FORMULACIÓN DE LA HIPÓTESIS

As for the InN , the AlN free-standing structures exhibited a downward buckling after release. The measurement from the stress pointers was inaccurate due to the buckling, but the mean residual stress has been estimated to be low as virtually no displacement of the indicator tip was observed. Contrary to what happened with the InN layer, the AlN films have been grown in a single step and uniform material is expected.

The XRD data showed wide peaks, so it has been speculated that the residual stress in the AlN layer is unevenly distributed. A thick relaxed layer is formed over a thin layer with less defect density but with larger residual strain. Only one AlN thickness has been used for the free-standing structure fabrication, 500 nm, so the determination of the thickness and stress of the adaptation layer has been done itera- tively by fitting the displacement of the cantilevers and the buckling of the H-shaped beams. The cantilevers were fitted using a parabolic function and using a simplified equation for the deflection of uniform material with a thin stressed layer:

δ = 3σL 2 4dE " 1 − (dr− ds) 2 d2 # (7.10) where dr is the thickness of the relaxed layer, ds the thickness of the stressed

layer, and d the total thickness of the cantilever. Using this equation and the numer- ical model for the H-shaped beam, the thickness and stress of the AlN adaptation

layer have been determined. It has been estimated that a layer of ∼ 50 nm has a residual tensile stress of 1 GP a, while the rest of the film is completely relaxed. This is of course a rough approximation to the real stress distribution in the layer, that empirically fits the measurement data. In reality a smooth evolution of the residual stress is expected. However, what seems clear from the models is that a thin layer close to the interface with the silicon has a large residual stress that is rapidly relaxed moving in the z axis, leaving a thick layer of AlN under a low residual stress state.

7.6

Conclusions

Nitride semiconductor free-standing test structures have been fabricated for the analysis and modeling of the main mechanical parameters for MEMS: flexural stiff- ness, residual strain and stress gradient. The material elastic modulus has been mea- sured and the stress distribution has been modeled in close agreement with the ob- served data. It is also worth noting that the fabrication technology optimized in this thesis, and already discussed in previous chapters, has been proven successful for producing free-standing structures of high crystal quality epitaxially grown nitride semiconductors.

The elastic modulus of the three main binaries of the III-N semiconductor system has been measured. The value for the alloys can be interpolated using the Vegard’s law from the three corner values, that are:

• EGaN ≈ 316 GP a

• EAlN ≈ 329 GP a

• EInN ≈ 137 GP a

The residual strain has been measured by XRD and the relaxation induced effects have been studied and modeled using special free-standing test structures. The fit of the developed models with the experimental data has been excellent for all the materials: GaN , AlGaN/GaN , AlN and InN .

In the case of InN and AlN layers, it has been seen that the material is completely relaxed and that the residual stress can be neglected in the design of the structures. Nevertheless, for structures with asymmetric clampings, a small buckling toward the substrate has been observed. The origin of this deformation has been modeled to be related with a small adaptation layer that is formed on the silicon substrate. The thickness of this layer is of few tenths of nanometers. In the case of the InN the

adaptation layer is believed to be coincident with the AlN buffer layer grown on the silicon for improving the nucleation and crystal quality of the InN . The stress of the thin AlN adaptation film has been estimated to be between 750 M P a and 1 GP a.

On the contrary, for the GaN layer a large bulk residual stress has been found. The mean stress value that has been measured is around 980 M P a ( = 3.1 · 10−3_).

Additionally, a severe out-of-plane buckling has been observed. The addition of a layer with lower residual stress at the bottom of the structure was necessary for suc- cessfully modeling the deformation of the structure. The stress of this layer has been estimated to be 820 M P a ( = 2.6·10−3_{). The explanation for this stress distribution is}

speculated to be a defect related relaxation of the lower GaN surface. These defects are believed to be induced during the structure release. These observations were made regardless of the GaN layer thickness and of the presence of a thin AlGaN barrier. Therefore it is believed to be an intrinsic effect of the processing of GaN free-standing structures.

