COMPUTER MODELING OF HYDROGEN INDUCTED MASS TRANSFER IN SEMICONDUCTORS
DOI:
https://doi.org/10.32782/tnv-tech.2023.2.13Keywords:
thermodynamics, equilibrium concentration, mass transferAbstract
In connection with the widespread use of copper conductors in microelectronics, the problem arises of modeling the processes that occur when active gases act on the substrate surface. The situation is further complicated by the circumstance that in order to obtain the final result facing a specific process, individual parts of the system are specifically placed under the influence of an external force. This complicates the thermodynamic modeling of systems in which both the location of the phase boundaries and the distribution of substances over the volume are essential. Based on thermodynamic principles, a model is proposed for the behavior of copper penetration into germanium from spots on the surface under the action of sprayed hydrogen. It has been suggested that some of the energy that is released on the surface is transferred to the crystal lattice and copper atoms and causes a shift in equilibrium. A differential equation is derived that describes the propagation of deviations from the equilibrium composition, and a method for compiling boundary conditions for it is also shown. The results of modeling the hydrogen-germanium-copper system are presented, and the dependence of the concentration of diffused copper on the concentration of superequilibrium atomized hydrogen is obtained. It has been proven that an increase in hydrogen atomization ensures an increase in the number of copper atoms in germanium. Thus, the stationary state of a chemical heterophase system, caused by a point source of perturbation of the chemical composition, is described using the minima of the functionals corresponding to the shift of the Gibbs free energy from the equilibrium value into the elementary cells of the system, the distribution of which over the system is described by differential equations of the form. In this case, due to the consideration of zones (elementary cells) bordering the phase boundary, not only the dissolution of an impurity in a solid body, but also sorption phenomena are described. The results of applying the model in an extended reactor for the H-H2 system are also presented, and the correspondence of the results to the classical scheme for solving the problem using mass transfer equations is shown.
References
Wenxiao Hu, Kai Chen, Tao Tao, et all. High-rate growth of single-crystal diamond with an atomically flat surface by microwave plasma chemical vapor deposition. Thin Solid Films. 2022. Nanjing, China. Vol. 763.
Lantos P.V., Jonson N.M., Street R.A. Light-enhanced hydrogen motion in SiH. Phys. Rev. Lett. 1991. Vol 67. no. 19.
Lavrenko V.A., Podchernyaeva I.A., Shchur D.V., Zolotarenko A.D., Zolotarenko, A.D. Features of Physical and Chemical Adsorption During Interaction of Polycrystalline and Nanocrystalline Materials with Gases. Powder Metallurgy and Metal Ceramics. Ukraine, 2018. Vol. 56, Issue 9–10. P. 504–511.
Юрченко І.О., Авраменко А.І., Щербак М.О. Фізична та колоїдна хімія Physical and colloidal chemistry. Ukraine : «Магнолія 2006», 2021. 950 с.
Boll R.H. Calculation of complex equilibrium with an unknown Number of Phases. Journ. Chem. Phys. Vol. 34, 1960. P. 1108–1110.
Sancier K.M., Morrison S.R. Wisendanger H.V.O. Catalysis and chemical reaction rat of hyrogen atom with germanium. J. Catalysis. 1966. Vol. 5. № 2. P. 361–365.
Mafliet W. Series solutions of nonlinear coupled reaction diffusion equations. J. Phys. Appl. № 23. 1991. P. 5499–5503.
Jacucci G.,Poseth M. Monte Carlo calculation of latticevacancies by the method of overlapping distribution. Solid State Comm. 1980. Vol. 33, 11. P/ 35–37.
Anderson J.O., Agen J. Models for numerical treatment of multicomponent diffusion in simple phases. Appl. Phys. Vol. 72, 1992. № 4. P. 1350–1353.
Wise H., Wood B.J. Reactive collision between gas and surface atoms. Adv. at. and mol. Phys. 1967. Vols. 3. P. 290–353.
Model calculations for hydride nucleations on oxide-coated metallic surfaces. J. alloys and Compounds. 1992. Vol. 1. P. 11–23.
Johnson N.M., Doland C., Ponce F. Hydrogen in crystalline semiconductors. A review of experimental results. Physica B. 1991. Vol. 1–4. № 3–20. P. 3–20.
De Groot, Masur S. Nonequilibrium thermodynamics. USA : Courier Corporation. 1984. P. 510.
De Groot. About thermodynamics irreversible heat and a mass exchange. Heat and mass transfer. Минск : Наука и технологии. 1965. P. 63–70.
Bumstead H. A., Gibbs J. W. Scientific Papers of J. Willard Gibbs. 2015. Thermodynamics. USA : Creative Media Partners, LLC.
Lopushanskaya A.M. (Ed.). Thermodynamics of irreversible processes : Sci. works. 1992. Ukraine : Academy of Sciences of the USSR of IOHRAN.
Раман Б.В. Механизм и кинетика сложных реакций. / Київ : Металургия, 1970.
Kressel G., Nelson G. In book: Physics of thin films. Київ, Наукова думка dumka, 1982. С. 79–144.
Kröger F. The Chemistry of Imperfect Crystals: Imperfection chemistry of crystalline solids. 1973. Holland : North-Holland Publishing Company.
