Effect of Internal Radiation on Process Parameters in the Global Simulation of Growing Large-Size Bulk β-Ga2O3 Single Crystals with the Czochralski Method

Xia Tang,Botao Song,Yue Yu,Botao Liu,Pengfei Han,Bing Gao,Sheng Liu

doi:10.3390/cryst11070763

Abstract

As a crystal grows, the temperature distribution of the crystal and melt will change. It is necessary to study the dynamic process of single-crystal growth. Due to the relatively low crystallization rates used in the industrial Czochralski growth system, a steady state is used to compute the temperature distribution and melt flow. A two-dimensional axisymmetric model of the whole Czochralski furnace was established. The dynamic growth process of large-size bulk β-Ga2O3 single crystal using the Czochralski method has been numerically analyzed with the parameter sweep method. In this paper, two cases of internal radiation and no internal radiation were compared to study the effect of radiation on the process parameters. The temperature distribution of the furnace, the temperature field, and the flow field of the melt was calculated. The temperature, the temperature gradient of the crystal, the temperature at the bottom of the crucible, and the heater power were studied for the crystals grown in the two cases of radiation. The results obtained in this study clearly show that the loss calculated by including the internal radiation is higher compared to that including the surface radiation.

Highlights

Gallium oxide has a wider band-gap than SiC and GaN, and its unique properties mean that it is used in many devices, including Schottky barrier diodes (SBDs), inverters equipment, circuits used in high-temperature, high-humidity and high-radiation environments, and field-effect transistors (FET) [5]
Two models of surface radiation and internal radiation are compared to study the effect of radiation on the process parameters
The temperature, the temperature gradient of the crystal, the temperature at the bottom of the crucible, and the heater power are studied when the crystal is growing in the two cases of radiation

Summary

Karayiannis

Gallium oxide has five polymorphisms, and other phases transform into the β phase at high temperatures. β-Ga2 O3 is the most stable crystal structure, with a melting point of 1800 ◦ C under atmospheric pressure [1,2]. Galazka et al [8] used the Czochralski method to grow β-Ga2 O3 single crystals that were 2–3 inches in diameter. Some authors believed that the surface tension of the melt being reduced by impurities is the cause of spiral growth [21,22]. The Czochralski method was used to grow large-diameter single crystals of Ge and Si and some oxide crystals [24,25,26]. The crystal growth furnace for growing oxide crystals using the Czochralski method includes a heater, a puller, a pulling shaft connected to a weighing cell, a pulling/rotating motor, and a PID (proportional, integral, differential) controller computer. Established a 2-dimensional global model, analyzed the flow field and temperature field by steady-state simulation, and calculated the growth of the phase interface of different sizes by a transient method. Dynamic modeling was used to analyze the effects of radiation on the process parameters during the whole growth process

Geometric Model

Mathematical Model

The Actual Governing Equations of the Model

Mesh Model and Boundaries

Results and Discussion

Conclusions