Investigation of Elastic Energy on Single Crystal GaN Nanobeams with Different Span

This research presents a novel technique which canmore efficiently fabricate different spans of nanobeams on the same substrate. It requires less time to prepare specimen and further shortens the process of aligning, clamping, and testing. Also, we probe into the elastic deformation properties of clamped freestandingGaN nanobeamswith different spans. In the bending process, displacement, D, corresponding to load, P is strongly dependent on the span of nanobeam at the same penetration depth and a distinct linearity is observed. Young’s moduli E of the GaN in this study are calculated as 171.3 GPa ±5.4% and 264.2GPa ±4.7% by strain energy methods, respectively, for the longer and shorter spans of nanobeams, serving as a simple supporting beam of elastic material under small deformation.The result shows that, even under small deformation, the rigidity enhancement helps the shorter nanobeam store more elastic energy.


Introduction
Since the conversion of mechanical energy into electric one has been realized as a nanogenerator for the recycle energy issue, Nitride-based one-dimensional nanomaterials have attracted much attention [1,2].Among them, the materials AlN, InN, and GaN are usually fabricated by bottom-up growing techniques and the top-down growing methods also involve in some GaN-based nanogenerator fabrication [3].This means that nanogenerator can be realized by semiconductor processing techniques.In nanogenerator experiment in which the kinetic energy is transferred into the elastic one, it is interesting to note that the output current is significantly dependent on the bended nanorods with different aspect ratio whereas the magnitudes of the deflecting kinetic energy are equal [3].Furthermore, the deflecting direction is perpendicular to the axial direction (-plane of GaN film) of nanorods which were stretched on the outer surface and were compressed on the inner surface [4], which consequently creates the rigidity.The shorter aspect ratio will produce more rigidity than that in longer one at the same displacement.This means that the shorter a nanorod is, the more energy is needed to bend a nanorod.Therefore, considering its elastic behavior, the shorter nanorod can store more energy.The mechanical characterization of onedimensional nanostructure with different aspect ratio has proven itself a fertile ground for further research.However, their sizes and configurations, which cannot be precisely tested by conventional measures, have posed great challenges to the mechanical characterization of nanostructures.To acquire better measurement, axial loading for uniaxial compression is adopted in experiments concerning mechanical behavior about one-dimensional GaN nanomaterials [5,6].In this method, the advanced group III nitride semiconductor nanotube fabrication technology makes intricate manipulations unnecessary.Besides, precise alignment of an individual nanotube is still a challenging task.Various novel methods have been developed to overcome the aligning problem, such as microelectromechanical system (MEMS) test [7][8][9], micro/nanoindentation tests [10][11][12][13], tensile tests [14], and bending tests [15][16][17], each of which has its contribution and advantages.Unfortunately, aligning, clamping, and testing of individual nanowire between two fixed ends still demand great specimen preparation time.
To offer a better solution, this report presents a novel, more efficient technique which can fabricate different spans of nanobeams on a homogeneous substrate.It requires less time to prepare specimen and shortens the process of aligning, clamping, and testing of individual nanobeam between two fixed ends.In this study, nanobeams, fabricated by focused ion beam (FIB, FEI Nova-200 NanoLab Compatible) with different spans, are clamped in between two homogeneous fixed ends as simple supporting beams.They are subjected to tension or compression loads in an in situ transmission electron microscopy.These bending tests of nanobeams install a conical tip inside the transmission electron microscopy (TEM) chamber, improving the visibility for alignment, load, and displacement.In addition to testing the elastic energy of nanobeams, we also conduct experiments for the linear relationship of stress and strain with different spans.

