WO2014200140A1 - Method for computer-aided simulation of atomic-resolution scanning thermoelectric microscope - Google Patents

Abstract

The present invention relates to a method for the computer-aided simulation of an atomic-resolution scanning thermoelectric microscope and, more particularly, to a simulation method in which a computer calculates a thermoelectric voltage V for displaying an atomic-level image of a predetermined local area of a material.

Description

Computer aided simulation method of atomic-resolution scanning thermoelectric microscope

The present invention relates to a computer aided simulation method of atomic level-resolution scanning thermoelectric microscopes.

One way to view the surface of a material in atomic-resolution is the Scanning Tunneling Microscope technology disclosed in US Pat. No. 4,343,993. Scanning tunneling microscopy is a technique for displaying atomic-resolution images of the surface of a material based on a vacuum tunneling current generated locally by applying an external voltage between the material and the probe. However, since an external voltage must be applied, Fermi electrons may be disturbed by the voltage, and the scanable area is narrow. In addition, a sharp probe must be made to generate a localized current, and the difficulty of this process is that the yield is not high.

A scanning thermoelectric microscope may be considered as an alternative to supplement the disadvantages of the scanning tunneling microscope, but in general, heat is known to be difficult to localize in space, so it is not practical to implement.

Recently, a technique for scanning the surface of a material in atomic-resolution using scanning thermoelectric microscope was published in 2013. S. Cho, S. D. Kang, W. Kim, E.-S. Lee, S.-J. Woo, K.-J. Kong, I. Kim, H.-D. Kim, T. Zhang, J. A. Stroscio, Y.-H. Kim, and H.-K. Lyeo, "Thermoelectric imaging of structural disorder in epitaxial graphene" arXiv: 1305.2845 (http://arxiv.org/abs/1305.2845).

However, even with this paper, a real device must be implemented to observe the surface of the material with a scanning thermoelectric microscope, and a technique for simulating the surface shape of the material without such a device has not been developed yet.

The present invention relates to a computer-aided simulation method of atomic-resolution scanning thermoelectric microscope, which aims to provide a method of knowing the surface morphology of a material through simulation without using the actual scanning thermoelectric microscope.

에 대한 원자 레벨 이미지 표시를 위한 열전압(thermoelectric voltage) V를 아래 수학식에 의해서 컴퓨터가 계산하는 시뮬레이션 방법에 관한 것이다.FIELD OF THE INVENTION The present invention relates to a computer-aided simulation method of atomic-resolution scanning thermoelectric microscopy, wherein a predetermined local region of a material

Computer simulations of the thermoelectric voltage V for atomic level image display for

From here,

: 적분변수

: Integral variable

S: Seebeck Coefficient

: 국지 영역의 온도 그래디언트(temperature gradient)

: Temperature gradient of the local area

은 국지 영역에 대한 지벡 계수(Seebeck coefficient)로서 전기전도도로 표현되는 소재의 고유 특성이다. 본 발명에서는 다음과 같이 정의되는 지벡 계수를 사용할 수 있다.

Is the intrinsic property of the material expressed as electrical conductivity as Seebeck coefficient for the local area. In the present invention, a Seebeck coefficient defined as follows may be used.

From here,

e: amount of electron charge

T: absolute temperature

E _F : Fermi Energy

f: Fermi-Dirac distribution function at temperature T

: 소재의 브릴루앙 영역(Brillouin zone)의 k 번째 지점에서 i번째 고유상태(eigenstate)

: I-eigenstate at the k-th point of the Brillouin zone of the material

: 소재의 브릴루앙 영역(Brillouin zone)의 k 번째 지점에서 i번째 고유값(eigenvalue)

Is the i th eigenvalue at the k th point of the Brillouin zone of the material.

δ: delta function

는 아래 수학식에 의해서 정의되는 것이 바람직하다.In the simulation method according to the present invention, the temperature change between the probe and the material surface is displayed.

Is preferably defined by the following equation.

: 탐침의 온도

: Probe temperature

: 소재의 온도

Material temperature

: 누적 분포 함수(cumulative distribution function; CDF)

Cumulative distribution function (CDF)

R: Tip radius of the probe

: 탐침의 팁 중앙

: Center of tip of probe

: 온도변화의 급작성 정도를 표시하는 가우시안 확장(Gaussian broadening)

: Gaussian broadening indicating the degree of sudden change in temperature change

The present invention provides a method for simulating atomic-resolution scanning thermoelectric microscopes.

