KR101575955B1 - Computer-aided simulation method for atomic-resolution scanning seebeck microscope images - Google Patents

Abstract

According to an embodiment, a compter-aided simulation method of an atomic-resolution scanning seebeck microscope image is provided, wherein a voltage probe corresponding to position r of the voltage probe The local thermoelectric voltage (V (r)) for the position r of the voltage probe is calculated by a computer according to the following equation to obtain the scan defocus microscope image.

: The thermoelectric voltage drop in the diffusive transport region in the tip and sample.

: Position-dependent Seebeck coefficient.
r : Distance measured from the point-shaped probe
r ': Material inner coordinate

:

A radially weighted temperature gradient by a factor of < RTI ID = 0.0 >

: Volume integral of temperature profile

Description

TECHNICAL FIELD [0001] The present invention relates to a computer-aided simulation method for an atom-level-resolution injection scanning electron microscope image,

According to one embodiment, a computer-aided simulation method of atomic level-resolution scanning thermo-microscopy is provided.

There is a Scanning Tunneling Microscope technique disclosed in U.S. Patent No. 4,343,993 as a way to view the surface of the material at atomic level-resolution. A scanning tunneling microscope is a technique for displaying an atomic level-resolution image of a workpiece surface based on a vacuum tunneling current that occurs locally by applying an external voltage between the workpiece and the probe. However, since an external voltage must be applied, there is a possibility that the Fermi electrons may be disturbed by the voltage and the scanable area is narrow. And a sharp probe must be made to generate a localized current, and the drawback is that the yield is not high due to the difficulty of this process.

A scanning thermoelectric microscope can be considered as an alternative to compensate for the disadvantages of such a scanning tunneling microscope, but it is generally not feasible to implement it because it is known that heat is difficult to localize in space.

Recently, a technique for viewing the surface of a material at atomic level-resolution using a scanning thermo-optic microscope has been disclosed in 2013, S. Cho, SD Kang, W. Kim, E.-S. Lee, S.-J. Woo, K.-J. Kong, I. Kim, H.-D. Kim, T. Zhang, JA 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 ), Nature Mater. 12 , 913.

It is necessary to simulate the surface shape of a specific material by using a computer to obtain an atomic level-resolution image from the surface of the material by using a scanning thermoelectric microscope as a practical device and to find an atomic structure corresponding to the acquired image.

According to one embodiment, there is provided a computer-generated simulation method of an atomic-level-resolution scanning dynamic microscope image, wherein the surface morphology of a material corresponding to an image obtained by an actual scanning thermo-microscope is simulated, The present invention is directed to providing a method that can be used in a variety of applications.

According to one embodiment, a compter-aided simulation method of an atomic-resolution scanning Seebeck microscope image is provided, wherein a voltage probe corresponding to position r of a voltage probe The local thermoelectric voltage (V (r)) for the position r of the voltage probe is calculated by a computer according to the following equation to obtain the scan defocus microscope image.

here,

Is a thermoelectric voltage drop in the diffusive transport region at the tip and sample,

Is the position-dependent Seebeck coefficient, r is the distance measured from the point probe, r 'is the inner coordinate of the workpiece,

silver

A radial weighted temperature gradient by a factor of < RTI ID = 0.0 >

May be a volume integral of the temperature profile.

In a simulation method according to an embodiment, the volume integral of the temperature profile

Is defined by the following equation.

From here,

May be an effective temperature drop at the interface between the tip and the sample.

In a simulation method according to an embodiment, the position-dependent < RTI ID = 0.0 >

Is calculated by the following equation.

Here, e is the electron charge amount, T is the absolute temperature,

E F is the Fermi energy, and f can be the Fermi-Dirac distribution function at the temperature T. [

In a simulation method according to an embodiment, the position-dependent < RTI ID = 0.0 >

Is derived from the Landauer formula by the following equation.

From here,

Is a tip-decking coefficient,

May be a sample Seebeck coefficient of the material.

In a simulation method according to an embodiment, the sample deblocking coefficient

Is defined by the following equation.

