A method for determining laser parameters for exciting laser plasma light source

Abstract

The present invention relates to the field of laser plasma technology. The present invention provides a method for determining laser parameters for exciting a laser plasma light source, comprising: determining a target material for exciting the laser plasma according to a laser plasma pre-excitation wavelength; determining an electron temperature of the laser plasma according to the target material of the laser plasma; determining parameters of the laser plasma light source based on the electron temperature of the laser plasma, the parameters including: laser wavelength, laser focal spot diameter and laser pulse width; wherein the expansion velocity of the laser plasma luminous area along the target normal direction is determined based on the laser wavelength. V , so that the expansion rate V , laser pulse width T and laser focal spot diameter D The relationship is satisfied: The present invention discloses an expression for the relationship between the optimal laser focal spot and the laser pulse width, so that the luminous efficiency of the laser plasma light source is maximized when the numerical relationship is satisfied.

Description

Technical Field

[0001] The present invention relates to the field of laser plasma technology, and in particular to a method for determining laser parameters for exciting a laser plasma light source. Background Art

[0002] The high-temperature laser plasma generated by laser ablation of solid or liquid targets can produce a high-brightness light source covering the far-infrared to X-ray band through a thermal radiation process. Among them, the extreme ultraviolet light source radiated by tin laser plasma line has been applied to extreme ultraviolet lithography machines and extreme ultraviolet quantity detection equipment. The laser plasma light source in the soft X-ray band is also used in transient imaging of laser fusion processes and material impact processes.

[0003] Previous studies have found that various laser parameters such as laser intensity, laser wavelength, laser focal spot size, and laser pulse width will affect the luminous efficiency of the plasma light source produced by laser ablation of solid or liquid targets.

[0004] At present, the method for selecting laser intensity and laser wavelength parameters is basically clear, but the method for selecting laser focal spot and laser pulse width is still unclear. Summary of the invention

[0005] The object of the present invention is to provide a method for determining laser parameters for exciting a laser plasma light source, which can solve at least one of the above-mentioned technical problems. The specific scheme is as follows:

[0006] According to a specific embodiment of the present invention, a method for determining laser parameters for exciting a laser plasma light source is provided, comprising:

[0007] Determining a target material for generating the laser plasma light source according to the wavelength of the pre-excited laser plasma light source;

[0008] determining the electron temperature of the generated laser plasma according to the target material of the laser plasma light source;

[0009] Determining laser parameters for exciting the laser plasma light source based on the electron temperature of the laser plasma, the laser parameters including: laser wavelength, laser focal spot diameter and laser pulse width;

[0010] Wherein, the expansion speed of the laser plasma luminous area along the target normal direction is determined based on the laser wavelength, so that the expansion speed, the laser pulse width and the laser focal spot diameter satisfy the relationship:

[0011]

[0012] in, V is the expansion velocity of the laser plasma luminous area along the target normal direction;

[0013] T is the pulse width of the laser;

[0014] D is the focal spot diameter of the laser.

[0015] Preferably, determining the expansion speed of the laser plasma along the light emitting area and along the target normal direction based on the laser wavelength comprises:

[0016] The ion sound velocity of the laser plasma is determined according to the electron temperature of the laser plasma; the electron temperature and the ion sound velocity satisfy the relationship:

[0017]

[0018] The ion sound velocity of the laser plasma and the expansion velocity of the laser plasma luminous area along the target normal direction satisfy the relationship:

[0019]

[0020] in,

[0021] Thu is the ion sound velocity of laser plasma;

[0022] is a constant related to the laser wavelength;

[0023] You is the electron temperature;

[0024] M is the atomic mass of the target substance;

[0025] Z It is the average ionization degree of ions in the light-emitting region when the target material is heated into plasma.

[0026] Preferably, the expansion velocity of the laser plasma luminous area along the target normal direction is expressed as:

[0027]

[0028] in, x is the spatial position of a unit in the laser plasma luminescence area, t is the expansion time of the laser plasma luminous area.

