激光熔融SiO2基底上银纳米颗粒分子动力学仿真 下载: 1274次
Objective As a technology of welding nanomaterials, nano-welding is not only an important “bottom-up” means for manufacturing nanostructures, but also a key technology for the development of high-performance integrated circuits with reliable interconnection points. Among all nano-welding methods, the nanometer brazing technology of melting nanomaterials under laser irradiation, as one of most reliable methods, is utilized to realize nano-device-level interconnection. This technology reduces the damage to the welding base materials, achieves the interconnection points with high mechanical strength, and even maintains the excellent electrical performance of the devices. However, the previous theoretical models of nano-welding have only considered the atomic configuration evolution process of nanoparticles at different temperatures, ignoring the effect of substrate materials on the energy exchange process for achieving the best welding quality. Moreover, the simulation of nanoparticle melting under laser irradiation without substrates cannot completely represent the evolution of actual atomic configuration of nanoparticles as a reliable interconnection node during the brazing process. Therefore, in view of the actual brazing process of nanometer brazing, the change of atomic configuration of Ag nanoparticles on a SiO2 substrate under laser irradiation is simulated and analyzed. More importantly, the adsorption energy between the substrate and nanoparticles during the melting process is discussed in detail. These results provide a theoretical basis for the realization of actual nanometer brazing.
Methods To obtain the melting evolution process of nanoparticles at the atomic level under laser irradiation, molecular dynamics (MD) simulation based on classical mechanics is used for establishing the simulation model. In the simulation model, single and multiple Ag nanoparticles are considered. Also, amorphous silica is obtained by the energy minimization process for supporting an energy-exchanging substrate in the melting evolution process of nanoparticles. This paper simulates the melting process of silver nanoparticles induced by a laser. In the melting simulation, geometric structure optimization is first executed as an initial system state. The laser irradiation energy is applied by controlling the corresponding evolution temperature of an atomic structure. The melting process utilizes a canonical ensemble NVT to carry out the relaxation of an atomic configuration. The Nose-Hoover thermostat method is used to set the temperature and bath time for matching the requirement of energy exchange. The boundary condition is an aperiodic boundary. Three bottom atoms of the amorphous SiO2 substrate are selected to exert fixed constraints in three directions in the simulation. After simulation, the atomic configuration and energy change are extracted and analyzed for the subsequent discussion of contact length, contact angle, and adhesion energy.
Results and Discussions When the applied temperature is low, the shape of silver nanoparticles is spherical. With the increase of applied temperature, the shape of silver nanoparticles gradually changes to a hemispherical shape (Fig. 2). The hemispherical shape is attributed to the restriction of the substrate at the interface between nanoparticles and SiO2 substrate during the evolution of atomic configuration. The changes of contact length and contact angle between silver nanoparticles and substrate at different temperatures are analyzed [Fig. 3(a)]. The contact length and contact angle increase first and then reach a flat state with the increase of temperature. The adsorption energy between a single silver nanoparticle and an amorphous SiO2 substrate versus temperature is discussed [Fig. 3(b)]. When the applied temperature is 400--1000 K, the adsorption energy increases linearly with temperature. When the temperature is higher than 1000 K, the adsorption decreases rapidly. The changes of the atomic configuration of two silver nanoparticles on the amorphous SiO2 substrate at different time are conducted (Fig. 4). The original two nanoparticles fuse into one after high-temperature relaxation. The adsorption energy of two silver nanoparticles melted on the substrate is significantly higher than that of a single nanoparticle, which was attributed to the increase of contact area (Fig. 7).
Conclusions In summary, based on the molecular dynamics method, the evolution process of the atomic configuration of 4 nm-diameter nanoparticles on SiO2 substrate at different temperatures is discussed, and the melting process of nanoparticles caused by laser irradiation in the actual brazing process is simulated. When the temperature reaches 800 K, the atomic configuration of a single Ag nanoparticle forms a hemispherical shape, and the adsorption capacity of a single Ag nanoparticle reaches the maximum at 1000 K. At a temperature of 1200 K, the atomic lattice change, sintering neck formation, and melting of two nanoparticles into a single particle occur. The atomic configuration can completely form a single nano-interconnection node. The adsorption capacity with a SiO2 substrate can reach the maximum, higher than the adsorption capacity of a single particle as an interconnection node. In addition, the adsorption energy increases first and then decreases with temperature based on different numbers of Ag nanoparticles and the SiO2 substrate. Therefore, there is an optimal critical temperature to maximize the adsorption energy and to ensure a stable nano-interconnect structure after welding. The above simulation results lay a theoretical foundation for the subsequent realization of laser melting of nanoparticles and nanomaterial brazing.
