Discerning Black Phosphorus Crystal Orientation ... - ACS Publications

Subscriber access provided by TUFTS UNIV

Functional Nanostructured Materials (including low-D carbon)

Discerning Black Phosphorus Crystal Orientation and Anisotropy by Polarized Reflectance Measurement Arnob Islam, Vida Pashaei, Hao Jia, Zenghui Wang, Jaesung Lee, Guojun Ye, Xianhui Chen, and Philip X.-L. Feng ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b05408 • Publication Date (Web): 25 Jun 2018 Downloaded from http://pubs.acs.org on July 6, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Applied Materials & Interfaces

Discerning Black Phosphorus Crystal Orientation and Anisotropy by Polarized Reflectance Measurement Arnob Islam1, Wei Du1, Vida Pashaei1, Hao Jia1, Zenghui Wang1, Jaesung Lee1, Guo Jun Ye2, Xian Hui Chen2, Philip X.-L. Feng1* 1

2

Department of Electrical Engineering & Computer Science, Case School of Engineering, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA

Hefei National Laboratory for Physical Science at the Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

Abstract Strong in-plane anisotropy of atomic layer and thin film black phosphorus (P) offers new device perspectives and stimulates increasing interests and explorations, where precisely determining the black P crystal orientation and anisotropic axes is a necessity. Here we demonstrate that the crystal orientation and intrinsic in-plane optical anisotropy of black P crystals in a broad thickness range (from ~5nm to ~300nm) can be directly and precisely determined, by polarized reflectance measurement alone, in visible range.

Combining

experiments with modeling of multi-reflection and interference, we elucidate the underlying principles and validate these measurements. The polarized reflectance method is not only easy to implement, but also deterministic, non-destructive, and effective for both on-substrate and suspended black P atomic layers and thin films. Keywords: Black Phosphorus, In-Plane Anisotropy, Crystal Orientation, Polarized Reflectance Measurement, Polarized Raman Spectroscopy.

*

Corresponding Author. Email: [email protected] -1ACS Paragon Plus Environment

ACS Applied Materials & Interfaces 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

INTRODUCTION The rapid growth of explorations in atomically thin crystals, including the forerunner semimetal graphene and the following compound semiconductors such as transition metal di-chalcogenides (TMDCs), has enabled a variety of two-dimensional (2D) device prototypes and demonstrated considerable potential for future-generation electronics and optoelectronics1,2. Black P crystal, an elemental semiconductor, has recently emerged as a new player, or for its ‘renaissance’3, in the arena of 2D materials. It offers very high hole mobility (~1,000 cm2V-1s-1)4,5, layer-dependent direct electronic band gap (~0.3 eV in bulk, up to ~2 eV in its single-layer limit) that covers an unusually wide range from visible to infrared (IR); these make black P an attractive candidate for future electronic and optoelectronic devices6,7,8,9. Further and importantly, black P distinguishes itself from other 2D crystals for its strong, intrinsic in-plane anisotropy benefited from its corrugated crystal structure in each atomic layer formed by the sp3 nonequivalent hybridization of each P atom, giving rise to strong in-plane anisotropy between the armchair (AC) and zigzag (ZZ) directions3. This fundamental structural anisotropy in black P leads to a plethora of anisotropic physical properties that in turn promise new exciting device concepts and functionalities. For examples, one can envision atomically thin modulators, polarizers 10 , and plasmonic devices exploiting its anisotropic optical properties along the AC and ZZ directions11. In addition, utilizing the in-plane anisotropic thermal properties of black P, thermoelectrics with high efficiency may be realized12. Besides, owing to higher electrical conductance and mobility, and optical absorption along AC direction, in order to realize high performance field effect transistors and photodetectors, metal electrodes need to be fabricated in such a way that carrier transport occurs along AC direction13,14. In all these potential applications, it is necessary to identify the crystal orientation

