Growth kinetics and structure of epitaxial garnet layers as functions of the mismatch of crystal lattice parameters

Abstract

We present an analysis of the kinetics and growth mechanism of liquid phase epitaxy (LPE) of garnets using the linear non-equilibrium thermodynamic approximation, as a function of the degree ƒ of mismatch of the crystalline lattice parameters in the film and substrate. The effect of mismatch on the rate of crystallization is determined by three factors: variation of the crystallization rate constant, variation of the heat of dissolution, and shifting of the effective saturation temperature of the melt in contact with a stressed crystal. As a rule, the last of these factors predominates: δT s ≳ 1 K for ƒ ≈ 3×10 -3 , δT s ≳ 10 K for ƒ ≈ 1×10 -2 and δT s ≈ 40 K for ƒ ≈ 2×10 -2 . An analysis is given of the effect of crystal anisotropy and local inhomogeneities on the value of δ T s, i.e. on the relative shift of the liquidus point. It is demonstrated that a set of characteristic values of ƒ exists whose ratios determine specific features of LPE in a chosen system. The occurrence of lamination of epitaxial films is discussed in relation to the last effect. The conclusions from the theory presented have been experimentally verified on garnet systems of composition (YBiSmCa) 3(FeGe) 5O 12 ( a = 12.508 Å) grown under conditions of compression stress on the substrates Sm 3Ga 5O 12 ( a = 12.439 Å), Gd 3Ga 5O 12 ( a = 12.383 Å) and Ca 3Ga 2Ge 3O 12 ( a = 12.250 Å), and with garnets of composition (SmYCa) 3(FeGe) 5O 12 ( a = 12.389 Å) grown under conditions of tensile stress on Nd 3Ga 5O 12 substrates ( a = 12.508 Å). The experimental data obtained are in reasonable agreement with the conclusions of the theory.