LABORATORIO

The elastic modulus of the material has been directly measured using the AFM force calibration method described in section 2.6, also sometimes referred to as AFM beam bending. Double clamped and single clamped beams of 4 µm width and various lengths were used in the experiments. In order to have a reliable calibration of the elastic constant of the tip, long probes with a large contact area were selected. The calibration was performed bending the tip as less as possible in order to ensure that the indentation depth at the surface was small enough in order to be neglected in the measurement postprocessing.

For minimizing the effect of the underetching at the clamping regions the silicon substrate was sacrificially etched using the SF6 dry etching, described at 4.3.2. The

films that were subject of this characterization have been described in section 7.3.

7.4.1

Elastic modulus of GaN

Suspended microstructures of GaN over Si(111) were characterized in order to extract the elastic modulus. The cantilevers fabricated with this material presented a severe out-of-plane buckling, indicative of large stress or stress gradient in the material. The determination of the exact stress state will be discussed in the following section.

The GaN layer had a thickness of 200 nm, as determined by SEM inspection. The effect of the thin AlN adaptation layer has been neglected for the purpose of this study, as dAlN  dGaN and both materials have similar elastic modulus. For the

measurement an AFM carbon-like-diamond tip was used. The elastic constant of the tip was determined from the resonance frequency and AFM assessment to be kAF M =

8.41 N/m. For ensuring the correct measurement the structure was measured from 5 µminside the clamping region and moving 1 µm every step. After measuring every structure, the tip deflection was newly calibrated in order to verify that the tip was not damaged during the measurement and validate the collected data. Cantilever lengths of 10 µm and 15 µm were used for the beam bending measurements.

The large stress observed in the material hindered the correct interpretation of the curves obtained for the double clamped beam structures, due to the large stress stiff- ening present in the device. Hence, only cantilever single clamped beams have been

Figure 7.6: Measurement of a GaN cantilever by AFM beam bending technique with

the fit using the average flexural elastic modulus that has been determined from the experimental data.

analyzed in order to fit the force calibration curve with (2.12). Excellent fits were ob- tained for the cantilever structures, as seen in figure 7.6. The values extracted for the various cantilevers with both lengths yielded very low data dispersion. The elastic modulus of the GaN cantilevers, working in vertical flexural mode, was calculated after statistic treatment of the measured data, reaching:

EGaN = 316 ± 21

7.4.2

Elastic modulus of AlN

AlN microstructures were also characterized using the AFM beam bending tech- nique. The AlN material was grown on Si(111) by MBE. The preliminary character- ization showed little residual strain in the AlN film. After the mechanization of the free-standing structures virtually no out-of-plane buckling and very low stress was measured for this materials, as discussed in depth in the following section.

The AlN film thickness was determined to be dAlN = 500 nmby SEM inspection.

As with the GaN a Diamond-Like-Carbon tip with kAF M = 8.41 N/m was used for

the characterization. Again, the structures were measured by starting well inside the clamping region and moving toward the opposite end of the structure by 1 µm steps. The measured data were validated by confirming that the tip suffered no degradation

Figure 7.7: Measurement of an AlN cantilever by AFM beam bending technique with

the fit using the average flexural elastic modulus that has been determined from the experimental data.

during the measurement by measuring after the end of the structure against the fixed substrate. The absence of residual stress allowed the use of (2.13) for fitting the data measured on double clamped beams. Therefore, both cantilever and double clamped beams were used for the flexural modulus determination of AlN . Cantilever lengths of 10 µm and 15 µm and double clamped beams with lengths of 10 µm and 20 µm were used.

The data measured for the double clamped beams showed large dispersion of the calculated flexural modulus. This is because of the large value of the coefficients of the elastic tensor of AlN and to the large thickness used for the structure fabrication. On the contrary, cantilever beams were successfully fitted using (2.12). The data calculated for the cantilever structures showed little dispersion, as seen in figure 7.7. The statistical treatment of these results provides a value of the flexural stiffness of AlN has been calculated to be

EAlN = 329 ± 24

7.4.3

Elastic modulus of InN

Finally, InN free-standing microstructures were also measured with the AFM bending technique. The InN was grown on Si(111) with a thin AlN interlayer that

Figure 7.8: Measurement of an InN cantilever by AFM beam bending technique with

the fit using the average flexural elastic modulus that has been determined from the experimental data.

has been neglected for the analysis of the measurements. The measured buckling of the cantilevers is very low. This fact and the absence of significant residual stress in preliminary XRD measurements lead to the assumption that little stress is accumu- lated in the structure, and that stress stiffening effects can be neglected.