-2ACS Paragon Plus Environment

Page 2 of 26

Page 3 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and precisely resolve the anisotropic axes (AC, ZZ) before one can utilize the unique anisotropic properties of the crystal. Considerable efforts have been made in determining black P crystal orientation. In material science studies, high resolution transmission electron microscopy (HR-TEM) has an edge in directly and unambiguously determining the crystal orientation of black P15. For characterizing functional devices, however, TEM’s demanding and complicated sample preparing procedures, time-consuming and destructive measurement limit its applications in device platforms. To date, polarized Raman spectroscopy is probably the most widely investigated method for determining black P crystal orientation3,16,17,18. In earlier studies, it has been claimed that the main axis of the 2 polar plot of Ag Raman intensity indicates the AC direction of black P crystal3,16,17,18. Later, it is 2 demonstrated that due to the multilayer interference effects, the measured Ag polarized Raman

spectra is not always reliable in determining crystal orientation19. There is hence great need for a deterministic, precise, efficient, and reliable approach to resolving the crystal orientation and anisotropic axes. In this paper, we present a comprehensive analysis and experimental demonstration of polarized reflectance measurement that can discern black P crystal orientation, incorporating several key factors including the thickness of black P crystal, wavelength of the probing laser, material and the structure of the substrate, in addition to the inherent optical anisotropy of black P. We implement careful polarized reflectance measurements on two important, generic types of devices: (i) black P flakes on 290 nm SiO2-on-Si substrate, and (ii) suspended black P devices on 2.2 µmdeep trenches on SiO2-on-Si substrate, with flake thickness ranging from ~6nm to ~300nm, by employing both 532 nm and 633 nm wavelengths for illumination. Further, we combine a -3ACS Paragon Plus Environment


theoretical model with the experimental results to determine the crystal orientation precisely. Our approach is capable of determining the crystal orientation directly, unambiguously, and quickly, while simultaneously avoiding damage to the measured samples, as it only requires very low laser power of around ~100200 µW.

Figure 1. Experimental system and basic principles of the angle resolved polarized reflectance measurement. (a) Schematic of the measurement system. The angle between polarization of incident light and horizontal axis on the same plane in clockwise direction is defined as rotation angle (φ). Inset shows the three dimensional (3D) crystal structure of black P. (b) Illustration of normal incident light with linear polarization along θ (in the x-y plane of the sample) propagating in z direction. (c) A refractive index ellipse in the x-y plane. (d) Angle-dependent reflectance obtained from polarized reflectance measurement where main axis of the polar plot (φM) will indicate either AC or ZZ direction. Illustrations of optical interference in black P on SiO2/Si substrate and suspended black P devices are shown in (e) and (f), respectively.

The inset in Figure 1a shows the crystal structure of black P, in which each P atom is connected with three adjacent P atoms, forming a stable linked ring structure3. This corrugated structure reduces the crystal symmetry, leading to a strong in-plane anisotropy in electrical, optical and thermal conductivities3. Optical constants display strong in-plane anisotropy, i.e., the refractive index (n) is different along the AC and ZZ directions. When black P is under linearly polarized normal incident light, the reflectance will be different in these two directions due to variation of n. Motivated by this idea, we design the angle-resolved polarized reflectance experiment to measure -4ACS Paragon Plus Environment

Page 4 of 26

Page 5 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the reflectance (R) along different in-plane directions to discern the anisotropy of black P. In addition, multi-layer interference effects are taken into account when determining the crystal orientation of black P flakes with different thicknesses, on substrates with different types of structures (shown in Figure 1e-f).

THEORETICAL MODELING In order to model polarized reflectance measurement, we consider linearly polarized normal incident light (propagation in +z direction) on black P (x-y plane). Black P is a biaxial crystal and its permittivity or refractive indices are different along three principal axis directions. Its two principal axis directions, AC and ZZ are along x and y directions, respectively (Figure 1b). We presume that the angle between the electric field of the polarized light and AC direction is θ. In order to determine R along θ, it requires the value of n along that direction. The variation of n in x-y plane will form an elliptical shape where n along AC ( nAC ) and n along ZZ ( nZZ ) are two axes of the ellipse (Figure 1c). Therefore, n along a given θ direction, n(θ), can be expressed as following (refer to Supporting Information, S1 for details)20:

n2   

n2ACn2ZZ . n2AC sin2   n2ZZ cos2 

(1)

A theoretical model is employed to calculate R for normal incidence of light on black P flakes on SiO2/Si substrates. For nAC and nZZ , we use the values reported in ref. 21. Based on the optical interferometry theory, substrate geometry and thickness of black P, R at a given  can be obtained by using the following expression22:



