Thermodynamic analysis of SiC polytype growth by physical vapor transport method

doi:10.1016/j.jcrysgro.2011.03.059

Journal of Crystal Growth

Volume 324, Issue 1, 1 June 2011, Pages 78-81

https://doi.org/10.1016/j.jcrysgro.2011.03.059 Get rights and content

Abstract

Crystal growth of a certain polytype of SiC in a process of physical vapor transport was studied on the basis of classical thermodynamic nucleation theory in conjunction with numerical results obtained from a global model. Formation of a certain polytype in the nucleation stage is determined by the energy balance among surface energy, formation energy and supersaturation. The preferential growth condition of a certain polytype was estimated. The value of supersaturation was estimated using a numerical model obtained by a global model that includes species transport as well as heat transport in a furnace. The results of calculation showed that 4H polytype is more stable than 15R, 6H and 3C polytypes. Free energy difference between 4H and 6H polytypes decreased when total pressure in the furnace decreased.

Introduction

SiC has a great potential for devices operating at high temperatures, high power and high frequency [1], [2], [3]. Bulk SiC crystals are commonly grown by the physical vapor transport (PVT) method. One of the most important and interesting properties of SiC is the different polytypes that are easily formed in a crystal during crystal growth. The cubic polytype of 3C has a bandgap of 2.3 eV, while other polytypes such as 4H and 6H have a bandgap of 3.2 eV. We therefore have to control polytypes of SiC to obtain electronic devices such as diodes and transistors in which band structure can be precisely controlled.

There have been several reports on control of polytypes of SiC [1], [4], [5], [6] since experimental and theoretical results have shown that several polytypes can be easily formed in a grown crystal. Fissel [1] reported results of stability analysis based on the classical thermodynamic nucleation theory with a certain condition of supersaturation. Fissel [1] discussed polytype stability based on two-dimensional (2D) and three-dimensional (3D) nucleation models [1], [7] including supersaturation, surface and formation energy of many polytypes under solid-source molecular beam epitaxy. These papers discussed on the nucleation theory that includes free energy calculation from the point of view of supersaturation of carbon. Calculation indicated that the formation of a polytype in the nucleation stage is determined by a set of growth parameters including substrate temperature, Si/C-ratio and C-flux.

In this study, we investigated the free energy of formation of 2D nucleation for the four polytypes, 3C, 4H, 15R and 6H, by using numerical results obtained by a global model reported elsewhere [8]. We developed a set of analysis systems that includes almost all of the effects in heat and mass transport processes, including compressible effect, convection effect, buoyancy effect, flow coupling of argon gas and species, and Stefan effect. Evaporation and deposition flux is provided according to the supersaturation of species at the seed or supercooling at the powder source. We used a global model [8], which can calculate vapor pressure of Si, SiC₂ and Si₂C by using a global heat and species transfer, which includes gas heat transfer, gas convection and species transfer of Si, SiC₂ and Si₂C, therefore supersaturation of carbon can be estimated. Then, we can obtain free energies of formation of 2D nucleation for the four polytypes 3C, 4H, 15R and 6H.

Section snippets

Calculations of heat and species transfer and free energy

A furnace growing a crystal with 2 in. diameter was selected to this work of a global simulation. The configuration of the furnace was reported elsewhere [9]. The SiC PVT growth system consists of SiC powder, a graphite crucible, an insulation shield, a graphite pedestal and induction coils. The SiC powder is placed inside the crucible, and the seed is attached to the bottom of the lid of the crucible. The diameter of seed is 50 mm. The global model takes into account all heat transfer processes

Calculated results

The left side of Fig. 1(a) shows the distribution of temperature from the powder to the seed, and the right side of Fig. 1(a) shows the distribution of vapor pressure of SiC₂ in growth chamber. The left side and the right side of Fig. 1(b) show a distribution comparison of vapor pressures of Si₂C and SiC₂, respectively. Argon pressure in the furnace was set to 1 Torr. The temperature of a seed was kept at 2270 K. The vapor pressures of the species Si, SiC₂ and Si₂C in argon gas on a seed

Conclusions

The formation of polytypes of SiC during crystal growth was studied by using thermal equilibrium analysis based on 2D nucleation. The results showed that free energy obtained from supersaturation becomes small near the periphery and the center of a seed crystal. Calculations also showed that the free energy difference between 6H and 4H polytypes becomes small when total pressure in a furnace is small. To improve the process to control polytype, supersaturation of carbon on a seed crystal should

Acknowledgments

This work was supported by a Grant-in-Aid for Scientific Research (B) 19360012 and a grant-in-aid for the creation of innovation through business-academy-public sector cooperation from the Japanese Ministry of Education, Science, Sports and Culture.

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Thermodynamic analysis of SiC polytype growth by physical vapor transport method

Abstract

Introduction

Section snippets

Calculations of heat and species transfer and free energy

Calculated results

Conclusions

Acknowledgments

J. Cryst. Growth

J. Cryst. Growth

Int. J. Heat Mass Transfer

J. Cryst. Growth

Thin Solid Film

J. Cryst. Growth

J. Cryst. Growth

Mater. Sci. Eng. B