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激光熔覆过程十分复杂,先后涉及到的物理过程有热传导、对流、辐射、熔化凝固等,在仿真中考虑其全部物理过程是不切实际的。因此,在保证仿真精度及降低计算难度的前提下,对研究问题作出了以下几点假设:(1)经典传热理论依然适用于此仿真模型;(2)仿真过程中不考虑瞬间的熔池内部流动对温度场的影响;(3)考虑仿真过程中的熔化潜热与对温度场的影响。
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如图1所示,考虑到激光辐照范围和计算量的情况,同时兼顾验证试验的准确性,设定基体模型长、宽、高尺寸为80 μm×60 μm×30 μm,基体上方覆盖一层厚度为2 μm的硼掺杂纳米硅薄膜,仿真主要比较单脉冲及多脉冲激光辐照后硅薄膜及基体表面温度场分布状况,激光熔池的尺寸以及热影响区的范围大小。同时,根据仿真结果,分析利于硼元素在硅中扩散的激光参数条件。考虑到计算量,在关键区域采取加密网格的方式提高运算精度,保证仿真结果更具有针对性。文中仿真主要验证激光熔覆过程中的热作用与硼元素扩散间的相互关系,故在硅基体与硅薄膜接触面区域及硅薄膜区域进行网格加密,重点探讨这两个区域受激光辐照的情况。
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激光束在激光加工过程中进行快速移动,所以激光热源可以视为不均匀的面热源。同时因为处于激光光斑中心点的温度最高,距离中心点越远的区域温度越低,因此采用高斯分布特征的不均匀面热源模型,以满足对热源能量分布特征的要求。热流密度公式为[7]:
$$ I=\frac{4P\omega \left(t\right)(1-R\left(T\right))}{\pi {r}_{b}^{2}ftr}{{\rm{exp}}}\left(-\frac{2{r}^{2}}{{r}_{b}^{2}}\right) $$ (1) 式中:
$ P $ 为激光功率;$ \omega \left(t\right) $ 为激光脉冲作用时间函数;$ R\left(T\right) $ 为材料随温度变化的反射率;$ r $ 为基体上任意一点到光斑中心的距离;$ {r}_{b} $ 为激光光斑半径;$ f $ 为激光重复频率;$ tr $ 为激光脉宽。 -
多脉冲激光熔覆纳米硅薄膜的三维热传导方程[6]为:
$$ {\;\rho C\dfrac{\partial T^{'}}{\partial t}=\dfrac{\partial }{\partial x}\left(k\dfrac{\partial T^{'}}{\partial x}\right)+\dfrac{\partial T^{'} }{\partial y}\left(k\dfrac{\partial T^{'}}{\partial T^{'} y}\right)+\dfrac{\partial }{\partial {\textit{z}}}\left(k\dfrac{\partial T^{'}}{\partial {\textit{z}}}\right)+Q\left(x,y,{\textit{z}},t\right)} $$ (2) 式中:
$\; \rho $ 为材料的密度;$ C $ 为材料的比热容;$T ^{'}$ 为温度场随时间变化的分布函数;$ k $ 为材料的热导率;$ t $ 为传热时间;$ Q $ 为内热源。 -
数值模拟过程中的初始条件即初始温度,设定初始工作温度为周围环境温度,即:
$$ T{|}_{t={t}_{0}}={T}_{0} = 293\;{\rm{K}} $$ (3) 在激光辐照材料前,硅薄膜与基体之间存在对流换热,激光能量加载后转变为热传导传热为主,同时材料与周围环境之间还存在辐射换热,因此随着时间的增加,边界条件的选择也随之变化。文中将边界条件分为两类:
(1)热流密度边界条件:即正处于激光辐照的区域所受到的边界条件,即[15]:
$$ -k\frac{\partial T}{\partial n}=q(x,y,{\textit{z}},t) $$ (4) 式中:
$ q(x,y,{\textit{z}},t) $ 为单位面积上的热流函数。(2)热交换边界条件:即被激光辐照后的区域以及尚未被激光辐照的其他区域,在实际应用中对流换热和辐射换热通常是同时存在的,因此方程为[16]:
$$ -k\frac{\partial T}{\partial n}={h}_{c}(T-{T}_{0})+\sigma \varepsilon ({T}^{4}-{{T}_{0}}^{4}) $$ (5) 式中:
$ {h}_{c} $ 为对流换热系数,约为$ 10\;{\rm{W}}\cdot {\rm{m}}^{-2}\cdot {{\rm{K}}}^{-1} $ ;$ T $ 为材料表面温度;$ {T}_{0} $ 为初始温度(环境温度);$ \sigma $ 为Stefan-Boltzmann常数,约为$ 5.67\times $ $ 1{0}^{-4}\;{\rm{W}}\cdot {\rm{c}}{\rm{m}}^{-2}\cdot {{\rm{K}}}^{-4} $ ;$ \varepsilon $ 为材料辐射率。在实际的激光加工过程中,正在被激光辐照区域主要处于“吸能”状态,对流和辐射换热很少,因此此时采用第一种热流密度边界条件;对于尚未被激光辐照的区域以及激光辐照后的区域均(对称面除外,其为绝热边界条件)存在与周围环境的对流和辐射换热,因此采用第二种热交换边界条件。
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材料由两个部分组成,分别是硅基体和硼掺杂纳米硅薄膜层。其中基体材料为P型单晶硅片(电阻率为1~3