1 is a conceptual diagram of a scanning thermoelectric microscope to which the method according to the present invention is applied.

2 is a view showing a simulation result image according to the present invention.

3 is a view showing an image displayed through an experiment according to the prior art.

Hereinafter, the present invention will be described in detail with reference to the accompanying drawings. The probe 10 of the scanning thermoelectric microscope is in contact with the graphene material 20 (graphene) at a first temperature T ₁ and the graphene material is at a second temperature T ₂ . It is desirable for the environment to maintain an ultra-high vacuum. For the sake of convenience, the drawings and the specification are described as graphene, but the simulation method of the present invention should not be construed as being limited to graphene.

The thermoelectric voltage is generated by the difference between the first temperature and the second temperature, which can be accurately measured by a high-impedance voltmeter in an actual scanning thermoelectric microscope.

)와 온도 구배(▽T)하의 입자 확산 구동력에 따라 전자 또는 대전 입자가 흐르게 된다. 국지 영역(

)에서 전체 전류 밀도

는 다음과 같이 표현된다.If there is a temperature gradient (▽ T) in the electrically conducting system,

And charged particles flow in accordance with the particle diffusion driving force under the " Local area (

Total current density

Is expressed as

Equation 1

은 국지 지벡 계수(local Seebeck coefficient)이다.σ is the electrical conductivity,

Is the local Seebeck coefficient.

이 확산 구동력으로서 열전압 발생의 기초가 된다. 온도 구배(▽T)는 소재의 고유 열전도도(thermal conductivity)와 탐침-소재간의 경계면 열전도율(interfacial conductance) 등 열전달 성질에 의해서 결정된다.

This diffusion driving force serves as a basis for generating thermal voltage. The temperature gradient ▽ T is determined by heat transfer properties such as the intrinsic thermal conductivity of the material and the interfacial conductance between the probe and the material.

In the measurement environment of FIG. 1, the thermal voltage is an open circuit condition, and in the open circuit condition, since the total current density is 0, Equation 1 is represented by Equation 2 as follows.

Equation 2

은 단지 열-유도 대전 분포

으로부터 야기되는 전기장이다. 가우스 법칙을 이 전기장과 대전 밀도 사이에 적용하면

가 되며, 따라서 다음과 같은 수학식 3이 도출된다.In the absence of an external electric field,

Is just a heat-induced charging distribution

Electric field resulting from Applying Gaussian law between this electric field and the charge density

Therefore, the following equation (3) is derived.

Equation 3

는 국지 지벡 계수

와 공간 온도 프로파일

로부터 정확하게 추적될 수 있다.Distribution of heat induced charge density

The local Seebeck coefficient

And space temperature profiles

Can be accurately tracked from

에 대한 포아송 방정식으로부터 유도되는 하트리 정전 포텐셜(Hartree electrostatic potential)

은 열전압과 등가이며, 위 수학식 3에 의해서 다음과 같은 수학식 4가 도출된다.

Hartree electrostatic potential derived from the Poisson equation for

Is equivalent to the thermal voltage, and the following Equation 4 is derived from Equation 3 above.

Equation 4

은 적분변수이다. 온도 구배(▽T)는 무한대에서 0이기 때문에 수학식 4는 다음과 같은 수학식 5로 단순화될 수 있다.From here

Is an integral variable. Since the temperature gradient ▽ T is 0 at infinity, Equation 4 may be simplified to Equation 5 as follows.

Equation 5

을 구하는 방법에 대해서 살펴 본다. 국부 지벡 계수는 이하의 방법 이외에 공지되어 있는 다른 방법으로 전기전도도, 전자투과함수, 국부상태밀도 등을 정의하여 도출하거나 구할 수 있으며, 이하의 내용에 국부 지벡 계수 정의가 제한되는 것으로 해석되어서는 아니된다. Next, a local Seebeck coefficient for atomic resolution

Let's look at how to obtain. The local Seebeck coefficient may be derived or obtained by defining electric conductivity, electron transmission function, local state density, etc. by other methods other than the following methods. do.

로 다음과 같은 수학식 6으로 표현될 수 있다.The local Seebeck coefficient in the structure shown in FIG. 1 is the energy-and position-dependent electron transmission function between the probe and the material from the Landauer formula.

It can be represented by the following equation (6).

