Modeling low-temperature mechanical behavior of water-containing porous silicon


Аuthors

Bardushkin V. V.1*, Shilyaeva Y. I.2, Kochetygov A. A.3**, Volovlikova O. V.2***, Dronov A. A.2****, Yakovlev V. B.3*****

1. Institute of Nanotechnology of Microelectronics of the Russian Academy of Sciences, Moscow, Russia
2. National Research University of Electronic Technology, Bld. 1, Shokin Square, Zelenograd, Moscow, Russia, 124498
3. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: bardushkin@mail.ru
**e-mail: aakcht@gmail.com
***e-mail: 5ilova87@gmail.com
****e-mail: mfh.miet@gmail.com
*****e-mail: yakvb@mail.ru

Abstract

This article solves to the problem of low-temperature mechanical behavior modeling of the «porous electrode — aqueous electrolyte» type systems applied in new generation electrochemical devices. The structures based on porous silicon membranes and water are under consideration. Analysis by the differential scanning calorimetry method revealed high temperature characteristics reproducibility of the ice particles melting peaks in porous silicon at successive cooling-heating cycles. This fact is indicative of constant geometric parameters of porous silicon. A mathematical model is developed for predicting the stress-strain state (up to the ultimate) generated during the water freezing under conditions of spatial delimitation inside the silicon matrix pores. The model accounts for the material structure, physical and mechanical characterristics, and the volumetric content of its components. Modeling rests upon the generalized singular approximation of the random fields theory and the concept of the stress and strain concentration operators (fourth-rank tensors), connecting average stresses (and strains) in the material with their local values within the limits each separate inhomogeneity element. Comparison of the tensions tensor largest diagonal component in the silicon matrix with the silicon tensile strength limit is being performed to evaluate the strain-stress state. The marginal state is being reached in the case when this maximum diagonal component value exceeds the said strength limit, i.e. the non-homogeneous material will crash as the result of the silicon matrix cracking. The conducted numerical model calculations revealed that the water freezing in the pores at sequential cooling-heating cycles does not have destructive effect on the porous silicon structures under consideration, which is in agreement with experimental data.

Keywords:

modeling, porous silicon, water, differential scanning calorimetry, freezing, melting, stress-strain state, generalized singular approximation of the random fields theory, stress and strain concentration operators, mechanical strength

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