This invention relates to the apparatus and the process for producing single crystals with little OSF generation and excellent dielectric strength of gate oxide films by adjusting the temperature gradient of the silicon single crystal in the direction of pulling. The apparatus is provided with a crucible which contains the melt of the single crystal material, a heating element which heats the melt, a pulling shaft to grow the single crystal, a protective gas inlet pipe, and a chamber which contains all above mentioned components. In addition, the apparatus is provided with a circular cylinder or a cylindrical shaped heat resistant and heat insulating component below the protective gas inlet pipe noted above. In the process of producing single crystals, the single crystal is pulled up through the circular cylinder or a cylindrical shape heat resistant and heat insulating component below the protective gas inlet pipe, and while the palled-up crystal is at high temperature the temperature gradient in it is held small and when the crystal is cooled to low temperature the temperature gradient is increased.