Encapsulation method under spectroscopic ellipsometry and method for measuring metal dielectric function

Abstract

The application relates to a packaging method under an ellipsometric spectrum and a metal dielectric function measurement method. A packaging material is used to package a material to be measured. A thickness relationship formula one, a relationship formula two and a relationship formula three are used to obtain a minimum d value of z2 and z1, z3 light spot area separation. The minimum d value is used for packaging, which can enhance the accuracy of the detection data of a detector. Then, a final packaging thickness is obtained by combining an error allowable range, and the accuracy of the metal dielectric function is improved.

Description

Technical Field

[0001] This invention relates to a packaging method for elliptic polarization spectroscopy and a method for measuring the dielectric function of metals, belonging to the field of optical measurement technology. Background Technology

[0002] In recent years, with the improvement of materials micro- and nano-fabrication and characterization capabilities, surface plasmonics has shown broad application prospects in fields such as spectroscopic measurement, metasurfaces, and photocatalysis. However, due to the high locality of electromagnetic fields, surface plasmons in metals exhibit high ohmic losses, making their application in fields requiring efficient energy conversion or information transmission, such as photoelectric detection, optical interconnects, and integrated optics, difficult. How to reduce the ohmic losses of surface plasmons is one of the most important research topics in plasmonics.

[0003] Compared to previously used noble metals such as gold and silver, sodium-based plasmonic micro / nano lasers and optical waveguides utilize sodium-based devices, reducing ohmic loss in the near-infrared band to below 50%. However, conventional dielectric constant testing methods remain inadequate for alkali metal systems under low-loss and packaging conditions; therefore, accurately and scientifically determining their optical constants is crucial.

[0004] Measuring the dielectric function of alkali metals in situ within a high-vacuum chamber presents challenges. Firstly, it requires a very high vacuum level within the chamber. Secondly, integrating the coating chamber with an ellipsometer is extremely complex, and it's difficult to avoid oxidation of the alkali metal during the coating process. Therefore, it's possible to measure the dielectric function of alkali metals after encapsulation using an ellipsometer. Existing patent 202110774099.0, "A Method for Measuring Elliptopolarimetry under Encapsulation Conditions," proposes obtaining the dielectric function of alkali metal materials after encapsulation using an ellipsometer. The optical path is as follows... Figure 1 As shown, the incident angle of the incident light is α, resulting in multi-level reflections. The ellipsometer detector collects the signal of the first reflected light. Based on Fresnel's formula, the relationship between the dielectric constant of different types of samples under packaging conditions and the direct measurement data of ellipsometric spectra is derived, yielding the analytical expression (6):

[0005]

[0006] Where ε m ε is the dielectric constant of the material being measured. s Let β be the dielectric constant of the encapsulation layer, and β be the angle of refraction of light after entering the encapsulation layer, according to Snell's law. It is determined that ρ is the ratio of the p-polarization component to the s-polarization component of the reflected light, which is directly measured by an ellipsometer, and T is calculated by the following formula:

[0007]

[0008] However, the problems that must be faced are: (1) the presence of the encapsulation layer will cause the incident light to be reflected in multiple levels. An encapsulation layer of unreasonable thickness will cause the required reflected light to intersect with other reflected light, making it impossible to accurately receive the required reflected light. (2) In practice, it is difficult to achieve a large area of ​​clean "encapsulation layer-metal" interface. There will be some small bubbles or other impurities in some areas. The incident white light also has a certain aperture. If the incident light shines on these impurities, the measurement results are often inaccurate. Therefore, each arm of the ellipsometer is usually equipped with a lens to reduce the size of the light spot that shines on the interface and to move the sample during the measurement process to keep the light spot on the clean "encapsulation layer-metal" interface. Due to the introduction of the lens, the light beam that shines on the interface is no longer parallel light, but a converging light beam with a certain divergence angle. Under this situation, the above measurement formula is applied and it is found that the dispersion effect of the encapsulation material will bring a certain error to the measurement, and the error cannot be ignored under certain conditions. Summary of the Invention

[0009] To address the problem of inaccurate measurements caused by the influence of other reflected light on the detector due to the encapsulation layer, this invention provides an encapsulation method for elliptic polarization spectroscopy measurement. When performing elliptic polarization spectroscopy measurements, the device using this encapsulation method separates the second-order reflected light (the light required by the detector) from the first-order and third-order reflected light, thus accurately detecting the second-order reflected light signal.

