Anisotropic Mechanical Properties of Black Phosphorus Nanoribbons

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Anisotropic Mechanical Properties of Black Phosphorus Nanoribbons Hao Chen, Peng Huang, Dan Guo, and Guoxin Xie J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b10644 • Publication Date (Web): 08 Dec 2016 Downloaded from http://pubs.acs.org on December 9, 2016

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The Journal of Physical Chemistry

Anisotropic Mechanical Properties of Black Phosphorus Nanoribbons †

†

*

*

Hao Chen, Peng Huang, Dan Guo, Guoxin Xie

State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China

1

ACS Paragon Plus Environment


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ABSTRACT: The mechanical properties of black phosphorus (BP) nanoribbons suspended

on

narrow

grooves

are

quantitatively

investigated

with

the

nano-indentation method on the basis of atomic force microscopy. The elastic moduli of BP nanoribbons are strongly related to the included angle between the lattice orientation and the groove. A theoretical model based on classical elasticity theory is established to explain the directional elastic modulus and matches well with the experimental results. The ideal elastic modulus of zigzag and armchair BP nanoribbons are about 65 GPa and 27 GPa, respectively, and this agrees with the simulation results by theoretical calculations. The obtained results in the present investigations would strengthen the understandings on the fascinating anisotropic properties of BP, which would be of great help for the future applications of BP in flexible electronics and nano-electro mechanical system (NEMS), etc.

2


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∎ INTRODUCTION Black phosphorus (BP) is a booming two-dimensional (2D) van der Waals (vdW) materials which has attracted intensive interest for its unique physical and electronic properties and they are widely used in nanoelectric devices, photoelectric devices and chemical sensors.1-4 BP film delivers a thickness dependent direct band gap ranging from 1.5 eV (monolayer) to 0.3 eV (bulk).5 Besides, few layer BP field effect transistors (FET) possess a high on/off ratio (up to 105) and a high carrier mobility (1000cm2/(Vs)).2 Compared with the graphene and transition-metal dichalcogenides (TMDS), BP emerges at the electronic intersection because the graphene behaves high mobility but with a negligible band gap while the MoS2 possesses a large band gap with a slow mobility.6-8 BP also shows fascinating anisotropic electrical properties for its puckered structure. For example, zigzag BP nanoribbons are metals while armchair BP nanoribbons are semiconductors according to the first-principles study, and this anisotropic transport behavior was also experimentally verified.9-12 In spite of the intriguing electrical properties of BP, the mechanical properties of BP-based nanodevices are crucial but remain less well investigated. Density functional theory based first-principles calculations verified the highly anisotropic elastic modulus and ultimate strain of single-layer BP under uniaxial deformation.13-17 A negative Poisson’s ratio and a third principle direction were also verified for monolayer BP.18,19 Molecular dynamics (MD) simulation is an alternative approach to study the mechanical properties of BP. Effects of thickness and temperature on the mechanical behaviors of BP have been studied with the MD method.20-22 The fracture 3



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strain was smaller along the zigzag direction than that along the armchair direction while the elastic modulus was on the contrary.23-26 The fracture mechanism in the armchair direction was due to a break in the interlayer bond angles while the fracture in the zigzag direction was attributed to the break in both bonds and intra-layer angles.25 Recent studies showed that strain could affect the electrical properties of BP remarkably.27,28 Therefore, it is essential to consider the mechanical anisotropy into the design of BP nanoelectronic and photoelectric devices. In contrast to the extensive theoretical researches on the mechanical properties of BP, less experimental analyses of few layer BP flakes have been conducted.8,29 Experimental results showed that the elastic modulus of BP flakes along the zigzag direction was almost twice of that along the armchair direction and agreed with the theoretical results.10 For the BP flakes suspended on circular holes, the elastic modulus increased with the reducing thickness while the breaking strength was independent of the thickness.30 Substantial influence was certified on the mechanical properties of few-layer BP and the effect was larger for the thinner ones.31 However, it is 2D nanoribbons that are usually used in the actual devices, so the mechanical properties of 2D nanoribbons deserve to be investigated. MD simulations proved that the Young’s modulus of the graphene nanoribbon was strongly related to the size and chirality.32 Considering the puckered structure of BP, the directional mechanical properties of BP nanoribbons are of more great concern than other 2D nanomaterials. Hitherto, the elastic moduli of BP nanoribbons were only obtained in the zigzag and armchair directions.10 However, the relationship between the elastic modulus of BP 4