R   

r1e 

i Φ1  Φ 2 

e

i Φ1  Φ 2 

 r2 e

 r1r2 e

 i  Φ1  Φ 2   i  Φ1  Φ 2 

 r3e

 i  Φ1  Φ 2 

 r1r3e

Page 6 of 26

 r1r2r3e 

 i  Φ1  Φ 2 

i Φ1  Φ 2 

 r2r3e 

i Φ1  Φ 2 

2

,

(2)

where

r1 

n0  n   n    n2 n  n3 , r2  , r3  2 n0  n   n2  n 3 n    n2

are the relative indices of refraction, Φ1 

2n   d1



and Φ 2 

(3)

2n2 d 2



are the phase shifts due to

optical path variations, d 1 is the thickness of black P and d 2 is the thickness of SiO2 layer. The Si layer is assumed to be a semi-infinite layer which is characterized by a wavelength-dependent refractive index n 3    ; the value is 4.21  0.010i for 532 nm and 4.14-0.0010i for 633 nm laser19. The thickness of SiO2 layer is 290 nm with refractive index n2    =1.47 for both wavelength19. n0 is the refractive index of air, which is 1. It can be seen from Eq. (2) that the R along AC (RAC) and ZZ (RZZ) can be obtained by setting the angle  as 0 and

 2

, respectively. R variation with respect to  is presented in the Supporting

Information, S1, where R maxima (Rmax) is observed along ZZ direction. Depending on the thickness of black P, wavelength of probing laser and structure of the substrate, Rmax can be observed either at ZZ or AC direction. Similarly, for suspended black P flakes, R(  ) can be calculated by considering 2.2µm air gap instead of 290nm SiO2 underneath black P flake. The RAC and RZZ as a function of black P thickness calculated by Eq. (2) is shown in Figure 2a for 532 nm laser. It can be seen that RAC and RZZ are largely dependent on thickness of black P (d1), which is originated from the constructive and destructive interferences in black P/SiO2/Si -6ACS Paragon Plus Environment

Page 7 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


multilayer interfaces. We calculate the ratio of reflectance (RZZ/RAC) along ZZ and AC directions and plot it as a function of d1, shown in Figure 2b. Similarly, for 633 nm laser, the calculated RZZ, RAC and RZZ/RAC for black P on SiO2/Si substrate with respect to d1 are also plotted in Figure 2c and Figure 2d respectively. Furthermore, RZZ, RAC and RZZ/RAC of suspended black P flakes are obtained for both 532nm and 633nm lasers, as shown in Figure 2e-h. In certain cases, where preknowledge of crystal orientation is desired before dry-transfer process22, we further provide the aforementioned calculations for black P on PDMS (semi-infinite and n1.4) shown in Figure 2i-l. In addition, as black P samples often need to be protected from environmental degradation by employing a protective layer (e.g., oxide layers, h-BN, parylene etc.), we can easily extend this model for a black P sample with an encapsulation layer. To implement this, one only needs to modify Eq. (2) to calculate reflectance by taking into consideration an additional layer on top of black P.



0.6 0.3 0.0

532nm

ZZ AC

a 0

50

3

100 150 200 250 Thickness (d1)(nm)

0.9 0.6 0.3 0.0

300

ZZ AC

e 0

50

100 150 200 250 Thickness (d1)(nm)

Black P PDMS

Reflectance (R)

0.9

Black P SiO2 Si

Reflectance (R)

Reflectance (R)

Black P SiO2 Si

300

ZZ AC

0.9 0.6 0.3 0.0

i 0

50

2

100 150 200 Thickness (d1)(nm)

250

300

1

1

0.6 0.3

c 50

100 150 200 250 Thickness (d1)(nm)

300

1

0.3

g 0

50

100 150 200 Thickness (d1)(nm)

250

1

10 100 Thickness (d1)(nm)

300

1

10 100 Thickness (d1)(nm) ZZ AC

0.9 0.6 0.3 0.0

k 0

50

2

100 150 200 250 Thickness (d1)(nm)

300

1

l

h

d 1

ZZ AC

0.6

0.0

1

Reflectance (R)

ZZ AC


RZZ/RAC

0.9

j

1

Reflectance (R)


RZZ/RAC

633nm

Reflectance (R)