Where e is the amount of electron charge, T is the absolute temperature, E F is the Fermi energy, f is the Fermi-Dirac distribution function at the temperature T,

May be a local density of states of electrons obtained from first-principles calculations of the material surface.

In the simulation method according to an embodiment, the effective temperature drop

Is calculated by the following equation.

From here,

Is the Boltzmann constant,

May be the phonon transmission probability of the tip-sample junction.

In the simulation method according to an embodiment, the effective temperature drop

Is an experimental

And theoretical

Which is derived by the following equation.

From here,

Is a thermoelectric voltage measured for a defect-free region,

May be the theoretical Seebeck coefficient of the material.

In the simulation method according to an embodiment, the effective temperature drop

Van der Waals energy

Which is a function based on the correlation between the input signal and the output signal.

From here,

May be a function involving a linear fit equation or an exponential function.

According to one embodiment, the atomic level-resolution image of a scanning electron microscope corresponding to the surface of a workpiece can be simulated using the Seebeck effect.

FIG. 1 illustrates a schematic of the atomic resolution of a scanning thermo-microscope according to one embodiment.
FIGS. 2A-2F may illustrate an experimental thermoelectric voltage image, a defocus coefficient image, a line profile, and a correlation for a non-defective region of n-doped independent graphene, according to one embodiment.
Figures 3A-3D illustrate an image of a thermoelectric voltage, a topographic image, and a profile for point defects according to one embodiment.
4A-4F may illustrate a simulated image and thermoelectric voltage of a Seebeck coefficient adjacent to a point defect in n-doped independent graphenes, according to one embodiment.
Figures 5a-d may illustrate the model, native density (DOS), van der Waals energy, Van der Waals topography of native free graphene, according to one embodiment.
FIGS. 6A-6F can illustrate locally averaged Jacobian coefficients, van der Waals energies, correlation between effective temperature drops, and thermoelectric voltages according to one embodiment.
FIGS. 7A-7D illustrate a model of defective free-standing graphene, electron density, van der Waals energy and Van der Waals topography, according to one embodiment.
Figures 8A-8D can illustrate the model, electron density, van der Waals energy, and van der Waals topography of single substituted nitrogen atoms according to one embodiment.
Figures 9A-9D can illustrate the model, electron density, van der Waals energy and van der Waals topography of defective free graphene, according to one embodiment.
10A-10D illustrate a simulated thermoelectric voltage image, a corresponding Fast Fourier Transform (FFT) image, an experimental thermoelectric image, and a corresponding fast Fourier transform image for a defective complex according to one embodiment can do.

Hereinafter, the present invention will be described in detail with reference to the accompanying drawings.

In the present specification, a scanning scanning microscope (SSM) may represent a scanning thermoelectric microscope (STM) using a Seebeck effect. According to one embodiment, a material surface can be simulated for a computer to find a material corresponding to an image of the material surface acquired by the scanning dynamic microscope.

Here, a scanning tunneling microscope (STM) uses tunneling to acquire a direct wavefunction image using a charge-transfer gap and a voltage bias. , The scanning-scanning microscope utilizes the Seebeck effect and can obtain a differential wavefunction image using a heat-transfer gap and a temperature bias.

In addition, in this specification, the scanning dynamic microscope image can represent an image obtained by the scanning dynamic microscope described above. The process by which the atomic level-resolution image of the workpiece surface corresponding to the scanned Zebec microscope image is simulated by a computer according to one embodiment is described in detail below.

Hereinafter, graphene has been mainly described as an example of the simulation of the scanning dynamic microscope image. However, the present invention is not limited to the graphene, and other materials having arbitrary atomic structures may be used as the simulation method Can be applied.

Herein, in the present specification, the Seebeck coefficient is a position-dependent Seebeck coefficient (or coherent Seebeck coefficient)

And a localized Seebeck coefficient S ( r ) (or S ( r ; r ' )).

It is known that heat can be diffused or incoherent transported by lattice vibrations, such as charge carriers and phonons, such as electrons and holes, in the material. It is therefore considered very difficult to perform local imaging of the electronic state of materials and materials using heat transport. Recently, however, Cho et al. Have performed local thermoelectric imaging with a heat-based scanning probe microscope at the surface of the epitaxial graphene to generate a series of atomic wave functions He reported that he got the image. This report can raise questions about how atomic variation in a unit cell can be measured in a heat transport experiment. In answer to this, not only does the imaging mechanism of scanning thermoelectric microscopy have to be identified, but fundamental physics of thermoelectric or Seebeck effects must be re-verified from normal length to atomic length scale.

