*33.01% (31.06%)- Limiting Highest Efficiencies obtained in \mathbf{n}^+(\mathbf{p}^+)-\mathbf{p}(\mathbf{n})\ Crystalline Silicon Junction Solar Cells at T=300 K, Due to The Effects of Heavy (Low) Doping and Impurity Size*

**DOI:**10.54647/physics14465 99 Downloads 5475 Views

**Author(s)**

**Abstract**

In our recent two works [1, 2], by basing on: (1) the effects of heavy(light) doping and donor (acceptor), d(a), size , which affect the total carrier-minority saturation current density J_{oI(II)}\equivJ_{En(p)o}+J_{Bp(n)o},\ J_{En(p)o}(J_{Bp(n)o}),\ being injected respectively into the heavily doped donor (acceptor)-Si emitter-lightly doped acceptor (donor)-Si base regions, HD[d(a)-Si]ER-LD[a(d)-Si]BR, of n^+(p^+)-p(n) junction solar cells, respectively, (2) an effective Gaussian donor-density profile to determine J_{En(p)o}, and (3) the use of two experimental points, we investigated the photovoltaic conversion factor n_{I(II)}, short circuit current density J_{scI(II)}, fill factor F_{I(II)}, and finally efficiency \eta_{I(II)}. Further, we obtained the highest maximal values of \eta_{I(II)}, \eta_{I(II)-max.}=31.55%\ (27.56%), being due to the taken large values of d(a)-radius, r_{d(a)}=0.163 (0.141) nm, which do not correspond to the of r_{S(Tl)}-radius, r_{S(Tl)}=0.10(0.19)\ nm\ [8], for the\ emitter\ thickness W=85\ \mu m and surface recombination\ velocity \ S ={10}^{-50}\ cm/s, for example, corresponding to the completely opaque COER, given in the COHD[d(a)-Si]ER, and for a low Tl(S)-acceptor(donor) density N_{a(d)}={10}^{16}{\rm cm}^{-3}, taken in the LD[a(d)-Si]BR, respectively.

In the present work, by basing on such a treatment method, but using now the usual physical conditions such as: W=15\ \mu m,{\ N}_{Bi(In)}={5\times10}^{20}\ {\rm cm}^{-3}\ and\ S\ =100\ (cm/s\ ), according to the highly transparent HD[Bi(In)-Si]ER-case, and then N_{In(Bi)}=5\times{10}^{18}{\rm cm}^{-3} for LD[In(Bi)-Si]BR, with r_{Bi(In)}=0.160(0.135)\ nm [8], we now get: \eta_{I(II)-max.}=31% (30.65%), respectively, which can be compared with the result \mathbf{\eta} =31% for W=15\ \mu m and S\ =100\ (cm/s\ ),obtained recently by Bhattacharya and John, using the numerical simulation method [3, 4].

**Keywords**

Donor (acceptor)-size effect; heavily doped emitter region; photovoltaic conversion factor; open circuit voltage; photovoltaic conversion efficiency

**Cite this paper**

H. Van Cong, K. C. Ho-Huynh Thi, P. Blaise, O. Henri-Rousseau, R. Brouzet, J. Sulian, M. Cayrol,
33.01% (31.06%)- Limiting Highest Efficiencies obtained in \mathbf{n}^+(\mathbf{p}^+)-\mathbf{p}(\mathbf{n})\ Crystalline Silicon Junction Solar Cells at T=300 K, Due to The Effects of Heavy (Low) Doping and Impurity Size
, *SCIREA Journal of Physics*.
Volume 7, Issue 3, June 2022 | PP. 80-103.
10.54647/physics14465

**References**

[ 1 ] | H. Van Cong, P. Blaise, and O. Henri-Rousseau, “Effects of Heavy Doping Impurity Size on Minority-Carrier Transport Parameters in Heavily (Lightly) Doped n(p)-Type Crystalline Silicon at 300K, Applied to Determine the Performance of Junction Solar Cells, “ SCIREA J. Phys. 2019, vol. 4, pp. 63-110, 2019. |

[ 2 ] | H. Van Cong, P. Blaise, and O. Henri-Rousseau, “Effects of Heavy Doping Impurity Size on Minority-Carrier Transport Parameters in Heavily (Lightly) Doped (n)-Type Crystalline Silicon at 300K, Applied to Determine the Performance of Junction Solar Cells, “ SCIREA J. Phys., Vol.4, pp. 126-162, 2019. |

[ 3 ] | S. Bhattacharya and S. John,” Beyond 30% Conversion efficiency in silicon solar cells: a numerical demonstration,” Sci. Rep., vol. 9, p 12482, 2019. |

[ 4 ] | S. Bhattacharya and S. John, APL Photonics, “Photonic crystal light trapping: Beyond 30% conversion efficiency for silicon photovoltaics,” vol. 5, p 020902, 2020. |

