CN115376631A - Method for acquiring dielectric function and electronic correlation degree of p-type transparent conductive film - Google Patents

Method for acquiring dielectric function and electronic correlation degree of p-type transparent conductive film Download PDF

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CN115376631A
CN115376631A CN202210979087.6A CN202210979087A CN115376631A CN 115376631 A CN115376631 A CN 115376631A CN 202210979087 A CN202210979087 A CN 202210979087A CN 115376631 A CN115376631 A CN 115376631A
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赵明琳
苟婷
徐晶
窦健泰
胡友友
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Abstract

The invention discloses a method for acquiring a dielectric function and electronic correlation of a p-type transparent conductive film, which comprises the steps of establishing a first evaluation model by combining simulated ellipsometric parameters and experimental ellipsometric parameters, initializing dispersion model parameters and film thickness based on a combined dispersion model, evaluating an ellipsometric spectrum to obtain optimal fitting parameters of the combined dispersion model so as to obtain a preliminary dielectric function, and then establishing a second evaluation model containing an optical calculation value and an electrical measurement value of film resistivity to obtain an optimal dielectric function of the film; finally, converting according to the optimal dielectric function to obtain photoconductivity, and calculating the normalized electronic correlation degree of the film sample by combining plasma frequency; the invention provides a numerical and physical dual evaluation system for the ellipsometry spectrum of the thin film material, an electrode is not required to be prepared, and the electronic correlation degree of the transparent conductive thin film can be nondestructively obtained through optical parameter calculation according to the measured effective optimal dielectric function.

