Effects of heavy doping and impurity size on minority-carrier transport parameters in heavily (lightly) n(p)-type crystalline silicon at 300K, applied to determine the performance of n^+-p junction solar cells, by H. Van Cong, P. Blaise, and O. Henri-Rousseau
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Abstract
The effects of heavy doping and donor (acceptor) size on the hole (electron)-minority saturation current density J_Eo (J_Bo ), injected respectively into the heavily (lightly) doped crystalline silicon (Si) emitter (base) region of n^+-p junction, which can be applied to determine the performance of solar cells, being strongly affected by the dark saturation current density: J_o≡J_Eo+J_Bo, were investigated. For that, we used an effective Gaussian donor-density profile to determine J_Eo, and an empirical method of two points to investigate the ideality factor n, short circuit current density J_sc, fill factor (FF), and photovoltaic conversion efficiency η, expressed as functions of the open circuit voltage V_oc, giving rise to a satisfactory description of our obtained results, being compared also with other existing theoretical-and-experimental ones. So, in the completely transparent and heavily doped (P-Si) emitter region, CTHD(P-Si)ER, our obtained J_Eo-results were accurate within 1.78%. This accurate expression for J_Eo is thus imperative for continuing the performance improvement of solar cell systems. For example, in the physical conditions (PCs) of CTHD (P-Si) ER and of lightly doped (B-Si) base region, LD(B-Si)BR, we obtained the precisions of the order of 8.1% for J_sc, 7.1% for FF, and 5% for η, suggesting thus an accuracy of J_Bo (≤8.1%). Further, in the PCs of completely opaque and heavily doped (S-Si) emitter region, COHD(S-Si)ER, and of lightly doped (acceptor-Si) base region, LD(acceptor-Si)BR, our limiting η-results are equal to: 27.77%,…, 31.55%, according to the E_gi-values equal to: 1.12eV ,…, 1.34eV, given in various (B,…, Tl)-Si base regions, respectively, being due to the acceptor-size effect. Furthermore, in the PCs of CTHD (donor-Si) ER and of LD(Tl-Si)BR, our maximal η-values are equal to: 24.28%,…, 31.51%, according to the E_gi-values equal to: 1.11eV ,…, 1.70eV , given in various (Sb,…, S)-Si emitter regions, respectively, being due to the donor-size effect. It should be noted that these obtained highest η-values are found to be almost equal, as: 31.51%≃31.55%, coming from the fact that the two obtained limiting J_o-values are almost the same.
Keywords
donor (acceptor)-size effect; heavily doped emitter region; ideality factor; open circuit voltage; photovoltaic conversion efficiency
Cite this paper
H. Van Cong, P. Blaise, O. Henri-Rousseau,
Effects of heavy doping and impurity size on minority-carrier transport parameters in heavily (lightly) n(p)-type crystalline silicon at 300K, applied to determine the performance of n^+-p junction solar cells, by H. Van Cong, P. Blaise, and O. Henri-Rousseau
, SCIREA Journal of Physics.
Volume 4, Issue 4, August 2019 | PP. 63-110.
References
| [ 1 ] | F. A. Lindholm, A. Neugroschel, C. T. Sah, M. P. Godlewski, and 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. |
| [ 2 ] | W. Shockley, “The theory of p-n junctions in semiconductors and p-n junction transistors,” Bell Syst. Tech. J., vol. 28, pp. 435-489, 1949; W. Shockley and H. J. Queisser, “ Detailed balance limit of efficiency of p-n junction solar cells.” J. Appl. Phys., vol. 32, pp. 510-519, 1961. |
| [ 3 ] | J. W. Slotboom, H. C. de Graaff, “Measurements of band gap narrowing in Si bipolar transistors,” Solid-State Electron., vol. 19, pp. 857-862, 1976. |
| [ 4 ] | M. A. Green, “Solar cell fill factors: general graph and empirical expressions,” Solid-State Electron., vol. 24, pp. 788-789, 1981; M. Leilaeioun and Z. C. Holman,”Accuracy of expressions for the fill factor of a solar cell in terms of open-circuit voltage and ideality factor,” J. Appl. Phys., vol. 120, pp. 123111, 2016. |
| [ 5 ] | R. M. Swanson and R. A. Sinton,“ Advances in Solar Energy,” edited by K. A. Bouer , American Solar Energy, Newark, Delaware, 1990. |
