Analysis of dislocation cell patterns in as-grown compound materials (GaAs, CaF2)

The present paper investigates the correlations between the cell dimension d of characteristic dislocation cell patterns and acting thermo-elastic stress τ at the growth of GaAs and CaF 2 crystals. The dislocation rearrangement into cell networks are due to plastic relaxation under external or internal stresses. We scaled the cell diameters d with dislocation density ρ and thermoelastic stress τ . The dislocation density, determined by etch pit density (EPD) analysis and the cell dimensions, revealed by etching of wafers were correlated with numerically modeled thermoelastic stress. In order to obtain realistic mean size of the 3D cells from the cross-sectional 2D cuts a stereological method in combination with an automatic image processing program was applied. Different d ( τ )-proportionalities in VCz and VGF GaAs crystals, due to the varying thermal conditions and stay times of the growing crystal at high temperatures, are observed. The results show that for thermoelastic stresses above 1 MPa the well-known universal relation d = αKGbτ −1 ( K , α -constants, G- shear modulus, b -Burgers vector) proved to be valid. At lower τ , typically for low-temperature-gradient growth like VCz-method, the exponent in the d ( τ )-correlation tends to be less than −1.