CN107655891B - Method for representing Van der Waals crystal optical anisotropy with nanoscale thickness - Google Patents

Method for representing Van der Waals crystal optical anisotropy with nanoscale thickness Download PDF

Info

Publication number
CN107655891B
CN107655891B CN201710956650.7A CN201710956650A CN107655891B CN 107655891 B CN107655891 B CN 107655891B CN 201710956650 A CN201710956650 A CN 201710956650A CN 107655891 B CN107655891 B CN 107655891B
Authority
CN
China
Prior art keywords
van der
der waals
sample
optical anisotropy
waveguide mode
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201710956650.7A
Other languages
Chinese (zh)
Other versions
CN107655891A (en
Inventor
戴庆
胡德波
杨晓霞
李驰
刘瑞娜
胡海
刘梦昆
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Institute of Nanoenergy and Nanosystems
Original Assignee
Beijing Institute of Nanoenergy and Nanosystems
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Institute of Nanoenergy and Nanosystems filed Critical Beijing Institute of Nanoenergy and Nanosystems
Priority to CN201710956650.7A priority Critical patent/CN107655891B/en
Publication of CN107655891A publication Critical patent/CN107655891A/en
Application granted granted Critical
Publication of CN107655891B publication Critical patent/CN107655891B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/84—Systems specially adapted for particular applications
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
    • G01N21/84—Systems specially adapted for particular applications
    • G01N2021/8477—Investigating crystals, e.g. liquid crystals

Landscapes

  • Physics & Mathematics (AREA)
  • Health & Medical Sciences (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • Biochemistry (AREA)
  • General Health & Medical Sciences (AREA)
  • General Physics & Mathematics (AREA)
  • Immunology (AREA)
  • Pathology (AREA)
  • Crystals, And After-Treatments Of Crystals (AREA)

Abstract

The invention provides a method for representing optical anisotropy of Van der Waals crystals with nanometer-scale thickness, which comprises the steps of exciting ordinary and extraordinary waveguide modes in the Van der Waals crystals by using a scattering type scanning near-field optical microscope (s-SNOM), carrying out near-field imaging on the waveguide modes, and further obtaining the optical anisotropy of the Van der Waals crystals by analyzing a near-field image. The method overcomes the limitation of the traditional characterization means on the sample size, and can accurately characterize the optical anisotropy of the uniaxial and biaxial Van der Waals crystal materials.