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nanoribbons and their lattice directions remains less investigated. Thus, this is experimentally and theoretically studied in the present work.

∎ EXPERIMENTAL SECTION Substrate Fabrication. Silicon (Si) substrates with arrays of grooves were designed and patterned through the photoetching method. The width of the groove was 1.5 μm and the depth was 500 nm. Optical Microscope. The optical images were captured with the optical microscope BX51 (OLYMPUS). Focused Ion Beam Etching. The black phosphorus flakes were sculptured into nanoribbons with the LYRA3 (TESACN) FIB-SEM instrument. The voltage in the FIB process was 30 kV and the beam current was 200 pA. Atomic Force Microscopy. The AFM images and height profiles were obtained by NTEGRA Prima (NT-MDT) and a tapping mode was used. AC 240TS-R3 probes (OLYMPUS) were adopted in the AFM experiments. The ramp rate for the indentation test was 1 Hz. A new AFM probe was adopted after one BP sample test was finished. The deflection sensitivities of the probe were calibrated on a standard clean sapphire wafer three times at different locations, and then the average values were obtained to diminish the accidental errors. The temperature and relative humidity in the experiment room were 25 ℃ and 14%, respectively. Raman Spectroscopy. The Raman spectra were obtained with the HR800 (HPRIBA) Raman instrument at room temperature using an Ar+ laser (514.5 nm) with 5



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a power of 1 mW. This could reduce the temperature influence on the structures of BP flakes.43,44 In the experiments, polarization of incident light changed from 0° to

360°, and the 0° direction of polarization was always set in the direction parallel to the groove on the Si substrate.

∎ RESULTS AND DISCUSSION Atomic force microscopy (AFM) has been widely used to measure the mechanical properties of nanomaterials, and the elastic modulus can be easily obtained through the force-indentation curves.33 Focused ion beam (FIB) etching is a universal method to sculpture 2D materials into arbitrary shapes.34 Raman spectroscopy is an effective way to confirm the lattice direction of BP nanoribbons.35 In this work, these techniques were combined to characterize the isotropic mechanical properties of BP nanoribbons. Few-layer thickness BP flakes were obtained by mechanical exfoliation from bulk BP crystal.29 Some BP flakes might cover one or several grooves after transferred onto the Si substrate. Total 7 BP samples were prepared and measured in the experiments. Figure 1a shows that the BP flake on the substrate is irregular under the optical microscope. In order to better reveal the anisotropic elastic properties of BP nanoribbons, we utilized FIB to sculpture the BP flakes and obtained rectangle suspended BP nanoribbons which were suitable for the following indentation test in the AFM experiments. Figure 1b is the schematic of FIB etching process. Figure 1c and 1d show the SEM images of a BP sample before and after FIB etching process. In 6


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the suspended part of BP flake over the groove, the widths of the BP nanoribbons after the FIB process ranged from 0.8 μm to 1.2 μm.

Figure 1. (a) Optical image of BP flake on the Si substrate with pre-patterned arrays of grooves. (b) The schematic of FIB etching process. (c), (d) SEM images of BP flake before and after the FIB etching process.

