Mechanics of shaped crystal growth from the melt

Abstract

We present the numerical formulation of the thermal stress driven steady-state dislocation generation during the growth of shaped crystals from the melt, with Czochralski (CZ) growth of solid cylinder III -V compound semiconductors as an example. We use and compare the Haasen-Alexander model, coupling dislocation multiplication and creep strain rates, and the Jordan model, based on thermoelastic stresses. Growth parameters may be chosen so as to produce an overall approximately flat interface, leading to reduced dislocation density in the majority of the crystal's cross section. Calculation of final dislocation density requires the initial dislocation density and all stress components along the solid-liquid interface, microstructural features which depend on the physical processes leading to solidification. The final dislocation density is not sensitive to the initial dislocation density along the solid-liquid interface, but strongly depends on the interface stress. Significant stress relaxation at the interface is required to produce experimentally observed "W" shaped dislocation patterns. Crystal growth direction and crystalline anisotropy couple elastic (lattice) and plastic (slip systems) crystalline anisotropy.

Solid mechanics and material strength studies on the melt growth of bulk single crystals

“…The parameters including in the HAS model are identified for Ge, Si, InSb, InP, GaAs, and so on [32][33][34][35].…”

“…Fig. 3 shows the dislocation density distributions for a GaAs bulk single crystal at 35,87,191,312,451 and 607 min after the CZ growth starts [44]. High dislocation density appears at the central and peripheral regions of the bulk single crystal.…”

“…In the HAS model, only the multiplication of dislocations is considered and the annihilation of dislocations is not considered. The modification of the HAS model was done by Lambropoulos and Wu [35] and Gondet et al [51] to include the effect of the annihilation of dislocations. The constitutive equation for Si including the effect of the oxygen atoms was proposed by Maroudas and Brown [53].…”

Dislocation density evaluation using dislocation kinetics model

“…The parameters including in the HAS model are identified for Ge, Si, InSb, InP, GaAs, and so on [10][11][12]20]. …”

An insight into dislocation density reduction in multicrystalline silicon

“…In principle, the reduction of dislocation densities from 10 6 -10 8 cm À 2 to as low as 10 3 -10 4 cm À 2 may lead to an improvement in the cell performance (from 13-14% to 420%). Hence, efforts have been made to suppress the harmful impact of dislocations on cell performance, to avoid the formation of dislocations during crystal growth [8,9] and to remove dislocations after ingot growth [10][11][12][13]. Despite numerous studies on the passivation of dislocations and the gettering of fast-diffusing metal impurities from dislocations, the improvement of cell performance after these processes is still very limited in regions with high dislocation densities (410 6 cm À 2 ) [14].…”