Effect of recombination process in femtosecond laser-induced modification on Ge crystal

doi:10.1088/1674-1056/abbbe9

Abstract

The dynamics of produced excited carriers under the irradiation of Ge crystal is investigated theoretically by using femtosecond laser pulse. A two-temperature model combined with the Drude model is also used to study the nonequilibrium carrier density, carrier and lattice temperatures, and optical properties of the crystal. The properties of the surface plasmon wave when excited are also studied. The influences of non-radiation and radiative recombination process on the photoexcitation of the semiconductor during pulse and the relaxation after the pulse are described in detail. The results show that the effects of Auger recombination on the nonequilibrium carrier density and optical properties of the crystal and the properties of the surface plasmon polariton are great, whereas the effect of radiative recombination is extremely small.

Keywords: two-temperature model Ge crystal Auger recombination radiative recombination surface plasmon polariton

Received: 11 June 2020
Revised: 31 July 2020
Accepted manuscript online: 28 September 2020

Fund: the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11804227).

Corresponding Authors: ^†Corresponding author. E-mail: liujukun@126.com

Cite this article:

Jia-Qi Ju(居家奇), Zi-Yao Qin(秦子尧), Ju-Kun Liu(刘聚坤), Hong-Wei Zhao(赵宏伟), Yao-Qing Huang(黄耀清), Rong-Rong Hu(胡蓉蓉), and Hua Wu(吴华)$ Effect of recombination process in femtosecond laser-induced modification on Ge crystal 2020 Chin. Phys. B 29 114208

Table 1.

Parameters of Ge crystal at 800-nm light.

Fig. 1.

Time-dependent dynamic behaviors of (a) carrier density and (b) carrier temperature on surface of Ge sample irradiated by 50-fs laser pulse of F = 0.1 J/cm² for different situations with I_p representing laser pulse.

Fig. 2.

Evolutions of (a) lattice temperature, (b) real part, and (c) imaginary part of dielectric constant, and (d) reflectivity on Ge surface, with black dash line in panel (a) denoting melting temperature.

Fig. 3.

Laser fluence-dependent (a) maximum carrier density, (b) carrier temperature, and (c) lattice temperature on surface of a 100-nm-thick Ge sample heated by 50-fs laser pulse for γ_R = 0, and γ_A and γ_R ≠ 0.

Fig. 4.

Calculated time evolutions of (a) surface electron and (b) lattice temperature for different electron–phonon relaxation times, with black dash line in panel (b) representing melting temperature.

Fig. 5.

Calculated relationship between (a) carrier density and real part of dielectric constant, and time evolutions of (b) imaginary part and (c) real part, with a denoting Drude model, and b referring to Drude model with the effect of state renormalization and band filling and band gap renormalization considered.

Fig. 6.

SP wavelength versus (a) carrier density and (b) laser fluence.

Fig. 7.

SP propagation length (a) parallel and (b) perpendicular to surface versus laser fluence.