Both the mechanical and electrical properties of BP are strongly related with the lattice orientation.10,36,37 Therefore, it is significant to identify the lattice orientation of BP samples and this is realized by polarized Raman measurements in this work. In Raman measurements, atoms of BP will gain energy from the incident light and vibrate in some particular ways. Figure 2a shows a typical Raman spectroscopy of BP with three major peaks at Raman shift of 360 cm-1, 437 cm-1, 464 cm-1. Interestingly, the intensity of Raman spectra of BP depends on the polarization of the incident light. For different modes, atoms of BP may vibrate in a direction perpendicular or parallel to the zigzag or armchair direction. Generally for a certain mode of vibration, the strongest signal in the spectroscopy occurs when the polarization of incident light is parallel to the vibration direction of atoms. Thus, it is possible to identify the 7



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crystallographic orientations through the method. In the experiments, polarization of incident light changed from 0° to 360°, and the 0° direction of polarization was always set in the direction parallel to the groove on the Si substrate. To observe the results for different Raman shifts, it was found that vibration

mode was more regular and reflected clearer periodicity. Thus, the regular

intensity signals were taken into particular account and used to determine the lattice orientations. Figure 2b shows the variation of intensity in Raman shift with the direction of polarized incident light. Raman spectroscopy results of BP sample in polar coordinates are shown in Figure 2c. The shape of intensity curve in the polar coordinate looks like a peanut, and the direction of the strongest and weakest signals in the spectroscopy are explicit and orthometric. The strongest signal of occurs when the incident light is parallel to the armchair direction that we can obtain the direction of the BP nanoribbon.

Figure 2. (a) Raman spectra of BP with the 514.5 nm excitation. (b) The intensity of changes with the different direction of polarized incident light. (c) Raman spectroscopy results of BP sample in polar coordinates.

The lattice orientations of BP nanoribbons were obtained through polarized Raman scattering measurements after the AFM indentation tests to minimize the influences 8


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on the mechanical properties caused by the laser beam and degradation. Figure 3 shows two representative lattice orientations of BP flakes measured by Raman spectroscopy. As shown in Figure 3a and 3b, the spectroscopy of vibration mode for the sample 1 indicates that the strongest intensity occurs at the incident light with polarization angle of 18°. It means that the included angle between the armchair direction of the sample and the grooves edges on the substrate is 18°. Thus, the included angle between the suspended nanoribbon and the zigzag direction is known to be 18°. Similarly, the included angle between the zigzag direction and the BP nanoribbon of sample 2 shown in Figure 3c and 3d is 77°.

Figure 3. Representative lattice orientation of BP flakes measured by Raman 9



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spectroscopy. (a) and (b) refer to sample 1, (c) and (d) refer to sample 2.

The AFM indentation method has been widely used to measure the mechanical properties of 2D materials suspended on holes or grooves.10,33,38 In this work, indentation tests were carried out on the suspended BP nanoribbons to obtain the force-indentation curves which could be used to calculate the elastic modulus. In order to reduce the effect of BP degradation on the mechanical properties, the BP nanoribbons were preserved in a vacuum chamber and the AFM indentation tests were accomplished in a couple of hours after being freshly prepared. The influence of exposure to air in several hours on the mechanical properties could be neglected.31,39 Figure 4a and 4d showed that no obvious bubbles were observed on the BP flakes and this also verified the validity of the experiments. What is more, no cracks were found on the BP flakes in the SEM or AFM images, and this proved that the influence of FIB process was negligible. By comparing the Raman spectra of BP nanoribbons before and after the FIB etching, no obvious difference was observed and this verified the good crystalline structures. The tapping mode was conducted to obtain the topography of BP nanoribbons to minimize the damage and then we could acquire the widths and lengths of the BP nanoribbons. Two representative AFM images and the corresponding sections are shown in Figure 4. The tip radius is 15 nm (±20%) to ensure the applied load right on the center of BP nanoribbon. The cantilever stiffness is about 2 N/m which is close to the stiffness of BP nanoribbons at the loading point and this can assure the good accuracy of the bending test.10 Since the cantilever stiffness varied with the different mounting conditions, it was calibrated for every new 10


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probe before the indentation test by thermal tune method.40 Totally 7 BP samples were fabricated in our research and the corresponding parameters are shown in Table 1.

