Chemistry, Physics and Technology of Surface

ISSN 2518-1238 (Online), ISSN 2079-1704 (Print)

The paper presents a system of equations that determines the effective lifetime of minority charge carriers in macroporous silicon. The system of equations was found from the diffusion equation of minority carriers recorded for the macroporous layer and the single-crystal substrate. The solution of nonstationary diffusion equation written for a macroporous layer and a single-crystal substrate is complemented by boundary conditions at the surfaces of a sample of macroporous silicon and at the interface between the macroporous layer and the single-crystal substrate. The effective lifetime of minority charge carriers in macroporous silicon on a single crystal substrate depends on such values as: the minority carrier lifetime in the bulk, the diffusion coefficient of charge carriers, the thickness of the single crystal substrate, the average diameter of the macropores, the average distance between the centers of macropores, the surface recombination rate, the volume fraction macropore. The effective recombination of excess charge carriers in macroporous silicon is determined by the recombination of excess charge carriers on the surface of macropores and limited by the diffusion of charge carriers from the single crystal substrate to the recombination surfaces in the macroporous layer. Using the system of equations, we calculated and shown in the figure the effective lifetime of minority charge carriers in macroporous silicon dependent on the depth of the macropores. To verify the accuracy of calculations performed using a system of analytical equations, which determines the effective lifetime of minority charge carriers in macroporous silicon on a single crystal substrate, we used a numerical method. The numerical method showed the coincidence of the calculations on the effective lifetime of minority carriers. When the depth of macropores is close to the size of the sample of macroporous silicon, a discrepancy of calculations is observed.

1. Ernst M., Brendel R., Ferre R., Harder N P. Thin macroporous silicon heterojunction solar cells. Phys. Stat. Sol. RRL. 2012. 6(5): 187. https://doi.org/10.1002/pssr.201206113

2. Ernst M., Brendel R. Macroporous silicon solar cells with an epitaxial emitter. IEEE J. Photovoltaics. 2013. 3(2): 723. https://doi.org/10.1109/JPHOTOV.2013.2247094

3. Juntunen M.A., Heinonen J., Vähänissi V., Repo P., Valluru D., Savin H. Near-unity quantum efficiency of broadband black silicon photodiodes with an induced junction. Nature Photonics. 2016. 10(12): 777. https://doi.org/10.1038/nphoton.2016.226

4. Otto M., Algasinger M., Branz H., Geseman B. Black silicon photovoltaics. Adv. Opt. Mater. 2015. 3(2): 147. https://doi.org/10.1002/adom.201400395

5. Bett A.J., Eisenlohr J., Höhn O., Repo P., Savin H., Bläsi B., Goldschmidt J.C. Wave optical simulation of the light trapping properties of black silicon surface textures. Opt. Express. 2016. 24(6): 434. https://doi.org/10.1364/OE.24.00A434

6. Karachevtseva L., Kartel M., Kladko V, Gudymenko O., Bo Wang, Bratus V., Lytvynenko O., Onyshchenko V., Stronska O. Functionalization of 2D macroporous silicon under the high-pressure oxidation. Appl. Surf. Sci. 2018. 434: 142. https://doi.org/10.1016/j.apsusc.2017.10.029

7. Ernst M., Brendel R. Modeling effective carrier lifetimes of passivated macroporous silicon layers. Sol. Energy Mater. Sol. Cells. 2011. 95(4): 1197. https://doi.org/10.1016/j.solmat.2011.01.017

8. Monastyrskii L.S., Sokolovskii B.S., Pavlyk M.R. Analytical and numerical calculations of photoconductivity in porous silicon. Ukr. J. Phys. 2011. 56(9): 902. https://doi.org/10.1155/2011/896962

9. Onyshchenko V.F., Karachevtseva L.A. Effective minority carrier lifetime and distribution of steady-state excess minority carriers in macroporous silicon. Him. Fiz. Tehnol. Poverhni. 2017. 8(3): 322. https://doi.org/10.15407/hftp08.03.322

10. Onyshchenko V.F., Karachevtseva L.A., Lytvynenko O.O., Plakhotnyuk M.M., Stronska O.Y. Effective lifetime of minority carriers in black silicon nano-textured by cones and pyramids. Semiconductor Physics, Quantum Electronics and Optoelectronics. 2017. 20(3): 325. https://doi.org/10.15407/spqeo20.03.325

11. Karachevtseva L.A., Onyshchenko V.F. Relaxation of excess minority carrier distribution in macroporous silicon. Him. Fiz. Tehnol. Poverhni. 2018. 9(2): 158. https://doi.org/10.15407/hftp09.02.158