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光载流子辐射技术已广泛应用于半导体材料性能的表征, 本文基于一种包含光子重吸收效应的光载流子辐射理论模型, 对单晶硅中光子重吸收效应对光载流子辐射信号的影响进行了详细的理论分析. 分析结果表明, 光子重吸收效应对光载流子辐射信号的影响主要取决于样品掺杂浓度、过剩载流子浓度和过剩载流子的分布. 由于过剩载流子浓度及其分布与材料电子输运特性密切相关, 电子输运参数的变化将导致光子重吸收效应的影响随之变化. 进一步分析了光子重吸收效应对具有不同电子输运特性的样品的电子输运参数的影响, 并提出了减小光子重吸收效应影响的方法.In microelectronic and photovoltaic industry, semiconductors are the base materials in which impurities or defects have a serious influence on the properties of semiconductor-based devices. The determination of the electronic transport properties, i.e., the carrier bulk lifetime (
$\tau $ ), diffusion coefficient (D) and front surface recombination velocity (S1), is important in the evaluation of semiconductor materials. In this paper, the influence of reabsorption of spontaneously emitted photons within silicon wafers on conventional frequency domain photocarrier radiometric (PCR) is theoretically analyzed. The model with photon reabsorption, proposed by our previous paper, in which both band-to-band absorption and free carrier absorption are taken into account, is used. It is shown that the influence strongly depends on not only the doping level, but also the excess carrier density and its distribution, which are sensitive to the electronic transport properties. The influences of photon reabsorption on PCR amplitude and phase increase with doping level and carrier lifetime increasing. While, as the diffusion coefficient and the front surface recombination velocity increase, the influence of photon reabsorption on PCR amplitude decreases but on PCR phase increases. If photon reabsorption is ignored in the determination of the electronic transport parameters for high-doping silicon wafers via multi-parameter fitting, there are large errors for the fitted results. For a sample with$\tau $ = 50 μs, D = 20 cm2/s, and S1 = 10 m/s, if the effect of photon reabsorption is ignored, the fitting results with conventional PCR model are 55.66 μs, 19.98 cm2/s, and 11.94 m/s, and the corresponding deviations from the true value are 11.33%, 0.10%, and 19.40%, respectively. In addition, simulation results show the effect of photon reabsorption can be greatly reduced with a suitable filter in front of the detector, while still enabling the majority of the emitted signal to be captured. For example, with a 1100 nm long-pass filter, the fitted results for the same sample above are 51.43 μs, 20.19 cm2/s, and 9.88 m/s with the relative errors of 2.86%, 0.95%, and 1.23%, respectively. It should be pointed out that an infinitely steep cut-on edge of the long-pass filter is assumed in our simulations, while in fact the influences of the filter on PCR signal and the fitted results should be further considered.-
Keywords:
- photocarrier radiometric /
- photon reabsorption /
- electronic transport parameters /
- free carrier absorption /
- silicon wafers
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图 2 单晶硅样品的带间吸收系数和自由载流子吸收系数及仿真的未考虑PR效应的PL谱
Fig. 2. Absorption coefficients
${\rm{\alpha }}$ BB and${\rm{\alpha }}$ FCA for a silicon wafer and a simulated PL without PR.
图 4 重吸收对PL谱的影响 (a)振幅; (b)相位
Fig. 4. Influence of PR on PL spectrum: (a) Amplitude; (b) phase.
图 3 PR对PCR信号的影响 (a)振幅; (b)相位; (c)相对误差
Fig. 3. Influence of PR on PCR signal: (a) Amplitude; (b) phase; (c) relative error.
图 5 r = 0 μm时 (a) 过剩载流子浓度纵向分布; (b)平均深度与调制频率的关系
Fig. 5. (a) Vertical excess carrier density distribution and (b) mean depth as a function of the modulation frequency at r = 0 μm.
图 6 载流子寿命变化时, PR效应对PCR信号的影响
Fig. 6. Influence of PR on PCR signal for silicon wafers with different carrier lifetimes.
图 7 载流子扩散系数变化时, PR效应对PCR信号的影响
Fig. 7. Influence of PR on PCR signal for silicon wafers with different diffusion coefficients.
图 8 前表面复合速率变化时, PR效应对PCR信号的影响
Fig. 8. Influence of PR on PCR signal for silicon wafers with different front surface recombination velocities.
图 9 掺杂浓度变化时, PR效应对PCR信号的影响
Fig. 9. Influence of PR on PCR signal for silicon wafers with different doping densities.
图 10 p型单晶硅中PR对拟合的电子输运参数的影响 (a)
$\tau $ ; (b) D; (c) S1Fig. 10. Influence of PR on the fitted electronic transport parameters for p-type silicon wafers: (a)
$\tau $ ; (b) D; (c) S1.
图 11 n型单晶硅中PR对拟合的电子输运参数的影响 (a)
$\tau $ ; (b) D; (c) S1Fig. 11. Influence of PR on the fitted electronic transport parameters for n-type silicon wafers: (a)
$\tau $ ; (b) D; (c) S1.