The theory of scanning thermo-microscopy having atomic resolution based on the intensive electron and heat transport characteristics can be presented herein. Theories, beginning with macroscopic general transport equations and electrostatic equations, can demonstrate the possibilities and mechanisms of atomic-level imaging techniques with thermoelectric measurements. Computer simulations of thermoelectric images can be used effectively to identify atomic scale defects in graphene combined with experimental results.

FIG. 1 illustrates a schematic of the atomic resolution of a scanning thermo-microscope according to one embodiment.

As schematically shown in Fig. 1, the probe 10 of the scanning thermo-microscope contacts the graphene 20 at a first temperature T1 and the graphene material at a second temperature T2. Measurements are made through a modified ultra-high vacuum atomic force microscope (AFM). For the sake of convenience, the graphene is described in the drawings and herein, but the method of simulation of the present invention should not be construed as limited to graphene. Due to the difference between the first temperature and the second temperature,

Can be formed in the vicinity of the tip-sample contact region, and at the interface between the tip and the sample

And the thermoelectric voltage with a phase difference of 180 degrees from the atomic height z ( r ) can be accurately measured by a high-impedance voltmeter in an actual scanning thermo-microscope. The measured local thermoelectric voltage can be expressed by the following equation (1).

here,

Shows the thermoelectric voltage drop in the diffusive transport region in both the tip and the sample,

And

Can represent a temperature-dependent Seebeck coefficient and an effective temperature drop at the interface between the tip and the sample. At this time, electrons and heat can be transported coherently. Coherent thermoelectric voltage < RTI ID = 0.0 >

May correspond to the atomic resolution observed in a scanning thermo-microscope, as described below.

Temperature gradient

Is present in a macroscopic electro-conductive system, the transport of electrons or charged particles is carried out by electrostatic fields E and gradients < RTI ID = 0.0 >

And particle diffusion under driving force. The electric current density J ( r ) at the local site is calculated from the general transport equation

. here,

Is the electrical conductivity, and S ( r ) may be the localized Seebeck coefficient or thermopower. The ideal voltmeter satisfies the open-circuit limit of J ( r ) = 0, so that a balance between the electrostatic force and the thermopower force acting on the charged particles is maintained, the built-in potential can be expressed by the following equation (2).

The temperature profile T ( r ) can be determined primarily by the heat transfer characteristics of the system, such as the thermal conductivity of the constituent material and the interfacial thermal conductivity between the materials. The above equation (2) can be derived from a macroscopic diffusion system, but it can also be applied to a microscopic system such as a microscope system. When no external field is applied, E ( r ) is the thermal diffusion-induced charge distribution,

Only the built-in electric field is generated. Gauss's law can be applied to internal field and charge density.

Lt; / RTI > Accordingly, the following Equation (3) can be derived using Equation (2).

From equation (3), the distribution of heat induced charges

Can be accurately traced back from the information of the localized Sebek coefficient S ( r ) and the temperature profile T ( r ).

Assuming that the AFM tip (AFM tip) is a point probe as shown in Fig. 1, the local thermoelectric voltage is the " Hartree-type "electrostatic potential

≪ / RTI > Where r is the position of the probe and V ( r ) can be the integral of r 'over the entire volume. At this time, in Equation (3) and infinity

= 0, the local thermoelectric voltage can be expressed by the following equation (4).

Local thermoelectric voltage V ( r )

Lt; RTI ID = 0.0 > radial < / RTI > weighted by a factor of &

(Not a line integral) of the local integral of the convoluted local deblocking coefficient S ( r ) Where r may be the distance measured from the point probe. Equation 4 is an exact mathematical expression that does not include any approximations and thus can be applied globally to other thermoelectric systems including non-contact STM settings.