Experiment
Firstly, a slice of GaN with a feature size ∼250 nm in width, 10 m in length, and 3 m in depth was peeled from single crystal GaN film by FIB (FEI Nova-200 NanoLab Compatible) at 5 keV.The single crystal GaN film was grown as prior study showed in a standard process by metal organic chemical vapor deposition (MOCVD) on sapphire (0 0 0 1) [3].Secondly, this single crystal GaN slice was then postpatterned and machined by FIB again with a tilted angle of 30 ∘ to generate a uniform set of suspended bridge structures of different lengths.
After fabrication, the geometric parameters of each nanobeam on the GaN substrate were measured from scanning electron microscope (SEM) observations.The length ranges are ∼1.5 and ∼2.0 m, while the width is  = ∼ 250 m.The thickness of the GaN nanobeams was examined by TEM cross-section observation to be  = ∼ 50-195 nm while the as-deposited thickness (-direction) was average 125 nm and formed a hexagonal columnar grain structure in -axis.
The fabrication process and cross-sectional structures of GaN nanobeams are depicted in Figure 1.The right part of Figure 1 reveals the transverse geometry of the fabricated nanobeam.The trapezoid shape is formed by the FIB machining of the GaN substrate.Surface morphologies and crosssectional views of these two GaN nanobeam samples were then examined by SEM and TEM.
Figures 2(a) and 2(b) are the tilted top view SEM images, showing the fabricated nanobeam samples with different length.The nanobeam length, , is defined as the suspending distance between two tops of supporting leg with column-like ends.Therefore, the 2 m and 1.5 m lengths of nanobeams are with aspect ratios of ∼10 and ∼7, respectively.In situ TEM was then performed to observe and evaluate the mechanical behavior of the GaN nanobeams with different aspect ratio.After the vertical alignment was completed, the displacement between the specimen and conical tip was measured by using a TEM with the loading device installed, given that TEM can precisely locate interfaces and sharply measure the displacement and contact point of the loading tip.All observations are conducted in an accelerating voltage of 15 kV under vacuum (1.5 × 10 −5 Pa).When the in situ experiment is being exercised, the loading rate of 10 nms −1 is applied continuously to load the tested specimen and then unloaded at the same rate while a preset maximum load displacement of 200 nm was reached.It is found that the maximum loading forces on sample I and sample II in penetration indentation depth of ∼200 nm (point (c) of the loading curve) were ∼30 N and ∼172 N, respectively.However, the eventful slope changes transpire in point (b) of Figures 3(a) and 3(b) when the loads get beyond ∼8 N and ∼20 N, while the maximum linear deflections are 90 nm and 80 nm in sample I and sample II, respectively.The linear elastic behavior of both nanobeam specimens became nonlinear when the loading force was continuingly increased beyond the point (b) in Figures 3(a) and 3(b).The sudden increase of slope suggests the existence of more complex elastic and plastic behaviors, particularly on the shorter span of GaN nanobeam system (sample II).In the shorter one (sample II), the slope was found to increase dramatically from ∼20 N to ∼172 N while the penetration depth is increasing from 80 nm to 200 nm as shown on point (b) to point (c) in Figure 3(b).Clearly, shorter specimen, namely, sample II, needs more load and work than longer ones to be pressed to the same depth of the pressed sample I.In indentation test, longer GaN nanobeam specimen shows more linear elasticity than shorter ones as shown in the contrast of sample I and sample II.More interestingly, both unloading curves return approximately to the original position.The perfect retreats of the loading and unloading curves indicate that the elastic energy can be stored and released in both of the indentation tests of the freestanding nanobeam systems without considering the aspect ratio.