[0029] Preferably, the laser plasma luminous area has a density, and the density expression of the laser plasma luminous area is:

[0030]

[0031] in, is the critical electron density of the laser, in cm -3 ;

[0032] is the wavelength of the laser, in μm;

[0033] For x The laser plasma luminous zone unit is located in t The electron density at time.

[0034] Preferably, the laser plasma pre-excitation wavelength is 13.5 nm.

[0035] Preferably, the laser wavelength is 1064 nm; the ion sound velocity, laser pulse width and laser focal spot diameter satisfy the relationship:

[0036]

[0037] Preferably, the laser wavelength is 10 μm; the ion sound velocity, laser pulse width and laser focal spot diameter satisfy the relationship:

[0038]

[0039] Preferably, the parameters also include: laser light intensity, and the laser light intensity decreases as the laser wavelength increases.

[0040] Preferably, the target material of the laser plasma is tin.

[0041] Preferably, the ion sound velocity of the laser plasma is 15 μm / ns.

[0042] Compared with the prior art, the above-mentioned solution of the embodiment disclosed in the present invention has at least the following beneficial effects:

[0043] The invention discloses an expression for the relationship between the best laser focal spot and the laser pulse width, so that the luminous efficiency of the laser plasma light source is maximized when the numerical relationship is satisfied. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The drawings herein are incorporated into the specification and constitute a part of the specification, showing embodiments consistent with the disclosure of the present invention, and together with the specification, are used to explain the principles disclosed in the present invention. Obviously, the drawings described below are only some embodiments disclosed in the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0045] Figure 1 A flow chart of a method for determining laser parameters for exciting a laser plasma light source provided by an embodiment of the present invention;

[0046] Figure 2 A schematic diagram of the positional relationship between the laser focal spot and the target normal light-emitting area provided in an embodiment of the present invention.

[0047] Reference numerals:

[0048] 1 Laser focus diameter, 2 Laser pulse width, 3 Target material, 4 Laser plasma, 5 Laser channel boundary of laser beam. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical scheme and advantages disclosed in the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments disclosed in the present invention, rather than all the embodiments. Based on the embodiments disclosed in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the protection scope disclosed in the present invention.

[0050] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a product or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such product or device. In the absence of more restrictions, the elements defined by the sentence "comprises a" do not exclude the presence of other identical elements in the product or device including the elements.

[0051] There are many factors that affect the luminous efficiency of laser plasma light sources produced by laser ablation of solid or liquid targets, such as laser intensity, laser wavelength, laser focal spot diameter, laser pulse width, and the interaction between laser and plasma. Solid or liquid target materials are the materials required for laser plasma light sources, and the radiation wavelength of the laser plasma light source produced by them can be selected and adjusted by replacing the target materials. In the known research related to the parameters of laser plasma light sources that affect the luminous efficiency of plasma light sources, adjusting the laser focal spot diameter, laser pulse width and corresponding laser intensity of the laser plasma light source can effectively improve the luminous efficiency of the laser plasma light source.

[0052] Taking a solid or liquid tin target as an example, laser ablation of a solid or liquid tin target generates extreme ultraviolet light with a wavelength of 13.5nm. As long as the diameter of the laser focus on the solid or liquid tin target is greater than a certain value, the luminous efficiency of the extreme ultraviolet light can reach the maximum. If the laser focus diameter continues to increase, the luminous efficiency will remain constant, while reducing the laser focus will lead to a decrease in luminous efficiency. However, there is currently no record that clearly states which parameters the laser focus diameter is related to, so it is impossible to determine the laser focus diameter and its related critical parameters.

[0053] Therefore, the present invention discloses a method for determining laser parameters for exciting a laser plasma light source, such as Figure 1 As shown, the following steps are included:

[0054] Step S1, determining the target material of the generated laser plasma light source according to the wavelength of the pre-excited laser plasma light source;

[0055] Step S2, determining the electron temperature of the generated laser plasma according to the target material of the laser plasma light source;

[0056] Step S3, determining parameters for exciting the laser plasma light source based on the electron temperature of the laser plasma, the parameters including: laser wavelength, laser focal spot diameter and laser pulse width;

[0057] Wherein, the expansion speed of the laser plasma luminous area along the target normal direction is determined based on the laser wavelength, so that the expansion speed, the laser pulse width and the laser focal spot diameter satisfy the relationship:

[0058]

[0059] in, V is the expansion velocity of the laser plasma luminous area along the target normal direction;

[0060] T is the laser pulse width;

[0061] D is the laser focal spot diameter.