In Equation (4), the volume integral can be divided into diffusion and coherent transport regions. In the diffusion transport region, the Seebeck coefficient and temperature profile can only be determined by the intrinsic properties of the material, such as electrical conductivity and thermal conductivity. From the Mott formula, the diffusion-Seebeck coefficient is

. here,

Is the Boltzmann constant, T is the absolute temperature, e is the electron charge,

Energy-dependent electrical conductivity, and E _F is the Fermi energy. The temperature profile T ( r ) is determined by the phonon mean-free-path and can vary slowly in the material, so the thermoelectric voltage

Can have almost constant values.

In the coherent transport region of the tip-sample interface, the transport of electrons and phonons across junctions is determined by the respective transmission probability and the electrical and thermal conductivity quantum (electrical and thermal conductance quanta). Coherent Seebeck coefficient

Is dependent on the tip position r (independent of the internal coordinate r ') and the electron transmission probability of the tip-sample junction,

From the Landauer formula.

. here,

May represent the electron transmission probability of the tip-sample junction.

The local coherent thermoelectric voltage can be expressed by the following equation (5).

Here, the volume integral of the temperature profile is

Lt; / RTI >

The

Can be sensitive to the temperature profile around the probe and the local geometry. Physically

May correspond to an interface temperature drop that is known to exist at the thermal boundary between two different thin film materials. In general, the interface temperature drop in a thin film can be affected by the vibrational spectra and the interaction strength of the materials involved.

For example, the effective temperature drop

From the Landauer formula using the phonon transmission probability of the tip-sample junction

. here,

Can represent the phonon transmission probability of the tip-sample junction.

Diffusion thermoelectric voltage

And the coherent thermoelectric voltage, the total local thermoelectric voltage can be derived from Equation (1). Through this, it is possible to explain how the thermal power profiling works for the PN junction and how the local thermoelectric imaging works smoothly from the micrometer to the sub-angstrom scale.

Coherent Seebeck coefficients (e.g., position-dependent Seebeck coefficients)

Can be expressed by Equation (6) below.

In the limit of weak coupling, the probability of electron transmission

silver

. ≪ / RTI > here,

Can represent the local electron density.

From the Landauer formula, coherent Seebeck coefficients

The

. Sample Seebeck coefficient

Can be expressed by the following Equation (7).

Here, f may be a Fermi-Dirac distribution function at a temperature T. At 300K

Fermi energy

Lt; RTI ID = 0.0 > eV < / RTI > The sample Seebeck coefficient is calculated from the Fermi energy

And may be positive or negative depending on the energy derivative or asymmetry of the input signal.

From the first-principles calculations on the material surface, the local electron density of the material

Can be obtained,

Is known, equation (1) can serve as a basis for thermoelectric image simulation in the tip-sample junction. Generally

May be difficult to know by experiment or simulation. Instead, as shown in Figure 2 below,

And theoretical

(E.g,

By inverting Equation 1 with < RTI ID = 0.0 >

Lt; / RTI > E.g,

.

FIGS. 2A-2F may illustrate an experimental thermoelectric voltage image, a defocus coefficient image, a line profile, and a correlation for a defect-free area in accordance with one embodiment.

2A is an experimental thermoelectric voltage image for a defect-free region of two-layer graphene on SiC (0001)

The pattern can also be observed.

FIG. 2B is an enlarged view of FIG. 2A. The experimental thermoelectric voltage can be sampled in a graphene unit cell marked with a parallelogram.

FIG. 2C can represent a computer simulated Jacobian modulus image of n-doped independent graphenes. The central pores and carbon atoms can be marked as 'V' and 'C', respectively.

Figure 2d shows the line profiles of the experimental thermoelectric voltage, the Seebeck coefficient and the Van der Waals energy along the line V-C-C-V in Figure 2c.

FIG.

And Van der Waals energy

. ≪ / RTI > Averaged over a disk radius of 0.5 angstroms locally

silver

. ≪ / RTI > (Figure 8). For example,

And Van der Waals energy

The correlation between

. ≪ / RTI > Here,

May include a linear fit equation or an exponential function. In the above-described Fig. 2E,

silver

= 118.05 + 1.6454

Lt; / RTI >

FIG. 2F can represent a reconstructed image of the theoretical thermoelectric voltage for n-doped independent graphenes.