$ {\Omega } \cdot {\rm{c}}{\rm{m}} $ ),硼掺杂纳米硅薄膜层为硼掺杂纳米硅浆料经丝网印刷至硅基体上,烘干后获得纳米硅薄膜,厚度为2 μm左右。根据相关研究,由于纳米材料特性,在仿真分析中假设硅薄膜的热导率为单晶硅材料的70%。激光熔覆是非线性瞬态热传导过程,材料的温度快速上升后急剧下降,其温度上升的时间尺度为纳秒量级。仿真中考虑材料的主要物理参数是常数,不随温度变化,具体参数如表1所示。
表 1 基体材料的热物性参数
Table 1. Thermal physical parameters of matrix materials
Material properties Solid state Liquid state Thermal conductivity[17]k/W·m−1·K−1 150 125 Specific heat capacity[17]$ {C}_{p}/ $J·kg−1·K−1 700 1000 Density[18]$ \rho / $kg·m−3 2329 2520 Melting point $ {T}_{m}/ $K 1685 Boiling point $ {T}_{v}/ $K 3538 Reflectivity $ R $ ($ {\lambda } $ = 532 nm)[19] 0.374 0.73 Latent heat of fusion $ H\_s/ $kJ·kg−1 1415.4
Numerical simulation and experimental study of multi-pulse laser cladding of B doped Si nano-film
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摘要: 为研究多脉冲激光的热累积效应对硼掺杂纳米硅薄膜熔覆过程的影响,采用单温模型,利用三维有限元方法对激光与硅薄膜的相互作用过程中温度场的分布进行了数值模拟,得到了多脉冲激光耦合情况下的温度场变化规律。仿真结果表明:与单脉冲相比,在多脉冲激光作用下,峰值温度增加了3.2%,熔池尺寸扩大了18.75%,同时热影响区范围也明显增加;激光辐照后,熔覆层表面温度下降,但基体温度仍会继续上升,多脉冲热累积效应为纳米硅薄膜中硼元素扩散提供了有利条件。最后,通过单脉冲及多脉冲激光熔覆实验,分析了熔覆硅薄膜后的熔覆层表面状况的差异,并获得了激光熔覆辅助硼元素扩散的一般规律,为硼掺杂纳米硅薄膜的激光辅助扩散技术在半导体器件中的应用提供了条件。Abstract: In order to study the influence of the thermal accumulation effect of the multi-pulse nanosecond laser on the cladding process of the boron(B) doped silicon(Si) nano-film, the single-temperature model and the three-dimensional finite element method were used to numerically analyze the distribution of temperature field during the interaction process between the laser and the Si film, then the law of temperature field change under multi-pulse coupling was obtained. Compared with a single pulse, the simulation results of the multi-pulse laser action shows that the peak temperature has increased 3.2%, the size of the molten pool has enlarged 18.75%, and the range of the heat-affected zone has also significantly increased; after the laser irradiation, the surface temperature of the cladding layer drops, while the substrate temperature will continue to rise. The multi-pulse heat accumulation effect provides favorable conditions for the B diffusion in the Si nano-film. Finally, through single-pulse and multi-pulse laser cladding experiments, the different conditions of the cladding layers were analyzed, and the general law of the B diffusion assisted by laser cladding was obtained. The technology of laser-assisted B doped Si nano-film will provide the foundation for the applications in semiconductor devices.