Description

Method for representing Van der Waals crystal optical anisotropy with nanoscale thickness
Technical Field
The invention relates to the field of Van der Waals crystal material performance measurement, in particular to a method for representing Van der Waals crystal optical anisotropy with nanoscale thickness by using a scattering type scanning near-field optical microscope.
Background
After graphene, new two-dimensional materials (such as hexagonal boron nitride, molybdenum disulfide, etc.) are emerging. These new two-dimensional materials (van der waals crystals) can be prepared by physical exfoliation or chemical growth methods. The two-dimensional material prepared by the physical mechanical stripping method can keep a better crystal structure, maintain good electrical and optical properties and be easily prepared into a high-quality functional device. Recently, the academia has proposed a new concept of van der waals heterojunction, which can regulate the function and performance of the prepared device by longitudinally stacking two-dimensional materials with different properties.
Whether a simple device is prepared by one two-dimensional material or a complex heterojunction device is prepared by a plurality of two-dimensional materials, the optimal design of the device can not be accurately mastered on the material performance. Van der waals crystals are layered structures, bonded by covalent bonds within layers, and bonded by van der waals forces between layers. Since the covalent bond action is much stronger than the van der waals force action, van der waals crystals exhibit strong anisotropy (mechanical, electrical and optical properties). To design and fabricate photovoltaic devices based on van der waals crystals, the optical anisotropy of the material must be accurately characterized. The conventional methods for characterizing the optical anisotropy of materials are mainly end-face reflection method and spectroscopic ellipsometry, however, neither method is suitable for characterizing the optical anisotropy of van der waals crystals, because they require the sample to have a size of at least 50 micrometers, while the van der waals crystal size obtained by mechanical peeling is generally in the order of several micrometers.
Therefore, a method capable of effectively characterizing the optical anisotropy of van der waals crystals of nanoscale thickness is required.
Disclosure of Invention
In order to solve the above problems, the present invention provides a method for characterizing van der waals crystal optical anisotropy in a nano-scale thickness, comprising the steps of:
the method comprises the following steps: placing the sample to be detected in SiO2On the Si substrate, one straight edge of a tested sample is parallel to a cantilever beam of a scattering type scanning near-field optical microscope (s-SNOM) needle tip;
step two: scanning the sample by the s-SNOM needle tip along the direction vertical to the cantilever beam of the scattering type scanning near-field optical microscope (s-SNOM) needle tip, and sequentially scanning four samples with different thicknesses to obtain a near-field image;
step three: fourier transform is respectively carried out on the near field images obtained in the second step, momentum space spectrograms corresponding to samples with different thicknesses are obtained, and apparent wave vector values K of ordinary (TE polarization) and extraordinary (TM polarization) waveguide modes are read from the imagesTEAnd KTM；
Step four, β according to the formula (1)o,e＝kTE,TM-k0Obtaining a true wave vector β DEG and β e of each waveguide mode by cos α sin β and the apparent wave vector obtained in the third step, wherein β DEG is the true wave vector of the ordinary waveguide mode, β e is the true wave vector of the extraordinary waveguide mode, and α is an incident wave vector K0And sampleAngle of plane of article, β is K0Projection K at the sample planexyThe included angle between the needle tip cantilever beam and the needle tip cantilever beam;
step five, respectively substituting the true wave vectors β DEG and β e of the sample corresponding to each thickness obtained in the step four into a formula (2) of an ordinary waveguide mode and a formula (3) of an extraordinary waveguide mode, and solving the in-plane dielectric constant epsilon of the van der Waals crystal to be measured through numerical values⊥And out-of-plane dielectric constant ε∥Whereby the optical anisotropy of the van der waals crystal to be measured is represented by its dielectric tensor, which is represented by formula (4);
Figure GDA0001596390800000021
Figure GDA0001596390800000022
Figure GDA0001596390800000023
wherein k is0＝2π/λ，k0Denotes the vacuum wave vector, ε1And epsilon2The dielectric constants of air and a sample to be measured are respectively, d is the thickness of the sample, and m and n are orders of an ordinary waveguide mode and an extraordinary waveguide mode respectively.
Preferably, the sample to be tested is a uniaxial and biaxial Van der Waals crystal with a transverse dimension of 100 μm or less.
Preferably, the tested sample is uniaxial and biaxial Van der Waals crystal, and the longitudinal thickness of the tested sample is less than or equal to 1 micron.
Preferably, the sample to be detected can be MoS2And BN nanoplatelets, wherein MoS2And BN are both uniaxial van der waals crystals.
The invention uses scattering type scanning near-field optical microscope (s-SNOM) to excite ordinary and extraordinary waveguide modes in van der Waals crystal, and carries out near-field imaging on the waveguide modes, and further obtains the optical anisotropy of the van der Waals crystal by analyzing the near-field image. The method overcomes the limitation of the traditional characterization means on the sample size, and can accurately characterize the optical anisotropy of the uniaxial and biaxial Van der Waals crystal materials.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.
Drawings
Further objects, features and advantages of the present invention will become apparent from the following description of embodiments of the invention, with reference to the accompanying drawings, in which:
fig. 1 shows a schematic diagram of a measurement experiment setup according to the present invention.
Fig. 2 shows the near field images obtained using the s-SNOM scanning 4 samples with different thicknesses.
Fig. 3 shows a momentum space spectrum corresponding to samples of different thicknesses obtained by fourier transform of the near-field image shown in fig. 2, respectively.
Detailed Description
The objects and functions of the present invention and methods for accomplishing the same will be apparent by reference to the exemplary embodiments. However, the present invention is not limited to the exemplary embodiments disclosed below; it can be implemented in different forms. The nature of the description is merely to assist those skilled in the relevant art in a comprehensive understanding of the specific details of the invention.
Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In the drawings, the same reference numerals denote the same or similar parts, or the same or similar steps.
Example 1
In the form of van der Waals crystals MoS2The nano-sheet is taken as an example, and the optical anisotropy of the nano-sheet is accurately characterized by using the method disclosed by the invention.
Referring to fig. 1-3, the present invention provides a method for characterizing van der waals crystal optical anisotropy at a nanoscale thickness, comprising the steps of:
fig. 1 is a schematic structural diagram of a measurement experiment setup in the present invention. As shown in fig. 1, to disperseCantilever of a radio scanning near-field optical microscope (s-SNOM) tip, where k is used as a reference0Denotes the vacuum wave vector, kxyIs k0Projection on the plane of the sample to be measured, α being kxyAnd k is0And α -38 deg., kxyThe angle between the near infrared laser and the edge of the sample to be measured is β -60 degrees, and when the lambda is 1530nm and the spot diameter is 3 mu m, the near infrared laser irradiates the tip of the s-SNOM to excite MoS2Ordinary and extraordinary waveguiding modes in the nanosheets, these modes being in MoS2The nanosheets propagate as cylindrical waves and are scattered at the sample boundary into the photodetector. Therefore, the image acquired by s-SNOM is mainly the fringe formed by the interference of scattered light from the tip and the edge of the sample.
Referring to fig. 1, in step one: MoS of a sample to be detected2The nano-sheet is arranged in SiO2On a/Si substrate, by reacting MoS2One straight edge of the nanosheet is parallel to a cantilever beam of a tip of a scattering-type scanning near-field optical microscope (s-SNOM), i.e., along the OY direction in FIG. 1;
referring to fig. 1 and 2, in step two: scanning an s-SNOM tip over a MoS in a direction perpendicular to a cantilever beam of the s-SNOM tip (i.e., in an OX direction as in FIG. 1)2Nanosheets, sequentially scanning four MoS's of different thicknesses2Nanosheets, obtaining near field images;
FIG. 2 is a graph of scanning 4 MoS's with different thicknesses using the s-SNOM2And obtaining a near field image by the nano sheet. Wherein the MoS measured2The thickness of the nano-sheet is 81nm, 103nm, 170nm and 198nm respectively.
Step three: and D, respectively carrying out Fourier transform on the near field images obtained in the step two, and obtaining momentum space spectrograms corresponding to samples with different thicknesses. Reading the apparent wave vector value K of the ordinary (TE) and the extraordinary (TM) waveguide modes from the momentum space spectrogramTEAnd KTM；
FIG. 3 shows MoS's corresponding to different thicknesses obtained by Fourier transform of the near-field image shown in step two2Momentum space spectrum, MoS, of the nanosheets2The thickness of the nanosheets was 81nm, 103nm, 170nm, 198nm, respectively, as read from FIG. 3Apparent wave vector K for the ordinary (TE) and extraordinary (TM) waveguide modesTE、KTM. Very thin MoS2The nano-sheet can only support one waveguide mode, namely a fundamental mode, and MoS with relatively thick thickness2Two distinct modes of nanoplatelets can be observed.
Step four, β according to the formula (1)o,e＝kTE,TM-k0Obtaining a true wave vector β ° and β e of each waveguide mode by cos α sin β and the apparent wave vector obtained in the third step, wherein β ° is the true wave vector of the ordinary waveguide mode, and β e is the true wave vector of the extraordinary waveguide mode;
step five, respectively substituting the true wave vectors β DEG and β e of the sample corresponding to each thickness obtained in the step four into a formula (2) of an ordinary waveguide mode and a formula (3) of an extraordinary waveguide mode, and solving the in-plane dielectric constant epsilon of the van der Waals crystal to be measured through numerical values⊥And out-of-plane dielectric constant ε∥Whereby the optical anisotropy of the van der waals crystal to be measured can be represented by its dielectric tensor, which is represented by formula (4);
wherein equation (2) is as follows:
Figure GDA0001596390800000051
wherein, the formula (3) is as follows:
Figure GDA0001596390800000052
according to the two transcendental equations of the formulas (2) and (3), the ordinary waveguide mode is transverse electric field (TE) polarization, and the in-plane wave vector of the ordinary waveguide mode only neutralizes in-plane MoS2Relative dielectric constant of (c); the extraordinary waveguide mode is Transverse Magnetic (TM) polarized with in-plane wave vectors related to the relative permittivity in-plane and out-of-plane. Thus, once at least two different thicknesses of MoS2The in-plane wave vectors of the ordinary waveguide mode and the extraordinary waveguide mode of the nanosheets are determined, and the in-plane out-of-plane relative dielectric constants can be derived from equations (2) and (3).
Wherein, due to MoS2Is a uniaxial van der Waals crystalThe optical axis of which is perpendicular to the sample plane, and the relative dielectric tensor can be written as:
Figure GDA0001596390800000061
wherein k is0＝2π/λ，k0Denotes the vacuum wave vector, ε1And epsilon2Respectively being air and SiO2D is MoS2The thickness of the nano-sheet, m and n are respectively the order of the ordinary waveguide mode and the extraordinary waveguide mode; epsilon⊥Is the in-plane relative permittivity (perpendicular to the optical axis), ε||Is the out-of-plane relative permittivity (parallel to the optical axis). In summary, uniaxial van der Waals crystal MoS2The relative dielectric tensor can be calculated, and the van der Waals crystal MoS can be accurately represented by using the relative dielectric tensor2Optical anisotropy of (2).
As can be seen from the figure: d1＝81nm,βo1＝2.735k0；d2＝103nm,βo2＝3.06k0) Substituting equation (2) can result in: epsilon⊥＝20.25，m＝0；
In the same way, d3＝170nm,βe1＝1.733k0；d4＝198nm,βe2＝2.007k0Substituting equation (3) can result in: epsilon||＝9.61，n＝0；
In conclusion: at 1530nm of optical communication wavelength, Van der Waals crystal MoS2The relative dielectric tensor of (a) can be quantitatively determined as:
Figure GDA0001596390800000062
the invention uses scattering type scanning near-field optical microscope (s-SNOM) to excite ordinary and extraordinary waveguide modes in van der Waals crystal, and carries out near-field imaging on the waveguide modes, and further obtains the optical anisotropy of the van der Waals crystal by analyzing the near-field image. The method overcomes the limitation of the traditional characterization means on the size of a sample, can accurately characterize the optical anisotropy of uniaxial and biaxial Van der Waals crystal materials, and can further utilize the Van der Waals crystal design to prepare a Van der Waals crystal-based photoelectric device.
Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.

