Micro-Opto-Electro-Mechanical Device Based on Flexible β-Ga2O3 Micro-Lamellas

1IPFN, Instituto Superior Técnico (IST), Campus Tecnológico e Nuclear, P-2695-066 Bobadela LRS, Portugal 2Instituto de Engenharia de Sistemas de Computadores-Microsystems and Nanotechnology (INESC-MN), Lisbon, Portugal 3i3N and Physics Department, University of Aveiro, 3810-193 Aveiro, Portugal 4CICECO and Materials and Ceramic Engineering (DEMaC), University of Aveiro, 3810-193 Aveiro, Portugal 5C2TN, Instituto Superior Técnico (IST), Campus Tecnológico e Nuclear, P-2695-066 Bobadela LRS, Portugal 6Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal 7Departamento de Física de Materiales, Universidad Complutense de Madrid, 28040 Madrid, Spain 8National Institute for Materials Science, Tsukuba 305-0044, Japan

The recent renewed interest in monoclinic β-Ga 2 O 3 arises from its potential for transparent optoelectronic devices up to UV due to its wide bandgap of ∼4.9 eV. [1][2][3][4][5][6] Furthermore, the large breakdown voltage of ∼8 MV cm −1 is another property that makes this semiconductor a promising material for high power electronics. 7 Several studies have been published on other applications using this semiconductor putting in evidence the advantages of its particular properties, as for example in LEDs, large transparent and conductive substrates, intelligent windows, etc. 3,8,9 By controlling the stoichiometry 10 and by doping with Sn, Si, or Mg it is furthermore possible to control its conductivity. [11][12][13] Two dimensional, high quality, flexible β-Ga 2 O 3 thin lamellas/membranes, produced from single crystals by mechanical exfoliation, demonstrated high potential for high power (opto) electronics, 14 as well as for mechanical applications such as microresonators. 15 Thermal actuators are devices in which the mechanical movement results from the thermal lattice expansion due to Joule heating when a current passes the device. 16 β-Ga 2 O 3 , with a high thermal stability (melting point above 1700°C 17 ) and low thermal conductivity, presents a relation (α/k) between the thermal expansion coefficient (α) and the thermal conductivity (k) similar to the structural materials (metals and polysilicon 16 ) conventionally used to design thermal actuators (see Table I which compares the relevant materials properties of several materials used in thermal actuators). In this context and considering that the relation (α/k) is among the most important parameters to evaluate the potential of an active material to design thermal actuators, 18 in this study flexible micro lamellas of β-Ga 2 O 3 are investigated. β-Ga 2 O 3 actuators are expected to be specially suited for applications in harsh temperature and radiation environments. The interest on electro-thermal actuators based on β-Ga 2 O 3 becomes even more relevant when additionally considering their optical properties, such as the high transparency in the UV and visible region as well as their waveguiding properties. 19 z E-mail: marcoperes@ctn.tecnico.ulisboa.pt Regarding the optical properties of β-Ga 2 O 3 , up to three different broad light emission bands have been revealed by luminescence studies with excitation above and below bandgap energy. These UV, blue and green bands, localized around 3.4, 3.0 and 2.4 eV, respectively, are assigned to different intrinsic defects in β-Ga 2 O 3 . 10,20,21 The UV band is being attributed to radiative recombination of free electrons with self-trapped holes or an exciton bound to an acceptor. 21,22 Concerning the blue band, it has been consensual that it is related with the oxygen vacancy concentration and, contrary to the UV band, this band can be observed under excitation below the bandgap energy. The blue band strongly depends on the sample preparation conditions and there are strong evidences that it is related with the electrical conductivity being only observed in conductive samples. 20 Binet et al. 23 estimated an activation energy for the deep trap involved in the UV and blue emission of ∼0.3 eV. Contrary to the UV and blue bands, the green band, localized at ∼2.4 eV, is usually attributed to impurities as for example Be, Ge and Sn. 10,22 In this work, a systematic study is performed in a device based on a flexible β-Ga 2 O 3 lamella anchored at both extremes on a rigid substrate. The temperature of the device was calibrated with the help of Raman and PL measurements. A vertical movement of the actuator of up to 42.38 μm, caused by thermal expansion, was observed and evidences the potential of this material for thermal actuators.

