Theoretical study on influence of photon reabsorption on photocarrier radiometric characteristics of silicon wafers

Wang Qian; Liu Wei-Guo; Gong Lei; Wang Li-Guo; Li Ya-Qing; Liu Rong

doi:10.7498/aps.68.20181889

Abstract

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:

Authors and contacts

School of Optoelectronic Engineering, Xi'an Technological University, Xi'an 710021, China

Corresponding author: Wang Qian, qian_wang521@163.com

Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 61704132, 61501363), Xi'an Intelligent Visiting Perception Key Laboratory Project (Grant No. 201805061ZD12CG45), and Principal Fund from Xi'an Technological University (Grant Nos. XAGDXJJ16007, XAGDXJJ18001).

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References

[1]	Schroder D K 2006 Semiconductor Material and Device Characterization Third Edition (New York: Wiley) pp 389-390
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Cited By

图 1 PCR技术原理示意图

Figure 1. Schematic diagram of PCR technique.

DownLoad: Full-Size Img PowerPoint

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

Figure 2. Absorption coefficients ${\rm{\alpha }}$_BB and ${\rm{\alpha }}$_FCA for a silicon wafer and a simulated PL without PR.

DownLoad: Full-Size Img PowerPoint

图 4 重吸收对PL谱的影响　(a)振幅; (b)相位

Figure 4. Influence of PR on PL spectrum: (a) Amplitude; (b) phase.

DownLoad: Full-Size Img PowerPoint

图 3 PR对PCR信号的影响　(a)振幅; (b)相位; (c)相对误差

Figure 3. Influence of PR on PCR signal: (a) Amplitude; (b) phase; (c) relative error.

DownLoad: Full-Size Img PowerPoint

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

Figure 5. (a) Vertical excess carrier density distribution and (b) mean depth as a function of the modulation frequency at r = 0 μm.

DownLoad: Full-Size Img PowerPoint

图 6 载流子寿命变化时, PR效应对PCR信号的影响

Figure 6. Influence of PR on PCR signal for silicon wafers with different carrier lifetimes.

DownLoad: Full-Size Img PowerPoint

图 7 载流子扩散系数变化时, PR效应对PCR信号的影响

Figure 7. Influence of PR on PCR signal for silicon wafers with different diffusion coefficients.

DownLoad: Full-Size Img PowerPoint

图 8 前表面复合速率变化时, PR效应对PCR信号的影响

Figure 8. Influence of PR on PCR signal for silicon wafers with different front surface recombination velocities.

DownLoad: Full-Size Img PowerPoint

图 9 掺杂浓度变化时, PR效应对PCR信号的影响

Figure 9. Influence of PR on PCR signal for silicon wafers with different doping densities.

DownLoad: Full-Size Img PowerPoint

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) S₁

Figure 10. Influence of PR on the fitted electronic transport parameters for p-type silicon wafers: (a) $\tau $; (b) D; (c) S₁.

DownLoad: Full-Size Img PowerPoint

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) S₁

Figure 11. Influence of PR on the fitted electronic transport parameters for n-type silicon wafers: (a) $\tau $; (b) D; (c) S₁.

DownLoad: Full-Size Img PowerPoint

图 12 加入滤光片前后PR对PCR信号的影响

Figure 12. Influence of PR on PCR signal with and without the filter.

DownLoad: Full-Size Img PowerPoint

[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 物理学报 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 物理学报 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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Vol. 68, Issue 4 - 2019-02-20

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