[ 5 ] | F. A. Lindholm, A. Neugroschel, C. T. Sah, M. P. Godlewski, H. W. Brandhorst, “A methodology for experimentally based determination of gap shrinkage and effective lifetimes in the emitter and base of p-n junction solar cells and other p-n junction devices, “IEEE Trans. Electron Devices ED, vol. 24, pp. 402-410, 1977. |

[ 6 ] | W.Shockley and H. J. Queisser “Detailed balace limit of efficiency of p-n junction solar cells,” J. Appl. Phys., vol. 32, pp. 510-519, 1961. |

[ 7 ] | M.A. Shibib, F.A. Lindholm, and F. Therez, “Heavily doped transparent-emitter region in junction solar cells, diodes, and transistors,” IEEE Trans. Electron Devices 1979, vol. ED-26, pp. 959-965, 1979. |

[ 8 ] | C. Kittel, “Introduction to Solid State Physics, pp. 84-100. Wiley, New York (1976). |

[ 9 ] | R.A. Logan, J.F. Gilbert, and F.A. Trumbore, “Electron mobilities and tunneling currents in silicon,” J. Appl. Phys., vol. 32, pp. 131-132, 1961. |

[ 10 ] | J. del Alamo, S. Swirhum, and R.M. Swanson, “Measuring and modeling minority carrier transport in heavily doped silicon,” Solid-State Electron., vol. 28, pp. 47-54, 1985. |

[ 11 ] | D. Chattopadhyay, and H.J. Queisser, “Electron scattering by ionized impurities in semiconductors,” Rev. Mod. Phys., vol. 53, pp. 745-768, 1981. |

[ 12 ] | J. del Alamo and R.M. Swanson, “Modeling of minority-carrier transport in heavily doped silicon emitters. Solid-State Electron., vol. 30, pp. 1127-1136, 1987. |

[ 13 ] | Z. Essa et al., “Doping profile measurement on textured silicon surface,” EPJ Photovoltaics, vol. 9, p.5, 2018. |

[ 14 ] | S.C. Jain, E.L. Heasell, and D.J. Roulston, “Recent advances in the physics of silicon p-n junction solar cells including their transient response,” Prog. Quant. Electron., vol. 11, pp.105-204, 1987. |

[ 15 ] | S.C. Jain and D.J. Roulston,” A simple expression for band gap narrowing in heavily doped Si, Ge, GaAs and strained layers. Solid-State Electron., vol. 34, pp. 453-465 (1991). |

[ 16 ] | D.B.M. Klaassen, J.W. Slotboom, and H.C. de Graaff, “Unified apparent band gap narrowing in n- and p-type silicon. Solid-State Electron. 1992, vol. 35, pp. 125-129, 1992. |

[ 17 ] | A. Zouari and A.B. Arab, “A simple formulation of the saturation current density in heavily doped emitters,” Can. J. Phys., vol. 81, pp. 1109-1120, 2003. |

[ 18 ] | J. W. Slotboom and H.C. de Graaff, “Measurements of band gap narrowing in Si bipolar transistors. Solid-State Electron,” vol. 19, pp. 857-862, 1976. |

[ 19 ] | M. A. Green, “Solar cell fill factors: general graph and empirical expressions. Solid-State Electron,” 1981, vol. 24, pp. 788-78, 1971. |

[ 20 ] | R.M. Swanson and R.A. Sinton, “Advances in Solar Energy,” edited by K. A. Bouer , American Solar Energy, Newark, Delaware, 1990. |

[ 21 ] | H. Van Cong, and S. Brunet, “Effective drift current densities in the n-type heavily doped emitter region of junction silicon solar cells. Solar Cells,” vol. 5, pp. 355-365, 1982. |

[ 22 ] | H. Van Cong, “A simple accurate solution to minority electron injection in the p-type heavily doped emitter region of silicon devices,” Physica Status Solidi A, vol. 149, pp. 619-628, 1995; H. Van Cong and G. Debiais, “About a conjunction between electrical and optical phenomena in p-type heavily doped silicon at room temperature,” Physica Status Solidi B, vol. 191, pp. 161-169, 1995. |

[ 23 ] | K. Masuko et al., “Achievement of more than 25% conversion efficiency with crystalline silicon heterojunction solar cell. IEEE J. Photovoltaic, vol. 4, pp. 1433-143, 2014. |

[ 24 ] | A. Fell, et al., “Input Parameters for the simulation of silicon solar cells in 2014,” IEEE J. Photovoltaics, vol. 5, pp. 1250-1263, 2015. |

