Method and system for constructing photoresist secondary electron generation model
By constructing a model for the generation of secondary electrons in photoresist and combining molecular dynamics and Monte Carlo simulations, the problem of simulating the distribution of secondary electrons in photoresist films was solved, and accurate simulation of the distribution of secondary electrons in extreme ultraviolet photoresist films was achieved, which can be applied to the field of photolithography.
Patent Information
- Application Number
- CN202310736474.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-06-20
- Publication Date
- 2025-12-26
- Estimated Expiration
- 2043-06-20
AI Technical Summary
Existing photolithography software lacks simulation studies on the distribution of secondary electrons in photoresist films. It mainly focuses on the ionization process caused by a single electron or photon in electron beam lithography, and fails to comprehensively simulate the distribution of secondary electrons.
A model for the generation of secondary electrons in photoresist is constructed. Through molecular dynamics simulation and Monte Carlo simulation, combined with photon number, photon coordinates and molecular ionization energy, the distribution of secondary electrons in the photoresist film is calculated, including elastic and inelastic scattering processes, and the coordinates of secondary electrons are output.
It achieves accurate and efficient simulation of the secondary electron distribution in extreme ultraviolet photoresist films, and can simulate the generation and effects of secondary electrons in different types of photoresists. The simulation process solves the technical problems of existing technologies and can be applied to other photolithography fields.
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Figure CN119167575B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of photoetching process, and more particularly to a method and system for constructing a photoresist secondary electron generation model. BACKGROUND
[0002] In the photoresist reaction mechanism, the photoresist will absorb photons to generate high-energy photoelectrons, and these high-energy photoelectrons are distributed in the photoresist film, undergo elastic and inelastic scattering processes, trigger further ionization and generate several secondary electrons. These secondary electrons will be adsorbed by a photoacid generator (PAG) and then dissociated to generate photoacid. Therefore, the size of the ionization energy determines the generation efficiency of the secondary electrons and their movement path, and the distribution of the secondary electrons in the film has a very great influence on the dissociation of the PAG to generate photoacid. The existing photoetching software has the following shortcomings: the current simulation research on secondary electrons is mainly for electron beam lithography, only the ionization process triggered by a single electron or photon is studied, and the distribution of secondary electrons in the film is not simulated. Therefore, for those skilled in the art, how to simulate the distribution of secondary electrons in the photoresist film is a problem to be solved. SUMMARY
[0003] Therefore, the present application provides a method and system for constructing a photoresist secondary electron generation model to solve the problems in the background art.
[0004] In order to achieve the above-mentioned purpose, the present application adopts the following technical solution: a method for constructing a photoresist secondary electron generation model, comprising the following specific steps:
[0005] S1, determining a simulated photoresist formula, and constructing a photoresist system model according to the photoresist formula;
[0006] S2, performing molecular dynamics simulation on the photoresist system model to obtain the density of the relaxed photoresist film, and outputting the center-of-mass coordinates of the molecules in the film;
[0007] S3, determining the number of photons in the photoresist film and randomly distributing them in the film to obtain the coordinates of the photons;
[0008] S4, determining the type of molecules ionized by the photons according to the distance from the photons to the center-of-mass coordinates, and obtaining the energy of the photoelectrons in combination with the ionization energy of the molecules;
[0009] S5, performing Monte Carlo simulation of the generation of secondary electrons at all photon positions in the photoresist film in combination with the energy of the photoelectrons and the coordinates of the photons to obtain the distribution of the secondary electrons in the photoresist film, and outputting the coordinates of the secondary electrons.
[0010] Optionally, the number of photons in the photoresist film is determined according to the simulated exposure dose and the absorption efficiency of the photons.
[0011] Optionally, the energy of the photoelectron is the photon energy minus the ionization energy of the molecule, wherein the ionization energy of different types of molecules is calculated by first-principle software.
