# Homogenization of Radial Temperature by a Tungsten Sink in Sublimation Growth of 45 mm AlN Single Crystal

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}·K

^{−1}) and small lattice and thermal expansion mismatch with GaN [1]. AlN has great potential in high-power and high-frequency electronic and deep ultraviolet (UV) optoelectronic industries [2]. AlN single crystal is usually grown by the physical vapor transport (PVT) method [3]. However, AlN crystal growth is difficult, especially in large sizes, with cracks occurring frequently [4]. To reduce the probability of crack occurrence, it is important to reduce the thermal stress by homogenizing the radial temperature distribution. There are two methods to achieve this. The first is to perform experiments using trial and error; however, this method is expensive and time consuming. The second is numerical simulation and optimization, which is low cost and highly efficient [5].

## 2. Simulation

#### 2.1. Geometric Model

#### 2.2. Mathematical Model

_{radi}is the radiative heat flux on the surface of the growth chamber and q

_{eddy}is the heat flux caused by the eddy current.

_{rr}, σ

_{ΦΦ}and σ

_{zz}represent the normal stress; τ

_{rz}represents the shear stress; c

_{ij}is the elastic constant; ε

_{rr}, ε

_{ΦΦ}, ε

_{zz}and ε

_{rz}are the strain components; α

_{r}, α

_{Φ}and α

_{z}are the thermal expansion coefficients and T

_{ref}is the reference temperature.

## 3. Results and Discussion

#### 3.1. Temperature Distribution

#### 3.2. Temperature Gradients in Radial and Axial Directions

#### 3.3. Thermal Stress in the Seed

#### 3.4. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) AlN sublimation growth furnace according to traditional design; (

**b**) AlN sublimation growth furnace according to improved design.

**Figure 2.**Temperature distributions for (

**a**) the original design, (

**b**) A design, (

**c**) B design and (

**d**) C design.

**Figure 4.**Temperature gradients of different types of crucibles (DT/Dz and DT/Dr represent the axial and radial temperature gradient, respectively).

**Figure 5.**Comparison of temperature gradients in crucibles with different heat sinks. A, B and C designs represent designs with different bottom fin lengths; 1 and 2 represent tungsten sinks with and without the holder and top fin, respectively.

**Figure 6.**Temperature distributions of the AlN seed in different design crucibles: (

**a**) original design; (

**b**) A design; (

**c**) B design; (

**d**) C design.

**Figure 7.**Thermal stress distributions of the AlN seed in crucibles with different designs: (

**a**) original design; (

**b**) A design; (

**c**) B design; (

**d**) C design.

Thermal Conductivity (W/m·K) | Density (kg/m ^{3}) | Heat Capacity (J/kg·K) | |
---|---|---|---|

Tungsten crucible | 180 | 19,300 | 135 |

Insulation | 0.5 | 170 | 2100 |

AlN powder | 22.55 | 270.34 | 1172.7 |

AlN seed | 320 | 3250 | 1197 |

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**MDPI and ACS Style**

Yu, Y.; Liu, B.; Tang, X.; Liu, S.; Gao, B.
Homogenization of Radial Temperature by a Tungsten Sink in Sublimation Growth of 45 mm AlN Single Crystal. *Materials* **2020**, *13*, 5553.
https://doi.org/10.3390/ma13235553

**AMA Style**

Yu Y, Liu B, Tang X, Liu S, Gao B.
Homogenization of Radial Temperature by a Tungsten Sink in Sublimation Growth of 45 mm AlN Single Crystal. *Materials*. 2020; 13(23):5553.
https://doi.org/10.3390/ma13235553

**Chicago/Turabian Style**

Yu, Yue, Botao Liu, Xia Tang, Sheng Liu, and Bing Gao.
2020. "Homogenization of Radial Temperature by a Tungsten Sink in Sublimation Growth of 45 mm AlN Single Crystal" *Materials* 13, no. 23: 5553.
https://doi.org/10.3390/ma13235553