[ 25 ] | H. Van Cong, and G. Debiais, “Energy band structure parameters and their data, derived from the measurements of minority carrier current density in heavily doped emitters of silicon devices,” Solar Ener. Mater. and Solar Cells, vol. 45, pp. 385-399, 1997; “Apparent band-gap narrowing and its data derived from the measurements of minority-carrier current density in heavily doped emitters of silicon devices,” Physica Status Solidi A, vol. 155, pp. 547-553, 1996; H. Van Cong, “ A new solution for minority-carrier injection into the heavily doped emitter of silicon devices,” Physica Status Solidi A, vol. 171, pp. 631-64, 1999. |

[ 26 ] | A. Richter, M. Hermle, and S.W. Glunz, “Reassessment of the limiting efficiency for crystalline silicon solar cells,” IEEE J. Photovoltaics, vol. 3, pp. 1184-1191, 2013. |

[ 27 ] | R.S. Davidsen, et al., “Black silicon laser-doped selective emitter solar cell with 18.1% efficiency. Sol. Energy Mater. Sol. Cells,” vol. 144, pp. 740-747, 2016. |

[ 28 ] | C. Battaglia, A. Cuevas, and S. de Wolf, “High-efficiency crystalline silicon solar cells: status and perspectives,” Energy Environ. Sci., vol. 9, pp. 1552-1576, 2016. |

[ 29 ] | M.A. Green, et al., “Solar cell efficiency tables (version 51),” Prog. Photovolt. Res. Appl., vol. 26, pp. 3-12, 2018. |

[ 30 ] | J.E. Lang, F.L. Madarasz, and P.M. Hemenger, “Temperature dependent density of states effective mass in non-parabolic p-type silicon,” J. Appl. Phys., vol. 54, pp. 3612-3612, 1983. |

[ 31 ] | M.A. Green, “Intrinsic concentration, effective densities of states, and effective mass in silicon,” J. Appl. Phys., vol. 67, pp. 2944-2954, 1990. |

[ 32 ] | H. Van Cong, “Band gap changes in excited intrinsic (heavily doped) Si and Ge semiconductors,” Physica B, vol. 405, pp. 1139-1149, 2010. |

[ 33 ] | R. Pässler, “Dispersion-related description of temperature dependencies of band gaps in semiconductors,” Phys. Rev. B, vol. 66, p. 085201, 2002. |

[ 34 ] | R. Pässler, “Semi-empirical descriptions of temperature dependences of band gaps in semiconductors,” Physica Status Solidi B, vol. 236, pp. 710-728, 2003. |

[ 35 ] | O. Henri-Rousseau, and P. Blaise, “Quantum Oscillators,” edited by John Wiley & Sons, Inc., Hoboken, New Jersey, 2011. |

[ 36 ] | A.B. Sproul, and M.A. Green, “Improved value for the silicon intrinsic carrier concentration from 275 to 375 K,” J. Appl. Phys., vol. 70, pp. 846-854, 1991. |

[ 37 ] | K. Misiakos, and D. Tsamakis, “Accurate measurements of the silicon intrinsic carrier density from 77 to 340 K,” J. Appl. Phys., vol. 74, pp. 3293-3297, 1993. |

[ 38 ] | R. Couderc, M. Amara, and M. Lemiti, “Reassessment of the intrinsic carrier density temperature dependence in crystalline silicon,” J. Appl. Phys., vol. 115, p. 093705, 2014. |

[ 39 ] | H. Van Cong, and G. Debiais, “ A simple accurate expression of the reduced Fermi energy for any reduced carrier density. J. Appl. Phys., vol. 73, pp. 1545-15463, 1993. |

[ 40 ] | H. Van Cong, and B. Doan Khanh, “Simple accurate general expression of the Fermi-Dirac integral and for j> -1,” Solid-State Electron., vol. 35, pp. 949-951, 1992; H. Van Cong, “New series representation of Fermi-Dirac integral for arbitrary j> -1, and its effect on for integer j,” Solid-State Electron., vol. 34, pp. 489-492, 1991. |

[ 41 ] | H. Van Cong, S. Abide, B. Zeghmati, and X. Chesneau, “Optical band gap in various impurity-Si systems from the metal-insulator transition study,” Physica B, vol. 436, pp. 130-139, 2014. |

[ 42 ] | H. Van Cong, “Effects of impurity size and heavy doping on energy-band-structure parameters of various impurity-Si systems,” Physica B, vol. 487, pp. 90-101, 2016. |

[ 43 ] | H. Van Cong, “Effects of donor size and heavy doping on optical, electrical and thermoelectric properties of various degenerate donor-silicon systems at low temperatures,” American Journal of Modern Physics, vol. 7, pp. 136-16, 2018. |

[ 44 ] | J. Wagner, and J.A. del Alamo, “Band-gap narrowing in heavily doped silicon: A comparison of optical and electrical data,” J. Appl. Phys., vol. 63, pp. 425-429, 1988. |

[ 45 ] | H. Van Cong, “Fermi energy and band-tail parameters in heavily doped semiconductors,” J. Phys. Chem. Solids, vol. 36, pp. 1237-1240, 1975. |