[1]	Garcial-Lechuga M, Puerto D, Fuentes-Edfuf Y, Solis J, Siegel J 2016 ACS. Photon. 3 1961 DOI: 10.1021/acsphotonics.6b00514
[2]	Murphy R D, Torralva B, Adams D P, Yalisove S M 2013 Appl. Phys. Lett. 103 141104 DOI: 10.1063/1.4823588
[3]	Kafka K R P, Austin D R, Li H, Yi A Y, Cheng J, Chowdhury E A 2015 Opt. Express 23 19432 DOI: 10.1364/OE.23.019432
[4]	Jia X, Yuan Y, Yang D, Jia T, Sun Z 2014 Chin. Opt. Lett. 12 113203 DOI: 10.3788/COL
[5]	Jia X, Jia T Q, Peng N, Feng D H, Zhang S A, Sun Z R 2014 J. Appl. Phys. 115 143102 DOI: 10.1063/1.4870445
[6]	Cheng K, Liu J, Cao K, Chen L, Zhang Y, Jiang Q, Feng D, Zhang S, Sun Z, Jia T 2018 Phys. Rev. B 9 184106 DOI: 10.1103/PhysRevB.98.184106
[7]	Liu J, Jia X, Wu W, Cheng K, Feng D, Zhang S, Sun Z, Jia T 2018 Opt. Express 26 6302 DOI: 10.1364/OE.26.006302
[8]	Yang M, Wu Q, Chen Z, Zhang B, Tang B, Yao J, Drevensek-Olenik I, Xu J 2014 Opt. Lett. 39 343 DOI: 10.1364/OL.39.000343
[9]	Liu J, Zhao H, Cheng K, Ju J, Feng D, Zhang S, Sun Z, Jia T 2019 Opt. Express 27 37859 DOI: 10.1364/OE.27.037859
[10]	Margiolakis A, Tsibidis G D, Dani K M, Tsironis G P 2018 Phys. Rev. B 98 224103 DOI: 10.1103/PhysRevB.98.224103
[11]	Petrakakis E, Tsibidis G D, Stratakis E 2019 Phys. Rev. B 99 195201 DOI: 10.1103/PhysRevB.99.195201
[12]	Polman A, Knight M W, Garnett E C, Ehrler B, Sinke W C 2016 Science 352 4424 https://science.sciencemag.org/content/352/6283/aad4424
[13]	Luo D, Su R, Zhang W, Gong Q, Zhu R 2020 Nat. Rev. Mater. 5 44 DOI: 10.1038/s41578-019-0151-y
[14]	Seo D, Gregory J M, Feldman L C, Tolk N H, Cohen P I 2011 Phys. Rev. B 83 195203 DOI: 10.1103/PhysRevB.83.195203
[15]	Zhu J, Zhu H, Xu H, Weng Z, Wu H 2018 Infrared Physics & Technology 92 13 https://www.sciencedirect.com/science/article/abs/pii/S135044951830015X
[16]	Cavalleri A, Siders C W, Rose-Petruck C, Jimenez R, Tóth C, Squier J A, Barty C P J, Wilson K R, Sokolowski-Tinten K, Horn von Hoegen M, von der Linde D 2001 Phys. Rev. B 63 193306 DOI: 10.1103/PhysRevB.63.193306
[17]	Fu J, Xu Q, Han G, Wu B, Sum T C 2018 Nat. Commun. 8 1300 https://www.nature.com/articles/s41467-017-01360-3#citeas
[18]	Sundaram S K, Mazur E 2002 Nat. Mater. 1 217 DOI: 10.1038/nmat767
[19]	Agassi D 1984 J. Appl. Phys. 55 4376 DOI: 10.1063/1.333007
[20]	Zollner S, Myers K D, Dolan J M, Bailey D W, Stanton C J 1998 Thin Solid Films 313 568 https://www.sciencedirect.com/science/article/abs/pii/S0040609097008869
[21]	Prince M B 1953 Phys. Rev. 92 681 DOI: 10.1103/PhysRev.92.681
[22]	Jiang L, Tsai H L 2005 Journal of Heat Transfer 127 1167 DOI: 10.1115/1.2035113
[23]	Liu J, Jia T, Zhao H, Huang Y 2016 J Phys. D: Appl. Phys. 49 435105 DOI: 10.1088/0022-3727/49/43/435105
[24]	Sokolowski-Tinten K, Von d L D 2000 Phys. Rev. B 61 2643 DOI: 10.1103/PhysRevB.61.2643
[25]	Wang L, Xu B B, Cao X W, Li Q K, Sun H B 2017 Optica 4 637 DOI: 10.1364/OPTICA.4.000637
[26]	Aspnes D E, Studna A A 1983 Phys. Rev. B 27 985 DOI: 10.1103/PhysRevB.27.985
[27]	Tsibidis G D, Barberoglou M, Loukakos P A, Stratakis E, Fotakis C 2012 Phys. Rev. B 86 115316 DOI: 10.1103/PhysRevB.86.115316
[28]	Carroll L, Friedli P, Neuenschwander S, Sigg H, Cecchi S, Isa F, Faist J 2012 Phys. Rev. Lett. 109 057402 DOI: 10.1103/PhysRevLett.109.057402
[29]	Auston D H, Shank C V, LeFur P 1975 Phys. Rev. Lett. 35 1022 DOI: 10.1103/PhysRevLett.35.1022
[30]	Alfano R R 1984 Semiconductors probed by ultrafast laser spectroscopy Academic Press 87
[31]	Yeh T T, Shirai H, Tu C M, Fuji T, Kobayashi T, Luo C W 2017 Sci. Rep. 7 40492 DOI: 10.1038/srep40492
[32]	Chen J K, Tzou D Y, Beraun J E 2005 Int. J. Heat Mass Transfer 48 501 DOI: 10.1016/j.ijheatmasstransfer.2004.09.015
[33]	Hwang T Y, Vorobyev A Y, Guo C 2009 Appl. Phys. Lett. 95 123111 DOI: 10.1063/1.3222937
[34]	Das S K, Messaoudi H, Debroy A, McGlynn E, Grunwald R 2013 Opt. Mater. Express 3 1705 DOI: 10.1364/OME.3.001705
[35]	Huang M, Zhao F, Cheng Y, Xu N, Xu Z 2009 ACS Nano 3 4062 DOI: 10.1021/nn900654v
[36]	Wang Y L, Zhao B, Min C J, Zhang Y Q, Yang J J, Guo C L, Yuan X C 2020 Chin. Phys. B 29 027302 http://cpb.iphy.ac.cn/CN/abstract/abstract75392.shtml
[37]	Raether H 1988 Surface plasmons on smooth and rough surfaces and on gratings Berlin Springer-Verlag 209