Figure 4. The AFM images and corresponding sections of two representative BP samples. (a) and (d) refer to the AFM images of two individual BP nanoribbons, (b) and (e) refer to the widths of the BP nanoribbons, (c) and (f) refer to the thickness of the BP nanoribbons. Table 1. Parameters of Different BP Samples No. Width/μm 1 0.81 2 1.17 3 1.06 4 1.07 5 1.13 6 1.13 7 1.26

Thickness/nm 66 134 102 151 58 83 75

/° 18 77 40 11 27 53 82

Figure 5a shows the schematic of AFM indentation test. The load is applied at the center of BP nanoribbon and the deformation of BP can be obtained by the following equation ∆ ∆

(1)

where is the deformation of BP nanoribbon, ∆Z is the scanning piezo 11



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displacement, ∆ is the deflection of AFM cantilever. The relationship between the applied load and the cantilever deflection is as follows

F= ∙ ∆

(2)

where F is the applied load, k is the stiffness of the AFM cantilever. As the both ends of BP samples are much larger than the nanoribbon, the BP nanoribbons are simplified to be a clamped-clamped beam model with a concentrated load at the center. Thus the relationship between the deformation and the load is described in equation 3.10

! " #$ "

!

δ +

'$ "

)

δ ( + δ $

(3)

where E is the effective elastic modulus of BP nanoribbon; t, w and l are the thickness, width and length of BP nanoribbon, respectively; T is the pretension of BP nanoribbon. When the indentation depth is small at the beginning, the load is mainly linear with deformation. With the increase of indentation, the load is related with the one order and cubic order of deformation. So equation 3 can be translated to equation 4.

We assume

+,!

! +, ! +,- ( * .+ * . #$ " ! '$ " !

+

)! +,* . $ !

(4)

is a dimensionless parameter, and the effective elastic modulus E can

be fitted according to the following equation (

/ 0 + 0 ( + 20 1

where A and B in the fitting equation are equal to

(5)

! #$ "

and

)! $

, respectively. Then

we can obtain the elastic modulus and the pretension that 3

#4$ "

(6)

$

(7)

!

5

!

12


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Figure 5. (a) Schematic of AFM indentation test carried on the suspended BP nanoribbon. (b) Fitting curve of the force on the dimensionless parameter δ/t. Several indentation tests were repeated on the same BP nanoribbon to acquire different force-indentation curves. Thus, the average elastic modulus and pretension could reduce the experimental errors to a large extent. Finally, the pretension of the BP nanoribbons on the Si groove T=0.14-0.44 N/m. For the thicker nanoribbons, the pretension is smaller than that of the thinner ones for their stronger structural stiffness. Similarly, the wider nanoribbons behave relatively smaller pretensions. Another reason for the resolving variation of the pretension are attributed to the different defects in the BP nanoribbons and the adhesion force with the substrate.41 The elastic modulus of BP nanoribbons ranges from 27.8 to 58.7 GPa and the standard deviations of each BP nanoribbon are shown in Figure 6. In the experiment, the BP flakes were mechanically exfoliated and the thickness of the flakes couldn’t be guaranteed with the same value. However, the effect of the thickness on the elastic modulus of BP flakes was neglected since the elastic modulus tends to be constant when the thickness is more than 30 nm.30 Recent discoveries also found that the elastic modulus and breaking strength of BP nanoflakes ranging from 4 nm to 30 nm were independent of 13