[0062] By using the above relationship, when the laser pulse width of the laser plasma light source used to ablate the target material is known, the size of the minimum laser focal spot diameter of the laser can be determined, thereby maximizing the luminous efficiency of the laser plasma light source; or when the luminous size of the laser plasma light source is limited, the optimal laser pulse width can be determined, thereby maximizing the luminous efficiency of the laser plasma light source.

[0063] Specifically, Figure 2 As shown, in the early stage of generating a laser plasma light source by laser ablation of a solid or liquid target material 3, the generated laser plasma 4 expands along the target normal direction, and the lateral surface area of ​​the laser plasma is very small, and its lateral expansion is not significant. Therefore, the laser plasma 4 is approximately a one-dimensional expansion along the target normal direction. At this time, the lateral position of the light-emitting area is basically within the laser channel boundary 5 of the laser beam, and the lateral size is approximately equal to the laser focal spot diameter 1, and the size of the light-emitting area along the target normal direction will increase with the one-dimensional expansion of the laser plasma.

[0064] When the expansion size of the laser plasma along the target normal increases to a size close to the laser focal spot diameter 1, the lateral surface area of ​​the laser plasma becomes very large and the lateral expansion cannot be ignored. The expansion of the laser plasma is converted from the initial one-dimensional expansion along the target normal direction to an axisymmetric quasi-spherical three-dimensional expansion. The dissipation of the laser plasma by the quasi-spherical three-dimensional expansion is more intense than that of the one-dimensional expansion. The generation rate of the laser plasma is balanced with the dissipation rate of the laser plasma by the three-dimensional expansion, so that the spatial distribution of the laser plasma reaches a steady state. Therefore, the maximum effective size of the laser plasma luminous area along the target normal direction is close to the laser focal spot diameter and no longer increases; at the same time, a large amount of high-temperature laser plasma quickly cools down and no longer emits light due to the lateral expansion overflowing the laser channel boundary 5, so that the lateral size of the laser plasma luminous area is still approximately equal to the laser focal spot diameter 1. Even if the laser continues to irradiate with the same laser pulse width 2, the laser plasma luminous area remains unchanged, and the newly generated laser plasma will also cool down and no longer emit light due to running out of the laser channel laterally, resulting in the subsequent laser pulses being wasted, and the luminous efficiency of the laser plasma light source begins to decrease.

[0065] Therefore, the maximum value of the product of the laser pulse width and the expansion speed of the laser plasma luminous area along the target normal direction, that is, the expansion scale of the luminous area along the target normal direction, should not be greater than the laser focal spot diameter, that is:

[0066]

[0067] in,

[0068] V is the expansion velocity of the laser plasma luminous area along the target normal direction;

[0069] T is the laser pulse width;

[0070] D is the laser focal spot diameter.

[0071] The expansion speed of the laser plasma luminous area along the target normal direction is related to the luminous wavelength of the laser plasma light source and the laser wavelength used. Specifically:

[0072] Step S1, determining a target material for generating a laser plasma light source according to the wavelength of a pre-excitation laser plasma light source;

[0073] Taking the extreme ultraviolet laser plasma light source with a wavelength of 13.5nm as an example, by measuring the spectrum emitted by the laser plasma, identifying the characteristic spectral lines, and comparing the measured characteristic spectral lines with the radiation transition wavelengths of known elements, it is possible to determine that the target material is tin.

[0074] Step S2: Determine the electron temperature of the generated laser plasma according to the target material of the laser plasma light source You .