[0012] Optionally, the photoelectron is generated at the photon, and the photoelectron undergoes elastic scattering and inelastic scattering, the inelastic scattering causes energy loss of the photoelectron, and a secondary electron is generated, and the cascade process of the secondary electron is obtained by tracking the photoelectron after energy loss and the generated secondary electron.
[0013] Optionally, the energy loss of the inelastic scattering is calculated by Bethe's law:
[0014]
[0015] Wherein, s is the electron mean free path, Z i is the atomic number of the i-th element, A i is the atomic mass of the target, J i is the ionization energy, E is the instantaneous energy of the electron, and p is the density of the photoresist film.
[0016] Optionally, the energy of the secondary electron is obtained using a uniform random number R:
[0017]
[0018]
[0019] Wherein, φ is the work function, is the average binding energy of the shell electron, E c is the parameter limiting the energy of the secondary electron, E s is the energy of the secondary electron.
[0020] Optionally, the specific steps for obtaining the secondary electron coordinates are:
[0021] Monte Carlo simulation of the secondary electron generated by a single photon is performed to obtain the free path, scattering angle and azimuth angle parameters in each elastic scattering or inelastic scattering process;
[0022] The simulation results of different photons are substituted into the photon coordinates to obtain the secondary electron distribution and secondary electron coordinates in the entire photoresist film.
[0023] In another aspect, a photoresist secondary electron generation model construction system is provided, comprising a photoresist model construction module, a first calculation module, a photon distribution module, a photoelectron energy calculation module, and a secondary electron distribution calculation module; wherein,
[0024] The photoresist model construction module is configured to determine a simulated photoresist formula and construct a photoresist system model according to the photoresist formula.
[0025] The first calculation module is configured to perform molecular dynamics simulation on the photoresist system model to obtain the density of the relaxed photoresist film and output the center-of-mass coordinates of the molecules in the film.
[0026] The photon distribution module is configured to determine the number of photons in the photoresist film and randomly distribute the photons in the film to obtain the photon coordinates.
[0027] The photoelectron energy calculation module is configured to determine the type of molecule ionized by the photon according to the distance between the photon and the center-of-mass coordinates, and obtain the energy of the photoelectron in combination with the ionization energy of the molecule.
[0028] The secondary electron distribution calculation module is configured to perform Monte Carlo simulation of the generation of secondary electrons at all photon positions in the photoresist film in combination with the energy of the photoelectron and the photon coordinates to obtain the distribution of the secondary electrons in the photoresist film and output the secondary electron coordinates.
[0029] The method further comprises a molecular ionization energy calculation module configured to calculate the ionization energy of different types of molecules by first-principle software.
[0030] Compared with the prior art, the method and system for constructing a photoresist secondary electron generation model provided by the present application have the following beneficial technical effects: the calculation model of the present application introduces parameters such as ionization energy, and through Monte Carlo simulation, the generation and distribution of secondary electrons in the exposure process of extreme ultraviolet photoresist are obtained. By calculating the motion path of the secondary electrons in the extreme ultraviolet photoresist, the distribution of secondary electrons in the film after exposure of photoresist of different types and ratios can be simulated, and accurate and efficient simulation of the distribution of secondary electrons in the extreme ultraviolet photoresist film is realized. It should be noted that the secondary electron generation model in the present application can not only be applied to extreme ultraviolet lithography, but also be applied to other lithography fields. BRIEF DESCRIPTION OF DRAWINGS
[0031] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only embodiments of the present application, and those skilled in the art can obtain other drawings according to the provided drawings without creative labor.
[0032] Figure 1 The method flowchart of the present application;
[0033] Figure 2 A system structure diagram of the present application;
[0034] Figure 3 A secondary electron motion path diagram of an embodiment of the present application;
[0035] Figure 4 A molecule distribution diagram in a photoresist film simulated in an embodiment of the present application;
[0036] Figure 5 A secondary electron coordinate diagram in a photoresist film in an embodiment of the present application. DETAILED DESCRIPTION
[0037] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present application.
[0038] The embodiments of the present application take an extreme ultraviolet photoresist as an example, and disclose a construction method of an extreme ultraviolet photoresist secondary electron generation model, as shown in Figure 1 The specific steps include the following.
[0039] S1, determining a simulated photoresist formula, and constructing a photoresist system model according to the photoresist formula;
[0040] S2, performing molecular dynamics simulation on the photoresist system model to obtain a relaxed photoresist film density, and outputting the center of mass coordinates of molecules in the film;
[0041] S3, determining the number of photons in the photoresist film, and randomly distributing the photons in the film to obtain photon coordinates;
[0042] S4, determining the type of molecules ionized by the photons according to the distance from the photons to the center of mass coordinates, and obtaining the energy of photoelectrons in combination with the ionization energy of the molecules;
[0043] S5, performing Monte Carlo simulation of secondary electron generation on all photon positions in the photoresist film in combination with the energy of the photoelectrons and the photon coordinates, obtaining the distribution of the secondary electrons in the photoresist film, and outputting the secondary electron coordinates.
[0044] Further, the number of photons in the photoresist film is determined according to the simulated exposure dose and the absorption efficiency of the photons in step S3.
[0045] Further, the energy of the photoelectrons is the photon energy minus the ionization energy of the molecules, wherein the ionization energy of different types of molecules is calculated by a first principle software.
[0046] Further, the photoelectron is generated at the photon, and the photoelectron undergoes elastic scattering and inelastic scattering, and the inelastic scattering causes energy loss of the photoelectron and generates a secondary electron. The cascade process of the secondary electron is obtained by tracking the photoelectron after energy loss and the generated secondary electron.
[0047] The photoelectron is generated by ionization of the photoresist by the photon, and the energy of the photoelectron is the energy of the photon minus the ionization energy. The photoelectron undergoes elastic scattering and inelastic scattering. The elastic scattering is related to the interaction between the electron and the nucleus, and the direction of the electron is changed, but no energy loss occurs. The inelastic scattering is the interaction between the incident electron and the electron of the target atom, and the energy is transferred from the incident electron to the orbital electron of the target atom, and a secondary electron is generated. Each elastic scattering or inelastic scattering process includes three parameters of free path, scattering angle and azimuth angle, which are obtained by Monte Carlo simulation, and finally the complete electron motion path is obtained.
[0048] Further, the specific steps for obtaining the secondary electron coordinates in step S5 are as follows:
[0049] Monte Carlo simulation is performed on the secondary electron generated by a single photon to obtain the free path, scattering angle and azimuth angle parameters in each elastic scattering or inelastic scattering process;
[0050] The simulation results of different photons are substituted into the photon coordinates to obtain the secondary electron distribution and secondary electron coordinates in the entire photoresist film.
[0051] Specifically, the calculation process of the secondary electron motion trajectory is as follows:
[0052] Elastic scattering: The secondary electron motion trajectory model includes elastic scattering that only changes the angle of electron motion without changing the energy, and inelastic scattering that causes energy loss of the electron and generates a secondary electron. The elastic scattering is related to the interaction between the high-energy electron and the nucleus. In this process, the direction of the electron is changed, but its energy remains unchanged. The elastic scattering uses the Mott cross section fitted by the Browning:
[0053]
[0054] where Z is the atomic number and E is the instantaneous energy of the electron (eV). Then the average distance between consecutive elastic scattering events, i.e. the average free path of elastic scattering Λ is calculated. el which is determined by the following formula:
[0055]
[0056] where n is the atomic density and a random number R (0-1) is used to calculate the electron mean free path As for the current elastic scattering event: As = -Λ - ln(R); (3)
[0057] Scattering angle of elastic scattering θ el is determined by the following equation:
[0058]
[0059] Azimuthal angle
[0060] Inelastic scattering: Inelastic scattering includes the interaction between the incident electron and the orbital electron of the target atom, and the energy is transferred from the incident electron to the target atom and its orbital electron. The energy loss of the incident electron is caused by electron, proton and phonon excitation, ionization and other processes. The inelastic scattering model used in the present embodiment is based on the continuous energy loss method (continuous deceleration approximation, CSDA), and is expressed in terms of energy loss per unit length. The inelastic mean free path of secondary electrons is calculated using an empirical formula for organic compounds:
[0061]
[0062] where p is the density, and the inelastic scattering cross section is derived using the following equation:
[0063]
[0064] The energy loss of each step is calculated by the Bethe law:
[0065]
[0066] where s is the electron mean free path, Z i is the atomic number of the i-th element, A i is the atomic weight of the target, J i is the ionization energy, E is the instantaneous energy of the electron, and p is the density of the photoresist film.
