Abstract
Numerical simulations of the transient temperature field and dislocation density distribution for a recently published silicon crystal heating experiment were carried out. Low- and high-frequency modelling approaches for heat induction were introduced and shown to yield similar results. The calculated temperature field was in very good agreement with the experiment. To better explain the experimentally observed dislocation distribution, the Alexander–Haasen model was extended with a critical stress threshold below which no dislocation multiplication occurs. The results are compared with the experiment, and some remaining shortcomings in the model are discussed.
Highlights
Dislocation-free silicon (Si) single crystals are grown with the Czochralski (CZ) and Floating-Zone (FZ) methods
A new numerical model in open-source library deal.II was developed for the simulation of the temperature field and the dislocation density dynamics
It is freely available as a new open-source solver package MACPLAS [20]
Summary
Dislocation-free silicon (Si) single crystals are grown with the Czochralski (CZ) and Floating-Zone (FZ) methods. In FZ and CZ processes, the initial dislocations are generated due to high temperature gradients arising during the contact of the crystalline seed with the melt These are eliminated using the Dash technique—by growing a long, thin neck until dislocations terminate at the crystal surface by the climb mechanism [1]. Recent attempts to develop new techniques without the Dash neck, such as the modified FZ method, have shown that in cases using large-area seeds, the dislocations always occur at high temperatures above 1200 °C [2,3] In this case, dislocation generation is believed to be caused primarily by high thermal stresses.
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