[0075] In the study of laser plasma, by measuring the X-ray energy spectrum emitted by the target material, the spectral line data of the tracer ion can be obtained, thereby determining the electron temperature of the laser plasma. You.

[0076] For the 13.5nm EUV laser plasma source used in EUV photolithography and EUV measurement equipment, the optimal electron temperature when ablating a solid or liquid tin target is You Around 30eV.

[0077] Step S3, based on the electron temperature of the laser plasma, determining the laser parameters for exciting the laser plasma light source, the laser parameters including: laser wavelength, laser focal spot diameter and laser pulse width. Wherein, based on the laser wavelength, determining the expansion speed of the laser plasma luminous area along the target normal direction includes the following steps:

[0078] Step S31: According to the electronic temperature You Determine the laser wavelength and laser intensity used to excite the laser plasma light source; taking the generation of extreme ultraviolet light with a wavelength of 13.5 nm as an example, a 1064 nm wavelength Nd:YAG laser can be used to ablate a tin solid or liquid target to generate a high-temperature tin laser plasma. At this time, the laser intensity is 1×10 11 W / cm 2 ; Carbon dioxide laser with a wavelength of 10 μm can also be used to ablate tin solid or liquid targets to produce high-temperature tin laser plasma. The laser intensity used at this time is 1×10 10 W / cm 2 .

[0079] Step S32, determining the expansion speed of the laser plasma luminous area along the target normal direction according to the laser wavelength, comprising the following steps:

[0080] Step S32-1: Based on the target material and the electron temperature

[0081] You Determining the ion sound velocity in laser plasmas Thu :

[0082]

[0083] in, You is the electron temperature;

[0084] M is the atomic mass of the target substance;

[0085] ZIt is the average ionization degree of ions in the light-emitting area when the target material is heated into laser plasma.

[0086] Furthermore, due to the ion sound velocity of the laser plasma Thu The expansion velocity of the laser plasma luminous area along the target normal direction satisfies the relationship:

[0087]

[0088] in, Thu is the ion sound velocity of laser plasma;

[0089] is a parameter related to the laser wavelength. Therefore, equation (1) can be further characterized as:

[0090]

[0091] in,

[0092] Thu is the ion sound velocity of laser plasma;

[0093] is a parameter related to the laser wavelength;

[0094] T is the laser pulse width;

[0095] D is the laser focal spot diameter.

[0096] It can be seen that the laser focal spot diameter of the plasma light source is D The laser pulse width T, laser wavelength and ion sound velocity Thu Are relevant.

[0097] Step S32-2: Expansion speed related to parameters of determination.

[0098] When lasers of different wavelengths used to excite laser plasma are irradiated on different target materials, the effective luminous areas of the laser plasma will be different due to the different critical densities of the generated lasers. The laser plasma generated in this area has different expansion speeds along the target normal direction. V , so the expansion velocity of the laser plasma luminous area along the target normal direction can be obtained by the following formula:

[0099]

[0100] in, x is the spatial position of a unit in the laser plasma luminescence area, t It is the expansion time of the laser plasma luminous area, that is, the laser ablation time.

[0101] Therefore, it is necessary to further determine the effective luminous area:

[0102] The luminous area of ​​laser plasma is distributed in the critical electron density of laser plasma. Nearby It covers a very wide area, but the light emitted by the laser plasma will be absorbed by the laser plasma in the process of leaving the luminous area. Therefore, it is necessary to use the absorption coefficient of the light at the laser plasma pre-excitation wavelength in the laser plasma multiplied by the density of the laser plasma luminous area, and then spatially integrate from the lowest density area to the high density area to obtain the proportion of light emitted at each spatial position that is absorbed, thereby determining the effective luminous area.

[0103] The density expression of the laser plasma luminous area is:

[0104]

[0105] in, is the critical electron density of the laser, in cm -3 ;

[0106] is the wavelength of the laser, ranging from 1 μm -10 μm ;

[0107] For x The laser plasma luminous zone unit is located in t The electron density at time.

