A substrate for manufacturing a semiconductor device is mainly made of high-purity single crystal silicon. The Czochralski method (hereinafter referred to as “ CZ method”) is, in general, used for manufacturing the single crystal silicon. The CZ method is performed by filling blocks of raw material polycrystalline silicon into a crucible provided in a semiconductor single crystal manufacturing apparatus, and melting the raw material polycrystalline silicon by a heater provided around the crucible. Then, a seed crystal held by a seed chuck is dipped into the melt, and the seed crystal is pulled up while rotating the seed chuck and the vitreous silica crucible in the same direction or opposite direction, to grow high-purity single crystal silicon. For this reason, the crucible needs to be manufactured to have an uniform quality so as to include a certain amount of impurities in order to introduce a certain amount of impurities into the grown ingot.
Conventionally, a rotating mold method is known as a method of manufacturing the above-mentioned vitreous silica crucible. This method is performed by heating and vitrifying an inner surface of a silica powder molded body deposited on an inner surface of a rotating mold, from a mold cavity side by use of heat plasma generated by arc discharge.
Parameters such as a value of discharge current supplied to the arc electrodes (arc current) and the position of the arc electrodes (the height of the electrodes, the deviated position of the electrodes) in generating heat plasma for heating the crucible are currently adjusted based on experience and intuition.
Therefore, parameters used for actual manufacturing can be estimated by simulating a temperature distribution, of a silica powder molded body inner surface, enabling manufacturing a vitreous silica crucible with quality higher than the standard. A finite element method or finite difference method is currently known for the simulation of thermal fluid (See Patent Document 1).