[0067] The energy of the secondary electron is obtained using a uniform random number R:
[0068]
[0069]
[0070] where φ is the work function (here the HOMO level is used for approximation), is the average binding energy of the shell electron (here the value of the ionization energy is taken), E c is a parameter limiting the energy of the secondary electron, E sEnergy of secondary electron.
[0071] The simulation of the generation process of secondary electrons and subsequent electrons can obtain the motion path of EUV photoresist and the number of generated secondary electrons. The scattering angle of incident electron θ inel Energy of secondary electron
[0072]
[0073] Scattering angle of secondary electron θ se Determined by the loss energy and electron energy:
[0074]
[0075] Where ΔE is the energy lost in the inelastic scattering process, the azimuth angle of the initial electron and the secondary electron All can be calculated by different random numbers R:
[0076] The probability of elastic scattering or inelastic scattering is determined by the cross section of elastic and inelastic scattering, and the probability is:
[0077] The model of the method can be used in the field of extreme ultraviolet lithography simulation. Taking the generation of secondary electrons of BPA-6BOC photoresist as an example, the ionization energy of the photoresist is 8.3eV, and the generated photoelectron energy is 84.7eV. The density of the thin film is obtained by molecular dynamics simulation, which is 1.2g / cm3, and the motion path of the photoelectron and the generated secondary electron is as shown in Figure 3 The simulated distribution of molecules in the photoresist thin film is as shown in Figure 4 The blue dots are photoresist molecules, the red dots are PAG, and the green dots are basic neutralizers.
[0078] Determine the distance between the photon and the surrounding molecules, confirm the type of molecules that will cause ionization, and combine the ionization energy of the molecules to obtain the energy of the photoelectron. All Monte Carlo simulation results of the photoelectron (for example) Figure 3 are substituted into the photon position, and finally the coordinates of the secondary electrons in the photoresist thin film are obtained, as shown in Figure 5 .
[0079] On the other hand, a system for constructing a secondary electron generation model of extreme ultraviolet photoresist is provided, as shown in Figure 2 , comprising a photoresist model construction module, a first calculation module, a photon distribution module, a photoelectron energy calculation module, and a secondary electron distribution calculation module; wherein,
[0080] The photoresist model construction module is used to determine the simulated photoresist formula and construct the photoresist system model according to the photoresist formula.
[0081] The first calculation module is configured to perform molecular dynamics simulation on the photoresist system model to obtain the density of the relaxed photoresist film and output the center-of-mass coordinates of the molecules in the film;
[0082] The photon distribution module is configured to determine the number of photons in the photoresist film and randomly distribute the photons in the film to obtain the coordinates of the photons;
[0083] The photoelectron energy calculation module is configured to determine the type of molecule ionized by the photons according to the distance between the photons and the center-of-mass coordinates, and obtain the energy of the photoelectrons in combination with the ionization energy of the molecules.
[0084] The secondary electron distribution calculation module is configured to perform Monte Carlo simulation of the generation of secondary electrons at all photon positions in the photoresist film in combination with the energy of the photoelectrons and the coordinates of the photons to obtain the distribution of the secondary electrons in the photoresist film and output the coordinates of the secondary electrons.