1

0

1

f

b

0.0

RZZ/RAC

RZZ/RAC

RZZ/RAC

2

RZZ/RAC

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 26


1


Figure 2. Theoretical analysis and modeling of polarized reflectance measurement. (a), (e) and (i) show the calculated R (532nm laser) along both AC and ZZ directions for black P on SiO2/Si, suspended black P on 2.2 µm deep trench, and black on PDMS, respectively. (b), (f) and (j) show the calculated RZZ/RAC of 532nm laser for black P on SiO2/Si, suspended black P and black on PDMS respectively. Similarly, using 633nm laser, theoretical modeling results of R ((c), (g) and (k)) and RZZ/RAC ((d), (h) and (l)) are shown for black P on SiO2/Si, suspended black P and black P on PDMS. Brown dashed line in RZZ/RAC plots denotes the value where RZZ/RAC=1.

From these calculations, we can make two possible projections with reasoning. Firstly, RZZ and RAC are largely dependent on d1, wavelength of probing laser, and the material and structure of the substrate. It is reasonable that these factors will influence the conditions of interference which in turn change R. Secondly, for thinner black P crystals on Si/SiO2 substrate ( RAC from atomic layer to 200nm thick black P (refer to Supporting Information, S1). Therefore, RZZ/RAC provides a criterion for determining crystal orientation in black P flakes on SiO2/Si substrate unambiguously. Based on these calculations, we can design polarized reflectance measurement to determine crystal orientation.

MEASUREMENTS AND RESULTS To experimentally validate and demonstrate polarized reflectance measurement, we use both black P flakes on SiO2/Si substrate and suspended black P flakes with known thickness (see Methods, Supporting Information, S2 and S3 for detail). We employ a home-built apparatus for polarized reflectance measurement (Figure 1a). In the system, both 532 nm and 633 nm lasers are integrated. A polarizer produces linearly polarized incident light onto black P flakes (focused by a 50 objective), while its rotation angle φ (defined as the angle between the linearly polarized incident light and the horizontal axis of the black P sample plane in clockwise direction, see Figure 1a) is controlled by a half-wave plate. The reflected light intensity is collected by a laser power meter as φ varies from 0 to 360o. The reflected light intensity from black P sample are calibrated by repeating the same measurement on metal electrodes which has isotropic optical property for a fixed incident illumination. In the polar plot, when R is plotted as a function of φ, a bow-tie shape is observed. Here main axis of the polar plot (φM) indicates the φ at which R is maximum (Figure 1d) (see Supporting Information, S4 for details about the measurement). From the aforementioned model, it is possible to know RZZ/RAC for a particular black P flake with d1, which will guide us to



determine the anisotropic axis (AC or ZZ) φM is indicating for that flake. If RZZ> RAC for a certain d1, it can be concluded that φM points to the ZZ direction for that flake or vice versa. As a result, by this polarized reflectance measurement, we can determine crystal orientation. It is expected that change of band structure of black P with thickness change can also change the refractive index. In order to address that, firstly, thickness of black P higher than 8L (~6nm) should have same refractive index as bulk, due to same band gap (~0.3 eV) as bulk23. Secondly, due to change of band structure, mostly imaginary part of refractive index can change, which dictates the absorption in black P. Therefore, for 1-8L black P, imaginary part of refractive index may be different from that of bulk black P, which is used in the calculation. However, in visible regime of interest (500-650nm) for the measurements, it has been found that theoretically calculated absorption co-efficient of 1-3L black P is not significantly different from that of thicker black P (>8L) (ref. 24 ), which indirectly indicates that in this particular wavelength range refractive index does not change much with the thickness. Therefore, considering this fact, our model should be fairly valid for monolayer or few-layer black P. At first, we demonstrate polarized reflectance measurement for black P flakes on SiO2/Si substrates. The polar plots in Figure 3a-d, 3e-f display the results of the measurement using two probing lasers. Figure 3a presents the bow-tie shaped polarized reflectance polar plot with φM=35o for the 6 nm-thick black P flake using 532nm laser. For the same flake, it can be observed that φM=35o when we use 633nm laser (Figure 3e). From the corresponding plots of RZZ/RAC for both lasers (solid lines of Figure 3m, 3n), it can be found that RZZ >RAC for the flake. Therefore, we can determine that φM of both Figure 3a and Figure 3e indicate the ZZ direction. Similarly, for black P flakes with thicknesses of 7.5 nm, 13 nm and 50 nm, main axes of polar plots (Figure 3bd, 3f-g) are also found along ZZ direction. Now if we calculate the RZZ/RAC (solid dots) from these -10ACS Paragon Plus Environment