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the thickness.31 Therefore, the relationship between the elastic modulus and the included angle is investigated and the result is shown in Figure 6. The included

angle means the angle between the BP nanoribbon and the zigzag direction. The

elastic modulus is strongly related to the direction of BP nanoribbon and the modulus comes to the maximum value in the zigzag direction, being agreement with the theoretical results.10,14 It can be inferred that the elastic modulus of BP nanoribbons is strongly dependent on the lattice orientation for its puckered structure. Hence, we assume the effective elastic modulus of BP nanoribbon with an arbitrary direction is a function of Ezag, Earm and , which represent the ideal elastic modulus of zigzag BP nanoribbon, the ideal elastic modulus of armchair BP nanoribbon and the included angle, respectively. The BP nanoribbons are orthotropic and the height is far less than the length and width, thus we can expect them to be in-plane structures. Then the stress-strain relations are given in equation 8.42

9: =:: 9 = 8 < 8 : ;: 0

=: = 0

>: >: 0 0 < 8 > < @ 8 > < ?: =## ?:

(8)

Where 9 and ; are the normal and shear strain, > and ? are the normal and shear stress, subscript 1 and 2 means the two orthotropic directions, respectively. =::

=: =:

BAC A

BCA C

, =

:

C

, =##

:

DAC

:

A

,

, E: and E: are the Poisson’s

ratios along different directions, F: is the shear modulus. For a BP nanoribbon with

arbitrary direction, a relation is needed between the stresses and strains in the principal material coordinates and those in the body coordinates. Therefore, the transformation equations for expressing stresses in an x-y coordinate system in terms 14


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of stresses in a 1-2 coordinate system are given as follows,

>G >G 9G 9: >: ) ) ) J 8 >H < 8 9H < I 8 9 < I @ 8 > < I @I 8 >H < @ ;GH ?GH ?GH ;: ?:

(9)

where is the angle from the x-axis to the 1-aixs, I is the transformation matrix, @ is the compliance matrix. KLM I 8 MNO MNOKLM

MNO KLM MNOKLM

2MNOKLM 2MNOKLM < KLM MNO

(10)

Finally we can obtain that :

:

A

KLM 1 +

:

C

MNO1 + (

:

DAC

BAC A

)MNO KLM

(11)

Thus, we utilize equation 11 to explain the anisotropic elastic modulus of BP nanoribbons. The directional elastic modulus and the fitting result are shown in Figure 6. We can acquire the ideal elastic modulus in the zigzag and armchair direction that 3RS ≈ 65.16 ± 4.45 GPa , 3\]^ ≈ 27.38 ± 2.35 GPa , F: ≈ 11.3 ± 0.75 GPa , E: ≈

0.93 ± 0.04. This theoretical model agrees well with the experimental results and can

predict the directional elastic modulus of BP nanoribbons (Figure 6). The results also match with the literature values.10,30

15



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Figure 6. The elastic modulus of BP nanoribbons varies with different included angles. The inset line is the theoretical fitting result.

∎ CONCLUSIONS In conclusion, we have measured the elastic modulus of suspended BP nanoribbons with AFM nano-indentation and the strongly isotropic mechanical properties of BP nanoribbons are proved by the experiments. The elastic modulus of BP nanoribbons along the zigzag direction is the largest and almost 2.4 times of that along the armchair direction. The elastic moduli of BP nanoribbons are strongly related to the included angle between the lattice orientation and the groove. A theoretical model is utilized to predict the direction-dependent elastic modulus of BP nanoribbons and 16


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agrees well with the experimental results. This unique isotropic mechanical properties of BP makes it an ideal candidate for the future electronic and optoelectronic applications.

∎ AUTHOR INFORMATION Corresponding Authors *

E-mail: [email protected]; [email protected]

Author Contributions †

H. Chen and P. Huang contributed equally to the work.

Notes The authors declare no competing financial interest.

∎ ACKNOWLEDGEMENTS This work was financially supported by National Natural Science Foundation of China (Grant Nos. 51375255, 51527901, 51321092).

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Anisotropic Mechanical Properties of Black Phosphorus Nanoribbons

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