Description

Method for acquiring dielectric function and electronic correlation degree of p-type transparent conductive film
Technical Field
The invention relates to a method for acquiring a dielectric function and electronic correlation of a P-type transparent conductive film, belonging to the technical field of ellipsometry.
Background
Common transparent conductive films are mostly doped with n-type, but p-type doped transparent conductive films are rare and have performance far behind that of n-type. The strong correlation system is an effective way for constructing the p-type transparent conductive film, on one hand, the strong coulomb acting force between electrons can strengthen the coupling between valence bands and promote the conduction of the p-type transparent conductive film; on the other hand, strong electron coupling promotes shielding of the plasma energy from the visible region and thus improves optical transparency. Therefore, the electron correlation degree is closely related to the development of the p-type transparent conductive film and is a key reference parameter for preparing the p-type transparent conductive film. The electron correlation can be represented by an effective mass, and the effective mass can be calculated by a dielectric function. In addition, the dielectric function can embody not only the optical characteristics but also the electrical characteristics of the transparent conductive thin film material. Therefore, the dielectric function and the electronic correlation degree of the p-type transparent conductive film material are obtained, the design and the preparation of a photoelectric device based on the p-type transparent conductive film material can be promoted, and the development of the related technical field and the application field is promoted. In the prior art, the electron correlation degree is generally obtained by a traditional magnetic measurement means, and the measurement means needs to prepare electrodes on a thin film material, so that the surface of the thin film is damaged.
Disclosure of Invention
The invention aims to: the invention aims to provide a method for acquiring a film dielectric function and an electronic correlation degree without preparing an electrode.
The technical scheme is as follows: the method for acquiring the dielectric function and the electronic correlation degree of the p-type transparent conductive film comprises the following steps of:
(1) Measuring the ellipsometry spectrum of the p-type transparent conductive film sample to obtain the ellipsometry parameter of the p-type transparent conductive film sample;
(2) Establishing a combined dispersion model containing a polar vibrator, a Delaude vibrator and a Lorentz vibrator, wherein the combined dispersion model is used for expressing the change rule of a dielectric function along with the wavelength;
(3) Establishing a first evaluation model by combining simulated ellipsometry parameters and experimental ellipsometry parameters, taking the measured ellipsometry spectrum as a target, initializing and setting the parameters and the film thickness of the dispersion model based on the combined dispersion model, and evaluating the ellipsometry spectrum by using an ellipsometry inversion calculation method to obtain the optimal fitting parameters and the film thickness of the combined dispersion model;
(4) Establishing a second evaluation model containing an optical calculation value and an electrical measurement value of the resistivity of the p-type transparent conductive film, and evaluating the ellipsometry spectrum to obtain an optimal dielectric function of the p-type transparent conductive film;
(5) And converting according to the optimal dielectric function to obtain photoconductivity, and calculating the normalized electronic correlation degree of the p-type transparent conductive film sample by combining plasma frequency obtained by fitting a Derad model.
Further, the formula of the first evaluation model is as follows:
Figure BDA0003799677780000021
psi is the amplitude ratio of p light and s light before and after reflection, delta is the phase difference of the two, subscript cal represents an ellipsometric parameter simulation calculation value, subscript exp represents an experimental value, error represents an error, and Q is the total wavelength number.
Further, the formula of the second evaluation model is:
PMSE=((ρ 0cal0exp )/ρ 0exp )×100%
where ρ is 0 Subscript cal represents a calculated value and subscript exp represents an experimental value, which are resistivity of the p-type transparent conductive thin film;
wherein the calculated value of the resistivity of the p-type transparent conductive film is the plasma frequency omega obtained by fitting p And the scattering time tau is calculated, and the calculation formula is as follows:
ρ 0cal =1/σ 0 =(ε 0 ω p 2 τ) -1
further, the judgment basis of obtaining the optimal dielectric function in the step (4) is that the value of the PMSE is 0-10%, otherwise, the step (3) is returned, the parameters of the joint dispersion model are initialized and set again or the step (2) is returned to adjust the number of the Lorentz vibrators, and the steps (3) and (4) are initialized again and repeated.
Further, in step (3), when the first evaluation function is a minimum value, a best fit parameter is obtained.
Further, the joint dispersion model comprises a polar oscillator, a Delaude oscillator and three to six Lorentz oscillators.
Further, the formula of the joint dispersion model is:
Figure BDA0003799677780000022
wherein the pole oscillator is composed of n0 Determining A, which respectively represents the central energy and the amplitude of the oscillator; the Delaud vibrator is determined by A and gamma and respectively represents the amplitude and the broadening coefficient of the vibrator; lorentz oscillator composed of A, E n0 And Γ, which respectively represent the amplitude, peak intensity and broadening coefficient of the oscillator, j represents the serial number of the Lorentz oscillator.
Further, the formula of the normalized electronic correlation degree in the step (5) is as follows:
m * =e 2 N e0 ω p 2
Z K =m band /m *
wherein N is e Is the carrier concentration,. Epsilon 0 Is the dielectric constant of vacuum, Z K Normalizing the parameter for the degree of electronic correlation, m band M is the effective mass of free non-interacting electrons * For reforming the electron effective mass, omega, of electron-electron interactions p Is the plasma frequency.
Further, in the step (5), the plasma frequency omega is obtained by fitting a Dereude model p And the scattering time τ is given by:
Figure BDA0003799677780000031
wherein omega and epsilon 2 The photoconductivity is obtained by dielectric function conversion, and the conversion expression is as follows:
σ 1 =ωε 0 ε 2
where ω is angular frequency, ε 2 Is the imaginary part of the complex dielectric function.
Has the beneficial effects that: compared with the prior art, the invention has the advantages that: a numerical and physical dual evaluation system is provided for the ellipsometry spectrum of the thin film material, so that the accuracy and effectiveness of obtaining the dielectric function of the p-type transparent conductive thin film are ensured; under the condition of not preparing an electrode, the electronic correlation degree of the transparent conductive film can be nondestructively obtained through optical parameter calculation according to the measured effective optimal dielectric function, and the method has the advantages of no disturbance, high precision, no destructiveness, high measuring speed and the like.