Experimental
Thin and flexible lamellas of β-Ga 2 O 3 , with dimensions of some mm length with a thickness lower than 10 μm with a (100) surface orientation were mechanically exfoliated from β-Ga 2 O 3 bulk crystals grown using the floating zone technique as described in Ref. 9. The mechanical exfoliation process using a thermal-release tape (REVAL-PHA) was done following the procedure described in Ref. 30. The thin lamellas of Ga 2 O 3 were transferred to a silicon wafer with a silicon oxide layer of 2 μm thickness that works as an electrical isolating layer.  Two lateral Au/Al contacts with a thickness of 100 nm and 200 nm, with a separation of about 1.5 mm were deposited on the surface of the β-Ga 2 O 3 lamellas by RF-sputtering at room temperature, the size and position of the contacts were defined using a hard mask. Two anchors were created by two pads of indium positioned on top of the two contacts and melted using a hot plate at 200°C during five minutes.
These two pads work also as electrical contacts.
In Figure 1a a schematic of this type of device is shown where the relative directions of the three main crystalline axes (a, b and c) of the β-Ga 2 O 3 lamella are indicated. The objective of these two anchors is to fix the two extremities of the lamella and force a vertical movement when a thermal expansion of the lamella takes place induced by selfheating when an electrical current passes through it. The deflection (vertical movement Z'-Z (see Figure 1a)) due to the thermal expansion of this kind of devices is given by the simple relation: where θ is the initial deflection angle when the device is unbiased, L is approximately half of the lamella length for small θ and L = Lα T is the elongation due to the thermal expansion with, α the thermal expansion coefficient and T the temperature variation associated to the Joule effect. Figure 1b shows an optical microscopy image of the studied device, with a dimension of 1500 × 600 μm 2 and a thickness of ∼5 μm (the thickness was estimated by Rutherford Backscattering spectrometry as described in Ref. 31. The optical characterization was performed by photoluminescence and micro-Raman spectroscopy. The photoluminescence (PL) spectra in the range between 200 nm and 800 nm were acquired using a CCD camera (JY Symphony) coupled to a monochromator with a diffraction grating of 1200 lines/mm (Triax 150 JY). As excitation source, a 240 nm LED (UVTOP 240) was used working with a power of 50 μW and a spot size of 4 × 4 mm 2 . The PL is collected and guided to the monochromator through an optical fiber with a core of 600 μm diameter. The presented spectra were corrected to the optical response of the PL system.
The micro-Raman analysis was conducted in backscattering configuration on a Jobin Yvon HR800 instrument (Horiba, Japan), using a 600 lines/mm grating and the 441.6 nm laser line of a HeCd laser (Kimmon IK Series, Japan). The excitation laser line was suppressed by a pair of edge filters placed in series, allowing Raman acquisition starting at 50 cm −1 . A 50x objective (spot size ∼2 microns, numeric aperture = 0.9, Olympus, Japan) was used to focus the laser light onto the sample and to collect the Raman radiation in a backscattering configuration and further direct the light to the spectrometer equipped with a Peltier cooled (223 K) back-thinned CCD detector. The apparatus was operated in the confocal mode, setting the iris to 0.25 mm and the acquisition time to 2 s with 3 accumulations. All the results presented in this paper using these different techniques were obtained in air.
A non-contact 3D optical profiler (S neox 3D, Sensofar) was used to measure the thickness and the deflection of the lamellas as a function of the applied current. This optical profiler is equipped with a black and white 1360 × 1024 pixels CCD sensor that, when combined with a display of 2560 × 1440 pixels, yields high resolution optical images. The vertical resolution in this equipment is further enhanced by a piezo assisted Z-axis deflection movement (limited to 200 μm) without any further mechanical components. The confocal mode was used to measure the deflection of the β-Ga 2 O 3 lamellas as a function of the applied current. This mode used an objective with 10x magnification and a numerical aperture (NA) of 0.30 having an optical resolution in  XY of 0.46 μm and a vertical resolution (Z) of 25 nm, for a visualization area of 1754 × 1320 μm 2 . In order to measure the thickness of the entire micro-lamella with better accuracy, interferometric analysis in Vertical Shift Interferometric (VSI) mode was used. In this case, a 10x objective was also used and it provides optical (XY) and vertical (Z) resolutions around 0.50 μm and 1 nm, respectively.
The electrical characterization was performed using a semiconductor device analyzer (AGILENT B1500). All the electrical characterization was performed at room temperature. Figure 2a shows the obtained I-V curve of this device where the metal-semiconductor-metal configuration can be described by the equivalent circuit presented in Figure 2b composed of two back-toback polarized Schottky diodes separated by a resistance. The almost linear and symmetric curve observed in this particular device suggests that the contacts are almost ohmic. However, I-V curves of other devices prepared in a similar way showed nonlinear and even asymmetrical curves. 31 This evidence suggests that heterogeneous distribution of interface defects, intrinsic and extrinsic, such as defects on the surface of the β-Ga 2 O 3 lamellas resultant from the exfoliation process, probably plays a major role in the electrical behavior. Despite these challenges in fabricating devices with reproducible electrical properties, it should be noted that all these devices exhibited similar properties in terms of self-heating and thermal expansion.