[1]	Numerical simulation of the thermal non-equilibrium flow-field characteristics of a hypersonic Apollo-like vehicle Minghao Yu(喻明浩)^†, Zeyang Qiu(邱泽洋), Bo Lv(吕博), and Zhe Wang(王哲). Chin. Phys. B, 2022, 31(9): 094702.
[2]	Improving the performance of a GaAs nanowire photodetector using surface plasmon polaritons Xiaotian Zhu(朱笑天), Bingheng Meng(孟兵恒), Dengkui Wang(王登魁), Xue Chen(陈雪), Lei Liao(廖蕾), Mingming Jiang(姜明明), and Zhipeng Wei(魏志鹏). Chin. Phys. B, 2022, 31(4): 047801.
[3]	Independently tunable dual resonant dip refractive index sensor based on metal—insulator—metal waveguide with Q-shaped resonant cavity Haowen Chen(陈颢文), Yunping Qi(祁云平), Jinghui Ding(丁京徽), Yujiao Yuan(苑玉娇), Zhenting Tian(田振廷), and Xiangxian Wang(王向贤). Chin. Phys. B, 2022, 31(3): 034211.
[4]	Improvement of femtosecond SPPs imaging by two-color laser photoemission electron microscopy Chun-Lai Fu(付春来), Zhen-Long Zhao(赵振龙), Bo-Yu Ji(季博宇), Xiao-Wei Song(宋晓伟), Peng Lang(郎鹏), and Jing-Quan Lin(林景全). Chin. Phys. B, 2022, 31(10): 107103.
[5]	Two-color laser PEEM imaging of horizontal and vertical components of femtosecond surface plasmon polaritons Zhen-Long Zhao(赵振龙), Bo-Yu Ji(季博宇), Lun Wang(王伦), Peng Lang(郎鹏), Xiao-Wei Song(宋晓伟), and Jing-Quan Lin(林景全). Chin. Phys. B, 2022, 31(10): 107104.
[6]	Single-beam leaky-wave antenna with wide scanning angle and high scanning rate based on spoof surface plasmon polariton Huan Jiang(蒋欢), Xiang-Yu Cao(曹祥玉), Tao Liu(刘涛), Liaori Jidi(吉地辽日), and Sijia Li(李思佳). Chin. Phys. B, 2022, 31(10): 104101.
[7]	Mode splitting and multiple-wavelength managements of surface plasmon polaritons in coupled cavities Ping-Bo Fu(符平波) and Yue-Gang Chen(陈跃刚). Chin. Phys. B, 2022, 31(1): 014216.
[8]	High-confinement ultra-wideband bandpass filter using compact folded slotline spoof surface plasmon polaritons Xue-Wei Zhang(张雪伟), Shao-Bin Liu(刘少斌), Ling-Ling Wang(王玲玲), Qi-Ming Yu (余奇明), Jian-Lou(娄健), and Shi-Ning Sun(孙世宁). Chin. Phys. B, 2022, 31(1): 014102.
[9]	Surface plasmon polaritons frequency-blue shift in low confinement factor excitation region Ling-Xi Hu(胡灵犀), Zhi-Qiang He(何志强), Min Hu(胡旻), and Sheng-Gang Liu(刘盛纲). Chin. Phys. B, 2021, 30(8): 084102.
[10]	Bound states in the continuum on perfect conducting reflection gratings Jianfeng Huang(黄剑峰), Qianju Song(宋前举), Peng Hu(胡鹏), Hong Xiang(向红), and Dezhuan Han(韩德专). Chin. Phys. B, 2021, 30(8): 084211.
[11]	High sensitive chiral molecule detector based on the amplified lateral shift in Kretschmann configuration involving chiral TDBCs Song Wang(王松), Qihui Ye(叶起惠), Xudong Chen(陈绪栋), Yanzhu Hu(胡燕祝), and Gang Song(宋钢). Chin. Phys. B, 2021, 30(6): 067301.
[12]	Super-resolution imaging of low-contrast periodic nanoparticle arrays by microsphere-assisted microscopy Qin-Fang Shi(石勤芳), Song-Lin Yang(杨松林), Yu-Rong Cao(曹玉蓉), Xiao-Qing Wang(王晓晴), Tao Chen(陈涛), and Yong-Hong Ye(叶永红). Chin. Phys. B, 2021, 30(4): 040702.
[13]	Design and verification of a broadband highly-efficient plasmonic circulator Jianfei Han(韩建飞), Shu Zhen(甄姝), Weihua Wang(王伟华), Kui Han(韩奎), Haipeng Li(李海鹏), Lei Zhao(赵雷), and Xiaopeng Shen(沈晓鹏). Chin. Phys. B, 2021, 30(3): 034102.
[14]	Plasmonic characteristics of suspended graphene-coated wedge porous silicon nanowires with Ag partition Xu Wang(王旭), Jue Wang(王珏), Tao Ma(马涛), Heng Liu(刘恒), and Fang Wang(王芳). Chin. Phys. B, 2021, 30(1): 014207.
[15]	Spoof surface plasmon polaritons excited leaky-wave antenna with continuous scanning range from endfire to forward Tao Zhong(钟涛), Hou Zhang(张厚). Chin. Phys. B, 2020, 29(9): 094101.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Effect of recombination process in femtosecond laser-induced modification on Ge crystal

Cite this article:

Online attention