Page 10 of 26

Page 11 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


polar plots, then it can be observed that they are in good agreement with the RZZ/RAC (solid lines) obtained from the model (Figure 3m, 3n). We also present experimental data of RZZ/RAC for some other black P flakes in Figure 3m and 3n and their polar plots with determined crystal orientation can be found in the Supporting Information, S5.

However, a slight discrepancy between

experimentally measured and theoretically calculated RZZ/RAC exists for thinner flakes less than 10 nm when we use 633 nm for measurement. This could stem from the low reflectance in this thickness range. From a closer look at Figure 2c, for 633nm laser, it can be found that for black P flakes thinner than 10nm, the reflectance is very low around 2-5%. As a result, given ~100μW incident laser power on the sample, the reflected power for the case of light polarized along ZZ (PR,ZZ) can be close to 1μW (considering losses incurred in the mirrors), which is close to the noise floor of the power meter used in the experiments. Therefore, although reflected power for the case of AC, PR,AC < 1μW is expected (RZZ > RAC), measured PR,AC cannot be lower than the ~1μW noise floor. This means that the experimentally obtained reflectance ratio (RZZ/RAC) could be lower and close to 1, and lower than the theoretically expected value (RZZ/RAC ~ 2, if PR,AC is not limited by noise floor of power meter). Nevertheless, measured RZZ/RAC is still higher than 1, which qualitatively enables the identification of the crystal orientation correctly.



60

6 nm

180 210

300

60

270

90

30

240

210

300

60

270

90

30

( A Mode), Green Laser (532 nm)

330

(i) 300

240

210

90

AC

330 270

90

0 330

(j)

330

270

210

300

270 90

60

(g)

120

210

300 60

4 210 8 330 300 240

(k)

270 90

90

(m)

a

b c

210

(h)

60

270 90

30

d

Model Experiment 10 100 Thickness (d1) (nm)

120

180

330

150

1

240

0

120

1

150

300

240

270

30

180

2

210

(d)

120

0 330

180

330

150

30

3

150

300

240

120

0

180

150 8 30 4 1800 0

30

300

240

60

50 nm 90

30

150

60

210

300

Black P

Si

ZZ

120

0

120

180

90

30

(c)

150

60

180

270

240

0

120

240

210

300

30

(f)

150

270

180

60

180

60

150

330

13 nm

120

0

120

0

7.5 nm 90

30

(b)

150

330

60

150

330

ZZ

120

0

0

2 g

90

30

(e)

Polarized Raman Spectroscopy

SiO2

AC ZZ

AC

(a)

Polarized Reflectance Red Laser (633 nm)

AC

RZZ/RAC

Polarized Reflectance Green Laser (532 nm)

ZZ

RZZ/RAC

Black P Flake

1

1

240

ef

g

h

Model Experiment

(n)

10 100 Thickness (d1) (nm)

120 150 10

0

180 210 270

180

330

240

(l)

300

210 270

On SiO2/Si



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 26

240

1 1

(o)


Figure 3: Polar plots of polarized reflectance and polarized Raman measurements with respect to rotation angles for black P flakes on Si/SiO2 substrate. Enclosures marked by dashed white lines represent the areas on the flakes where measurements are performed. Thickness of each flake (d1) is noted at the lower right corner of the optical image (scale bar: 4µm). Polar plots of polarized reflectance measurements (radial axis represents normalized reflectance from 0.5 to 1) using (a)-(d) 532nm laser and (e)-(h) 633nm laser are shown along with the plot of RZZ/RAC, with respect to d1 (m, n) in corresponding rows of probing lasers. Arrows along their main axes denote the crystal direction to which they are aligned. Polar plot of Ag2 mode intensities (normalized by maximum, radial axis from 0 to 1) obtained from (i)-(l) polarized Raman spectroscopy (i-l) are shown with (o) the plot as a function of d1. Brown and purple arrows on the optical images and polar plots of flakes denote AC and ZZ directions.