2A and 2B are graphs showing the relationship between the thermoelectric voltage measured for a defect-free region in a bilayer graphene on SiC

. ≪ / RTI > Figure 2c shows the theoretical bekking coefficients for an n-doped free-standing graphene calculated from equation (7)

. ≪ / RTI > AFM tip and graphene samples coated with diamond can interact through van der Waals (vdW) interaction,

Can be evaluated at the vdW equilibrium height calculated as the Lennard-Jones potential for the pristine graphene as shown in FIG. 5 below. In FIGS. 2B and 2C, the experimental thermoelectric image and the theoretical thermoelectric power image can show a reasonable degree of similarity. In particular, the center void of a carbon hexagon represents a more negative signal in both experimental and theoretical results than a carbon atom site. This characteristically differs from STM, which draws more current at charge-rich atomic sites. However,

Only thermoelectric voltage

Can not be reproduced from the atomic corrugation observed in the line profile.

In order to identify the role of temperature in the length scale of the coherent transport,

Can deduce. Inferred

And vdW energy

There may be an almost linear correlation as shown in FIG. 2E. This linear correlation

May be sensitive to inter-atomic thermal coupling at the tip-sample interface. In other words, a large interfacial temperature drop can be predicted in the case of weak thermal coupling (carbon atom sites), and a small interfacial temperature drop can be predicted in case of strong bonding (central pore of carbon hexa).

As a result,

Can exhibit atomic variations on a subangstrom scale from carbon atom sites to hexagonal voids. Therefore, it may be proposed that the atomic-level resolution at local thermovoltage is due to changes at atomic level in coherent electron transport through the Seebeck coefficient and at atomic level of coherent heat transport through thermal conduction have. Figure 2f

And the linear fitting formula

Can be used to illustrate the theoretical thermoelectric voltage of a simulated raw, independent graphene.

3A-3D illustrate an image of the thermoelectric voltage, a topographic image, and a profile for a point defect according to one embodiment.

3A shows a large-area scan image of the thermoelectric voltage for a point defect in a two-layer graphene on SiC.

FIG. 3B may represent a small area scanned image of the thermoelectric voltage at a point rotated about the point defect in FIG. 3A, and FIG. 3C may represent a simultaneously obtained topographic image.

Figure 3d can show the height profile along the dashed line ('1') and the thick line ('2') in Figure 3c. Compared to the line profile of the dotted line ('1') and the thick line ('2'), it can be seen that one carbon atom is defective on the dotted line ('1').

Wow

The atomic scale defects on the graphene surface can be identified by comparing the simulated thermoelectric voltage image with the experimental thermoelectric image. 3A and 3B can show thermoelectric images of point defects of two-layer graphene on SiC. Through topographic analysis in Figures 3c and 3d, it can be deduced from experiments that point defects are associated with a single carbon atom site.

Figures 4a-4f illustrate a simulated image of the < RTI ID = 0.0 > Seebeck < / RTI > coefficients (Figures 4a, 4b, 4F). ≪ / RTI >

Figures 4A and 4D may show simulated images and thermoelectric voltages of a Seebeck coefficient for point defects of a single carbon vacancy (VC).

Figures 4b and 4e can show the simulated image and thermoelectric voltage of the Seebeck coefficient for point defects of the substituted nitrogen atoms (NC).

Figures 4C and 4F can show simulated images and thermoelectric voltages of the Jacobian coefficients for point defects of the carbon vacancy and substituted nitrogen defect complexes (VC-OC).

Here, each atomic model can be represented by an inset.

To map the defect to the atomic model, a single carbon vacancy (VC; Figs. 4A and 4D), a substitutional nitrogen (NC; Figs. 4B and 4E) It is possible to simulate the thermoelectric image of the carbon vacancies and substituted nitrogen defect complexes (VC-OC; Fig. 4C to Fig. 4F) in the fins.

