Thermal Stress Distribution Of GaAs And InP Crystals In LEC Growth And Of GaAs Crystal In LEFZ Growth

The GaAs and InP crystals as compound semiconductors are the basic microelectronics and photoelectron materials. The dislocation in the crystals can seriously influence the electrical and optic characteristics. The presence of dislocations in grown crystal has been attributed to thermal stress in the crystal. To estimate the density and distribution of dislocation, the stress distributions in Liquid Encapsulation Czochralski (LEC) growth of 3 in. (0.075m) diameter single-crystal GaAs and InP and in Liquid Encapsulation Floating zone (LEFZ) growth 3in.(0.075m) diameter single-crystal GaAs have been calculated by using finite element numerical methods. It has been assumed that the crystals are in a steady axisymmetric state with isotropic linearly elastic body. In accordance with different flow and heat transfer under the effect of boron oxide thickness, axial magnetic field strength as well as the rotation of crystal, the thermal stress distribution in LEC growth of GaAs crystal has been calculated;Corresponding to the different flow and heat transfer under the various boron oxide thickness and rotation of crystal and feed rod ,the thermal stress distribution in LEFZ growth of GaAs crystal has been obtained;In accordance with different flow and heat transfer under the effect of boron oxide thickness, axial magnetic field strength, crystal pulling rate and rotation of crystal and crucible, the thermal stress distribution in LEC growth of InP crystal has been calculated. All calculations above consider the effect of the growing interface shape. The conclusions in LEC growth of GaAs are: 1) The maximum Von Mises thermal stresses are located at the outer surface of the GaAs crystal, which have different values under different conditions, changing between 7.41MPa and 21.5MPa; 2) When the flow in the B2O3 encapsulation is much weak, the maximum Von Mises stresses are above the B2O3 encapsulation surface in the outer surface. When the flow in the B2O3 encapsulation is much strong, the maximum thermal stresses are below the B2O3 encapsulation surface; 3) If the growing interface is concave (concave to the melt) near the periphery of the crystal and much more concave, the maximum thermal stresses are close to the growing interface below B2O3 encapsulation and much larger. The growing interface has an obvious infection on the distribution and values of the thermal stresses. The results in LEFZ growth of GaAs show that: 1) The maximum Von Mises thermal stresses are always in the right side of GaAs crystal. As the B2O3 encapsulation gets thicker, the maximum thermal stress gets less. As the crystal rotation speed becomes larger, the maximum thermal stress gets a little larger. Moreover, the rotation of feed rod has little effect on the maximum thermal stress. 2) The stress distribution, the maximum and average thermal stresses along the growing interface have the relation with the growing interface. The growing interface is more flat, the maximum and average stress along the interface gets less; vice versa. Comparing the convex interface, the concave interface can lead to the larger stress along the growing interface. The results in LEC growth of InP show that: 1) The maximum stresses locate at the center of the melt/crystal interface in most cases. The stress distribution in the crystal is mainly affected by the total heat flow from the melt/crystal interface and the growing interface. As the B2O3 encapsulation gets thicker, the interface deflection gets larger but not obvious and the total heat flow from the melt/crystal interface becomes less, so the maximum thermal stress gets less. As the magnetic filed strength gets larger, the total heat flow from the melt/crystal interface becomes larger, and the growing interface turns convex into concave, which lead to the maximum thermal stress gets larger corresponding to the stronger magnetic filed strength. As a higher pulling rate is associated with a more release of the latent heat that the crystal can take away, the maximum thermal stress gets larger. With increasing the crystal rotation, the total heat flow from the melt/crystal interface gets larger and the growing interface turns convex into concave, so the maximum thermal stress gets larger. Corresponding to the different crucible rotation speeds, the total heat flow from the melt and crystal interface changes little and the growing interface is nearly same, so the difference of the maximum thermal stress under various crucible rotations is small; 2) The changing trend of the maximum thermal stress is consistent with that of the total heat flow from the melt/crystal interface. The more total heat flow from the melt and crystal interface, the larger the maximum thermal stress vice versa; 3) When the growing interface is convex which includes concave near the center and convex near the periphery, the isotherms deflection in the center along the growing interface and below B2O3 encapsulation height in the outer surface of crystal gets large, which leads to two peaks stresses there and the values of the peaks stresses are almostly same. When the growing interface is concave, the stress distribution in the growing interface nearly takes on the trend of decreasing along radius direction.