1 引言
基于纳米材料的新型纳米器件是后摩尔时代电子领域发展的重要方向之一。一维、二维纳米材料作为沟道材料及电极材料,能提高器件的电学、光学性能,进而有利于新一代芯片的研制[1-3]。其中,纳米连接作为一种实现纳米材料之间互连以及纳米材料与电极之间互连的关键技术,不仅决定着器件的性能及可靠性,同时还是一种“自下而上”构建功能性纳米结构的重要手段[4]。目前,利用化学处理、激光辐照、电子束辐照、冷焊等方法,可以实现纳米线之间的直接互连以及纳米线与电极之间的直接互连,得到较好的电学、力学性能[5-7]。另外,通过熔融纳米颗粒、纳米线等钎焊材料,纳米钎焊技术也可实现纳米材料的连接。纳米钎焊与直接互连相比,减少了焊接母材的损伤,同时可以实现不同纳米材料之间的互连,有利于获得具有高机械强度和优异电学性能的连接结构[8-9]。
利用激光技术可以对纳米材料进行直接操作如烧结[10-12],因此,通过激光辐照可以实现纳米颗粒的熔融,并将其应用于纳米材料的钎焊[13-14]。对激光辐照纳米颗粒进行纳米材料焊接的深入研究,有利于实现高性能纳米钎焊及器件研制。同时,通过对激光辐照纳米颗粒的过程进行研究,可以进一步分析焊接过程中纳米颗粒原子构型以及周围热场、电场分布的变化,并探讨不同因素对焊接效果的影响[15-16]。Ren 等[17-18]利用双温方程计算了飞秒激光作用下纳米颗粒的热场和电场分布,并研究了激光作用时间、颗粒大小、颗粒间距等因素对纳米颗粒周围热场及电场的影响。Pan等[19]利用分子动力学计算了激光加热下金纳米颗粒焊接过程中的烧结颈形成过程。Yang等[20-21]计算了不同加热速率下不同尺寸的两个纳米颗粒的原子构型变化。然而,上述所有仿真模型仅仅考虑了纳米颗粒在不同温度下的原子构型演化过程,忽略了焊接能量交换过程中基底材料对焊接质量的影响,缺乏激光辐照下基底材料的纳米颗粒熔化仿真,因此研究结果无法完整表征纳米钎焊过程中纳米颗粒作为可靠互连结点的实际原子构型演化过程。本文针对实际的纳米钎焊过程,仿真分析了激光辐照SiO2基底上Ag纳米颗粒的原子构型变化,并对熔融过程中基底与纳米颗粒之间的吸附能等进行了分析。研究结果为纳米钎焊的实现提供了理论参考。
2 模型建立
基于激光辐照实现纳米颗粒熔融的主要机理是激光辐照纳米颗粒产生的热场对钎料的作用[19-21]。在外加温度场下,通过模拟纳米颗粒的原子演化过程,可对不同激光功率辐照下纳米颗粒的熔化演化过程进行研究[15]。因此,本文通过设置不同的加热条件,模拟激光作用下银纳米颗粒的分子动力学行为, 从而获得不同温度场下纳米颗粒在SiO2基底上的原子构型演化过程。模型建立如下:首先,建立银纳米颗粒模型,以面心立方结构的银晶格为基础,综合考虑计算量及计算结果的准确性,构建了直径为4 nm的银纳米颗粒,单个颗粒共包含1961个银原子,银纳米颗粒的构型如
图 1. SiO2基底上Ag纳米颗粒的原子模型。(a) Ag纳米颗粒;(b) SiO2基底;(c)颗粒与衬底的装配
Fig. 1. Atom models of Ag nanoparticle on SiO2 substrate. (a) Ag nanoparticle; (b) SiO2 substrate; (c) assembly of Ag nanoparticle on SiO2 substrate
基于几何结构优化后的原子构型,进行了不同温度下的分子动力学仿真。分子动力学仿真参数设置如下:由于几何结构系统处于能量最低的平衡状态,默认初始的原子为随机状态,在此状态下原子的初始速度符合初始温度下的Maxwell-Boltzmann分布;将系综设置为NVT系综,NVT系综是温度可控的,默认系统不是孤立系统,可与周围虚拟的热浴进行能量交换,从而能够更好模拟不同外加温度场作为虚拟热浴场对原子构型的影响;为了抑制NVT系综中温度的振荡对原子构型的影响,虚拟热浴温度控制方法采用Nose-Hoover 恒温器对热浴温度和热浴时间进行设置,步长为2 fs,仿真时间为40 ps,以保证充分的能量交换;边界条件为非周期性边界,由于银纳米颗粒与无定型SiO2基底的相互作用只发生在表面,因此在仿真中仅选取无定型SiO2基底底部的三层原子,对其在三个方向上施加完全约束。在上述分子束模拟条件下,对原子构型和能量变化进行提取与分析。
3 分析与讨论
3.1 激光辐照下单个银纳米颗粒的仿真分析
图 2. 激光辐照导致的不同温度下单个银纳米颗粒的熔化原子构型变化。(a)400 K;(b)600 K;(c)800 K;(d)1000 K;(e)1200 K;(f)1500 K
Fig. 2. Snapshots for atomic melting configuration of single laser-irradiated Ag nanoparticle at different temperatures.(a) 400 K; (b) 600 K; (c) 800 K; (d) 1000 K; (e) 1200 K; (f) 1500 K