| [ 6 ] | H. P. D. Lanyon, “The Physics of heavily doped junction solar cells,” Solar Cells, vol. 3, pp. 289-311, 1981; 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; H. Van Cong and S. Brunet, S. Charar, J. L. Birman, and M. Averous, “Optical and electrical energy gaps of the n-type impure silicon at 300 K,” Solid State Commun., vol. 45, pp. 611-614, 1983. |
| [ 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, vol. ED-26, pp.959-965, 1979; M. A. Shibib and J. G. Fossum, “Limitations on the open-circuit voltage imposed by and regions in silicon solar cells,” J. Appl. Phys., vol. 52, pp. 1072-1075, 1981. |
| [ 8 ] | J. del Alamo and R. M. Swanson, “The physics and modeling of heavily doped emitters,” IEEE Trans. Electron Devices 1984, vol. ED-31, pp. 1878-1888, 1984; J. del Alamo, S. Swirhum, and R. M. Swanson, “Measurement of steady-state minority-carrier transport parameters in heavily doped n-type silicon,” IEEE Trans. Electron Devices, vol. ED-34, pp. 1580-1589, 1987. |
| [ 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; J. del Alamo, S. Swirhum, and Swanson R. M., “Simultaneous measurement of hole lifetime, hole mobility, and band gap narrowing in heavily doped n-type silicon,” Int. Electron Devices Meet. Tech. Dig., vol. 31, pp. 290-293, 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 ] | 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, N. Taleb, B. Sermage, C. Broussillon, B. Bazer-Bachi, and M. Quillec, “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., vol. 35, pp. 125-129, 1992; D. B. M. Klaassen, “A unified mobility model for device simulation-II, ”Temperature dependence of carrier mobility and lifetime. Solid-State Electron., vol. 35, pp. 961-967, 1992. |
| [ 17 ] | A. Zouari, 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 ] | N. Stem and M. Cid, “Studies of phosphorus Gaussian profile emitter silicon solar cells,” Materials Research, vol. 4, pp. 143-152, 2001. |
| [ 19 ] | V. Bahrami-Yekta and T. Tiedje, “Limiting efficiency of indoor silicon photovoltaic devices,” Optics Express, vol. 26, pp. 28238-28248, 2018. |
| [ 20 ] | F. H. Alharbi and S. Kais, “Theoretical limits of photovoltaics efficiency and possible improvements by intuitive approaches learned from photosynthesis and quantum coherence, ”Renewable and sustainable energy reviews,” vol. 43, pp. 1073-1089, 2015. |
| [ 21 ] | A. Cuevas, J. G. Fossum, and R. T. Young, “Influence of the dopant density profile on minority-carrier current in shallow, heavily doped emitters of silicon bipolar devices,” Solid-State Electron., vol. 28, pp. 247-254, 1985. |
| [ 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, M. Shigematsu, T. Hashiguchi, D. Fujishima, M. Kai, N. Yoshimura, T. Yamaguchi, Y. Ichihashi, T. Mishima, N. Matsubara, T. Yamanishi, T. Takahama, M. Taguchi, E. Maruyama, and S. Okamoto, “Achievement of more than 25% conversion efficiency with crystalline silicon heterojunction solar cell,” IEEE J. Photovoltaic, vol. 4, pp. 1433-1435, 2014. |
| [ 24 ] | A. Fell, K. R. McIntosh, P. P. Altermatt, G. J. M. Janssen, R. Stangl, A. Ho-Baillie, H. Steinkemper, J. Greulich, M. Müller, B. Min, K. C. Fong, M. Hermle, I. G. Romijn, and M. D. Abbott, “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; H. Van Cong and G. Debiais, “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. 631-645, 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, H. Li, A. To, X. Wang, A. Han, J. An, J. Colwell, C. Chan, A. Wenham, M. S. Schmidt, A. Boisen, O. Hansen, S. Wenham, and A. Barnett, “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, Y. Hishikawa, E. D. Dunlop, D. H. Levi, J. Hohl-Ebinger, and A. W. Y. Ho-Baillie, “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; O. Henri-Rousseau, Physique Théorique et Réalité, edited by Collection Etudes, Presses Universitaires de Perpignan, 2018. |
| [ 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; A. B. Sproul and M. A. Green, “Intrinsic carrier concentration and minority-carrier mobility of silicon from 77 to 300 K,” J. Appl. Phys., vol. 73, pp. 1214-1225, 1993. |
| [ 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 for arbitrary a and 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. 136-165, 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. |