Because the electrons of the VC defect are located below the Fermi energy (FIG. 7), the thermal power and thermoelectric images show a bright image at the defect site as opposed to the experimental image. On the other hand, since the electrons of the NC and VC-OC defects are located above the Fermi energy (Figures 8 and 9 below), the thermal power and thermoelectric image show a dark image similar to the experimental image. While the size of the dark part is well matched to the NC, the symmetric structure may well match the image of the VC-OC. Since the atomic oxygen exists in the sample growth environment and the formation energy of the VC-OC is sufficiently smaller than the VC, the point defect in the experiment is likely to be VC-OC have. 10,

= -0.6 mV, the simulation results that include positive signals can reproduce some prominent features when compared to the experimental image. Indeed, in the experiment, positive thermoelectric signals adjacent to a defect site can be reflected in wave function superposition, atom-to-atom thermal coupling, substrate effect, and limited current simulation scheme

Can be associated with the details of.

It may be important to compare the thermo-based scanning thermo-microscope with the STM. Both techniques share a common feature and function as a type of scanning probe microscope that provides a real spatial image of the wave function. The difference between the two techniques is that the STM measures the tunnel current by applying a voltage drop across the vacuum-tunneling gap, while the thermo-microscope can detect a temperature drop across the heat transfer gap or across the interface The voltage difference can be measured. As a result, STM shows the zero-order perturbation of the Fermi electrons by voltage bias, while the thermoelectric microscope shows the first-order perturbation by temperature bias. In this regard, scanning thermo-microscopy can be useful for analyzing the Fermi electronic state separately from STM even at room temperature.

Hereinafter, first-principles calculations will be described in detail.

In Equation (7), the significance of the Seebeck coefficient can be obtained using local electron density and Kohn-Sham wavefunctions from the first-principles density-functional theory calculations of graphene have. VASP software can be used to calculate the total energy of the floor condition. (12x12) graphene supercell can be used to model point defects (VC, NC, ... VC-OC) in graphene. When the Dirac point is 0 eV, the Fermi energy E _F = 0.3 eV can be used to calculate the local density of the electrons. In Equation (7)

T = 315K can be used to calculate.

Atomically-varying effective temperature drops are described in detail below.

Experimental

And theoretical

Locally averaged within a particular disk radius R to inverse < RTI ID = 0.0 > (1) <

Can be used. This is a way to consider the finite size effect of the probe. In Figures 2E-2F, R = 0.5 angstroms of locally averaged

Can be used. For comparison, as shown in FIG. 6, R = 0.3 angstroms of locally averaged

And existing

Can be used.

Inferred

(Van der Waals) energy calculated with the Leonard-Jones 12-6 potential (12-6 potentials) expressed as Equation (7)

And almost linear correlation or almost exponential correlation.

here,

And

May each be an atomic position of the tip and sample,

And

May be the Lennard-Jones parameters. The tip can be modeled as a single carbon atom. For carbon, nitrogen and oxygen atoms

And

The parameters can be listed in Table 1,

And

Can be used. Van der Waals energy has an atom-atom distance of 15

, And the equilibrium height z ( r ) with the minimum van der Waals energy is

. ≪ / RTI >

Hereinafter, the statistically defined Fermi temperature will be described in detail.

We can understand the in-depth physics of the sample Jacobian coefficients expressed in Equation 7 (which can also be expressed in the form of Equation 9 below).

Is defined as the entropy of the electron, the energy differential of the entropy can correspond to the reciprocal of the temperature, and can be expressed by the following equation (10).

here,

May be a position-dependent statistically-defined Fermi temperature of the material. The newly defined Fermi temperature of the actual material

Fermi temperature ", which can be applied only to a three-dimensional free electron gas model,

Lt; RTI ID = 0.0 > a < / RTI > generalized version. At this time, the Seebeck coefficient can be expressed by the following Equation (11).

Equation (11) describes the thermal equilibrium temperature ( T ) and Fermi temperature

As shown in FIG. The statistically defined Fermi temperature is the material characteristic, not the actual temperature,

Lt; / RTI > may be positive or negative depending on the slope of the slope. In Equation (11), the Seebeck coefficient is conceptually an electronic heat capacity,

And a thermally conductive quantum

To the electron-related thermal properties of the material, such as < RTI ID = 0.0 > For example, the Seebeck coefficient and the electronic thermal capacity can be expressed by the following equation (12).