Finally, an effect of the underetching of the clampings has also been observed. The etching beneath the clampings induces a deformation on the asymmetrically clamped structures. The deformation is due to the uneven stress relaxation because of the different boundary conditions on the layer faces due to the ambient and the substrate. This uneven relaxation produces an upward deformation of the structures, in the case of tensile residual stress. This deformation is incremented if the clampings are underetched, as the slope has been found to be proportional to the underetch length, using the numerical model. This effect produces a large deformation of the GaN asymmetric structures, together with the stress gradient generated during the GaN growth. Therefore double clamped structures have to be used for the design of GaN based MEMS structures. If a stress-free working point is required by the device design, an H-shaped beam can be used as the simulations show a complete relaxation of the central beam. Anyway, the deformation is low due to the stiffness of the two longitudinal beams.

Nanocrystalline diamond resonators

The technology developed in this thesis, described in the second part of this dis- sertation, has been used to produce NCD free-standing structures that have been statically and dynamically characterized. The characterization of these structures al- lowed the determination of the mechanical parameters of the NCD layers as well as the measurement of the resonator performance. The acquired knowledge was used for modeling and designing more complex structures, described later in chapter 9.

8.1

Introduction and motivation

The intrinsic mechanical properties of diamond, such as its high Young’s modulus, fracture strength, and low mass density [35], make diamond a perfectly suited mate- rial for high frequency and harsh environment MEMS [251, 252]. Depending on the deposition conditions the mechanical properties of the NCD can be modified [45], but when the grain size of NCD is larger than 50 nm the properties of this material approach to those of the crystalline diamond [35]. The details on the superlative properties of NCD have already been presented in the chapter 1.

NCD has been employed for the fabrication of RF switches [253] and several types of resonators [53, 64, 254–256]. In these devices the outstanding mechani- cal properties of diamond have been exploited to reach high resonant frequencies (640 M Hz [53]) and low switching times [251, 253].

Other functioning principles have yielded very high frequency NCD resonators, such as the disk resonator by Wang et al. [63], operating at 1.51 GHz with Q = 11555. In other published work, Gaidarzhy et al. [54] claim a cantilever type resonator fab- ricated with NCD operating at frequencies as high as 1.441 GHz and a frequency- quality factor product of Qf = 1013 _{Hz. In a recent work, Yang et al. [257] have}

used ultrathin NCD layers (50 nm) for the fabrication of resonant membranes sus- pended by two nanoscale tethers operating in torsional mode in the 10 M Hz range, with quality factors above 103_{. NCD has been also used in piezoelectrically actuated}

devices [258], but this type of devices will be specifically addressed in chapter 9. Finally, NCD can also be used for other type of sensors, such as gas sensors [259].

Extremely high quality factors have been reported for NCD beam resonators op- erated at the M Hz range at room temperature (∼ 10000) [260]. Other recent works claim the fabrication of NCD resonant structures with Q = 28800 [261], although this value is still far from the quality factor obtained for similar devices fabricated with single crystal diamond (∼ 500000) [260]. Nevertheless, NCD is much easier to produce, process and integrate with other materials. Consequently, NCD is the more suitable material for functional MEMS from the carbon material family.

All these published results provide sufficient ground for claiming that NCD is an excellent material for MEMS sensors and actuators fabrication for high frequency and high Q applications. Moreover, the excellent thermal and chemical stability of NCD allows the usage of the fabricated devices in harsh environment applications. Hence the fabrication of NCD MEMS is one of the objectives in this thesis.

For a correct design of the device performance and the actuation principles, sim- ple devices have to be fabricated and characterized in order to asses the material properties and the performance limiting factors. At a later stage, the obtained knowl- edge may be used for the design of complex structures. In this chapter this first research step is addressed. Simple beam resonators have been fabricated for the analysis of the material properties and device performance using magnetomotive ac- tuation.

The technology developed in the previous part of this thesis was used for the fabrication of metal/NCD free-standing structures. The structures were completely covered by a T i/Au/N i (20 nm/100 nm/80 nm) metal stack that served as both etch mask and current conductor for the magnetomotive actuation. Various NCD materials have been used and the mechanical properties of the NCD and the resonant structures have been calculated. Finally, behavioral models were derived for their use in the design of more complex structures, which will be described in chapter 9.