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Optical method for calculating the dopant concentration of doped amorphous semiconductors

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Abstract

An optical method is proposed to calculate the dopant (e.g., boron or phosphorus) concentration in doped amorphous semiconductors. The basic principle of this method is that the effective density of valence electrons and the coordination number of the samples could be obtained by f-sum rule and dispersion energy model, respectively. A computational model is derived from this method and applied to doped amorphous silicon (a-Si:H) films with the results of spectroscopic ellipsometry and Fourier transform infrared spectroscopy measurements. It is found that the predicted concentrations of boron and phosphorus in doped a-Si:H samples are quite consistent with the actual results from secondary ion mass spectroscopy test, for the samples with the dopant content higher than 1021 cm−3.

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Data Availability Statement

Research data will be made available upon request. This manuscript has associated data in a data repository. [Authors’ comment: All data included in this manuscript are available upon request by contacting with the corresponding author.]

References

  1. N.F. Mott, Electrons in disordered structures. Adv. Phys.-X 16(61), 49–144 (1967). https://doi.org/10.1080/00018736700101265

    Article  ADS  Google Scholar 

  2. R.A. Street, Doping and the Fermi energy in amorphous silicon. Phys. Rev. L 49(16), 1187 (1982). https://doi.org/10.1103/PhysRevLett.49.1187

    Article  ADS  Google Scholar 

  3. W. Beyer, W. Hilgers, P. Prunici, D. Lennartz, Voids in hydrogenated amorphous silicon materials. J. Non-Cryst. Solids 358(17), 2023–2026 (2012). https://doi.org/10.1016/j.jnoncrysol.2011.09.030

    Article  ADS  Google Scholar 

  4. M.H. Brodsky, R.S. Title, K. Weiser, G.D. Pettit, Structural, optical, and electrical properties of amorphous silicon films. Phys. Rev. B 1, 2632 (1970). https://doi.org/10.1103/PhysRevB.1.2632

    Article  ADS  Google Scholar 

  5. S.G. Greenbaum, W.E. Carlos, P.C. Taylor, Local bonding arrangements of boron in doped hydrogenated amorphous silicon. J. Appl. Phys. 56(6), 1874–1877 (1984). https://doi.org/10.1063/1.334203

    Article  ADS  Google Scholar 

  6. M.T.M. Tanaka, T. Matsuyama, T. Matsuyama, T. Sawada, S. Tsuda, S.I. Nakano, H. Hanafusa, Y. Kuwano, Development of new a-Si/c-Si heterojunction solar cells ACJ-HIT (artificially constructed junction-heterojunction with intrinsic thin-layer). Jpn. J. Appl. Phys. 31, 3518–3522 (1992). https://doi.org/10.1143/JJAP.31.3518

    Article  ADS  Google Scholar 

  7. M. Stutzmann, The doping efficiency in amorphous silicon and germanium. Philos. Mag. B 53(1), L15–L21 (1986). https://doi.org/10.1080/13642818608238962

    Article  ADS  Google Scholar 

  8. Y. Lee, H. Kim, S.M. Iftiquar, S. Kim, S. Kim, S. Ahn, Y.-J. Lee, V.A. Dao, J. Yi, Study of stacked-emitter layer for high efficiency amorphous/crystalline silicon heterojunction solar cells. J. Appl. Phys. 116, 24 (2014). https://doi.org/10.1063/1.4905013

    Article  Google Scholar 

  9. S.H. Wemple, M. DiDomenico, Optical dispersion and the structure of solids. Phys. Rev. Lett. 23(20), 1156–1160 (1969). https://doi.org/10.1103/PhysRevLett.23.1156

    Article  ADS  Google Scholar 

  10. F. Demichelis, E. Minetti-Mezzetti, A. Tagliaferro, E. Tresso, P. Rava, N.M. Ravindra, Optical properties of hydrogenated amorphous silicon. J. Appl. Phys. 59(2), 611–618 (1986). https://doi.org/10.1063/1.336620

    Article  ADS  Google Scholar 

  11. A. Hadjadj, N. Pham, P. Roca I Cabarrocas, O. Jbara, G. Djellouli, Ellipsometry investigation of the amorphous-to-microcrystalline transition in a-Si:H under hydrogen-plasma treatment. J. Appl. Phys. 107, 8 (2010). https://doi.org/10.1063/1.3393273

    Article  Google Scholar 

  12. A. Fontcuberta i Morral, P. Roca i Cabarrocas, C. Clerc, Structure and hydrogen content of polymorphous silicon thin films studied by spectroscopic ellipsometry and nuclear measurements. Phys. Rev. B 69, 125307 (2004). https://doi.org/10.1103/PhysRevB.69.125307

    Article  ADS  Google Scholar 

  13. A.H.M. Smets, W.M.M. Kessels, M.C.M. van de Sanden, Vacancies and voids in hydrogenated amorphous silicon. Appl. Phys. Lett. 82(10), 1547–1549 (2003). https://doi.org/10.1063/1.1559657