为了更加深入地分析温度对其原子构型的影响,对不同温度下银纳米颗粒与基底的接触长度和接触角度进行了分析。
图 3. 不同温度下Ag纳米颗粒与SiO2之间接触参数和吸附能的变化。(a)接触长度与接触角;(b)吸附能
Fig. 3. Contact parameters and adhesion energies between Ag nanoparticle and SiO2 substrate at different temperatures. (a) Contact length and contact angle; (b) adhesion energy
为了研究激光辐照纳米颗粒时银颗粒与基底的相互作用,进一步对银纳米颗粒与无定型SiO2基底之间的吸附能进行计算:
式中:EInteraction为银纳米颗粒与无定型SiO2基底之间的相互作用能; ETotal为银纳米颗粒与无定型SiO2基底的总能量;EAg为银纳米颗粒的能量;
由于原子构型的能量为单点能量,因此在计算原子能量的过程中,需要将所有的约束条件去除。另外,EInteraction是有正负性的,该参量为正值时表示相互作用能为排斥能,为负值时表示相互作用能为吸附能,而EInteraction的大小表征能量的强弱。在本文中,银纳米颗粒与SiO2基底之间的作用能计算值都为负值,表明它们之间的相互作用是一种相互吸附的作用。为了对其进行比较,后续均采用其绝对值进行分析。单个银纳米颗粒与无定型SiO2基底之间的吸附能随温度的变化曲线如
3.2 激光辐照下多个银纳米颗粒的仿真分析
多个纳米颗粒在不同温度下与基底相互作用的情况则有所不同。纳米颗粒具有极高的表面能,因此在高温下纳米颗粒之间首先出现互熔的现象。首先研究了加热温度为1200 K时不同时刻的两个4 nm银纳米颗粒在无定型SiO2基底上原子构型的变化,如
图 4. 不同激光加热时间下两个Ag纳米颗粒的熔化原子构型。(a)0;(b)0.6 ps;(c)2 ps;(d)4 ps;(e)6 ps;(f)8 ps;(g)10 ps;(h)12 ps;(i)18 ps;(j)30 ps;(k)34 ps;(l)40 ps
Fig. 4. Snapshots for atomic melting configuration of two Ag nanoparticles under different laser heating time. (a) 0;(b) 0.6 ps; (c) 2 ps; (d) 4 ps; (e) 6 ps; (f) 8 ps; (g) 10 ps; (h) 12 ps; (i) 18 ps; (j) 30 ps; (k) 34 ps; (l) 40 ps
图 5. 激光加热过程中两个Ag纳米颗粒的非键能
Fig. 5. Non-bond energy of two Ag nanoparticles during laser heating
在分析了基底上多个纳米颗粒的原子构型随时间的变化之后,获得了两个银纳米颗粒在不同温度下弛豫之后的原子构型图,如
图 6. 激光辐照导致的不同温度下两个银纳米颗粒的熔化原子构型变化。(a)400 K;(b)600 K;(c)800 K;(d)1000 K;(e)1200 K;(f)1500 K
Fig. 6. Snapshots for atomic melting configuration of two laser-irradiated Ag nanoparticles at different temperatures. (a) 400 K; (b) 600 K; (c) 800 K; (d) 1000 K; (e) 1200 K; (f) 1500 K
基于上述获得的不同温度下弛豫的原子构型,进行了银纳米颗粒与基底之间的吸附能计算。
图 7. 不同温度下两个Ag纳米颗粒与SiO2之间的吸附能
Fig. 7. Adhesion energies between two Ag nanoparticles and SiO2 substrate at different temperatures
4 结论
基于分子动力学方法,探讨了SiO2基底上直径为4 nm的纳米颗粒在不同温度下的原子构型演化过程,模拟了钎焊过程中激光辐照颗粒导致的纳米颗粒熔融过程。当温度达到800 K时,单个Ag纳米颗粒的原子构型为半球形,在1000 K温度下,单个Ag纳米颗粒的吸附能达到最大;当温度为1200 K时,两个纳米颗粒出现原子晶格变化,并形成烧结颈,进而熔融为单个颗粒,可完全形成单个纳米互连结点,且此时与SiO2基底的吸附能达到最大,高于单个颗粒作为互连结点的吸附能。另外,不同个数的Ag纳米颗粒与SiO2基底之间的吸附能随着温度的升高都出现先升高后降低的现象,因此存在最佳的临界温度,在该温度下吸附能达到最大,焊接后可获得稳定的纳米互连结构。上述仿真结果为后续基于激光熔融纳米颗粒实现纳米材料钎焊提供了参考。
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