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Key words:
- B doped Si nano-film /
- laser cladding /
- multi-pulse laser /
- temperature field /
- B diffusion
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图 6 不同时刻下的三维温度场分布。(a)
${{t}}=140 \;{\rm{n}}{\rm{s}}$ ; (b)${{t}}=1\;250 \;{\rm{n}}{\rm{s}}$ ; (c)${{t}}=1\;390 \;{\rm{n}}{\rm{s}}$ ; (d)${{t}}=2\;500 \;{\rm{n}}{\rm{s}}$ ; (e)${{t}}=2\;640 \;{\rm{n}}{\rm{s}}$ ; (f)${{t}}=3\;750 \;{\rm{n}}{\rm{s}}$ Figure 6. Three-dimensional temperature field distributions at different moments. (a)
${{t}}=140 \;{\rm{n}}{\rm{s}}$ ; (b)${{t}}=1\;250 \;{\rm{n}}{\rm{s}}$ ; (c)${{t}}=1\;390 \;{\rm{n}}{\rm{s}}$ ; (d)${{t}}=2\;500 \;{\rm{n}}{\rm{s}}$ ; (e)${{t}}=2\;640 \;{\rm{n}}{\rm{s}}$ ; (f)${{t}}=3\;750 \;{\rm{n}}{\rm{s}}$ 图 10 硅薄膜的单脉冲与多脉冲激光熔覆特性比较。(a) 硅薄膜的单脉冲熔覆形貌;(b) 单脉冲熔覆后去除多余硅薄膜;(c) 硅薄膜的多脉冲熔覆形貌;(d) 多脉冲熔覆后去除多余硅薄膜;(e) 单脉冲熔覆后背场形貌;(f)多脉冲熔覆后背场形貌
Figure 10. Cmparison with the characters of single and multi-pulse laser cladding of Si film. (a) Morphology of single pulse cladding of Si film; (b) Morphology of single pulse cladding after remove redundant Si film; (c) Morphology of muti-pulse cladding of Si film; (d) Morphology of muti-pulse cladding after remove redundant Si film; Morphology of back surface field form by (e) single pulse laser cladding and (f) muti-pulse laser cladding
表 1 基体材料的热物性参数
Table 1. Thermal physical parameters of matrix materials
Material properties Solid state Liquid state Thermal conductivity[17]k/W·m−1·K−1 150 125 Specific heat capacity[17] $ {C}_{p}/ $ J·kg−1·K−1700 1000 Density[18] $ \rho / $ kg·m−32329 2520 Melting point $ {T}_{m}/ $ K1685 Boiling point $ {T}_{v}/ $ K3538 Reflectivity $ R $ ($ {\lambda } $ = 532 nm)[19]0.374 0.73 Latent heat of fusion $ H\_s/ $ kJ·kg−11415.4 -
[1] Liu Hongxi, Zhao Yanshuang, Zhang Xiaowei, et al. Microstructure and high-temperature oxidation resistance of laser cladding in-situ synthesis Ti-Al-Si composite coatings [J]. Optics and Precision Engineering, 2019, 27(2): 316-325. (in Chinese) doi: 10.3788/OPE.20192702.0316 [2] Anas Ahmad Siddiqui, Avanish Kumar Dubey. Recent trends in laser cladding and surface alloying [J]. Optics & Laser Technology, 2021, 143: 106619. [3] Som M, Chetan S S. Deep diffusion of phosphorus in silicon using microsecond-pulsed laser doping [J]. Materials Science in Semiconductor Processing, 2017, 59: 10-17. doi: 10.1016/j.mssp.2016.11.011 [4] Lin W J, Chen D M, Chen Y F, et al. Green-laser-doped selective emitters with separate BBr3 diffusion processes for high-efficiency n-type silicon solar cells [J]. Solar Energy Materials and Solar Cells, 2020, 210: 110462. doi: 10.1016/j.solmat.2020.110462 [5] Yang N, Li S, Yuan X, et al. Driving-in effect and gettering degradation induced by laser doping using borosilicate glass as dopant source [J]. Journal of Materials Science: Materials in Electronics, 2019, 30: 6895-6901. doi: 10.1007/s10854-019-01004-w [6] Liu Kui, Liu Yaxin, Niu Junjie, et al. Simulation of temperature field distribution finite element during laser cladding TiCN coatings on titanium alloy [J]. Laser Journal, 