Claims (3)

1. A method for characterizing van der waals crystal optical anisotropy at nanoscale thicknesses, comprising the steps of:
s1: placing the sample to be detected in SiO2On the Si substrate, one straight edge of the tested sample is parallel to the cantilever beam of the scattering type scanning near-field optical microscope tip;
s2: scanning a tested sample by a scattering type scanning near-field optical microscope needle tip along a direction vertical to a needle tip cantilever beam, and sequentially scanning four tested samples with different thicknesses to obtain a near-field image;
s3: fourier transform is respectively carried out on the near field images obtained in the second step, momentum space spectrograms corresponding to samples with different thicknesses are obtained, and apparent wave vector values K of the ordinary and the extraordinary waveguide modes are read from the momentum space spectrogramsTEAnd KTM；
S4 according to formula (1) βo,e＝kTE,TM-k0Obtaining a true wave vector β DEG and β e of each waveguide mode by cos α sin β and the apparent wave vector obtained in the third step, wherein β DEG is the true wave vector of the ordinary waveguide mode, β e is the true wave vector of the extraordinary waveguide mode, and α is an incident wave vector K0The included angle between the measured sample plane and β is K0Projection K on the plane of the measured samplexyThe included angle between the needle tip cantilever beam and the needle tip cantilever beam;
s5, respectively substituting the true wave vectors β DEG and β e of the tested sample corresponding to each thickness obtained in the step four into a formula (2) of the ordinary waveguide mode and a formula (3) of the extraordinary waveguide mode, and solving the in-plane dielectric constant epsilon of the tested sample through numerical values⊥And out-of-plane dielectric constant ε∥From this measured sampleThe optical anisotropy of the article is represented by its dielectric tensor, which is represented by equation (4);
wherein, formula (2), formula (3) and formula (4) are as follows:
Figure FDA0002396764600000011
Figure FDA0002396764600000012
Figure FDA0002396764600000021
wherein k is0Denotes the vacuum wave vector, k0＝2π/λ，ε1And epsilon2The dielectric constants of air and a sample to be measured are respectively, d is the thickness of the sample, and m and n are the orders of an ordinary waveguide mode and an extraordinary waveguide mode respectively.
2. The method for characterizing van der waals crystal optical anisotropy at nanoscale thicknesses according to claim 1, wherein the samples tested are uniaxial and biaxial van der waals crystals with transverse dimensions ≦ 100 μm.
3. The method for characterizing van der waals crystal optical anisotropy at nanoscale thickness according to claim 1 or 2, wherein the sample to be tested is uniaxial and biaxial van der waals crystal with a longitudinal thickness of 1 μm or less.
CN201710956650.7A 2017-10-13 2017-10-13 Method for representing Van der Waals crystal optical anisotropy with nanoscale thickness Active CN107655891B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710956650.7A CN107655891B (en) 2017-10-13 2017-10-13 Method for representing Van der Waals crystal optical anisotropy with nanoscale thickness