[0010] The adopted technical solution is as follows: an encapsulation method under elliptic polarization spectroscopy, which uses an encapsulation material to encapsulate the material to be tested, and the thickness of the encapsulation layer is obtained by the following method:

[0011] Equation 1 is used to obtain the relationship between the position z1 of the primary reflected light spot on the detector and the encapsulation thickness d, where the primary reflected light is the light rays after the incident light is reflected by the surface of the encapsulation layer.

[0012] Equation 2 is used to obtain the relationship between the spot position z2 of the secondary reflected light on the detector and the encapsulation thickness d. The secondary reflected light is the incident light that is reflected once by the alkali metal interface of the encapsulation material.

[0013] Equation 3 is used to obtain the relationship between the position z3 of the third-order reflected light spot on the detector and the encapsulation thickness d. The third-order reflected light is the incident light that is reflected twice by the encapsulation material-alkali metal interface.

[0014] The minimum d value for separating the z2 and z1, z3 spot regions is obtained by using relational formulas 1, 2, and 3. The minimum d value is the minimum thickness d1 of the encapsulation material.

[0015] As a preferred embodiment, the first relation is:

[0016]

[0017] The second relation is:

[0018]

[0019] The third relation is:

[0020]

[0021] In the formula: α is the incident angle of the central beam, β is the refraction angle of the central beam, θ is the deviation angle of the incident beam relative to the central beam, γ is the refraction angle, f is the focal length of the lens, l is the distance from the detector plane to the lens, H is the depth of the lens focal point F from the upper surface of the encapsulation layer, and n is the refractive index of the encapsulation layer; the central beam is the central ray of the beam, that is, the ray located at the center of the beam.

[0022] The minimum thickness value d1 of the encapsulation material is obtained according to formulas (1), (2), and (3). Taking d>d1 can separate the spot areas of z2 from z1 and z3.

[0023] On the other hand, to address the problem of poor dielectric function accuracy under encapsulation conditions, this invention provides a method for measuring the dielectric function of a metal using elliptic polarization spectroscopy. This method involves encapsulating the material under test, then placing it under an elliptic polarimeter detector to measure the spectral signal of the metal, and obtaining the dielectric function of the metal based on the spectral signal. The encapsulation thickness d has a minimum value d1 and a maximum value d2, where d1 is obtained as follows:

[0024] (1) Obtain the relationship between the position z1 of the primary reflected light spot on the detector and the encapsulation thickness d, where the primary reflected light is the light after the incident light is reflected by the surface of the encapsulation layer.

[0025] (2) Obtain the relationship between the position z2 of the secondary reflected light on the detector and the encapsulation thickness d, where the secondary reflected light is the incident light reflected once by the metal interface of the encapsulation material.

[0026] (3) Obtain the relationship between the position z3 of the third-order reflected light on the detector and the encapsulation thickness d, where the third-order reflected light is the incident light reflected twice by the encapsulation material-metal interface;

[0027] The minimum d value for separating the z2 and z1, z3 spot regions is obtained by using relational formulas 1, 2, and 3. The minimum d value is the minimum thickness d1 of the encapsulation material.

[0028] The method for obtaining d2 is as follows: the relative error η corresponding to the packaging thickness d is obtained according to formula (4).

[0029]

[0030] Where: ε m The measured dielectric function, For ε m The partial derivative with respect to α, where α is the incident angle of the central beam and θ′ is the deflection angle of the incident ray. If the ellipsometer measures the light signal at z0, the deflection angle θ′ can be solved by the equation z2(θ)=z0 containing d.

[0031] That is: θ′ is the angle of deviation of the incident beam at position z0 of the 2nd reflected light relative to the center beam;

[0032] The maximum value of the packaging thickness d, d2, is obtained based on the maximum allowable value of the relative error η.

[0033] The encapsulation thickness d of the encapsulation material satisfies d1 <d<d2。

[0034] As a preferred option, the encapsulation material is silicon dioxide.