Result and Discussion
As we know, axial tensile force is also introduced when the nanobeam systems are displaced at the center section in this study.Therefore, the enhancement of nanobeam rigidity and nonlinearity in force versus displacement variation is transpired [18].Furthermore, assuming the prestretch was produced when the film was being grown by MOCVD, in a nanobeam fabrication can be neglected in the same specimen, the load-deflection behaviors in a given indentation test will be affected by four factors [19]: geometrical nonlinearity introduced by kinematic effects, plastic deformation, increasing contact area during indentation, and rate dependent material effect.Fortunately, limiting displacements in the bending test can minimize the influence of these four factors.
Given the elastic behavior shown in the experimental data, when at low displacement, the loading force of both nanobeams increased linearly with the displacement.This means that both GaN nanobeam systems exhibited linear elastic characteristics, when they were operated in low displacement.Under large deformation, the theoretical bases of the nanobeam test obey the classical beam theory with concern in substrate deformation [20].
Under small deformation (line (a)-(b) in Figures 3(a) and 3(b)), the deflection, , is linearly proportional to the lateral load, .Therefore, we define the slope, .On the other hand, for small deformation of unloading curves (line (d)-(e) in Figures 3(a) and 3(b)), the data of the recovery also exhibit a linear relationship between unload and deflection.We define the slope, .It is found that the slope  is almost the same as the slope  in Figure 3(a), further suggesting a good linear elastic behavior observed in higher aspect ratio of GaN nanobeam system, compared to that in lower aspect ratio of GaN nanobeam system.
For a given nanobeam sample with available values of sample length and thickness, the linear relationship between stress and strain in simple tension or compression can be expressed by the equation  = , in which , , and  are displacement, correspondence to load, and a constant of proportionality, respectively.The equation is commonly known as Hook's law, a rule only applied to ordinary tension and compression.Young's modulus is then obtained by measuring the nanobeam displacement as a function of the applied load.For a two-end fixed beam used here, Young's modulus cannot be determined from merely a slope of deflection versus load.We have to also consider linear elastic beam bending theory.The possibility of linear elastic deformation is discussed below.We assume that the GaN nanobeam systems are simple supporting beam systems, subjected to a vertical loading  (-direction).The linear force  is proportional to  and its value is  0 when  =  0 .Then  = ( 0 / 0 ), and the work is When an elastic material is deformed, this work can be stored in the form of potential energy.In this case, potential energy is strain energy  which can be expressed by the equation The displacement is where , , and  are the moment of inertia, Young's modulus, and span of the clamped portion of the beam, respectively.The moments of inertia on -axis of nanobeam systems are calculated as  = 8.64 × 10 −5 m 4 and 6.65 × 10 −5 m 4 for the lengths of 2.0 m (sample I) and 1.5 m (sample II), respectively.The beam's deflections at the point where  is applied are 90 nm and 80 nm.The force is assumed to change linearly as a function of bending displacement when the experiment was conducted on the curve of point (a) to point (b) in Figures 3(a) and 3(b).The average loading forces on deflection displacement of 90 nm and 80 nm are obtained as 8.01 ± 0.23 N and 20.32 ± 0.43 N, respectively.Therefore, we can estimate Young's modulus  from formula (3) by equating the work done to the strain energy in the nanobeam.Young's modulus  in this study is calculated as 171.3 GPa ±5.4% and 264.2 GPa ±4.8% for the longer nanobeam system (sample I) and shorter nanobeam system (sample II), respectively.Table 1 depicts the data and calculating results of GaN nanobeam systems with different spans.It is found that the enhancement of nanobeam rigidity, a byproduct of axial tensile force, is strongly dependent on the span of nanobeam even under small deformation.Notably, the axial direction of a deflected nanobeam in this experiment is not on -axis of GaN film examined in nanogenerator studies but is perpendicular to the -axis of nanobeam.
A series of in situ TEM images of sample I, as shown in Figure 4, presents the elastic-plastic behavior described by the data of Figure 3(a).Figure 4(a) shows the nanobeam before the deflecting experiment.When the tip gradually loads downward to the nanobeam at the beginning of the nanoindentation, the conical tip can easily bend the clamped GaN nanobeam because it is freestanding, with no barrier to restrict the bending process.
When a certain bending indentation depth has been achieved, as shown on point (b) in Figure 3 The maximum loading force deforming the nanobeam by the conical tip on point (c) in Figure 3(a) is given in Figure 4(c).Here, the relative location between conical tip and nanobeam can be easily targeted.This image shows that the loading force is not a perfectly concentrated load, suggesting the transition from single point bending indentation of a beam to surface stretching indentation.Moreover, the locations which are not contacted by the conical tip possess good elastic recovery.
Another dramatic slope switch can be found in Figure 4(d) corresponding to point (d) in Figure 3(a).Figure 4(e) corresponding to point (e) in Figure 3(a) shows the finished view of the deflected nanobeam, as expected, in which the nanobeam recovered perfectly to the original location as shown in Figure 4(a).