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710956650.7A CN107655891B (en) 2017-10-13 2017-10-13 Method for representing Van der Waals crystal optical anisotropy with nanoscale thickness

Publications (2)

Publication Number Publication Date
CN107655891A CN107655891A (en) 2018-02-02
CN107655891B true CN107655891B (en) 2020-04-21

Family

ID=61118780

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710956650.7A Active CN107655891B (en) 2017-10-13 2017-10-13 Method for representing Van der Waals crystal optical anisotropy with nanoscale thickness

Country Status (1)

Country Link
CN (1) CN107655891B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114879002B (en) * 2022-05-07 2023-03-24 北京科技大学 Single-pixel image recognition system based on Van der Waals photoelectric detector

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS61182553A (en) * 1985-02-08 1986-08-15 Hitachi Ltd Detector of abnormality in isotropic substance
EP2767830A1 (en) * 2013-02-18 2014-08-20 Laboratoires Expanscience Method for determining the maturation of the skin surface of a subject.
US20150039238A1 (en) * 2013-08-02 2015-02-05 Board Of Trustees Of The University Of Illinois Dispersion-Relation Fluorescence Spectroscopy
CN103995053A (en) * 2014-03-13 2014-08-20 天津大学 Method for detecting isotropic material surface Young modulus by using surface acoustic wave technology

Also Published As

Publication number Publication date
CN107655891A (en) 2018-02-02

Similar Documents

Publication Publication Date Title
Casiraghi et al. Rayleigh imaging of graphene and graphene layers
Chang et al. Extracting the complex optical conductivity of mono-and bilayer graphene by ellipsometry
Li et al. Layer number identification of intrinsic and defective multilayered graphenes up to 100 layers by the Raman mode intensity from substrates
Qiu et al. A general metrology of stress on crystalline silicon with random crystal plane by using micro-Raman spectroscopy
CN104359600B (en) Method for measuring stress optical coefficient of optical thin film
Evans et al. Laser actuation of cantilevers for picometre amplitude dynamic force microscopy
Wang et al. Imaging grain microstructure in a model ceramic energy material with optically generated coherent acoustic phonons
Qiu et al. Mechanical behavior study of microdevice and nanomaterials by Raman spectroscopy: a review
Li et al. Mapping the near-field spin angular momenta in the structured surface plasmon polariton field
Sun et al. Polariton waveguide modes in two-dimensional van der Waals crystals: an analytical model and correlative nano-imaging
Ureña et al. Strain in silicon nanowire beams
Xin et al. Optical anisotropy of black phosphorus by total internal reflection
CN107655891B (en) Method for representing Van der Waals crystal optical anisotropy with nanoscale thickness
Cui et al. In-plane anisotropic mechanical properties of two-dimensional NbOI2
Jeyar et al. Tunable nonadditivity in the Casimir-Lifshitz force between graphene gratings
Liu et al. Near-field ellipsometry for thin film characterization
Dab et al. Dependence of apertureless scanning near-field spectroscopy on nanoscale refractive index changes
Patrini et al. Photonic bands in patterned silicon-on-insulator waveguides
Deng et al. Directly measuring flexoelectric coefficients μ 11 of the van der Waals materials
CN112764133B (en) Polarization phase modulation device based on two-dimensional germanium selenide and design method thereof
Liu et al. Reflection-based near-field ellipsometry for thin film characterization
Li et al. Nondestructive and in situ determination of graphene layers using optical fiber Fabry–Perot interference
Sopinskii Determination of optical constants of a biaxially anisotropic film by standard multiangle monochromatic ellipsometry
Adamson Ellipsometry of anisotropic graphene-like two-dimensional materials on transparent substrates
Chen et al. Study of black phosphorus anisotropy on silicon photonic waveguide

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant