Simulation calculation method for thermal electron energy loss based on balance pulse and application thereof

Abstract

The invention provides a thermal electron energy loss simulation calculation method based on balanced pulses and application thereof, and the calculation method comprises the following steps: according to set laser parameters, based on formulas (1) and (2), employing LAMMPS software to calculate and obtain a Te-t relationship; wherein S is a function of S (z, t) and is obtained according to a formula (3); according to the relation of Te-t, the instantaneous thermal electron emission current density J (t) is calculated by adopting a formula (4); a formula (5) is adopted to calculate the thermal electron emission energy flux density qem (t); time integration is carried out on qem (t), and energy loss caused by hot electron emission in the double-pulse process is obtained through a formula (6). According to the technical scheme, energy loss caused by hot electron emission in the double-pulse process can be calculated according to the laser parameters, and therefore sintering quality is improved while hot electron emission is restrained by adjusting energy distribution and delay time of the double pulses.

Description

Technical Field

[0001] This invention relates to the field of laser sintering technology, and in particular to a simulation calculation method for the thermionic energy loss based on balanced pulses and its application. Background Technology

[0002] Femtosecond lasers, with their ultrashort pulses and high peak power, possess unique advantages in precision material processing. They can control energy deposition within an extremely small spatial range, thereby minimizing the heat-affected zone and achieving high-precision manufacturing. Since its application in micromachining, this technology has become an important component of high-precision device manufacturing. Particularly in the field of additive manufacturing, femtosecond laser sintering of metal nanoparticles (such as copper nanoparticles) can prepare high-resolution conductive structures at low temperatures, providing a new avenue for the development of electronic devices and flexible equipment. During sintering, the femtosecond laser induces localized melting and neck growth in the nanoparticles, achieving sub-micron-level processing precision. However, this process requires a precise balance between the competing relationship between material sintering and removal: moderate energy flux enables "cold processing" with minimal heat-affected zone; excessive energy triggers localized thermal effects or even ablation, while insufficient energy leads to decreased sintering efficiency. Copper nanoparticles have attracted significant attention due to their excellent conductivity and low cost, but their interaction with femtosecond lasers involves multiple complex mechanisms, including electronic excitation, non-equilibrium heat transfer, and atomic diffusion, which are not yet fully understood.

[0003] One of the main challenges in this field is the intense ablation caused by the thermionic effect. Ultrafast laser excitation generates a large number of non-equilibrium electrons, and the resulting Coulomb repulsion can cause the material to be ejected before sintering via a "thermoe explosion" mechanism. Energy is then transferred to the crystal lattice through an electron-phonon coupling process, driving melting and sintering. To circumvent this effect, various process strategies have been developed, including using photosensitive nanoparticles as localized heat sources or employing multiple low-energy-current femtosecond pulses for cumulative sintering to reduce the intensity of a single pulse. The dual-pulse excitation strategy, by dividing the energy into two pulses with picosecond delays, can effectively reduce the peak electron temperature and decrease material removal. However, the atomic-scale mechanism of copper nanoparticle sintering in dual-pulse mode remains unclear. In traditional methods, the energy loss due to thermionic emission during dual-pulse processes is assumed to be a fixed value. However, the energy loss due to thermionic emission can vary depending on the laser parameters. The understanding of the relationship between laser parameters and sintering quality requires further refinement, which limits the further application of this technology in high-precision electronic manufacturing. Summary of the Invention

[0004] To address the above technical problems, this invention discloses a simulation calculation method for the thermionic energy loss based on equilibrium pulses and its application.

[0005] The technical solution adopted by this invention is as follows: A simulation calculation method for the thermionic energy loss based on equilibrium pulses, characterized by comprising the following steps: Step S1: Based on the set laser parameters, calculate using LAMMPS software according to formulas (1) and (2). T e -t Relationship; (1) (2) in m i , v i It is the atoms of the laser-sintered material i Quality and speed U The potential energy of the system, This represents the force exerted by the potential energy field on atom i; a negative sign is added because the system always tends to evolve towards a lower, more stable state. Langevin thermostat for describing electron-lattice energy transfer; C e , k e , G p , S These are the electron's heat capacity, thermal conductivity, electro-acoustic coupling coefficient, and input energy, respectively. T e , T l Indicates the temperature of electrons and the temperature of the crystal lattice; in, S for S ( z , t The function of ) is obtained according to formula (3): (3) In formula (3), z , L op It refers to the depth and skin depth along the incident direction of the laser pulse. J abs , τ p These are the energy flux density and pulse width of the laser pulse. t d It is the pulse time interval, i.e., the pulse delay time, and t is the total time for laser emission; Step S2, according to T e -tThe instantaneous thermionic emission current density is calculated using formula (4) based on the relationship between the two. J(t) ; (4) in, A 0 =1.20173×10 6 Am -2 K -2 , where is Richardson's constant; Φ represents the work function of copper. k B =8.617333×10 -5 eVK -1 , where is the Boltzmann constant; Step S3: Calculate the thermionic emission energy flux density using formula (5). q em ( t ) ; (5), where Φ J =Φ×e Step S4, for q em ( t By performing time integration, the energy loss due to thermionic emission during the double-pulse process is obtained using formula (6). (6).

[0006] As a further improvement of the present invention, the material for laser sintering is copper.

[0007] As a further improvement of the present invention, a beam splitter and a displacement platform can be used to split the laser beam and introduce a delay.

[0008] This invention discloses the application of the simulation calculation method for hot electron energy loss based on the equilibrium pulse as described above, which is used to compare and analyze the relationship between electron temperature evolution and laser sintering parameters under different energy ratios, so as to select appropriate laser sintering parameters, wherein the laser sintering parameters include the pulsed laser energy ratio and the time interval of the laser pulse.

[0009] This invention discloses a simulation method for reducing the thermionic temperature and improving sintering quality based on a balanced pulse. The method uses the above-described simulation calculation method for thermionic energy loss based on balanced pulses to calculate the thermionic energy loss of different pulse laser energy ratios and laser pulse time intervals, and compares the results to obtain laser sintering parameters with lower energy loss, thereby improving sintering quality.

[0010] Compared with the prior art, the beneficial effects of the present invention are as follows: Using the technical solution of this invention, the energy loss caused by thermionic emission during the double-pulse process can be calculated based on the laser parameters. Based on this, the effect of delayed double-pulse laser on electron temperature regulation can be studied at the atomic scale. Furthermore, by adjusting the energy distribution and delay time of the double pulse, the sintering quality can be improved (such as promoting neck growth) while suppressing thermionic emission, thus providing a theoretical basis for optimizing the fabrication of copper-based micro / nano devices. Attached Figure Description

[0011] Figure 1 This is the electron / lattice temperature-time curve obtained in an embodiment of the present invention.

[0012] Figure 2 This is the highest electron temperature-delay curve obtained in the embodiments of the present invention.

[0013] Figure 3 The neck size ratio (R) under different time delays in embodiments of the present invention. neck / R0) varies with lattice temperature ( T l The curves of change are shown, where (a), (b), and (c) represent schemes E1, E2, and E3, respectively.

[0014] Figure 4 This describes the variation of melting time with time delay under different energy ratios in embodiments of the present invention. Detailed Implementation

[0015] The preferred embodiments of the present invention will be described in further detail below.

[0016] Using a beam splitter and a displacement platform, the laser beam can be split and a small delay can be introduced. The following example uses copper nanoparticles as the material to be sintered, and the microscopic behavior of the nanoparticles under femtosecond laser irradiation is observed. This can be simulated by coupling the two-temperature equation (TTM) with molecular dynamics (MD). The temperature rise of the material under femtosecond laser irradiation can be described by the following two equations: (1) (2) in, m i , v i It refers to the atomic mass and velocity of the material being laser-sintered. U The potential energy of the system, Langevin thermostat for describing electron-lattice energy transfer; C e , k e , G p ,S These are the electron's heat capacity, thermal conductivity, electroacoustic coupling coefficient, and input energy, respectively; the electron's heat capacity and thermal conductivity are... T e The function, T e , T l It represents the temperature of electrons and the temperature of the crystal lattice.

[0017] Among them S for S ( z , t The function of ) can be obtained from the source term of the equation according to formula (3): (3) in z , L op It refers to the depth and skin depth along the incident direction of the laser pulse. J abs , τ p These are the energy flux density and pulse width of the laser pulse. t d t is the time interval between laser pulses, and t is the total time for laser emission.

[0018] In this embodiment, the copper nanoparticles have a diameter of 6 nanometers, which is much smaller than the laser wavelength and typical laser spot size used in the experiment. Therefore, the incident light field can be approximated as spatially uniformly distributed in the transverse (xy) plane. Based on this assumption, the absorbed energy is considered to be uniformly distributed across the particle cross-section and decays exponentially along the incident light direction (z direction) with the optical penetration depth Lop as a characteristic. Under this approximation, equation (3) preserves the time distribution characteristics and inter-pulse delay of the double Gaussian pulse, while only resolving the depth-dependent absorption behavior.

[0019] The simulation region was set as a 16nm×12nm×12nm cube, and the region for TTM-MD simulation was divided into multiple small cells. Each cell is an "electron" region with the same internal temperature. The model solves the heat conduction equations between the source term and other cells using FDM (2). It should be noted that in MD, there is no concept of "electron". The "electron" here is actually a variable heat source in a user-defined function, that is, the atom is in a hot bath called "free electron gas". The function defines a finite electron temperature, so that the hot bath is heated by the atom through a Langevin thermostat in the form of a finite heat pool, thereby realizing the energy exchange between the "electron system" and the atomic system in the MD simulation that only considers the behavior of the atom.

[0020] With 70J / m 2 The total energy flux density was simulated under the condition of a double pulse (35 / 35) with a delay of 4 ps-12 ps and the electron / lattice temperature changing over time, as shown in the figure. Figure 1 It can be seen that the maximum temperature of electrons decreases with the introduction of delay, indicating that the introduction of delay has a certain regulatory effect on electron temperature and can effectively suppress the damage of thermionic emission to the processed surface. To evaluate whether thermionic emission is significant under the parameters of this study, this embodiment uses the Richardson-Dushmann equation to calculate the instantaneous thermionic emission current density. J ( t As shown in formula (4) (4) in, A 0 =1.20173×10 6 Am -2 K -2 , where is Richardson's constant; Φ represents the work function of copper. k B =8.617333×10 -5 eVK -1 , where is the Boltzmann constant.

[0021] The corresponding thermionic emission energy flux density q em ( t Then, it can be calculated using formula (5): (5) Where, Φ J =Φ×e, where Φ is the work function in eV, e is the electron charge, and e represents the energy factor related to the average energy of the emitted electron. Finally, according to formula (6), through... q em ( t The total emission energy can be obtained by time integration, which represents the energy loss due to thermionic emission during the double pulse process.

[0022] (6) Given that the work function of copper nanoparticles varies with size and surface conditions, calculations were performed using the above method, taking the two-pulse case as examples for Φ=4.5 eV and Φ=4.8 eV respectively. The hot electron energy loss results for the two conditions are shown in Table 1.

[0023] Table 1 Results of thermionic energy loss under two operating conditions

[0024] The calculation process used in calculating the "traditional method" in Table 1 is as follows: First, in the traditional method (i.e., the single-pulse case), a pulse delay is set. t d =0ps. At this point, the two terms within the curly braces describing the time distribution of the two pulses in formula (3) completely overlap, which is equivalent to the simultaneous incidence of two pulses, i.e., degenerates into a single-pulse model. The energy source term at this point... S ( z , t Substituting these equations into the two-temperature equations (1) and (2) describing electron-lattice nonequilibrium heat conduction, the electron temperature can be obtained by solving them. T e The evolution relationship with time t, and its typical curve is as follows: Figure 1 0ps in.

[0025] Subsequently, based on T e ( t The instantaneous thermionic emission current density is calculated using the Richardson-Dushmann formula (4) based on the relationship between the changes in the thermionic emission current and the Richardson-Dushmann formula (4). J ( t Since only a single pulse excitation is considered at this time, the only variable in formula (4) is... T e ( t ) .

[0026] Next, the thermionic emission energy flux density is further calculated according to formula (5). q em ( t This formula multiplies the emission current density by the average energy of each electron (determined by the work function Φ and the electron charge e), thus obtaining the energy loss rate per unit time and per unit area due to thermionic emission.

[0027] Finally, for q em ( t Integrating over the entire pulse duration, the total energy loss due to thermionic emission during the double pulse (which degenerates into a single pulse) is obtained according to formula (6). This integral result is the value listed in "Energy Loss of Traditional Method" in Table 1, reflecting the energy loss caused under no-delay conditions.

[0028] The results in Table 1 show that, under a pulse delay of 12 ps, the emission loss at work functions of 4.5 eV and 4.8 eV is reduced to approximately 5% and 4.8% of that under the single-pulse condition, respectively. This clearly demonstrates that increasing the pulse delay can significantly reduce the thermionic emission loss, and that double-pulse irradiation can effectively reduce the thermionic temperature, thereby suppressing thermionic emission.

[0029] Compared with traditional methods (equivalent to) t d Compared to a single pulse with a pulse duration of 0 ps, ​​the solution in this embodiment introduces a controllable pulse delay time. t d This allows the laser energy to be divided into two pulses with a time interval, which are then incident sequentially, effectively reducing the peak electron temperature (e.g., Figure 1 As shown in the figure, this suppresses thermionic emission.

[0030] To further investigate the influence of dual-pulse energy distribution on non-equilibrium processing, this embodiment designs three energy ratio schemes based on a total energy density of 70 J / m²: Group E1 (35 / 35, evenly distributed), Group E2 (50 / 20, high-low energy combination), and Group E3 (20 / 50, low-high energy combination).

[0031] By comparing and analyzing the relationship between electron temperature evolution and sintering parameters under different energy ratios, the regulation law of energy distribution on processing kinetics was revealed.

[0032] like Figure 2 As shown, the energy injection sequence significantly affects the electron temperature dynamics. Simulation data indicates that in the short delay range (<10 ps), the maximum electron temperature exhibits a quasi-exponential decay trend with increasing delay time; when the delay time reaches 10 ps, ​​the temperature drop exceeds 300 K. Notably, the energy distribution pattern has a significant difference in its effect on temperature control efficiency: when using a high-low energy combination (E2 group), the temperature control sensitivity in the short delay range (within approximately 10 ps) is significantly enhanced (temperature decrease rate reaches 6.01 × 10⁻⁶ K). 13 K / s); while the low-high energy combination (E3 group) exhibits a slow temperature relaxation process (rate approximately 3.53 × 10 K / s); 13 This difference stems from the temperature dependence of the electron-lattice coupling rate: the higher the electron temperature relative to the lattice temperature, the greater the electron-phonon coupling rate, prompting the hot electrons excited by the high-energy pulse to be transferred to the lattice system more quickly through the non-equilibrium energy transfer channel. Therefore, compared with the low-high energy combination, at the same delay time, the energy remaining in the electronic system after adding a second pulse is less. Thus, in the short delay range (within approximately 10 ps), the remaining energy of the E2 group electronic system is reduced by 7.5% compared to the E3 group, confirming that the high-low energy combination has better electron temperature control capability.

[0033] To visually compare the effects of different energy percentages on the sintering neck, the cross-sectional size of the two particles was calculated through simulation. The radius of this cross-section is the neck size, thus yielding the neck size under different energy percentages. Figure 3 As shown, it can be observed that different energy percentages all exhibit the characteristic of increasing neck size ratio with increasing time delay.