Conclusions
This research investigates a novel technique which can fabricate different span of nanobeams on a substrate and it does not require significant amounts of specimen preparation time for aligning, clamping, and testing of individual nanobeam between two fixed ends.In this study, nanobeams fabricated by focused ion beam with different spans are clamped in between two homogeneous fixed ends as simple supporting beams, subjected to load in an in situ TEM.These in situ TEM analyses provide details of bending to stretching-induced mechanical deformation.
It is found that a more conspicuous linear elastic behavior is observed in indentation test of longer GaN nanobeam specimen (sample I).Young's moduli have also been studied by strain energy method with presuming GaN nanobeams as simply supported beam systems of elastic material.The slopes of the - curves standing for the linear relationship between  International Journal of Photoenergy stress and strain at the initial phase of tests prove that the enhancement of nanobeam rigidity is strongly dependent on the span of nanobeam even under small deformation.

Figure 1 :
Figure 1: A schematic illustration showing a single crystal GaN nanobeam machined by FIB and a nanomechanical test and loading direction of a nanobeam in TEM.The right part is a cross-section view of GaN nanobeam with a cross-section area of 0.03125 m 2 after machining by FIB.

Figures 3 (
Figures 3(a) and 3(b) show the loading-unloading characteristics of the nanoindentation test, targeting these two different spans of single crystal GaN nanobeams with an aspect ratio of ∼10 (i.e., sample I) and an aspect ratio of ∼7 (i.e., sample II), operating in in situ TEM at room temperature, respectively, whereas the (a)-(b)-(c)/(c)-(d)-(e) symbols denote the experimental loading/unloading data, respectively.It is found that the maximum loading forces on sample I and sample II in penetration indentation depth of ∼200 nm (point (c) of the loading curve) were ∼30 N and ∼172 N, respectively.However, the eventful slope changes transpire in point (b) of Figures3(a) and 3(b) when the loads get beyond ∼8 N and ∼20 N, while the maximum linear deflections are 90 nm and 80 nm in sample I and sample II, respectively.The linear elastic behavior of both nanobeam specimens became nonlinear when the loading force was continuingly increased beyond the point (b) in Figures3(a) and 3(b).The sudden increase of slope suggests the existence of more complex elastic and plastic behaviors, particularly on the shorter span of GaN nanobeam system (sample II).In the shorter one (sample II), the slope was found to increase dramatically from ∼20 N to ∼172 N while the penetration depth is increasing from 80 nm to 200 nm as shown on point (b) to point (c) in Figure3(b).Clearly, shorter specimen, namely, sample II, needs more load and work than longer ones to be pressed to the same depth of the pressed sample I.In indentation test, longer GaN nanobeam specimen shows more linear elasticity than shorter ones as shown in the contrast of sample I and sample II.

Figure 2 :Figure 3 :
Figure 2: Tilted 45 ∘ top-view FESEM images of nanobeams with 2.0 m (a) and 1.5 m (b) in length and 250 nm in width after being machined by FIB.
(a) corresponding to Figure 4(b), a dramatic slope change occurs.Such change later brings about rigidity when the loading exceeds the linear elastic of the nanobeam.At this moment, the property of the nanomechanical action starts to change: the linear beam-like behavior is now turned into a nonlinear one.

Figure 4 :
Figure 4: A sequence of images extracted from a video recording of sample I, corresponding to the indentation experiment performed in point (a) to point (e) of Figure 3(a), showing the deformation stages: (a) the GaN nanobeam before loading, (b) at the end of linear loading, (c) the bended nanobeam at peak load, (d) during unloading at the end of nonlinear or plastic deformation, and (e) nearly no residual deformation after full separation.

Table 1 :
The experimentally measured data and calculating results of GaN nanobeam systems with different span.