Dislocations in crystals

Silicon carbide as a representative wide band-gap semiconductor has recently received wide attention due to its excellent physical, thermal and especially electrical properties. It becomes a promising material for electronic and optoelectronic device under high-temperature, high-power and high-frequency and intense radiation conditions. During the Silicon Carbide crystal grown by the physical vapor transport process, the temperature gradients induce thermal stresses which is a major cause of the dislocations multiplication. Although large dimension crystal with low dislocation density is required for satisfying the fast development of electronic and optoelectronic device, high dislocation densities always appear in large dimension crystal. Therefore, reducing dislocation density is one of the primary tasks of process optimization. This dissertation aims at developing a transient finite element model based on the Alexander-Haasen model for computing the dislocation densities in a crystal during its growing process. Different key growth parameters such as temperature gradient, crystal size will be used to investigate their influence on dislocation multiplications. The acceptable and optimal crystal diameter and temperature gradient to produce the lowest dislocation density in SiC crystal can be obtained through a thorough numerical investigation using this developed finite element model. The results reveal that the dislocation density multiplication in SiC crystal are easily affected by the crystal diameter and the temperature gradient. Generally, during the iterative calculation for SiC growth, the dislocation density multiples very rapidly in the early growth phase and then turns to a relatively slow multiplication or no multiplication at all. The results also show that larger size and higher temperature gradient causes the dislocation density enters rapid multiplication phase sooner and the final dislocation density in the crystal is higher.

The dislocation density in the Gallium Arsenide (GaAs) crystal is generated by the excessive thermal stresses during Czochralski (CZ) growth process. A constitutive equation which couples the dislocation density with the plastic deformation is employed to simulate the dislocation density in the crystal. The temperature distribution in the crystal during growth process is obtained by solving the quasi-steady-state (QSS) heat transfer equation. The thermal stresses induced by the temperature distribution are calculated by finite element method. The resolved shear stress (RSS) in each slip system is obtained by stress transformation. The dislocation motion and multiplication in each slip system are simulated using the constitutive equation and the total dislocation density in the crystal is obtained. The dislocation density is also found to be affected by the growth orientation, growth speed, ambient temperature and the radius of the crystal. The dislocation density in GaAs crystals grown from different growth orientation and crystal radius at various ambient temperatures will be calculated so that the influence of these growth parameters on the dislocation density can be understood. Consequently, one can control the growth parameters to reduce the dislocation density generated in the crystal during the CZ growth process.

Thermal stresses are induced by temperature variations in gallium arsenide(GaAs) crystal growth. The thermal stresses cause plastic deformations by dislocation and dynamic interaction in the crystal. In this study, firstly the temperature distribution in the Czochralski technique (CZ) growth of GaAs crystal is obtained according to the Jordan model. Secondly a visco-plastic response function for the GaAs crystal is developed from the Haasen model. Finally a nonlinear finite element model is employed to simulate the dislocation generation during CZ growth of GaAs crystal.

The generation and multiplication of dislocations in Gallium Arsenide (GaAs) and Indium Phosphide (InP) single crystals grown by the Vertical Gradient Freeze (VGF) process is predicted using a transient crystallographic finite element model. This transient model is developed by coupling microscopic dislocation motion and multiplication to macroscopic plastic deformation in the slip system of the grown crystals during their growth process. During the growth of InP and GaAs crystals, dislocations are generated in plastically deformed crystal as a result of crystallographic glide caused by excessive thermal stresses. The temperature fields are determined by solving the partial differential equation of heat conduction in a VGF crystal growth system. The effects of growth orientations and growth parameters (i.e., imposed temperature gradients, crystal radius and growth rate) on dislocation generation and multiplication in GaAs and InP crystals are investigated using the developed transient crystallographic finite element model. Dislocation density patterns on the cross section of GaAs and InP crystals are numerically calculated and compared with experimental observations. For crystals grown along [001] and [111] orientations, the results show that more dislocations are generated as the temperature gradient, the crystal growth rate and the crystal radius increase. For the same growth process, it shows that the crystal grown along [111] orientation is a favorable growth direction to grow lower dislocation density crystals. All the results show a famous "W" shape and four fold symmetry dislocation density pattern in GaAs and InP crystals grown from both orientations regardless of crystal growth parameters, which agree well with the patterns observed in actual grown crystals. Therefore, this developed crystallographic model can be employed by crystal grower to design an optimal growth parameters and orientations for growing low dislocation density in advanced semiconductor and optical crystals.

Dislocations in Gallium Arsenide (GaAs) and Indium Phosphide (InP) single crystals are generated by excessive stresses that are induced during the crystal growth process, and the fabrication and packaging of microelectronic devices/circuits. The presence of dislocations has adverse effects on the performance, lifetime and reliability of the GaAs and InP-based devices/circuits. It is well known that dislocation density can be significantly reduced by doping impurity atoms into the GaAs and InP crystal and/or decreasing the thermal stresses in these crystals during their growth process. In order to reduce the dislocation density generated in the GaAs and InP crystals, the influence of crystal growth parameters and doping impurity atoms on the dislocations reduction in GaAs and InP crystals has to be understood. Therefore, a transient finite element model was developed to simulate the dislocation generation in GaAs and InP crystals grown from the melt. A viscoplastic constitutive equation that couples a microscopic dislocation density with a macroscopic plastic deformation is employed to formulate this transient finite element model, where the dislocation density is considered as an internal state variable and the doping impurity is represented by a drag-stress in this constitutive model. GaAs and InP single crystals grown by the vertical gradient freeze (VGF) process were adopted as examples to study the influences of doping impurity and growth parameters on dislocations generated in these grown crystal. The calculated results show that doping impurity can significantly reduce dislocation generation and produces low-dislocation-density or dislocation free GaAs and InP single crystals. It also shows that the dislocations generated in GaAs and InP crystals increase as the crystal diameter and imposed temperature gradient increase, but do not change or increase slightly as the crystal growth rate increases. Therefore, this finite element model can be effectively used by crystal growers to select acceptable levels of doping impurity, crystal diameter, temperature gradient, and growth rate to produce the lowest dislocation density in GaAs and InP crystals through a thorough numerical investigation using this developed finite element model.