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FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 shows PtCoO in the practice of the present invention 2 Fitted photoconductivity map of the film.
FIG. 3 shows PtCoO according to an embodiment of the present invention 2 Resistivity of the film as a function of temperature.
FIG. 4 shows PtCoO according to an embodiment of the present invention 2 Dielectric function diagram of the film.
FIG. 5 is a graph of the best-fit parameters of the joint dispersion model in an embodiment of the invention.
FIG. 6 shows PtCoO according to an embodiment of the present invention 2 Film related parameters.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
As shown in FIG. 1, ptCoO is used in the present embodiment 2 For example, the method for obtaining the dielectric function and the electronic correlation degree of the p-type transparent conductive film comprises the following steps:
step 1: measurement of PtCoO 2 Obtaining the ellipsometry parameters (psi, delta) of the film sample by ellipsometry of the transparent conductive film, wherein psi is p-light and s-light before and after reflectionThe amplitude ratio of (2) and (Δ) are phase differences between them.
Specifically, ptCoO was measured using a spectroscopic ellipsometer manufactured by Wuhan Yiguan technologies, ltd 2 Ellipsometry of the film. The measurement was carried out at room temperature with the incident angle fixed at 65 ℃ and the wavelength range of the measurement from 245 to 1000nm.
Step 2: and establishing a combined dispersion model comprising a polar oscillator, a Delaude oscillator and six Lorentz oscillators.
The function expression of the joint dispersion model established in the embodiment of the invention is represented by formula (1):
Figure BDA0003799677780000032
wherein the pole oscillator is composed of n0 And A, determining and respectively representing the central energy of the vibrator and the amplitude of the vibrator. The de-rod oscillator is determined by A and gamma, and represents the amplitude and the broadening coefficient of the oscillator respectively. Lorentz resonators A, E n0 And Γ, which respectively represent the amplitude, peak intensity and broadening coefficient of the oscillator, and j represents the serial number of the Lorentz oscillator.
In the present embodiment, the joint dispersion model is a rule that the dielectric function of a material changes with wavelength by a specific functional expression. The polar oscillator is used for describing dispersion generated by absorption of ultraviolet and infrared bands beyond 245-1000nm, is a zero-scattering zero oscillator and only affects the real part of a dielectric function; the Droude oscillator is used for describing the influence of free electrons (current carriers) in a low-frequency region on a dielectric function; the Lorentzian oscillator is used for describing the transition characteristics between bands in a high-frequency band region.
And step 3: the method comprises the steps of taking measured ellipsometric spectra as a target, setting model parameters and initial film thickness values based on a combined dispersion model, performing one-time evaluation by using an ellipsometric inversion calculation method and combining a first evaluation model constructed by simulated ellipsometric parameters and experimental ellipsometric parameters to obtain a preliminary dielectric function of a film sample, wherein PtCoO is set in the embodiment of the invention 2 The initial thickness of the film was 15nm.
The algorithm of the thin film optical inversion calculation includes, but is not limited to, simulated annealing-ant colony algorithm and simulated annealing algorithm.
The criterion for obtaining the preliminary dielectric function is the magnitude of the numerical evaluation function, and when the evaluation function is the minimum, the corresponding result is obtained, and the evaluation function is shown in fig. 6. The evaluation function MSE expression is represented by equation (2):
Figure BDA0003799677780000041
where Q represents the total number of wavelengths, cal represents the calculated ellipsometric parameter simulation, exp represents the experimental value, and error represents the error.
The optimal fitting parameters of the combined dispersion model obtained by performing the first evaluation on the ellipsometry spectrum are shown in fig. 5, and the optimal thickness of the film is 15.2nm.
And 4, step 4: establishment of PtCoO-containing structures 2 The second evaluation model is a physical evaluation function, and the second evaluation model is used for carrying out secondary evaluation and judgment on the ellipsometry analysis result to obtain the optimal dielectric function of the film, and comprises the following specific steps:
step 4-1: plasma frequency ω used in embodiments of the invention p And the scattering time τ is obtained by fitting the photoconductivity by a de-roud model, and the fitting formula thereof is represented by formula (3):
Figure BDA0003799677780000042
in the embodiment of the invention, the dielectric function is converted by formula (4) to obtain the photoconductivity, and the conversion expression is as follows:
σ 1 =ωε 0 ε 2 (4)
in the embodiment of the invention, the photoconduction spectrum of the film can be further obtained by mutual conversion between the obtained initial optimal dielectric function and the photoconduction, and the obtained fitting result is shown in figure 2 and is at the plasma frequency omega p =4.32×10 15 s -1 And scattering time τ =2.96 × 10 -13 s is the best fit obtained, where the vacuum dielectric constant is ε 0 =8.9×10 -12 F/m。
Step 4-2: from the obtained plasma frequency omega p And calculating two physical parameters of scattering time tau to obtain resistivity rho 0 The calculation formula is represented by equation (5):
ρ 0 =1/σ 0 =(ε 0 ω p 2 τ) -1 (5)
the resistivity obtained by calculation through a formula is rho 0cal = 2.03. Mu. Omega. Cm, and the resistivity at room temperature obtained in practical experiments is rho 0exp =1.85 μ Ω cm, and the experimental results are shown in fig. 3.
Step 4-3: constructing a physical evaluation function including an optically calculated value and an electrically measured value of the resistivity of the film based on the calculated resistivity and the experimentally obtained resistivity, the expression of which is represented by formula (6):
PMSE=((ρ 0cal0exp )/ρ 0exp )×100% (6)
the physical evaluation function PMSE obtained by calculation is 9.72 percent, which shows that the obtained dielectric function is reasonable, namely the measured PtCoO 2 The optimal dielectric function of the transparent conductive film is shown in fig. 4.
And 5: by the obtained plasma frequency omega p The effective mass m of the reformed electrons whose electron-electron interaction can be calculated * The calculation formula is represented by equation (7):
m * =e 2 N e0 ω p 2 (7)
wherein N is e =4.5×10 22 cm -3 Basic charge e =1.6 × 10 as carrier concentration -19 C, vacuum dielectric constant of epsilon 0 =8.9×10 -12 F/m, m is obtained by calculation * =69.53×10 -31 kg。
The normalized electronic correlation degree can be further calculated and obtained according to the above result, and the calculation formula is represented by formula (8):
Z K =m band /m * (8)
wherein m is band And m * Respectively, a free non-interacting electron effective mass and a reformed electron effective mass comprising electron-electron interactions, wherein m band =9.1×10 -31 kg, then calculating to obtain the electronic correlation degree of Z K =0.13. The relevant parameters of an embodiment of the present invention are shown in fig. 6.

