Nanoidentation results and correlation with the defect structure of the nonpolar a-plane GaN epilayers

In order to correlate the defect structure of the samples with the nanoidentation results regarding the nanohardness (H) and reduced elastic modulus (E*), the defect densities must be measured. Combining the TEM observations from both XTEM and plan view geometries was necessary since the high density of PDs that are present in the nonpolar material makes difficult their distinction from the lattice dislocations. In Section 3.1.2.2 it was presented how the different defects are determined by employing TEM diffrac-

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tion contrast experiments. Table 3.VII summarizes the samples with the experimental H and E* values while the defect densities were presented in Table 3.III.

The measured defect content of the specimen was found to drastically influence the H and E* values. Increase of the dislocation density resulted in a significant increase of both the resistance to plastic deformation which is quantified by the H value, and the resistance to elastic deformation which corresponds to the E* value. Figure 3.14 shows this trend which is followed by considering both the overall TD density and PD density.

If the PDs are excluded, this dependence is not followed since the lattice TDs are fewer than the PDs and do not appear to regulate the slip processes.

Table 3.VII: Summary of the investigated samples with the experimental H and E* values.

Sample H (GPa)

E*

(GPa)

A 17.01 327.88

B 15.12 289.75

C 9.42 242.48

D 9.16 283.11

E 16.19 305.78

F 14.31 288.56

Figure 3.14: (a) H and (b) E* values as a function of overall TD and PD dislocation density. An increase of the density of the dislocations results to an increase of both H and E* (courtesy of Dr.

P. Kavouras).³²

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The load-unload curves for two representative samples which consist of high and low TD densities (samples E and D) is shown in Figure 3.15. Both samples exhibited the characteristic “pop-in” discontinuities as shown in the insets of Figure 3.15. In the case of sample E, with the high defect content, the pop-in appeared earlier and this is a trend which all the investigated samples are following. Figure 3.16 illustrates the dependence of the critical load (Pc) in which the critical pop-in occurs with the dislocation density. It is noted that in the sample with the lowest dislocation density (sample C), a pop-in event was not observed.

Based on these results, it is clear that an increase of the dislocation density is as- sociated with an increase in the hardness H and stiffness E*. This can be explained if the deformation mechanism of the nonpolar III-nitride epilayers under the nanoindenter tip is considered. Previous studies have shown that deformation is realized by nucleation of dislocation loops, and glide along the basal planes that are perpendicular to the surface in the case of the nonpolar material.^34,35 This is the primary slip system for GaN and the resolved shear stress is maximum on these planes for the given deformation geometry.

Figure 3.15: Load-unload curves for samples E and D (high and low defect density respective- ly). The insets show in higher magnification the pop-in discontinuities of the two samples. The positions of the pop-in events on the loading part of the curves clearly show the decrease in the pop-in load with increasing defect density (courtesy of Dr. P. Kavouras).³²

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Figure 3.16: Dependence of pop-in depth with the dislocation density. The pop-in depth shows an exponential decrease with increasing the TD density (courtesy of Dr. P. Kavouras).³²

According to the above, the process of basal-plane slip requires a higher resolved shear stress with increasing density of defects that lie on the basal plane. In particular, during the process of plastic deformation, the motion of the gliding dislocations will be stalled by the pre-existing TDs in the sample. This corresponds to an increased required energy for maintaining the dislocation glide on the basal plane. This interaction gives rise to an overall dragging effect on the advancing deformation wake. The 1/6<2023>

partial dislocations are sessile on the basal plane due to the c/2 BV component. Hence these defects cannot accommodate the imposed nanoindentation stress by gliding themselves. On the contrary, they hinder the motion of the nucleated dislocation loops.

The more the TDs, the more intense this effect is, thus making the sample less suscepti- ble to plastic deformation.

This is schematically shown in Figure 3.17 where the red lines correspond to TDs that are generated under the nanoindenter tip and glide along the deformation wake and it shows how their motion is hindered by the pre-existing TDs in the sample (solid grey lines). Moreover, when a critical density of new generated TDs is present, the sin- gle pop-in event in the loading segment of the load-displacement curves occurs due to the triggering of a burst of collective dislocation nucleation as a result of the high local stress under the indenter tip.^{34, 35}

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Figure 3.17: Schematic illustration of the sample during the indentation that shows how new TDs (red lines) are generated under the nanoidenter tip and glide along the advancing defor- mation wake. Their motion is hindered by the pre-existing TDs.

Such pop-ins mark the onset of plasticity. In literature both cases have been re- ported, i.e. the indentation in a-plane GaN does not produce pop-in discontinuities,³⁶ or they produce clearly visible pop-ins.³⁴ The lack of pop-ins has been attributed to the en- hanced defect concentration near the surface but possible reasons that lead to different results appear to be the different indentation conditions, the defect contents of the test- ed thin films, or the combination of epilayer/substrate.

The results show that the early occurrence of the pop-in in nonpolar orientation is favored by the increased TD density. This could be attributed to the existence of more sites for nucleation of new glissile dislocations from the specimen’s surface (i.e. under the nanoidenter tip). Indeed the pre-existing TDs distort the specimen’s surface by in- troducing steps and pits which favor the easy nucleation of glissile dislocations when a critical load is reached. However, after the nucleation, the large pre-existing TD density hinders the motion of the dislocations, as discussed in the previous paragraphs.

According to the results in this study, the heavily defected a-plane GaN films ex- hibited a response analogous to that obtained from c-plane GaN. Good quality a-plane epilayers were found to exhibit lower hardness than c-plane ones.³⁷ This behavior is an- ticipated since slip is straightforward in a-plane GaN geometry but, in the case of c- plane GaN, it requires formation of horizontal slip bands. The two orientations are simi- lar only when slip is obstructed in a-plane material through the pre-existing TDs. It is also interesting to note that in c-plane GaN, multiple pop-ins occur that are associated with multiple successive slip bands.³⁸ On the other hand, this is not required in the a- plane and therefore only single pop-in events were observed.

The lack of pop-in in the sample C does not mean a lack of elastic–plastic transi- tion and this is based on the fact that residual indents were observed after the load–

unload process in this sample. Therefore, it should be assumed that the onset of plastici-

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ty occurs with very narrow pop-in, most likely due to the low density of pre-existing de- fects that is unlikely to cause a collective dislocation nucleation.