Figures 5a-d may illustrate the model, native density (DOS), van der Waals energy, Van der Waals topography of native free graphene, according to one embodiment.

Figure 5a may represent a ball-and-stick model of a pristine free-standing graphene.

Figure 5b can represent the electron density of the native free graphene. The zero energy can indicate a charge-neutrality point or a Dirac point (bold dotted line). The thin dotted line in FIG. 4 can mark the Fermi energy (0.3 eV) for use in the thermoelectric simulation.

FIG. 5c is a cross-

Lt; RTI ID = 0.0 > a < / RTI >

FIG. 5D can represent a computer simulated image of van der Waals topography z ( r ) at minimum energy.

FIGS. 6A-6F can illustrate locally averaged Jacobian coefficients, van der Waals energies, correlation between effective temperature drops, and thermoelectric voltages according to one embodiment.

FIG. 6A may represent a computer simulated image of locally averaged Jacobian coefficients within R = 0 angstroms.

FIG. 6B may represent a computer simulated image of locally averaged Jacobian coefficients within R = 0.3 angstroms.

Figure 6C can show the correlation between van der Waals energy deduced from R = 0 angstroms and effective temperature drop.

Figure 6d can show a correlation between van der Waals energy deduced from R = 0.3 angstroms and effective temperature drop.

6E can show a reconstructed image of the thermoelectric voltage for R = 0 angstroms.

FIG. 6F may show a reconstructed image of the thermoelectric voltage for R = 0.3 angstroms.

FIGS. 7A-9D can illustrate the model, electron density, van der Waals energy and van der Waals topography of a defective freestanding graphene according to one embodiment.

Figure 7a may represent a ball-bar model of defective free grains of single carbon vacancies (VC).

Figure 7b can show the local electron density of a dangling-bound C3 atom at the electron density of the defective free graphene in a single carbon vacancy (VC). Young Energy can indicate an existing Dirac Point. The thick dotted lines indicate the existing Fermi energy of the defective graphene. The fine dotted line may indicate the elevated Fermi energy (0.3 eV) used in the thermoelectric simulation (Figs. 4A-4D).

Figure 7c is a graph of the van der Waals energy

Lt; RTI ID = 0.0 > a < / RTI >

Fig. 7d can represent a computer simulated image of van der Waals topography z ( r ) at minimum energy.

Figures 8A-8D can illustrate the model, electron density, van der Waals energy, and van der Waals topography of single substituted nitrogen atoms according to one embodiment.

Figure 8a can represent a co-rod model of defective free grains with a single substituted nitrogen atom (NC).

Figure 8b shows the local electron density for nitrogen atoms and three neighboring carbon atoms at the electron density of defective free grains of single substituted nitrogen atom (NC), marked with a medium-thick line. The zero energy can indicate the dealing point. The thick dotted lines indicate the existing Fermi energy of the defective graphene. The fine dotted line may indicate the Fermi energy (0.3 eV) used in the thermoelectric simulation (Figs. 4B-4E).

FIG. 8c is a cross-

Lt; RTI ID = 0.0 > a < / RTI >

FIG. 8D can represent a computer simulated image of van der Waals topography z ( r ) at minimum energy.

FIGS. 9A-9D can illustrate the model, electron density, van der Waals energy and Van der Waals topography of a VC-OC defective independent graphene in accordance with one embodiment.

Figure 9a may represent a ball-bar model of defective free graphene with a defect complex VC-OC. Where the oxygen atoms can be marked with a dark color.

Figure 9b shows the local electron state for an atom around the vacancy with the electron density of the defective free graphene in the defect complex VC-OC. Young Energy can indicate an existing Dirac Point. The thick dotted lines indicate the existing Fermi energy of the defective graphene. The fine dotted line can indicate the Fermi energy (0.3 eV) used in the thermoelectric simulation (Figures 4C-4F).

Figure 9c is a graph of the van der Waals energy

Lt; RTI ID = 0.0 > a < / RTI >

Figure 9d can represent a computer simulated image of van der Waals topography z ( r ) at the minimum energy.