Claims (9)

1. A method for acquiring a dielectric function and an electronic correlation degree of a p-type transparent conductive film is characterized by comprising the following steps:
(1) Measuring the ellipsometry spectrum of the p-type transparent conductive film sample to obtain the ellipsometry parameter of the p-type transparent conductive film sample;
(2) Establishing a combined dispersion model containing a polar vibrator, a Delaude vibrator and a Lorentz vibrator, wherein the combined dispersion model is used for expressing the change rule of a dielectric function along with the wavelength;
(3) Establishing a first evaluation model by combining simulated ellipsometry parameters and experimental ellipsometry parameters, taking the measured ellipsometry spectrum as a target, initializing and setting the parameters and the film thickness of the dispersion model based on the combined dispersion model, and evaluating the ellipsometry spectrum by using an ellipsometry inversion calculation method to obtain the optimal fitting parameters and the film thickness of the combined dispersion model;
(4) Establishing a second evaluation model containing an optical calculation value and an electrical measurement value of the resistivity of the p-type transparent conductive film, and evaluating the ellipsometry spectrum to obtain an optimal dielectric function of the p-type transparent conductive film;
(5) And converting according to the optimal dielectric function to obtain photoconductivity, and calculating the normalized electronic correlation degree of the p-type transparent conductive film sample by combining plasma frequency obtained by fitting a Derad model.
2. The method for obtaining the dielectric function and the electronic correlation of the p-type transparent conductive film according to claim 1, wherein the formula of the first evaluation model is as follows:
Figure FDA0003799677770000011
psi is the amplitude ratio of p light and s light before and after reflection, delta is the phase difference between the two, subscript cal represents the ellipsometric parameter simulation calculation value, subscript exp represents the experimental value, error represents the error, and Q is the total wavelength number.
3. The method for obtaining the dielectric function and the electronic correlation of the p-type transparent conductive film according to claim 1, wherein the formula of the second evaluation model is as follows:
PMSE=((ρ 0cal0exp )/ρ 0exp )×100%
where ρ is 0 For the resistivity of the p-type transparent conductive film, the subscript cal represents the calculated value and the subscript exp represents the experiment; wherein the calculated value of the resistivity of the p-type transparent conductive film is the plasma frequency omega obtained by fitting p And the scattering time tau is calculated, and the calculation formula is as follows:
ρ 0cal =1/σ 0 =(ε 0 ω p 2 τ) -1
4. the method for obtaining the dielectric function and the electronic correlation of the p-type transparent conductive film as claimed in claim 1, wherein the optimal dielectric function obtained in the step (4) is determined according to the value of PMSE of 0-10%, otherwise, the step (3) is returned, the parameters of the joint dispersion model are reinitialized, or the step (2) is returned to adjust the number of Lorentz vibrators, and the steps (3) and (4) are repeated.
5. The method for obtaining the dielectric function and the electronic correlation of the p-type transparent conductive film as claimed in claim 1, wherein in the step (3), when the first evaluation function is a minimum value, a best fit parameter is obtained.
6. The method for obtaining the dielectric function and the electronic correlation of the p-type transparent conductive film according to claim 1, wherein the joint dispersion model comprises one polar oscillator, one Drude oscillator and three to six Lorentz oscillators.
7. The method for obtaining the dielectric function and the electronic correlation of the p-type transparent conductive film according to claim 1, wherein the formula of the joint dispersion model is as follows:
Figure FDA0003799677770000021
wherein the pole oscillator is composed of n0 Determining A, which respectively represents the central energy and the amplitude of the oscillator; the Delaud vibrator is determined by A and gamma and respectively represents the amplitude and the broadening coefficient of the vibrator; lorentz oscillator composed of A, E n0 And Γ, which respectively represent the amplitude, peak intensity and broadening coefficient of the oscillator, and j represents the serial number of the Lorentz oscillator.
8. The method for obtaining the dielectric function and the electronic correlation of the p-type transparent conductive film as claimed in claim 1, wherein the normalized electronic correlation in the step (5) is represented by the following formula:
m * =e 2 N e0 ω p 2
Z K =m band /m *
wherein N is e Is the carrier concentration, ε 0 Is a dielectric constant of vacuum, Z K Normalizing the parameter for the degree of electronic correlation, m band M is the effective mass of free non-interacting electrons * To reform the electron effective mass, omega, for electron-electron interactions p Is the plasma frequency.
9. The method for obtaining the dielectric function and the electron correlation degree of the p-type transparent conductive film as claimed in claim 1, wherein the plasma frequency ω is obtained by fitting a Drude model in the step (5) p And the scattering time τ is:
Figure FDA0003799677770000022
the photoconductivity is obtained by dielectric function conversion, and the conversion expression is as follows:
σ 1 =ωε 0 ε 2
where ω is angular frequency, ε 2 As the imaginary part of the complex dielectric function.
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