Results and Discussion
In order to assess the thermal expansion of the actuator, it was first necessary to establish the calibration of the beam temperature as a function of the applied electrical power (note that this calibration may be different for different devices due to the varying size of exfoliated crystals and due to the above mentioned variations in contact properties). For this, temperature and power dependent Raman and PL measurements were performed on the same device. Figure 3a shows the μ-Raman spectra of a bulk β-Ga 2 O 3 crystal taken at temperatures from RT to 798 K where the sample temperature was adjusted using a heatable sample stage. Figure 3b shows μ-Raman spectra as a function of the applied power (without external heating), measured in the middle of the lamella between the two electrodes. For each measurement, the focal distance was realigned to maximize the Raman signal in order to compensate the defocussing caused by the vertical movement of the crystal as the power is increased. The intense and sharp Raman peaks (similar to those of the bulk β-Ga 2 O 3 crystal) confirm the good structural quality of the exfoliated micro-lamellas obtained by mechanical exfoliation. Due to the limitations of the spectral resolution and due to the superposition with two strong bands of the silicon substrate, in these spectra only 8 peaks (from the 15 predicted by group theory and previously observed 33 ) associated to the A g and B g modes of β-Ga 2 O 3 were identified. In agreement with Doyng et al. and Rao R. et al., 34,35 these 8 peaks can be classified in three main groups: the high-frequency group associated to the stretching and bending of the GaO 4 tetrahedra (770-500 cm −1 ), the mid-frequency group associated to the deformation of the Ga 2 O 6 octahedra (480-310cm −1 ) and the low-frequency group associated to the liberation and translation of the tetrahedral-octahedra chains (below 200 cm −1 ). Comparing both Raman studies, it is observed that the peaks shift to lower wavenumbers both for higher applied powers and higher temperatures. Figure 3c plots the Raman peak position of the B g 3 and A g 10 modes as a function of the temperature extracted from the spectra in Fig. 3a. These two modes where chosen for being the most intense peaks and for being sensitive to the stretching and bending of the GaO 4 tetrahedral and to the deformation of the Ga 2 O 6 octahedra in agreement with. 35 The dependence of the peak shift with the temperature of the different Raman modes is well described by the empirical Cui formula: 36 where A and B are fitting parameters, ω 0 is the Raman phonon wavenumber at 0 K and k B is the Boltzmann constant, h the Planck constant and c the speed of light in vacuum. The temperature dependences of both A g 10 and B g 3 modes are well fitted by expression 2 (see Figure 3c); this fact suggests that the effects of bending induced by the Joule-heating (responsible for the vertical movement) play a minor role on the Raman shift suggesting that the temperature should be the main responsible for the observed Raman shifts. Rewriting expression 2 by solving it for T and using the fitted parameters (A,B and ω 0 ), a calibration curve of the expected temperature for a certain applied power can be determined. Figure 3d shows the determined temperature as a function of the applied power considering the wavenumbers of both Raman modes (B g 3 and A g 10 ) in the spectra shown in Figure 3b. As an independent confirmation of the temperature calibration as well as to understand the effects of the temperature on the luminescence properties of the exfoliated lamellas, a PL study as a function of the temperature was performed in a similar lamella used to fabricate the thermal device, but not anchored to the substrate in order to avoid any strain induced by the lamella bending. The PL spectra are dominated by an asymmetric broad band with a maximum at ∼3.0 eV (see Figure 4a). The dependence on the temperature is characterized by a strong quenching without any energy shift. Comparing to different reported works, 20,23,37 this asymmetric band is assigned to an overlap of the two emission bands, UV and blue, located at ∼3.4 eV and 3.0 eV, respectively. Based on the Urbach law, Binet et al. estimated an activation energy of 0.3 eV for the thermal quenching of the blue band and associated this band to a deep acceptor level 0.3 eV above the valence band maximum. 23 The UV band, on the other hand, was associated to self-trapped excitons supported by recent computational results. 38 Electron paramagnetic resonance studies estimated an activation energy of about 0.19 eV for this process. 39 In this study, we adopt the activation energy estimated by Binet et al. for the blue band, although the underlying process is still under debate since density functional simulations point to typical acceptor levels above 1.3 eV in Ga 2 O 3 . 40 Indeed, the dependence of the integrated PL intensity measured (i.e. englobing both bands) is well fitted (see Figure 4c) assuming an activation energy of 0.3 eV, using the conventional law for the thermal quenching 41 described by: [3] where I 0 is the intensity at 0 K, A is a constant describing the relation between radiative and non-radiative recombination lifetimes and E a is the activation energy. Figure 4b shows the PL spectra as a function of the applied power. The differences in the shape of the spectra compared with the study with the temperature are due to different interference effects that occur due to the different collection angles. 42 Effectively, because the Ga 2 O 3 lamellas are very small and thin, with our PL setup it is difficult to keep the same collection conditions (namely the collection angle) used for the temperature study. As performed in the Raman study, in order to avoid the influence of changes on the collection zone due to the vertical movement, for each spectrum acquired at different power the PL signal was maximized.