    Article  ADS  Google Scholar 

  14. M.V.Z. Remeš, P. Torres, U. Kroll, A.H. Mahan, R.S. Crandall, Optical determination of the mass density of amorphous and microcrystalline silicon layers with different hydrogen contents. J. Non-Cryst. Solids 227–230, 876–879 (1998). https://doi.org/10.1016/S0022-3093(98)00207-5

    Article  ADS  Google Scholar 

  15. W. Liu, L. Zhang, F. Meng, W. Guo, J. Bao, J. Liu, D. Wang, Z. Liu, Characterization of microvoids in thin hydrogenated amorphous silicon layers by spectroscopic ellipsometry and Fourier transform infrared spectroscopy. Scr. Mater. 107, 50–53 (2015). https://doi.org/10.1016/j.scriptamat.2015.05.018

    Article  Google Scholar 

  16. J.J. Hopfield, Sum rule relating optical properties to the charge distribution. Phys. Rev. B 2(4), 973–979 (1970). https://doi.org/10.1103/PhysRevB.2.973

    Article  ADS  Google Scholar 

  17. S.H. Wemple, M. DiDomenico, Behavior of the electronic dielectric constant in covalent and ionic materials. Phys. Rev. B 3(4), 1338–1351 (1971). https://doi.org/10.1103/PhysRevB.3.1338

    Article  ADS  Google Scholar 

  18. G.E. Jellison, F.A. Modine, Parameterization of the optical functions of amorphous materials in the interband region. Appl. Phys. Lett. 69(3), 371–373 (1996). https://doi.org/10.1063/1.118064

    Article  ADS  Google Scholar 

  19. W. Liu, L. Zhang, S. Cong, R. Chen, Z. Wu, F. Meng, Q. Shi, Z. Liu, Controllable a-Si:H/c-Si interface passivation by residual SiH4 molecules in H2 plasma. Sol. Energy Mater Sol. Cells 174, 233–239 (2018). https://doi.org/10.1016/j.solmat.2017.09.009

    Article  Google Scholar 

  20. E. Shiles, T. Sasaki, M. Inokuti, D.Y. Smith, Self-consistency and sum-rule tests in the Kramers–Kronig analysis of optical data: applications to aluminum. Phys. Rev. B 22(4), 1612–1628 (1980). https://doi.org/10.1103/PhysRevB.22.1612

    Article  ADS  Google Scholar 

  21. T. Haage, U.I. Schmidt, H. Fath, P. Hess, B. Schröder, H. Oechsner, Density of glow discharge amorphous silicon films determined by spectroscopic ellipsometry. J. Appl. Phys. 76(8), 4894–4896 (1994). https://doi.org/10.1063/1.357267

    Article  ADS  Google Scholar 

  22. J.P.F.C. Ance, J.M. Berger, F. De Chelle, Calculation model for valence electrons and hydrogen concentration in a-Si:H. Phys. Stat. Sol. (B) 113, 105 (1982). https://doi.org/10.1002/pssb.2221130110

    Article  ADS  Google Scholar 

  23. C.A.N.M. Ravindra, J.P. Ferraton, J.M. Berger, F. De Chelle, S. Robin, Refractive index dependency on optical gap in amorphous silicon-part II. Si prepared by chemical vapour deposition. Infrared Phys. 23, 223–232 (1983). https://doi.org/10.1016/0020-0891(83)90040-4

    Article  ADS  Google Scholar 

  24. C.A.N.M. Ravindra, S.P. Coulibaly, F. De Chelle, J.M. Berger, J.P. Ferraton, A. Donnadieu, Refractive index dependency on optical gap in amorphous silicon-part I. Si prepared by glow discharge. Infrared Phys. 23, 99–108 (1983). https://doi.org/10.1016/0020-0891(83)90019-2

    Article  ADS  Google Scholar 

  25. D. Franta, D. Nečas, L. Zajíčková, I. Ohlídal, J. Stuchlík, D. Chvostová, Application of sum rule to the dispersion model of hydrogenated amorphous silicon. Thin Solid Films 539, 233–244 (2013). https://doi.org/10.1016/j.tsf.2013.04.012

    Article  ADS  Google Scholar 

  26. D. Franta, D. Nečas, L. Zajíčková, I. Ohlídal, J. Stuchlík, Advanced modeling for optical characterization of amorphous hydrogenated silicon films. Thin Solid Films 541, 12–16 (2013). https://doi.org/10.1016/j.tsf.2013.04.129

    Article  ADS  Google Scholar 

  27. D.J.L.R.E. Norberg, P.A. Fedders, Non-bonded hydrogen in a-Si:H. J. Non-Cryst. Solids 227, 124–127 (1998). https://doi.org/10.1016/S0022-3093(98)00267-1

    Article  ADS  Google Scholar 

  28. K. Mui, F.W. Smith, Optical dielectric function of hydrogenated amorphous silicon: tetrahedron model and experimental results. Phys. Rev. B 38(15), 10623–10632 (1988). https://doi.org/10.1103/PhysRevB.38.10623