The layer thickness was measured by SEM inspection to be approximately dInN =

400 nm. Contrary to the GaN and AlN cases, the stiffness of the structures is ex- pected to be low. Therefore, a silicon AFM tip was used for the AFM trials. The spring constant of the testing tip was calculated to be kAF M = 4.87 N/m. As for the

other materials, the tip deflection was calibrated prior and after each measurement to ensure that the data extraction is correct and that it is not affected by degradation. The low residual stress allowed the usage of both cantilever and double clamped structures for the determination of the flexural rigidity. Cantilever lengths of 10 µm and 15 µm and double clamped beams with lengths of 10 µm and 20 µm were used.

The elevated thickness of the InN and the rigidity of the double clamped structure caused the data fitted for these structures to have higher residuals than for cantilever beams. Nevertheless, the data obtained for both structures was similar and has been statistically treated without distinction. An example of the trace measured for a cantilever has been shown on figure 7.8. In this figure, the good agreement between the theoretical plot using the mean value of the calculated InN flexural stiffness can be observed. The data on this figure can be compared with the fits for GaN and AlN ,

figures 7.6 and 7.7, respectively. The value of the flexural stiffness of InN has been calculated to be

EAlN = 137 ± 10

7.4.4

Result discussion

The static AFM beam bending technique has been successfully used for determin- ing the vertical flexural elastic modulus of GaN , AlN and InN ,and the obtained values have been summarized in table 7.3. It is readily observed that the values are very close to those theoretically predicted using (7.2) and the elastic constants published in the literature.

Many reviews on the mechanical properties of nitride semiconductors have been published, as for example [103, 235, 236]. In what follows the values obtained for the measured materials are compared with those published in the literature in order to asses the mechanical quality of the epitaxial material that is grown on Si(111) by MBE.

The values of the flexural strength of GaN calculated from the elastic constants reported in the literature yield 327 GP a for high quality epitaxial layers [237], 312 GP a for single crystal [230] and 295 − 319 GP a for theoretical calculations [103, 238]. Early works on GaN cantilever structures yielded low elastic modulus values (E ≈ 250 GP a) [239]. However, measurements on GaN by microindenta- tion have yielded similar results [240] to the obtained in this thesis, being the most commonly reported values between 295 GP a and 325 GP a as summarized in [233], although other author claim to have measured E = 330 GP a [241]. Measurements of GaN nanowires provide Young’s modulus with a very large scattering of the ob- tained values, reported elastic modulus from 220 GP a to 400 GP a are cited in [242] and in [243]. As can be seen, the measured value is relatively high compared to the reported values in the literature. Therefore, the crystalline quality is excellent and

Material Measured E [GP a] Literature reported E [GP a] AlN 329 ± 24 ∼ 345 [232]

GaN 316 ± 21 295 − 325[233] InN 137 ± 10 140 − 160[234]

Table 7.3: Flexural elastic modulus of the III-N binaries measured by AFM force calibra-

the defect density is not sufficient to affect the elastic properties of the GaN . This fact is important, as it suggests that the properties on the GaN thin film are not affected by the micromachining and that the devices can be designed as on a standard layer.

The value obtained for the elastic modulus of AlN is very high and close to 345 GP a, which is the value commonly reported in the literature [103,232,244,245]. The calculated flexural stiffness differs less than 5% from the prediction. The small reduction in the elastic modulus with respect to the previously reported values for single crystal cantilevers [232] can be attributed to the large defect density present in such a thick AlN layer (500 nm).

The value measured for InN is in accordance with the published values evaluated by other techniques on various substrates. In an early work Edgar et al. [246] estab- lished the basic mechanical parameters of InN . In this work, the elastic modulus was found to vary between 150 GP a and 190 GP a, depending on the growth tem- perature. In other works, the calculations and measurements of the InN have been reviewed and a great scattering of the calculated and measured data is reported. Val- ues between 115 GP a and 208 GP a are given for InN [103,235,247–249], although the most commonly reported values span from 140 GP a to 160 GP a. In fact, Lu et

al. [234] claim to have measured E = 149 GP a on InN cantilevers grown on an

AlN buffer. In comparison with the data found in the literature the value measured is slightly lower. It is believed to be so low due to the difficulty of growth of the material, that has an impact on the elastic modulus of the film. Further discussion is presented for the characterization of the residual stress in the following section.

7.5

Residual stress and relaxation of free-standing struc-