Further, we perform the same sets of measurements for suspended black P flakes with different thicknesses (Figure 4). Similar to the black P flakes on SiO2/Si substrate, φM indicates ZZ direction for thinner suspended black P flakes with thicknesses of 16 nm, 20 nm and 21 nm (Figure 4a-c, Figure 4e-g). On the 82 nm-thick flake, however, it is found that φM,633φM,532=90. Based on our model, for d1 = 82 nm, RZZ > RAC for 532 nm (Figure 4m), which indicates that φM,532 points towards the ZZ direction (Figure 4d). On the other hand, for 633 nm laser, RZZ < RAC (Figure 4n) -12ACS Paragon Plus Environment

Page 13 of 26

which implies that φM,633 indicates the AC direction (Figure 4h).

From the agreement of

measurement results and the model, it can be concluded that our proposed method is also valid for suspended black P flakes.

ZZ 16 nm 60 30

2

( Ag Mode), Green Laser (532 nm)

210

300

60

270

90

30

240

330

210

300 60

270 90

30

240

330 300

270 90

30

240

90

240

180

330

(d)

60

120

30 0

(m)


120

270 90

(n)

150

0

Model Experiment 1

240 120

180

e g f

1

210

30

180

1

240

180

60

150

d

Model Experiment

150

210 330 300 240 (h)

90

90

30

330 270

270

a c b

1

210

300

120

120 150

180 0

300

90

0

150

60

180

270

82 nm `

30

0

120

0

210

300

30

(g)

150

60

180

60

210

150

330

Si

AC

120

0

120

180

90

30

(c)

150

60

180

90

240

0

(f)

150

270

30

120

0

210

60

180

60

180

300

21 nm

120 150

330

Black P SiO2

ZZ

ZZ

0

(b)

150

90

30

120

0

(e)

Polarized Raman Spectroscopy

180

330

60

150

ZZ 20 nm

120

0

(a)

Polarized Reflectance, Red Laser (633 nm)

90

AC

AC

RZZ/RAC

Polarized Reflectance, Green Laser (532 nm)

AC

RZZ/RAC

Black P Flake

h


10 Suspended



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

330

(i) 300

210 270

240

330

(j) 300

210 270

240

330

(k) 300

210 270

330

240

(l) 300

210 270

240

1

(o)


Figure 4: Polar plots of polarized reflectance and polarized Raman measurements with respect to rotation angles for suspended black P flakes. Thickness of the suspended portion of each flake is noted at the lower right corner of the optical image (scale bar: 4µm). Polar plots of polarized reflectance measurements (radial axis represents normalized reflectance from 0.5 to 1) using 532nm (a)-(d) laser and (e)-(h) 633nm laser are shown along with the plot of RZZ/RAC with respect to d1 (m, n) in corresponding rows of probing lasers. Arrows along their main axes denote the crystal directions to which they are aligned. (i)-(l) Polar plots of

Ag2 mode intensities (normalized by maximum,

radial axis from 0 to 1) obtained from polarized Raman spectroscopy are shown with (o) the plot as a function of d1. Brown and purple arrows on the optical images and polar plots of flake denote AC and ZZ directions.

We also perform polarized Raman spectroscopy shown in Figure 3i-l and 4i-l by using 532 nm laser (see S6 in Supporting Information for details) on the same black P flakes (both on substrate and suspended) and compare with the results measured using our proposed polarized reflectance



method. It is observed that our method is in excellent agreement with the polarized Raman measurement (taking into account multi-layer interference effects19,23,24, detailed discussions in S7 and S8 of Supporting Information) in determining crystal orientation. From careful observation, it can be found that there is a very slight inconsistency between crystal orientations determined by our method and polarized Raman spectroscopy. This could be generated if the incident laser illumination is not ideally perpendicular to the sample; in such a case, reflectance maxima may not be observed for the incident light polarized along crystallographic directions (AC or ZZ) of black P. Further, we manually control the polarization angle by rotating the half-wave plate, which might introduce some imperfection during measurements. From these results, it is obvious that polarized reflectance measurement is a fast and facile method for discerning crystal orientations.