图 12 加入滤光片前后PR对PCR信号的影响
Fig. 12. Influence of PR on PCR signal with and without the filter.
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[1] Schroder D K 2006 Semiconductor Material and Device Characterization Third Edition (New York: Wiley) pp 389-390
[2] Drummond P J, Bhatia D, Kshirsagar A, Ramani S, Ruzyllo J 2011 Thin Solid Films 519 7621
Google Scholar
[3] Guidotti D, Batchelder J S, Finkel A, Gerber P D 1989 J. Appl. Phys. 66 2542
Google Scholar
[4] Wang K, Kampwerth H 2014 J. Appl. Phys. 115 173103
Google Scholar
[5] Ikari T, Salnick A, Mandelis A 1999 J. Appl. Phys. 85 7392
Google Scholar
[6] Cheng J, Zhang S 1991 J. Appl. Phys. 70 6999
Google Scholar
[7] Zhang X, Li B, Gao C 2006 Appl. Phys. Lett. 89 112120
Google Scholar
[8] 王谦, 刘卫国, 巩蕾, 王利国, 李亚清 2018 67 217201
Google Scholar
Wang Q, Liu W G, Gong L, Wang L G, Li Y Q 2018 Acta Phys. Sin. 67 217201
Google Scholar
[9] Mandelis A, Batista J, Shaughnessy D 2003 Phys. Rev. B 67 205208
Google Scholar
[10] Li B C, Shaughnessy D, Mandelis A 2005 J. Appl. Phys. 97 023701
Google Scholar
[11] Sun Q M, Melnikov A, Mandelis A, Pagliar R H 2018 Appl. Phys. Lett. 112 012105
Google Scholar
[12] 刘俊岩, 宋鹏, 秦雷, 王飞, 王扬 2015 64 087804
Liu J Y, Song P, Qin L, Wang F, Wang Y 2015 Acta Phys. Sin. 64 087804
[13] Wang Q, Li B C 2015 J. Appl.Phys. 118 215707
Google Scholar
[14] Li B C, Shaughnessy D, Mandelis A, Batista J 2004 J. Appl. Phys. 95 7832
Google Scholar
[15] Wang Q, Li B C, Ren S D, Wang Q 2015 Int. J. Thermophys. 36 1173
Google Scholar
[16] Tai R, Wang C, Hu J, Mandelis A 2014 J. Appl. Phys. 116 033706
Google Scholar
[17] Melnikov A, Mandelis A, Tolev J, Chen P, Huq S 2010 J. Appl. Phys. 107 114513
Google Scholar
[18] Liu J Y, Song P, Wang F, Wang Y 2015 Chin. Phys. B 24 97801
Google Scholar
[19] Liu J Y, Mandelis A 2010 J. Phys. Conf. Ser. 214 012107
Google Scholar
[20] Wang J, Mandelis A, Melnikov A, Hoogland S, Sargent E H 2013 J. Phys. Chem. C 117 23333
Google Scholar
[21] Hu, L L, Liu M X, Mandelis A, Sun Q M, Melnikov A, Sargent E H 2018 Sol. Energy Mater. Sol. Cells 174 405
Google Scholar
[22] Trupke T 2006 J. Appl. Phys. 100 063531
Google Scholar
[23] Schinke C, Hinken D, Schmidt J, Bothe K, Brendel R 2013 IEEE J. Photovoltaics 3 1038
Google Scholar
[24] Nguyen H T, Rougieux F E, Baker-Finch S C, Macdonald D 2015 IEEE J. Photovoltaics 5 77
Google Scholar
[25] Diab H, Arnold C, Lédée F, Trippé-Allard G, Delport G, Vilar C, Bretenaker F, Barjon J, Lauret J, Deleporte E, Garrot D 2017 J. Phys. Chem. Lett. 8 2977
Google Scholar
[26] Giesecke J A, Kasemann M, Schubert M C, Würfel P, Warta W 2010 Prog. Photovoltaics Res. Appl. 18 10
Google Scholar
[27] Mitchell B, Trupke T, Weber J W, Nyhus J 2011 J. Appl. Phys. 109 083111
Google Scholar
[28] Pazos-Outón L M, Szumilo M, Lamboll R, Richter J M, Crespo-Quesada M, Abdi-Jalebi M, Beeson H J, Vrućinić M, Alsari M, Snaith H J, Ehrler B, Friend R H, Deschler F 2016 Science 351 1430
Google Scholar
[29] Xu Y, Tennyson E M, Kim J, Barik S, Murray J, Waks E, Leite M S, Munday J N 2018 Adv. Optical Mater. 6 1701323
Google Scholar
[30] Wang Q, Liu W G 2017 J. Appl. Phys. 122 165702
Google Scholar
[31] Zhang X R, Li B C, Liu X M 2008 J. Appl. Phys. 104 103705
Google Scholar
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