350 rub
Journal Nanotechnology : the development , application - XXI Century №4 for 2021 г.
Article in number:
Mathematical model of the pressure distribution on silicon wafers during two-sided polishing
Type of article: scientific article
DOI: https://doi.org/10.18127/j22250980-202104-06
UDC: 621.923
Authors:

I.I. Danilov1, N.G. Nazarov2, D.D. Dmitriev3, S.N. Sinavchian4, V.S. Sinavchian5

1–5 Bauman Moscow State Technical University (Moscow, Russia)

Abstract:

The production of a modern solid-state integrated circuits uses silicon semiconductor wafers as a blank. The accuracy of the geometric shape of the plates required for this is ensured during finishing polishing operations. The most productive is double-sided polishing. The calculation of the evolution of the geometric shape of the plate during polishing requires the development of a mathematical model of the pressure distribution on silicon wafers, taking into account the main factors.

Objective – to develop a mathematical model of pressure distribution on silicon wafers during two-sided polishing.

A mathematical model of the elastic-deformed state of an axisymmetric geometric silicon wafer with two-sided polishing, allowing calculating pressure diagrams on the wafers, has been developed.

The use of the research results allows to develop the mathematical model of the polishing process of silicon wafers and to calculate the optimal technological modes of this operation.

Pages: 60-67
For citation

Danilov I.I., Nazarov N.G., Dmitriev D.D., Sinavchian S.N., Sinavchian V.S. Mathematical model of the pressure distribution on silicon wafers during two-sided polishing. Nanotechnology: development and applications – XXI century. 2021 V. 13. № 4. P. 60–67. DOI: https://doi.org/10.18127/j22250980-202104-06 (in Russian)

References
  1. Orlov P.N. Almazno-abrazivnaya dovodka detalej: Obzor. Ser. S-H-4. M.: NIIMASH. 1972. 200 s.  (in Russian).
  2. Orlov P.N., Savelova A.A., Poluhin V.A., Nesterov YU.I. Dovodka precizionnyh detalej mashin / Pod red. G.M. Ippolitova. M.: Mashinostroenie. 1978. 256 s. (in Russian).
  3. Timoshenko S.P., Gud'er D. Teoriya uprugosti. Izd. 2-e. M.: Nauka. 1979. 560 s. (in Russian).
  4. Danilov I.I. Raschet davleniya v zone kontakta poverhnostej detali i instrumenta pri dvustoronnem polirovanii. V sb.: Povyshenie stojkosti metallorezhushchego instrumenta: Mater. Mezhotraslevyh nauchno-tekhn. konf., soveshch., semin. i vystavok / Pod red. L.S. Kerbikova. M.: VIMI. 1981. S. 94–98 (in Russian).
  5. Orlov P.N., Danilov I.I. Osobennosti matematicheskogo modelirovaniya dvustoronnego abrazivnogo polirovaniya .  Voprosy sudostroeniya. Ser. Tekhnologiya morskogo priborostroeniya. 1984. Vyp. 5. S. 21–29 (in Russian).
  6. Snitko N.K. Stroitel'naya mekhanika: Uchebnik dlya vuzov. Izd. 3-e, pererab. M.: Vysshaya shkola. 1980. 431 s. (in Russian).
  7. Biderman V.L. Mekhanika tonkostennyh konstrukcij. Statika. M.: Mashinostroenie. 1977. 488 s. (in Russian).
  8. Verlan' A.F., Sizikov V.S. Metody reshenij integral'nyh uravnenij s programmami dlya EVM. Kiev: Naukova dumka. 1978. 292 s. (in Russian).
  9. Kamke E. Spravochnik po obyknovennym differencial'nym uravneniyam. M.: Nauka. 1976. 576 s. (in Russian).
  10. Korenev B.G. Vvedenie v teoriyu besselevyh funkcij. M.: Nauka. 1971. 287 s. (in Russian).
  11. Yanke E., Emde F., Lesh F. Special'nye funkcii. Formuly, grafiki, tablicy. Izd. 3-e. stereotipnoe / Pod red. L.I. Sedova. M.: Nauka. 1977. 342 s. (in Russian).
  12. Tihonov A.N., Vasil'eva A.B., Sveshnikov A.G. Differencial'nye uravneniya. M.: Nauka. 1979. 232 s. (in Russian).
  13. Korenev B.G. Zadachi teorii teploprovodnosti i termouprugosti. M.: Nauka. 1980. 400 s. (in Russian).
Date of receipt: 13.09.2021
Approved after review: 27.09.2021
Accepted for publication: 28.10.2021