2016, 37(8): 27-32. (in Chinese) [7] Xu Long, Hong Juan, Wang Wei. Simulation analysis and experimental study on nanosecond laser cladding silicon nano film [J]. Chinese Journal of Lasers, 2019, 46(4): 0402008. (in Chinese) [8] Cai Zhixiang, Zeng Xiaoyan. Development and applications of laser micro cladding [J]. Chinese Optics, 2010, 3(5): 405-414. (in Chinese) doi: 10.3969/j.issn.2095-1531.2010.05.001 [9] Guo Ming, Zhang Yongxiang, Zhang Wenying, et al. Thermal damage of monocrystalline silicon irradiated by long pulse laser [J]. Infrared and Laser Engineering, 2020, 49(3): 0305002. (in Chinese) doi: 10.3788/IRLA202049.0305002 [10] Zhang Yongbin, Bing Ren, Lang Dingmu. Calculation for nano-second pulsed laser cladding temperature field and analysis of thin film removal mechanism [J]. Applied Laser, 2012, 32(6): 464-468. (in Chinese) doi: 10.3788/AL20123206.464 [11] Yan Xiaodong, Ren Ning, Tang Fuling, et al. Numerical simulation of movable nanosecond pulse laser etching of metal/polyimide [J]. Chinese Journal of Lasers, 2017, 44(4): 0402008. (in Chinese) [12] Wang Zhen, Fu Wenjing, Zhang Rongzhu. Numerical simulation of femtosecond laser multi-pulse ablation of metal iron [J]. Infrared and Laser Engineering, 2019, 48(7): 0706002. (in Chinese) doi: 10.3788/IRLA201948.0706002 [13] Zhang Liang, Ni Xiaowu , Lu Jian, et al. Numerical simulation of vaporization effect of long pulsed laser interaction with silicon [J]. Optics and Precision Engineering, 2011, 19(2): 437-444. (in Chinese) doi: 10.3788/OPE.20111902.0437 [14] Li Zhiming, Nie Jinsong, Hu Yuze, et al. Heat accumulation effects on the ablation of silicon with high frequency femtosecond laser [J]. Laser & Infrared, 2017, 47(4): 410-415. (in Chinese) doi: 10.3969/j.issn.1001-5078.2017.04.004 [15] Zhang Mingxin, Li Zhiming, Nie Jinsong, et al. Heat accumulation effect of multi-pulse femtosecond laser ablation of silicon [J]. Optoelectronic Technology, 2018, 38(4): 224-230. (in Chinese) [16] Bahrami A, Helenbrook B T, Valentine D T, et al. Fluid flow and mixing in linear GTA welding of dissimilar ferrous alloys [J]. International Journal of Heat and Mass Transfer, 2016, 93: 729-741. doi: 10.1016/j.ijheatmasstransfer.2015.10.058 [17] Zhang Kaifeng, Cheng Guanggui, Zhang Zhongqiang, et al. Numerical simulation of solidification process of molten silicon in horizontal tube [J]. Hot Working Technology, 2017, 46(9): 93-96. (in Chinese) [18] Sun Peng, Li Mo, Yang Qingxin, et al. Numerical simulation of the accumulative photo-thermal effect in silicon under illumination with sequential laser pulses [J]. Journal of Terahertz Science and Electronic Information Technology, 2018, 16(1): 158-163. (in Chinese) [19] Shen Zhonghua, Ni Xiaowu, Lu Jian. Theoretical calculation for thermal effect of the semiconductors induced by the laser pulse [J]. Journal of Optoelectronics · Laser, 1998, 9(4): 76-78. (in Chinese) [20] Hong Juan, Xuan Rongwei, Huang Haibin, et al. B-doped nano-Si-Paste by picosecond laser cladding [J]. Chinese Journal of Lasers, 2016, 43(9): 0902006. (in Chinese) doi: 10.3788/CJL201643.0902006