgap energy of the GaN films decreased, accompanied by an increase in the lattice strain. After Kr¹⁹⁺ ion irradiation, its value gradually decreased from (3.3562±0.1667) to (2.9394±0.1469) eV. As the ion fluence increased up to 1.0×10¹² Kr ions/cm², the optical bandgap energy of GaN films decreased to (3.2372±0.1618) eV, with a rapid increase in strains from 0.005% to 0.06%. Above this fluence, its value sharply decreased to (2.9394±0.1469) eV under a strain value of approximately 0.32%. Similar changes in bandgap energy were observed in Ne⁸⁺-ion-irradiated GaN specimens. The value of optical bandgap energy decreased from (3.3562±0.1667) to (2.8645±0.1617) eV after Ne⁸⁺ ion irradiation. When the ion fluence was lower than 1.0×10¹³ Ne⁸⁺/cm², the bandgap energy slowly reduced to (3.2916±0.1645) eV after the lattice strain rapidly increased to 0.06%. Above this fluence, the bandgap energy rapidly decreased to (2.9258±0.1629) eV and the strain enhanced to 0.44% from 0.06%. As the irradiation fluence further increased up to 1.0×10¹⁵ Ne ions/cm², its value decreased to (2.8645±0.1617) eV under a slow increase in lattice strain from 0.44% to 0.68%. The interaction of ions with GaN films caused various defects in the bandgap, resulting in a reduction in the optical bandgap energy. In other words, the generation of defects led to the establishment of localized states between the valence and conduction bands, which reduced the bandgap energy [48]. In addition, for lower fluence irradiation, a slow reduction in bandgap energy was observed owing to the generation of single defects and accumulation of strain. At a relatively higher fluence irradiation for both ions, the observed significant reduction in the bandgap energy of the irradiated GaN films was attributed to the creation of dislocations, lattice distortions, and stacking faults due to strain release. In general, these results agree well with the HRXRD analysis.

However, the exponential shape of the optical absorption edge in the UV-Vis spectrum reflects the structural disorder in dielectrics and semiconductors [49-51]. Some research groups have investigated disordered and amorphous materials using the Urbach energy obtained from the absorption edge of the UV-Vis spectrum curves [52-55]. The Urbach energy has been successfully applied to characterize the total structural disorder in ion- and neutron-irradiated crystals and glasses, as well as in thin films and nanoparticles [53-55]. This enabled us to clarify the atomic disorder levels using qualitative and quantitative methods based on the shapes of the formed spectral curves. Similarly, lattice disorders in crystalline semiconductors (GaN) induced by ion irradiation can be characterized by the Urbach energy. The irradiation-dependent Urbach energy was deduced from the absorption spectra.

The absorption coefficient (α) can be achieved from the UV-Vis spectrum and α is characterized using the following equation [48]:(6)where Eu is the Urbach energy (Urbach bandtail). This can be calculated by plotting the absorption coefficient (ln α) versus photon energy (hν). Eu characterizes the static and dynamic disorders in materials and embodies the state density tail length at the energy band boundary. Its boundary is located at the onset of a sharp drop in transmittance in the UV-Vis curves shown in Fig. 4.

Based on the UV-Vis curves shown in Fig. 4, we found that the energy-band boundary of the unirradiated GaN specimen was approximately 3.28 eV. For Kr¹⁹⁺ ion-irradiated GaN specimens, the values of the energy band boundary were approximately 3.12, 2.97, and 2.78 eV, corresponding to 1.0×10¹¹, 1.0×10¹², and 1.0×10¹³ Kr¹⁹⁺/cm², respectively (Fig. 4a). Meanwhile, for Ne⁸⁺ ion-irradiated GaN specimens with fluences of 1.0×10¹¹, 1.0×10¹², 1.0×10¹³, 1.0×10¹⁴, and 1.0×10¹⁵ Ne ions/cm², the corresponding values of the energy band boundary were approximately 3.28, 3.26, 3.23, 2.59, and 2.42 eV, respectively (Fig. 4b). Near the energy-band boundary, Eu can be computed using ln α~hv plots. The Eu values of all GaN films, including those unirradiated and those irradiated with two types of ions at different fluences, were computed. The Urbach energy of the non-irradiated GaN film was approximately (0.1735±0.0086) eV. After Kr¹⁹⁺ ion irradiation at fluences of 1.0×10¹¹, 1.0×10¹², and 1.0×10¹³ Kr ions/cm², the corresponding values of Urbach energy were (0.3056±0.0152), (0.3075±0.0153), and (0.3307±0.0165) under approximate lattice strains of 0.005%, 0.06%, and 0.32%, respectively. Meanwhile, for Ne⁸⁺ ion irradiation, the values of Urbach energy were (0.2887±0.0144), (0.2953±0.0147), (0.3122±0.0156), (0.3401±0.0170), and (0.3526±0.0176) eV, corresponding to fluences of 1.0×10¹¹, 1.0×10¹², 1.0×10¹³, 1.0×10¹⁴, and 1.0×10¹⁵ Ne⁸⁺/cm² irradiation, with approximate lattice strains of 0, 0.008%, 0.06%, 0.44%, and 0.68%, respectively. Obviously, the Urbach energy increased with respect to lattice strains and ion fluences after the GaN films were irradiated by the two types of ions with different fluences. This occurs because disorder is created and localized states are formed owing to irradiation [56, 57]. However, we found that as the Kr¹⁹⁺ ion fluence increased to 1.0×10¹² Kr ions/cm², the Urbach energy slowly increased from (0.1735±0.0086) to (0.3075±0.0153) eV, with a rapid increase in strains from 0.005% to 0.06%. When the irradiation fluence further increased to 1.0×10¹³ Kr ions/cm², the values of Urbach energy significantly increased to (0.3307±0.0165) eV under a slow increase to 0.32% from 0.06% in lattice strain value. Ne⁸⁺ ion-irradiated GaN specimens showed similar change to that obtained with Kr¹⁹⁺ ions. As the fluence was lower than 1.0×10¹³ Ne⁸⁺/cm², the Urbach energy also slowly increased from (0.1735±0.0086) to (0.3122±0.0156) eV after the lattice strain rapidly increased up to 0.06%. Above this fluence, its value sharply increases to (0.3401±0.0170) eV. In this case, the strain value increased slowly to 0.44%. As its fluence further increased to 1.0×10¹⁵ Ne⁸⁺/cm², the Urbach energy value mildly increased to (0.3526±0.0176) eV under a strain value of 0.68%. These results were consistent with those reported by other research groups [58, 59]. It should be noted that when the irradiation fluence exceeded a certain value, the significant increase in Urbach energy was ascribed to the production of dislocations, lattice distortions, and stacking faults owing to the release of strains. This result is in good agreement with the average distortion parameters and dislocation densities deduced from the HRXRD curves. According to Fig. 3 and the computed data (average distortion, dislocation density, bandgap energy, and Urbach energy), we can conclude that severe lattice damage occurs and the defect concentration remarkably increases during the process of strain release. This leads to a significant decrease in the optical bandgap energy and an evident increase in Urbach energy.