[0035] The beneficial effects of this invention include: the encapsulation method in this invention can separate the secondary reflected light received by the detector from the primary and tertiary reflected light, ensuring the accuracy of spectral reception and improving detection precision;

[0036] The method for measuring the dielectric function of metals in this invention allows the metal to be directly placed on an elliptic polarization spectroscopy detector for spectral detection under encapsulation conditions, and precise measurement can be achieved by adjusting the encapsulation thickness. Attached Figure Description

[0037] Figure 1 Light path diagrams of primary, secondary, and tertiary reflected light on the packaging material;

[0038] Figure 2 The actual optical path diagrams of the first-order reflected light, second-order reflected light, and third-order reflected light after the lens is installed;

[0039] Figure 3 The relationship between the light spot areas corresponding to z1, z2, and z3 and the package thickness;

[0040] Figure 4 Graph showing the variation of relative error with wavelength for different package thicknesses;

[0041] In the diagram, 1st represents the first-order reflected light, 2nd represents the second-order reflected light, and 3rd represents the third-order reflected light. The ellipsometer detector only collects the second-order reflected light signal. Detailed Implementation

[0042] The present invention will be further explained in detail below with reference to specific embodiments, but it should be understood that the scope of protection of the present invention is not limited to the specific embodiments.

[0043] Example 1

[0044] A method for measuring the dielectric function of a metal using elliptic polarization spectroscopy includes the following steps:

[0045] S01 selects an encapsulation material that does not react with the metal to be encapsulated, is optically transparent, allows light to enter the encapsulation material-metal interface, and the encapsulation material can isolate the metal from the outside air;

[0046] S02 Calculate the package thickness d

[0047] (1) Obtain the minimum thickness value d1;

[0048] The encapsulation thickness d of the encapsulation material refers to the thickness of the encapsulation material on the side of the encapsulation device that receives the incident light. Obtaining a suitable encapsulation thickness ensures that the second-order reflected light spot detected by the ellipsometer detector (elliptic polarization spectroscopy detector) is separated from the other levels of reflected light, thus ensuring the accuracy of the detection data.

[0049] Based on ray tracing methods, the positions of each stage of reflected light in the actual optical path on the detector are obtained, such as... Figure 2 As shown, light passes through the first convex lens and is incident on the packaged device. After reflection, it passes through the second convex lens and is incident on the ellipsometer for detection. In the figure, α is the incident angle of the principal ray (central beam), " is the refraction angle of the central beam after passing through the packaged material, θ is the deviation angle of the incident beam relative to the central beam, γ is the refraction angle of the incident beam after passing through the packaged material, f is the focal length of the first convex lens, l is the distance from the light receiving plane of the ellipsometer to the second convex lens, H is the depth of the lens focal point F from the upper surface of the packaged layer, n is the refractive index of the packaged layer, and d is the thickness of the packaged layer. The figure shows an incident light with a deviation angle of θ and the three reflected rays produced by it. The ray directly reflected by the surface of the packaged layer is the first-order reflected light (1st reflected light), the ray reflected once at the packaged material-metal interface is named the second-order reflected light (2nd reflected light), and the ray reflected twice at the packaged material-metal interface is named the third-order reflected light (3rd reflected light).

[0050] The positions of the 1st, 2nd, and 3rd reflected light transmitted onto the detector's light-receiving plane, z1, z2, and z3, are respectively represented by their expressions as follows:

[0051]

[0052]

[0053]

[0054] Adjusting the distance H between the lens focal point and the upper surface of the encapsulation material can reduce the size of the light spot illuminating the "encapsulation material-metal" interface. The value of H is approximately obtained using formula (4):

[0055]

[0056] Where θ0 is the maximum deviation angle.

[0057] The spot regions at positions z1, z2, and z3 of the 1st reflected light under different thicknesses are obtained using formulas (1), (2), and (3), respectively. These regions are then plotted, and the minimum thickness value d1 where the three spot regions do not overlap is identified within the plot. The range of the reflected light spot region at a given thickness is obtained by considering the range of the deviation angle θ. The range of θ is... Right now Where D is the beam aperture.

[0058] (2) Obtain the maximum thickness value d2

[0059] Due to the dispersion effect of the encapsulation layer, the incident angle of the 2nd reflected light captured by the detector is not α, but deviates from α by a small angle θ′, i.e., α+θ′. The larger the encapsulation thickness d, the larger the deviation angle θ′, and the greater the systematic error it causes. To reduce the systematic error, it is necessary to limit the encapsulation thickness, and obtain the maximum thickness value d2 according to the allowable error requirements.

[0060] If the ellipsometer measures the optical signal at z0, the deflection angle θ′ is obtained through z2(θ)=z0, and the resulting relative error η is:

[0061]

[0062] In the formula, α is the incident angle of the central beam, and ε m The dielectric constant of a metallic material obtained using existing methods is specifically ε. m To obtain using formula (6), which is the formula involved in the background art:

[0063]

[0064] The maximum package thickness value d2 is obtained based on the maximum permissible error η and formula (5).