DISCUSSIONS Among all the techniques developed so far for determining crystal orientation of black P, polarized Raman spectroscopy has been the most popular. Recently, it has been demonstrated that classical interference effects due to multiple reflections in black P / substrates layers must be considered and corrected, otherwise they may lead to totally opposite conclusions19. The interference effects depend not only on the polarization of light because of the different n along the AC and ZZ directions, but also on d1 and excitation wavelength. One needs to consider an enhancement factor (F), a factor by which the intrinsic Raman signal is enhanced or modified due to multilayer interference effects. F is defined as the ratio between Raman intensity considering multi-layer interference effects (Iʹ) and the intrinsic Raman signal intensity for semi-infinite black P crystal without any multi-reflection (I0), F= Iʹ/I0. This enhancement process is illustrated in Figure 5a,


Page 14 of 26

Page 15 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


which includes enhancement of the excitation light intensity and scattered light intensity due to multilayer interference in black P. To illustrate the enhancement of the Raman intensity, we compare the Raman intensity of a thin layer of black P qualitatively with that of a semi-infinite bulk black P where no enhancement takes place (Figure 5a). Due to the different n of black P in AC and ZZ directions, F along AC ( FAC ) and ZZ ( FZZ ) are also different. We define the ratio of F along ZZ and AC directions as   FZZ / FAC . We present the calculated  for both on-SiO2/Sisubstrate and suspended cases in Figure 3o and 4o respectively25, 26, using the nAC and nZZ reported in literature for 532 nm excitation18 (see Supporting Information S7). It is found that for a fixed excitation wavelength,  depends on d1, material and structure of substrates. 2 Correction of interference effects is needed to reveal the intrinsic Ag mode Raman intensities,

I ( ) , from the measured results, which can be done by dividing the measured Raman intensity of

Ag2 mode, I ( ) , by the corresponding calculated F(φ), I ( ) 

I ( ) . However, pre-knowledge F ( )

of crystal orientation by other means, e.g., HR-TEM, is required before calculating F(φ). After correction, φM of polar plot of I ( ) should indicate AC direction. From polarized Raman spectroscopy, we can obtain a major (maxima) and a minor (minima or secondary maxima) axes when we plot I ( ) , which are shown as I major and I m inor respectively in the polar plot (Figure 5b).  We assume that two crystal directions of black P are along these two axes but we cannot tell which one is AC or ZZ. Now we can consider two special cases (shown in Figure 5b and Figure 5c): (i) Case-1: I major : I minor   :1 and (ii) Case-2: I major : I minor   :1 . It can be shown that for Case-1, polarized Raman spectroscopy alone can identify crystal orientation without any necessity to perform correction of interference effects (Figure 5b), whereas for Case-2, it is not possible for polarized Raman spectroscopy alone to determine crystal orientation (Figure 5c) (see details in the -15ACS Paragon Plus Environment


Supporting Information, S8). From this discussion, we see that polarized Raman spectroscopy alone is unable to identify crystal orientation unambiguously in all cases. On the contrary, in our polarized reflectance measurement, multi-reflection interference is taken care of from the beginning and does not require separate complicated correction procedure after measurement to determine crystal orientation. In order to verify the accuracy of our method, when we compare the crystal orientation determined by our method with the polarized Raman measurement, we

a δP

Black P

Scattering Enhancement

carefully chose the black P flakes which fall under Case-1 (except 50nm flake in Figure 3). Excitation Enhancement

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 26

x

SiO2 Bulk Black P

Excitation

V

Raman Scattering

Si Raman Signal Intensity

Ef

Ei

Before Correction Case-1 major

:

minor

60

90

120

major

30

Hypothesis-1 AC

150

0

180 minor

330 300

270

ZZ

210

240

90

150

30

270

Case-2

60

90

30

60

120

ZZ

150

150 180

330

240

210

300

Reject: IZZ 90

30

120 150

120

0

210

300

90

AC

Valid

minor

60

ZZ

180

330

After Correction for Hypothesis -2

120

0

6 nm

b

:

60 30

Hypothesis-2

> η:1

4.34:1 >1.28:1

major

After Correction for Hypothesis -1

60

AC

270

240

IAC 90

30

120 150

< η:1

1.12:1

Discerning Black Phosphorus Crystal Orientation ... - ACS Publications

Recommend Documents