Similar to the temperature dependent results, the PL intensity quenches for higher applied power (increased Joule heating) without changes in the line shape; for powers above 100 mW the quenching is almost complete. Rewriting Equation 3 in order to have an expression for T as function of the normalized integrated intensity ( I (T ) I 0 ), the temperature of the flake resultant from the self-heating for each of the power dependent spectra was estimated. As shown in Figure 4d, following this methodology, the estimated temperatures are in excellent agreement with the estimates based on the Raman study. These self-consistent results confirm that, on the one hand, the Raman peak positions are not strongly influenced by the bending of the crystal and that, on the other hand, the luminescence quenching of intrinsic defect luminescence can be used as a tool to calibrate the temperature of the beam as a function of the applied power. It is worth mentioning that similar luminescence quenching behavior was observed when a current was applied during cathodoluminescence and ionoluminescence measurements for more than 250 cycles (not shown) suggesting that this effect is stable and reproducible.
In order to characterize the mechanical movement of the device, the vertical displacement and deformation of the Ga 2 O 3 lamella as a function of the applied power was measured using an optical profiler. Examples are presented in Figures 5a and 5b showing the optical images of the unbiased device and after applying a power of 194.9 mW (I = 5 mA and V = 38.98 V), respectively. A buckling of the lamella is clearly observed when applying dc currents from 0 to 5 mA to the device with a vertical elevation of more than 40 μm for the highest tested current. From the optical images the buckling profiles of the micro-lamella were extracted and are plotted in Figure 5c. From this figure is possible to confirm that the center of the profile as function of the dc current keeps almost constant as expected for this kind of device. From these profiles, the length of the beam parallel to the b axis as a function of the applied power was calculated by integration (see Figure 5d). This figure shows that the evolution of the beam length between the two contacts is almost linear, namely, in the region of higher applied power. The non-linearity for low powers can be justified considering that when the vertical displacement starts the thermal contact to the substrate decreases significantly. For high power, the air becomes the main channel of thermal losses because most of the lamella loses direct contact to the substrate. This is supported by the fact that the heat transfer coefficient (h) of air is considerably lower than that of the SiO 2 /Si substrate. 43 Considering that β-Ga 2 O 3 has a center of symmetry, no piezoelectric effects are expected 8,17 which means that the effect reported here should be purely thermal. Indeed, Figure 5d compares the beam length as a function of the applied power with the theoretical beam length estimated considering the lattice thermal expansion of β-Ga 2 O 3 along the b axis being described by α = 4.2 × 10 −6 K −124 using the standard definition for the linear thermal expansion L = L × α a × T . Figure 5d shows that the elongation estimated by the expression for the linear thermal expansion fits very well the tendency of the elongation measured as a function of the applied power/temperature. This result corroborates that all the mechanical movement is effectively due to a thermal expansion.

Conclusions
A thermal actuator based on a flexible lamella of β-Ga 2 O 3 anchored to the substrate at the two extremes was designed and successfully tested. When a current is applied to the β-Ga 2 O 3 lamella, an elongation occurs along the b axis of the crystal due to thermal lattice expansion resulting in a buckling of the lamella and thus a ver-tical movement. These results reveal the potential of β-Ga 2 O 3 microlamellas/membranes for electro-thermal actuators. The Joule-heating responsible for the elongation affects also the optical emission, namely the emission intensity of the UV and blue bands. The thermal quenching of these emission bands allows calibrating the temperature of the β-Ga 2 O 3 lamella. μ-Raman results corroborate the Joule-heating effect responsible for the luminescence quenching. Furthermore, the good agreement between calibration curves derived from PL and Raman studies demonstrates that the effect of strain due to bending on the Raman spectra is insignificant.
This work demonstrates that combining the thermal, optical and electrical properties of flexible micro-lamellas or membranes of β-Ga 2 O 3 , this material can be considered for the design of new kinds of micro-opto-electro-mechanical (MOEMs) devices such as camera focus systems, micro-mirrors and optical and microwave couplers. On the other hand, the results presented in this paper demonstrate also the potential of β-Ga 2 O 3 in devices where the self-heating processes could play an important role, such as for example in-situ damage recovery of detectors for ionizing radiation or for the recovery of aging effects in electronic devices.