Equation 6

는 페르미 에너지, f는 온도 T에서의 페르미-디랙 분포 함수(Fermi-Dirac distribution function)이다.Where e is the amount of electron charge, T is the absolute temperature,

Is the Fermi energy, f is the Fermi-Dirac distribution function at temperature T.

은 국부 상태 밀도

로 근사화될 수 있고 이를 수학식 7에 표시하면 다음과 같다.The electromagnetic wave functions of both the metal probe and the electrically conductive material overlap by contact. When this wave function overlap is insignificant

Silver local state density

It can be approximated by and represented in Equation 7 as follows.

Equation 7

은 소재의 브릴루앙 영역(Brillouin zone)의 k 번째 지점에서 i번째 고유상태(eigenstate)이고,

는 소재의 브릴루앙 영역(Brillouin zone)의 k 번째 지점에서 i번째 고유값(eigenvalue)이다. 여기에서 δ는 델타 함수(delta function)를 의미한다.

Is the i th eigenstate at the k th point of the Brillouin zone of the material,

Is the i th eigenvalue at the k th point of the Brillouin zone of the material. Here, δ means a delta function.

Equation 6 may be rewritten as Equation 8 as follows.

Equation 8

It can be seen from Equation 8 that the Seebeck coefficient is strongly related to the electrical state near the Fermi level.

For thermoelectric image simulation with atomic resolution, a step function temperature change is required at the interface between the spherical probe and the material surface, and the spherical temperature profile is assumed to be expressed as

Equation 9

는 탐침의 온도,

는 소재의 온도,

는 누적 분포 함수(cumulative distribution function; CDF), R는 탐침의 팁 반경,

: 탐침의 팁 중앙,

: 온도 변화의 급작성 정도를 표시하는 가우시안 확장(Gaussian broadening)을 가리킨다. 그리고 탐침의 팁과 소재의 접촉 거리(z₀)는 소재면 상에서 일정하게 유지된다.

Is the temperature of the probe,

Is the temperature of the material,

Is the cumulative distribution function (CDF), R is the tip radius of the probe,

: Center of tip of probe,

: Refers to Gaussian broadening, which indicates the degree of sudden change in temperature change. And the contact distance z ₀ between the tip of the probe and the workpiece is kept constant on the workpiece surface.

In the application of the simulation method according to the present invention, a temperature profile different from Equation 9 may be used, and Equation 9 is not the only temperature profile to which the present invention is applied.

FIG. 2 (a) shows the Seebeck coefficient displayed by the computer-aided simulation method according to the present invention, and FIG. 2 (b) shows the simulated thermoelectric voltage image. Simulation of the images shown in (a) and (b) of FIG. 2 was performed on n-doped pure graphene. A part shown in white in FIG. 2B is an atom, and a part shown in black is a void. 3 shows an image of a defect-free region of bilayer graphene on silicon carbide (SiC) as an image tested by the method disclosed in the above-described S. Cho paper. have. Notable identity is found between FIGS. 2B and 3.

The conditions of the simulation shown in FIG. 2 are T = 315K, z ₀ = 3 ms, ΔT = 3K, R = 0.75 ms, δ = 0.3 ms, respectively.

Although the present invention has been described above with reference to the accompanying drawings, the scope of the present invention is determined by the claims below and should not be construed as limited to the foregoing description. And it should be understood that improvements, changes, and / or modifications apparent to those skilled in the art of the invention described in the claims are included in the scope of the present invention.

Claims (3)

In the computer-aided simulation method of atomic-resolution scanning thermoelectric microscope, Predetermined local area of the material

Computer simulation of the thermoelectric voltage (V) for atomic level image display for

From here,

: Integral variable S: Seebeck Coefficient

: Temperature gradient of the local area The method according to claim 1, The Seebeck coefficient is defined by the following equation, Simulation method.

e: amount of electron charge T: absolute temperature E _F : Fermi Energy f: Fermi-Dirac distribution function at temperature T

: I-eigenstate at the k-th point of the Brillouin zone of the material

Is the i th eigenvalue at the k th point of the Brillouin zone of the material.

Delta function The method according to claim 1 or 2, To indicate the temperature change between the probe and the material surface

Is a simulation method defined by the following equation.

: Probe temperature

Material temperature

Cumulative distribution function (CDF) R: Tip radius of the probe

: Center of tip of probe

Gaussian broadening

Images