[0065] S03 selects the package thickness d such that d1 < d < d2;

[0066] S04 Based on the encapsulation layer with suitable material, thickness, and flat surface obtained in the first three steps (for example, using SiO2 as the encapsulation layer, a thickness of 1.5mm is more suitable), use an elliptic polarizer to measure and fix the light spot on the clean "encapsulation material-metal" interface, read the required data, and substitute it into formula (6):

[0067]

[0068] The accurate dielectric constant ε of the measured metal can then be calculated. m .

[0069] Example 2

[0070] Unlike Example 1, it is not necessary to obtain the maximum thickness value d2. After obtaining the minimum thickness value, the package thickness is obtained by taking the value and verifying the error. Specifically, in S02, after obtaining the minimum thickness value d1, the value d′ is taken in the range of d > d1, and substituted into formula (5) to obtain the relative error of the dielectric function measured under d′. If the relative error is within the allowable range, the package can be packaged with a package thickness of d′. If the relative error exceeds the allowable range, the package thickness is reduced and the error is calculated until the condition is met.

[0071] The following example, using SiO2 as the encapsulation material to encapsulate metal Au, illustrates the value of the encapsulation thickness d.

[0072] Based on formulas (1), (2), and (3)

[0073] The parameters are set as follows: α = 1.13 rad, f = 40 mm, l = 350 mm, D = 4 mm

[0074] The light spot regions under different encapsulation layer thicknesses were obtained and plotted as follows: Figure 3 As shown, through Figure 3 We know that d1 = 1.44;

[0075] Under the condition that d > d1, taking d = 1.5mm, d = 2.0mm, and d = 2.5mm, according to formula (5), the relative error of the real and imaginary parts with wavelength is obtained when the package thickness d = 1.5mm, d = 2.0mm, and d = 2.5mm, as shown in the figure. Figure 4 ,according to Figure 4 You can choose the package thickness within the tolerance range.

[0076] Example 3

[0077] An encapsulation method for elliptic polarization spectroscopy involves encapsulating the material under test with an encapsulation material. When the material is placed on an ellipsometer detector for measurement, the second-order reflected light received by the detector's light-receiving plane is separated from the first-order and third-order reflected light. The thickness of the encapsulation layer of the material under test is obtained through the following method:

[0078] Equation 1 is used to obtain the relationship between the position z1 of the primary reflected light spot on the detector and the encapsulation thickness d, where the primary reflected light is the light rays after the incident light is reflected by the surface of the encapsulation layer.

[0079] Equation 2 is used to obtain the relationship between the spot position z2 of the secondary reflected light on the detector and the encapsulation thickness d. The secondary reflected light is the light that is reflected once by the incident light through the encapsulation material-alkali metal interface.

[0080] Equation 3 is used to obtain the relationship between the position z3 of the third-order reflected light spot on the detector and the encapsulation thickness d. The third-order reflected light is the incident light that is reflected twice by the encapsulation material-alkali metal interface.

[0081] The first relation is:

[0082]

[0083] Relationship 2 is:

[0084]

[0085] Relationship 3 is:

[0086]

[0087] In the formula: α is the incident angle of the central beam, β is the refraction angle of the central beam, θ is the deviation angle of the incident beam relative to the central beam, γ is the refraction angle, f is the focal length of the lens, l is the distance from the detector plane to the lens, H is the depth of the lens focal point F from the upper surface of the encapsulation layer, and n is the refractive index of the encapsulation layer.

[0088] The minimum thickness value d1 of the encapsulation material is obtained according to formulas (1), (2), and (3). Taking d > d1 can separate the spot areas of z2 from z1 and z3.

[0089] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method of encapsulation under spectroscopic ellipsometry, characterized in that: The to-be-tested material is packaged by using a packaging material, and the thickness of the packaging layer is obtained by the following method: The light passes through the first convex lens and is incident on the packaged device, is reflected and then passes through the second convex lens and is incident on the ellipsometric detector for detection; Acquiring the position of the light spot of the first reflected light on the detector A relationship formula one between the package thickness d and the first reflected light, which is the light reflected by the surface of the package layer The relationship formula one is: Equation (1) Acquiring the position of the light spot of the secondary reflected light on the detector A second relationship between the package thickness d and the secondary reflected light, which is the light reflected once by the package material-metal interface; The relationship formula two is: Equation (2) Acquiring the light spot position of the three-stage reflected light on the detector A third relationship between the package thickness d and the three-stage reflected light, which is light reflected twice by the package material-metal interface; The relationship formula three is: Equation (3) wherein: is the central beam incidence angle, is the central beam refraction angle, is the off-center beam angle relative to the central beam, is the refraction angle, is the second convex lens focal length, is the distance from the detector plane to the second convex lens, is the first convex lens focal point F distance from the encapsulation layer upper surface depth, n is the refractive index of the encapsulation layer; The minimum thickness value of the separation of the light spot region is d1, and the packaging thickness d>d1; the minimum thickness value d1 of the packaging material is obtained according to formula (1), formula (2) and formula (3). The light spot region and The light spot region, The minimum thickness value of the separation of the light spot region is d1, and the packaging thickness d>d1; the minimum thickness value d1 of the packaging material is obtained according to formula (1), formula (2) and formula (3).