    Article  ADS  Google Scholar 

  29. J.B. Boyce, S.E. Ready, Nuclear-magnetic-double-resonance investigation of the dopant microstructure in hydrogenated amorphous silicon. Phys. Rev. B 38(16), 11008–11018 (1988). https://doi.org/10.1103/PhysRevB.38.11008

    Article  ADS  Google Scholar 

  30. W. Liu, J. Shi, L. Zhang et al., Light-induced activation of boron doping in hydrogenated amorphous silicon for over 25% efficiency silicon solar cells. Nat. Energy 7(5), 427–437 (2022). https://doi.org/10.1038/s41560-022-01018-5

    Article  ADS  Google Scholar 

Download references

Acknowledgments

We acknowledge the useful discussions about this method with Dr. Zhuopeng Wu. This work was supported by projects of the National Natural Science Foundation of China (62074153 and 62004208), Strategic Priority Research Program and the Joint Fund of Chinese Academy of Sciences (XDA17020403), and the project of Shanghai Municipal Science and Technology Committee (19DZ1207602 and 20dz1207100).

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Authors and Affiliations

  1. Research Center for New Energy Technology (RCNET), Shanghai Institute of Microsystem and Information Technology (SIMIT), Chinese Academy of Sciences (CAS), Jiading, Shanghai, 201800, People’s Republic of China

    Zhenfei Li, Liping Zhang, Wenzhu Liu, Youlin Yu, Shenglei Huang, Xiaodong Li, Yuhao Yang, Kai Jiang, Fanying Meng & Zhengxin Liu

  2. University of Chinese Academy of Sciences (UCAS), Shijingshan, Beijing, 100049, People’s Republic of China

    Zhenfei Li, Liping Zhang, Wenzhu Liu, Youlin Yu, Shenglei Huang, Xiaodong Li, Kai Jiang, Fanying Meng & Zhengxin Liu

  3. School of Physical Science and Technology, ShanghaiTech University, Shanghai, 201210, People’s Republic of China

    Shenglei Huang

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  1. Zhenfei Li
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Appendix

Appendix

Assuming there is a binary or ternary amorphous semiconductor. The molecular formula is Ax1Bx2C1 − x1 − x2, where the number of outshell electrons in element A, B and C is a, b and c, respectively. And nA, nB, nC are atomic concentrations per unit volume.

Considering the contributions of the effective number of valence electrons from each element, we can deduce that:

$$ n_{{\text{v}}} = {\text{a}}n_{{\text{A}}} + {\text{b}}n_{{\text{B}}} + {\text{c}}n_{{\text{C}}} $$

With the dispersion energy model, we have:

$$ E_{{\text{d}}} = 2\beta \left[ {\frac{{n_{{\text{v}}} }}{{n_{{\text{A}}} + n_{{\text{B}}} + n_{{\text{C}}} }}} \right]^{3} $$
$$ E_{{\text{d}}} = 2\beta \left[ {ax_{1} + {\text{b}}x_{2} + {\text{c}}\left( {1 - x_{1} - x_{2} } \right)} \right]^{3} $$
$$ x_{1} = \frac{{n_{{\text{A}}} }}{{n_{{\text{A}}} + n_{{\text{B}}} + n_{{\text{C}}} }} $$
$$ x_{2} = \frac{{n_{{\text{B}}} }}{{n_{{\text{A}}} + n_{{\text{B}}} + n_{{\text{C}}} }} $$
$$ 1 - x_{1} - x_{2} = \frac{{n_{{\text{C}}} }}{{n_{{\text{A}}} + n_{{\text{B}}} + n_{{\text{C}}} }} $$

Assuming that element C does not exist, it is now possible to calculate the content of each element in the binary samples:

$$ n_{{\text{A}}} = \frac{{n_{{\text{v}}} }}{{{\text{a}} - {\text{b}}}}\left( {1 - {\text{b}}\sqrt[3]{{\frac{2\beta }{{E_{{\text{d}}} }}}}} \right) $$
$$ n_{{\text{B}}} = \frac{1}{{\text{b}}}\left( {n_{{\text{v}}} - {\text{a}}n_{{\text{A}}} } \right) $$

For ternary samples, one of these elements needs to be characterized by other means. In the previous discussion, we used FTIR to obtain the H content for doped a-Si:H films. Here we assume that the content of element B can be obtained, we can deduced that:

$$ n_{{\text{A}}} = \frac{{n_{{\text{v}}} }}{{{\text{a}} - {\text{c}}}}\left( {1 - {\text{c}}\sqrt[3]{{\frac{2\beta }{{E_{{\text{d}}} }}}}} \right) + \frac{{{\text{c}} - {\text{b}}}}{{{\text{a}} - {\text{c}}}}n_{{\text{B}}} $$
$$ n_{{\text{C}}} = \frac{1}{{\text{c}}}\left( {n_{{\text{v}}} - {\text{a}}n_{{\text{A}}} - {\text{b}}n_{{\text{B}}} } \right) $$

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Li, Z., Zhang, L., Liu, W. et al. Optical method for calculating the dopant concentration of doped amorphous semiconductors. Eur. Phys. J. Plus 137, 862 (2022). https://doi.org/10.1140/epjp/s13360-022-03027-5

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