[0034] Since the above calculations do not consider heat dissipation and a time delay constraint needs to be introduced, for each set delay time... t d Simulation calculations were performed according to formulas (1) and (2) of this scheme, and the corresponding lattice temperatures were obtained. T l Curves of evolution over time (e.g.) Figure 1 (As shown). Then, from each T l - t The moment when the lattice temperature first reaches the material's melting point is extracted from the curve; this moment is... Figure 4 The ordinate value of the corresponding data point in the image represents the change in melting time with delay time for different energy percentages. Figure 4 As shown. Differentiating the curves, we can see that the slope of E1 approaches 1 around 30 ps, ​​indicating that the maximum time delay for group E1 is 30 ps. Similarly, differentiating for group E3, we find that the slope approaches 1 at a delay of 20 ps. For group E2, due to the high energy of the first pulse, the particle melting process is rapidly propelled and is unaffected by the second pulse; therefore, the maximum delay is also at 20 ps. In summary... Figure 3 The conclusion is that the greater the time delay, the better the sintering. The balanced pulse E1 group has the greatest advantage. Furthermore, the thermionic emission energies of these three groups were calculated, as shown in Table 2, with the balanced pulse (E1) group exhibiting the lowest emission energy.

[0035] The above experiments demonstrate that sintering quality can be significantly improved simply by optimizing the energy ratio and timing of the dual pulses, rather than by simply increasing the total energy. This provides theoretical support for the process optimization of femtosecond laser sintering.

[0036] Table 2 Total Energy Emitted at Different Energy Ratios

[0037] The above method can be used to compare and analyze the relationship between electron temperature evolution and laser sintering parameters under different energy ratios. By comparison, laser sintering parameters with lower energy loss can be obtained to improve sintering quality. The laser sintering parameters include the pulsed laser energy ratio and the time interval of the laser pulse.

[0038] The above technical solution is applicable not only to dual pulses but also to multi pulses.

[0039] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A simulation calculation method for the thermionic energy loss based on equilibrium pulses, characterized in that, Includes the following steps: Step S1: Based on the set laser parameters, calculate using LAMMPS software according to formulas (1) and (2). T e -t Relationship; （1） （2） in m i , v i It refers to the atomic mass and velocity of the material being laser-sintered. U The potential energy of the system, Langevin thermostat for describing electron-lattice energy transfer; C e , k e , G p , S These are the electron's heat capacity, thermal conductivity, electro-acoustic coupling coefficient, and input energy, respectively. T e , T l Indicates the temperature of electrons and the temperature of the crystal lattice; in, S for S ( z , t The function of ) is obtained according to formula (3): （3） In formula (3), z , L op It refers to the depth and skin depth along the incident direction of the laser pulse. J abs , τ p These are the energy flux density and pulse width of the laser pulse. t d t is the time interval between laser pulses, and t is the total time for laser emission; Step S2, according to T e -t The instantaneous thermionic emission current density is calculated using formula (4) based on the relationship between the two. J(t) ; （4） in, A 0 =1.20173×10 6 Am -2 K -2 , where is Richardson's constant; Φ represents the work function of copper. k B =8.617333×10 -5 eVK -1 , where is the Boltzmann constant; Step S3: Calculate the thermionic emission energy flux density using formula (5). q em ( t ) ; (5), where Φ J =Φ×e Step S4, for q em ( t By performing time integration, the energy loss due to thermionic emission during the double-pulse process is obtained using formula (6). （6）。 2. The simulation calculation method for hot electron energy loss based on equilibrium pulses according to claim 1, characterized in that: The material being laser-sintered is copper.

3. The simulation calculation method for hot electron energy loss based on equilibrium pulses according to claim 1, characterized in that: The laser beam is split using a beam splitter and a displacement platform, and a delay is introduced.

4. The application of the simulation calculation method for hot electron energy loss based on equilibrium pulses as described in any one of claims 1 to 3, characterized in that: This is used to compare and analyze the relationship between electron temperature evolution and laser sintering parameters under different energy ratios, in order to select appropriate laser sintering parameters, which include pulsed laser energy ratio and laser pulse time interval.

5. A simulation method for reducing the thermionic temperature and improving sintering quality based on a balance pulse, characterized in that: The thermionic energy loss based on the balanced pulse energy loss as described in any one of claims 1 to 3 is calculated using the simulation calculation method. The thermionic energy loss of different pulse laser energy ratios and laser pulse time intervals is compared to obtain laser sintering parameters with lower energy loss.

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