[0108] Since the absorption ratio of laser plasma changes with the spatial position of the luminous area, the higher the density, the stronger the absorption, so the effective luminous area will move below Density regional shift. Take the example of using a 1064nm wavelength Nd:YAG laser to ablate a tin solid or liquid target to produce a 13.5nm extreme ultraviolet laser plasma light source. Since the extreme ultraviolet light will be absorbed by the tin plasma in the process of passing out of the light-emitting area, the absorption coefficient of the 13.5nm extreme ultraviolet light in the tin plasma is multiplied by the density of formula (3), and then the spatial integration from the lowest density area to the high density area is used to obtain the proportion of the extreme ultraviolet light emitted at each spatial position that is absorbed. Among them, the absorption coefficient can be obtained through the standard data query of the atomic and molecular database.

[0109] According to numerical calculations based on the data table of the atomic and molecular database, it can be found that only the extreme ultraviolet light produced in the low-density area below 0.1 times the laser critical electron density can be transmitted, that is, the effective light-emitting area is at 0.1 times the laser critical electron density, and the extreme ultraviolet light produced in the higher density area is almost completely absorbed by the tin plasma.

[0110] According to formula (3), the position of 0.1 times the laser critical density is At Substituting the numerical value into formula (2), the expansion velocity of the laser plasma in the luminous region along the target normal direction can be obtained as: V =2.7 Thu . Thu About 15 μm / ns is the ion sound velocity of the tin laser plasma with an electron temperature of 30 eV. At this time, the formula for the optimal values ​​of the laser focus diameter and the laser pulse width is When a 10 μm wavelength carbon dioxide laser is used to ablate a tin solid or liquid target to generate a tin high-temperature laser plasma that emits a 13.5 nm extreme ultraviolet laser plasma light source, due to the low density of the high-temperature plasma generated by the long-wavelength laser and the weak absorption of extreme ultraviolet light, the same method as above is used to calculate that its effective light-emitting area is near 1 times the laser critical density. According to formulas (3) and (2), the expansion velocity of the plasma in this area along the target normal direction can be obtained as V = Thu At this time, the formula for the optimal values ​​of laser focal spot diameter and laser pulse width is: .

[0111] Example 1

[0112] It is known that the pre-excitation wavelength of the extreme ultraviolet laser plasma light source is 13.5nm. The Nd:YAG laser with a wavelength of 1064nm is used to ablate the tin solid or liquid target. The required laser intensity is 1×10 11 W / cm 2 The optimal laser plasma electron temperature is about You is 30eV, the ion sound velocity of laser plasma Thu About 15μm / ns.

[0113] Since the effective light-emitting area generated by the 1064nm wavelength laser is in the low-density area below 0.1 times the laser critical density, the expansion speed of the plasma in this area along the target normal direction is At this time, the optimal values ​​of the laser focal spot diameter and the laser pulse width satisfy the formula: If the pulse width of the laser is limited to 10ns, the minimum laser focal spot diameter should be controlled D At 400μm. Example 2

[0114] It is known that the pre-excitation wavelength of the extreme ultraviolet laser plasma light source is 13.5nm. The Nd:YAG laser with a wavelength of 1064nm is used to ablate the tin solid or liquid target. The required laser intensity is 1×10 11 W / cm 2 The optimal laser plasma electron temperature is about You is 30eV, the ion sound velocity of laser plasma Thu About 15μm / ns. Since the effective light-emitting area produced by the 1064nm wavelength laser is in the low-density area below 0.1 times the laser critical density, the expansion speed of the plasma in this area along the target normal direction is At this time, the optimal values ​​of the laser focal spot diameter and the laser pulse width satisfy the formula: If the size of the extreme ultraviolet light source is required to be controlled to be 50μm, the maximum laser pulse width T is approximately 50 / (2.7×15)≈1.2ns.

[0115] Example 3

[0116] It is known that the extreme ultraviolet laser plasma light source with a pre-excitation wavelength of 13.5nm uses a 10μm wavelength carbon dioxide laser to ablate tin solid or liquid targets, and the required laser intensity is 1×10 10 W / cm 2 The optimal laser plasma electron temperature is about You is 30eV, the ion sound velocity of laser plasma Thu About 15μm / ns.