2. A method for measuring the dielectric function of a metal using ellipsometric spectroscopy, characterized by: The to-be-tested metal is packaged under the packaging condition, and then is placed under the detector to measure the spectral signal of the metal, and the dielectric function of the metal is obtained according to the spectral signal; the light passes through the first convex lens and is incident on the packaged device, is reflected and then passes through the second convex lens and is incident on the ellipsometric detector for detection; The thickness of the packaging material is obtained by the following method: Acquiring the position of the light spot of the first reflected light on the detector A relationship formula one between the package thickness d and the first reflected light, which is the light reflected by the surface of the package layer The relationship formula one is: Formula (1) Acquiring the position of the light spot of the secondary reflected light on the detector A second relationship between the package thickness d and the secondary reflected light, which is the light reflected once by the package material-metal interface; The relationship formula two is: Equation (2) Acquiring the light spot position of the three-stage reflected light on the detector A third relationship between the package thickness d and the three-stage reflected light, which is light reflected twice by the package material-metal interface; The relationship formula three is: Equation (3) wherein: is the central beam incidence angle, is the central beam refraction angle, is the incident beam deviation angle from the central beam, is the refraction angle, is the second convex lens focal length, is the distance from the detector light receiving plane to the second convex lens, is the first convex lens focal point F distance from the encapsulation layer upper surface depth, n is the refractive index of the encapsulation layer; The minimum d value of the spot area separation is the minimum thickness value d1 of the encapsulating material, and the minimum thickness value d1 of the encapsulating material is obtained according to formula (1), formula (2) and formula (3). With , The minimum d value of the spot area separation is the minimum thickness value d1 of the encapsulating material, and the minimum thickness value d1 of the encapsulating material is obtained according to formula (1), formula (2) and formula (3).

3. The method for measuring the dielectric function of a metal using spectroscopic ellipsometry as claimed in claim 2, wherein: According to formula (4), the relative error corresponding to the packaging thickness d is obtained , Equation (4) In the formula: is the dielectric function measured from formula (6), is the central beam incidence angle, is the incidence beam deviation angle relative to the central beam; The maximum value d2 of the encapsulation thickness d is obtained according to the maximum allowed value of the relative error of 0.5%. The packaging thickness d of the packaging material satisfies d1 < d < d2.

4. The method for measuring a metal dielectric function using an ellipsometric spectrum according to claim 2, wherein: The packaging material is silicon dioxide.

5. The method for measuring the dielectric function of a metal using spectroscopic ellipsometry as claimed in claim 2, wherein: The incident light spot of the detector is irradiated on the clean packaging material-metal interface.

6. The method for measuring a metal dielectric function using an ellipsometric spectrum according to claim 2, wherein: The relationship diagram of the spot positions of the first-order reflected light, the second-order reflected light and the third-order reflected light and the packaging thickness is drawn according to the formula (1), the formula (2) and the formula (3), and the minimum value d of the separation of the second-order reflected light and the first-order reflected light and the third-order reflected light is obtained according to the relationship diagram, and the minimum d value is the minimum packaging thickness d1.

7. The method for measuring a metal dielectric function using an ellipsometric spectrum according to claim 2, wherein: Plotting the relative error for different package thicknesses A plot of the variation of the error with the wavelength of the incident light, from which the package thickness d for which the error is allowed is obtained.

8. The method for measuring a metal dielectric function using an ellipsometric spectrum according to claim 2, wherein: The packaging thickness d is in the range of d>d1, and the relative error corresponding to the packaging thickness d is calculated by substituting the formula (4) The relative error is checked Whether the relative error is in the allowable error range, if yes, the packaging is made according to the packaging thickness, if no, the value of the packaging thickness is reduced, and the corresponding relative error is calculated again Until the error meets the requirements.

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