[0085] The molecular ionization energy calculation module is further included and is configured to calculate the ionization energy of different types of molecules by using first-principle software.
[0086] The embodiments in the specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiments, the description is relatively simple because it corresponds to the method disclosed in the embodiments. The relevant parts can be referred to the description of the method.
[0087] The above description of the disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for constructing a photoresist secondary electron generation model, characterized in that, The specific steps include the following: S1, determining a simulated photoresist formula, and constructing a photoresist system model according to the photoresist formula; S2, simulating the film density of the photoresist system model, and outputting the center of mass coordinates of molecules in the film; S3, determining the number of photons in the photoresist film, and obtaining the photon coordinates; S4, determining the type of molecules causing molecular ionization according to the distance from the photon to the center of mass coordinates, and obtaining the energy of photoelectrons in combination with the ionization energy of the molecules; S5, performing Monte Carlo simulation of secondary electron generation for all photon positions in the photoresist film in combination with the energy of the photoelectrons and the photon coordinates, obtaining the distribution of secondary electrons in the photoresist film, and outputting the secondary electron coordinates.
2. The method of claim 1, wherein the method further comprises: determining a secondary electron yield of the photoresist; and determining a thickness of the photoresist. The number of photons in the photoresist film is determined according to the simulated exposure dose and the absorption efficiency of the photons.
3. The method of claim 1, wherein the method further comprises: determining a secondary electron yield of the photoresist; and determining a thickness of the photoresist. The energy of the photoelectrons varies with the ionization energy of the molecules, wherein the ionization energy of different types of molecules is calculated by first-principle software.
4. The method of claim 1, wherein the method further comprises: Photoelectrons are generated at the photons, and the photoelectrons undergo elastic scattering and inelastic scattering, the scattering process of the photoelectrons is simulated to obtain the cascade process of the photoelectrons and secondary electrons.
5. The method of claim 4, wherein the method further comprises: The energy loss of the inelastic scattering is calculated by Bethe's law: where s is the electron free path, Z i is the atomic number of the i-th element, A i is the atomic weight of the target, J i is the ionization energy, E is the electron instantaneous energy, and p is the photoresist film density.
6. The method of claim 4, wherein the method further comprises: The energy of the secondary electrons is obtained using a uniform random number R: where φ is the work function, is the average binding energy of the outer shell electrons, E c is a parameter that limits the energy of the secondary electrons, E s is the energy of the secondary electrons.
7. The method of claim 1, wherein the method further comprises: determining a secondary electron yield of the photoresist; and determining a thickness of the photoresist. The specific steps for obtaining the secondary electron coordinates are as follows: The Monte Carlo simulation results of different photons are substituted into the photon coordinates to obtain the distribution of secondary electrons and the secondary electron coordinates in the entire photoresist film.
8. A photoresist secondary electron generation model construction system characterized by comprising: It includes a photoresist model construction module, a first calculation module, a photon distribution module, a photoelectron energy calculation module, and a secondary electron distribution calculation module; wherein, The photoresist model construction module is used to determine a simulated photoresist formula, and construct a photoresist system model according to the photoresist formula; The first calculation module is used to simulate the film density of the photoresist system model, and output the center of mass coordinates of molecules in the film; The photon distribution module is used to determine the number of photons in the photoresist film, and obtain the photon coordinates; The photoelectron energy calculation module is used to determine the type of molecules causing molecular ionization according to the distance from the photon to the center of mass coordinates, and obtain the energy of photoelectrons in combination with the ionization energy of the molecules; The secondary electron distribution calculation module is used to perform Monte Carlo simulation of secondary electron generation for all photon positions in the photoresist film in combination with the energy of the photoelectrons and the photon coordinates, obtain the distribution of secondary electrons in the photoresist film, and output the secondary electron coordinates.
9. The system for constructing a secondary electron generation model of a photoresist according to claim 8, wherein It also includes a molecular ionization energy calculation module for calculating the ionization energy of different types of molecules by first-principle software.
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