[0117] Since the wavelength of the CO2 laser used is relatively long, the effective light-emitting area produced by the laser is near 1 times the laser critical density. The expansion speed of the plasma in this area along the target normal direction is V = Thu .

[0118] At this time, the optimal values ​​of the laser focal spot diameter and the laser pulse width satisfy the formula: If the pulse width of the laser is limited to 80ns, the laser focal spot diameter . Further, by comparing Example 1 and Example 3, it can be seen that the laser intensity decreases with the increase of the laser wavelength. This is because the longer the laser wavelength, the lower the rate of ablating the plasma, and the smaller the laser power and laser intensity consumed at the same plasma temperature. In summary, the determination of the laser parameters is related to the laser wavelength used to excite the laser plasma light source, the target material, and the expansion rate of the laser plasma light-emitting area along the target normal. When the wavelength of the laser plasma light source and any of the limiting conditions of the laser focus or the laser pulse width are known, the selection method according to the present invention can determine the critical value of the other parameter and ensure that the laser plasma light source has the maximum luminous efficiency.

[0119] The above embodiments are only used to illustrate the technical solutions disclosed in the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments disclosed in the present invention.

Claims

1. A method for determining laser parameters for exciting a laser plasma light source, characterized in that: include: Determining a target material for generating the laser plasma light source according to the wavelength of the pre-excited laser plasma light source; determining the electron temperature of the generated laser plasma according to the target material of the laser plasma light source; Determining laser parameters for exciting the laser plasma light source based on the electron temperature of the laser plasma, the laser parameters including: laser wavelength, laser focal spot diameter and laser pulse width; Wherein, the expansion speed of the laser plasma luminous area along the target normal direction is determined based on the laser wavelength, so that the expansion speed, the laser pulse width and the laser focal spot diameter satisfy the relationship: ， in, V is the expansion velocity of the laser plasma luminous area along the target normal direction; T is the laser pulse width; D is the laser focal spot diameter.

2. The method according to claim 1, characterized in that The step of determining the expansion speed of the laser plasma luminous area along the target normal direction based on the laser wavelength comprises: The ion sound velocity of the laser plasma is determined according to the electron temperature of the laser plasma; the electron temperature and the ion sound velocity satisfy the relationship: ， The ion sound velocity of the laser plasma and the expansion velocity of the laser plasma luminous area along the target normal direction satisfy the relationship: ， in, Te is the electron temperature; M is the atomic mass of the target substance; Z is the average ionization degree of ions in the luminous region when the target material is heated to plasma; Cs is the ion sound velocity of the laser plasma; is a constant related to the laser wavelength.

3. The method according to claim 2, characterized in that The expression of the expansion speed of the laser plasma luminous area along the target normal direction is: , in, x is the spatial position of a unit in the laser plasma luminescence area, t is the expansion time of the laser plasma luminous area.

4. The method according to claim 3, characterized in that The laser plasma luminous area has a density, and the density expression of the laser plasma luminous area is: , in, is the critical electron density of the laser, in cm -3 ; is the wavelength of the laser, in μm; For x The laser plasma luminous zone unit is located in t The electron density at time.

5. The method according to claim 2, characterized in that: The laser plasma pre-excitation wavelength is 13.5 nm.

6. The method according to any one of claims 2 to 5, characterized in that: The laser wavelength is 1064 nm; the ion sound velocity, laser pulse width and laser focal spot diameter satisfy the relationship:

7. The method according to any one of claims 2 to 5, characterized in that: The laser wavelength is 10 μm; the ion sound velocity, laser pulse width and laser focal spot diameter satisfy the relationship:

8. The method according to claim 1, characterized in that The parameters also include: laser light intensity, and the laser light intensity decreases as the laser wavelength increases.

9. The method according to claim 1, characterized in that: The target material of the laser plasma is tin.

10. The method according to claim 2, characterized in that The ion sound velocity of the laser plasma is 15 μm / ns.

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