Modeling of dislocation dynamics in germanium Czochralski growth

Abstract

Obtaining very high-purity germanium crystals with low dislocation density is a practically difficult problem, which requires knowledge and experience in growth processes. Dislocation density is one of the most important parameters defining the quality of germanium crystal. In this paper, we have performed experimental study of dislocation density during 4inch germanium crystal growth using the Czochralski method and comprehensive unsteady modeling of the same crystal growth processes, taking into account global heat transfer, melt flow and melt/crystal interface shape evolution. Thermal stresses in the crystal and their relaxation with generation of dislocations within the Alexander-Haasen model have been calculated simultaneously with crystallization dynamics. Comparison to experimental data showed reasonable agreement for the temperature, interface shape and dislocation density in the crystal between calculation and experiment.

A Coupled Approach to Compute the Dislocation Density Development during Czochralski Growth and Its Application to the Growth of High-Purity Germanium (HPGe)

“…This requires adding nodes at the propagating crystal/melt interface and, subsequently, setting dislocation densities in the new nodes. They used two approaches for the setting, as described in more detail in [8]. They found a reasonable agreement with the six experimental data points of etch pit density (EPD).…”

“…Numerical simulations are a valuable tool for detailed investigations of the Cz crystal growth, including such aspects as the global heat transfer, melt flow, thermal stresses, and dislocation density distribution. While a large amount of literature exists on modelling the Cz Ge crystal growth, see, e.g., [7][8][9], computing the dislocation density evolution is still a great challenge. The time evolution of the temperature field in the growing crystal has to be calculated accurately considering the growth process in the furnace.…”

“…A fully transient calculation was performed by Artemyev et al for the Czochralski growth of Ge [8]. They used the software package CGSim to perform a transient calculation of the crystal growth in the cylindrical part of the process.…”

Numerical Modeling of Heat Transfer and Thermal Stress at the Czochralski Growth of Neodymium Scandate Single Crystals

“…[ 6 ] A temporal analysis is also the prerequisite to perform computations including the dislocation dynamics, as, e.g., by the Alexander–Haasen model. [ 8 ]…”

Quasi-Transient Calculation of Czochralski Growth of Ge Crystals Using the Software Elmer

“…Dislocation multiplication is driven by thermal stresses, and thus, tuning the thermal field in the crystal is of severe importance. In the case of Czochralski growth with resistance heating, numerical results have been presented by Artemyev et al using the software package CGsim (http://str-soft.com/products/CGSim/) and compared with experimental results [2]. In the case of inductive heating, which is required to grow Ge crystals for detectors, the tuning of the thermal field is much more challenging.…”