10A-10D illustrate a simulated thermoelectric voltage image for a VC-OC defect complex, a corresponding Fast Fourier Transform (FFT) image, an experimental thermoelectric image, and a corresponding Fast Fourier Transform An image can be shown.

10A,

= -0.6 mV to represent a thermoelectric voltage image for a computer simulated Vc-Oc defect complex.

FIG. 10B may represent a fast Fourier transform image of the image of FIG. 10A. In FIG. 10B, the arrow A corresponds to the reciprocal lattice and the arrow B results from the intervalley scattering of the Fermi wave vector k F.

Fig. 10C can correspond to the experimental thermoelectric image shown in Fig. 3A.

FIG. 10D can be a fast Fourier transform image of the image shown in FIG. 10C. In FIG. 10D, the arrow A corresponds to the reciprocal lattice, and the arrow B results from the intervalley scattering of the Fermi wave vector k F. The arrow C indicates the surface of the SiC (0001)

It is derived from reconstruction.

Although the present invention has been described with reference to the accompanying drawings, it is to be understood that the scope of the present invention is determined by the claims that follow, and should not be construed as being limited to the above description. It is to be understood that improvements, changes and modifications that are obvious to those skilled in the art are also within the scope of the invention as set forth in the claims.

10: Probe
20: Material

Claims (16)

A compter-aided simulation method of atomic-resolution scanning seebeck microscope image,
A local thermoelectric voltage ( V ( r )) for the position r of the voltage probe is calculated by the following equation (1) to obtain the scanning probe microscope image corresponding to the position r of the voltage probe at the workpiece surface, Computed by the computer,
Simulation method.

From here,

: The thermoelectric voltage drop in the diffusive transport region in the tip and sample.

: Position-dependent Seebeck coefficient.
r : Distance measured from the point-shaped probe
r ': Material inner coordinate

:

A radially weighted temperature gradient by a factor of < RTI ID = 0.0 >

: Volume integral of temperature profile The method according to claim 1,
The volume integral of the temperature profile

Is defined by the following equation: < RTI ID = 0.0 >
Simulation method.

From here,

: An effective temperature drop at the interface between the tip and the sample, The method according to claim 1,
The position-dependent <

Is calculated by the following equation: < EMI ID =
Simulation method.

From here,
e : electron charge amount
T : absolute temperature

: Electron transmission probability
E F: Fermi energy
f : Fermi-Dirac distribution function at temperature T The method according to claim 1,
The position-dependent <

Is derived from the Landauer formula by the following equation: < RTI ID = 0.0 >
Simulation method.

From here,

: Tip Seebeck coefficient

: The sample's Seebeck coefficient 5. The method of claim 4,
The sample <

Is defined by the following equation: < EMI ID =
Simulation method.

From here,
e : electron charge amount
T : absolute temperature
E F: Fermi energy
f : Fermi-Dirac distribution function at temperature T

: The local density of states of electrons obtained from first-principles calculations of the material surface. 3. The method of claim 2,
The effective temperature drop

Is calculated by the following equation: < EMI ID =
Simulation method.

From here,

: Boltzmann constant

: Tip - probability of phonon transmission of sample junction 3. The method of claim 2,
The effective temperature drop

Is an experimental

And theoretical

≪ RTI ID = 0.0 >
Simulation method.

From here,

: The thermoelectric voltage measured for a defect-free region

: The theoretical Seebeck coefficient of the material 3. The method of claim 2,
The effective temperature drop

Van der Waals energy

Which is a function based on the correlation between the input signal and the input signal,
Simulation method.

From here,

: A function that contains a linear fitting function or an exponential function A method for computer-aided simulation of an image of a scanning electron microscope,
The local thermovoltage V (r) for position r of the voltage probe is calculated by the computer according to the following equation to obtain the scan deflection microscope image corresponding to position r of the voltage probe at the workpiece surface:
Simulation method.

From here,
S ( r ; r ' ): localized Seebeck coefficient

:

Lt; RTI ID = 0.0 > radial < / RTI > weighted by a factor of &
r: Distance measured from the point-shaped probe
r ': Material inner coordinate delete delete delete delete delete delete delete

Images