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Layer-number determination of two-dimensional

materials by optical characterization

You Zheng (郑优), Changyong Lan (兰长勇), Zhifei Zhou (周智飞), Xiaoying Hu (胡晓影),

Tianying He (何天应), and Chun Li (李春)*

State Key Laboratory of Electronic Thin Films and Integrated Devices, and School of Optoelectronic Information,

University of Electronic Science and Technology of China, Chengdu 610054, China

*Corresponding author: lichun@uestc.edu.cn

Received October 29, 2017; accepted December 12, 2017; posted online January 29, 2018

Initiated by graphene, two-dimensional (2D) layered materials have attracted much attention owing to their

novel layer-number-dependent physical and chemical properties. To fully utilize those properties, a fast and

accurate determination of their layer number is the priority. Compared with conventional structural charac-

terization tools, including atomic force microscopy, scanning electron microscopy, and transmission electron

microscopy, the optical characterization methods such as optical contrast, Raman spectroscopy, photolumines-

cence, multiphoton imaging, and hyperspectral imaging have the distinctive advantages of a high-throughput

and nondestructive examination. Here, taking the most studied 2D materials like graphene, MoS

, and black

phosphorus as examples, we summarize the principles and applications of those optical characterization

methods. The comparison of those methods may help us to select proper ones in a cost-effective way.

OCIS codes: 120.6200, 160.4760, 180.5655, 310.6860.

doi: 10.3788/COL201816.020006.

Micromechanical exfoliated graphene opened the research

field of two-dimensional (2D) materials. Since then, more

and more 2D layered materials, including molybdenum

sulfide (MoS

), hexagonal boron nitride (h-BN), black

phosphorus (BP), and so on, have been reported and have

attracted great interest. Compared with conventional

electronic and optical materials, 2D materials show many

unique properties such as record-high charge carrier

mobility, strong light–matter interaction, and superior

mechanical properties

[1–3]

, which implies promising appli-

cations for novel devices

[4]

. However, many of those fasci-

nating properties are strongly dependent on their layer

numbers (LNs). For example, monolayer graphene has

a zero ban dgap, while bilayer graphene on SiC substrate

has a finite bandgap of ∼0.26 eV

[5]

. Monolayer MoS

is a

direct bandgap semiconductor, but bilayer MoS

is an

indirect one. While the bandgap of BP decreases as the

number of layers increases from monolayer (1.5–2.0 eV)

to bulk (0.2 eV)

[6]

. In addition, at present, it is still a great

challenge to precisely contro l the LN of 2D materials in

large scale, although there are many methods for prepar-

ing 2D materials including micromechanical exfoliation

[7]

epitaxial growth

[8]

, chemical vapor deposition (CVD)

[9]

and liquid phase exfoliation

[10]

. Therefore, it is critical to

find an efficient and reliable way to identify their LNs,

which is important for both fundamental research and in-

dustrial application.

Among the numerous thickness characterization meth-

ods, atomic force microscopy (AFM), scanning electron

microscopy (SEM), and transmission electron microscopy

(TEM) are the most intuitive approaches. Nevertheless,

these structural characterization methods are usually

low in throughput, prone to sample damage, and strict

with substrate choosing. For example, during the measur-

ing process of AFM in contact mode, the cantilever tip

always needs contacting with the sample, which may

cause irreversible physical damage to the samples. In

the SEM observation, conductive substrates are required

to eliminate the charge accumulation. The low-voltage

mode is much sensitive to small surface features but de-

creases the signal-to-noise ratio. The TEM characteriza-

tion requires sophistica ted skills and experiences with

sample preparation. For optical characterization, due to

the strong LN-dependent light–matter interactions of

2D materials, the variation of optical signals collecting

from the scattering, absorption, or light emission can be

correlated to the LNs. Therefore, by detecting these opti-

cal signals and interpreting their peak position, intensity,

and line shape associated with LNs, their exact LNs can be

accurately determined. Such an optical characterization is

nondestructive, with high throughput, and reliable. Here,

we review the principles and recent development of the

commonly adopted optical characterization methods,

and compare their advantages and limitations.

This review is organized as follows. After the introduc-

tion, we first focus on the most frequently used method,

the reflective optical contrast, to identify the LNs of 2D

materials laying on nontransparent substrates. Particu-

larly, we summarize the reported strategies on improving

the visibility of 2D materials by engineering the reflection

contrast of the substrates. Then, Raman and photolumi-

nescence (PL) characterizations of typical 2D materials

(graphene, MoS

, and BP) are briefly reviewed. The mul-

tiphoton spectrum relying on nonlinear absorption is

one of the focuses in another section. Other methods

mainly regarding the identification of 2D materials on

COL 16(2), 020006(2018) CHINESE OPTICS LETTERS February 10, 2018

transparent substrate are also discussed. Finally, we

present a summary and an outlook for the research field.

We note that during our preparation of this review, an-

other comprehensive review paper mainly focusing on

Raman characterization was published

[11]

, which is also

a valuable reference for the optical characterization of

2D materials.

Undoubtedly, reflective optical contrast is the most

direct and convenient method to identify the LNs of 2D

materials, and is especially useful for finding monolayer

microflakes from the micromechanical exfoliated samples

in checking under microscopy

[12]

. Owing to their ultrathin

features, the optical transmittances are very high (∼97.7%

for monolaye r graphene), making them generally invisib le

on most substrates. Thanks to a special substrate of Si

wafer capped with a 300 nm SiO

, monolayer graphene

can be vividly seen by the naked eye

[13]

. A more clear con-

trast image can be obtained by observing the sample

under conventional reflective optical microscopy. This

simple and effective technique of direct visualization of

atomically thin materials not only makes the great success

of graphene, but also offers a quick way to identify other

monolayer materials, which greatly accelerates the explo-

ration of new 2D materials.

To explain this amazing phenome non, Blake et al.

[14]

first proposed a strict calculation using the Fresnel prin-

ciple. When light is incident from air onto a 2D material

laying on a dielectric substrate, multiple reflections at the

interfaces occur and optical interference within the

medium of multilayer structure will modify the intensity

of reflection from 2D material. As shown in Fig.

1(a), the

optical contrast is defined as the difference between the

light reflection intensity from the 2D materials deposited

on substrate and that from the bare substrate. The calcu-

lating formula can be written by C ¼ðR

sub

− R

subþfilm

Þ∕

sub

, where R

sub

and R

subþfilm

represent the reflectance

of substrate and 2D materials, respectively. Via well-

established recursive

[15]

and transfer matrix methods

[16–18]

both of which are derived from the Fresnel principle, this

enhancement effect can be theoretically calculated

and found to be well matched with the experimental

results

[19]

.AsshowninFig.1(b), the calculation result

shows that the optical contrast of monolayer graphene

on SiO

has two visualization channels. One is for

∼90 nm SiO

and the other i s for ∼300 nm SiO

with a

slightly wider range. Note that a near 1 0% optical con-

trast around 550 nm is enough for direct eye recognition.

Figure

2(a) shows the contrast spectra of different gra-

phene layers on th e 300 nm SiO

substrate. The c orre-

sponding o ptical images of the samples are shown in

Fig.

2(b)

[19]

. As can be seen, with LN increasing, the con-

trast clearly consistently increases.

This method is also found very effective for other 2D ma-

terials. To maximize the reflection contrast for easier dis-

tinction, many structures of the substrates have been

proposed. For example, Lee et al.

[20]

proposed that a struc-

ture of Ag film covered with 81 nm SiO

as the light cavity

also shows ∼10% optical contrast with a much broader

range than that of conventional 300 nm SiO

substrate.

Teo et al.

[16]

have theoretically studied the visibility of gra-

phene on different types of substrates, including metals,

semiconductors, and insulators. They found that by coat-

ing a polymethylmethacrylate (PMMA) layer on the

graphene/dielectric substrate the contrast can be further

improved. Table

1 summarizes the recently reported struc-

tures for enhancing optical contrast on nontransparent sub-

strates. Obviously, the maximum contrast is strongly

wavelength dependent. Therefore, a narrow bandpass filter

is typically required to improve the contrast.

It is worth mentioning that reflective optical contrast is

a very efficient method to identify monolayer 2D materials

on the above-mentioned reflectively enhanced substrates.

However, to quantitatively determine the LN by this

method, one needs to measure the reflection spectra

and fit them with the calibrated LN-dependent reflection

of the same material on the same substra te. It als o should

Fig. 1. (a) Schematic of the optical contrast definition. (b) A

color plot of the contrast as a function of the wavelength and

the SiO

thickness

[14]

Fig. 2. (a) Contrast spectra of graphene with different LNs on

300 nm SiO

substrate. (b) The optical images of all the samples

in (a). The graphene flakes in a, b, c, d, e, and f are more than

10 layers and the thickness increases from a to f

[19]

COL 16(2), 020006(2018) CHINESE OPTICS LETTERS February 10, 2018

020006-2

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