Method of controlling single crystal diameter
When pulling and growing a single crystal from a raw material melt by the Czochralski method, a boundary between the single crystal and the raw material melt is imaged by an optical sensor, and also the weight of the single crystal is measured by a weight sensor, a diameter value of the single crystal is calculated on the basis of first measured values of the diameter of the single crystal derived from image data captured by the optical sensor and second measured values of the diameter of the single crystal derived from weight data captured by the weight sensor, and a pulling rate of the single crystal and the temperature of the raw material melt are adjusted on the basis of the calculated diameter value to thereby control the diameter of the single crystal, and thus it is possible to accurately measure the diameter of a growing single crystal.
1. A method for controlling the diameter of a single crystal when pulling and growing the single crystal from a raw material melt by the Czochralski method, comprising:
a first step of imaging a boundary between the single crystal and the raw material melt by an optical sensor, and also measuring a weight of the single crystal by a weight sensor;
a second step of calculating a diameter value of the single crystal on the basis of first measured values of the diameter of the single crystal derived from image data captured by the optical sensor and second measured values of the diameter of the single crystal derived from weight data captured by the weight sensor;
a third step of adjusting a pulling rate of the single crystal and a temperature of the raw material melt on the basis of the calculated diameter value to thereby control the diameter of the single crystal;
a fourth step of accumulating said first and second measured values; and
a fifth step of updating coefficients of formulae used for calculation of the diameter value on the basis of average values of said accumulated first and second measured values for a predetermined time period,
wherein the fifth step is carried out during the growth of the single crystal for every execution of the second step or at a predetermined frequency.
2. The method for controlling the diameter of a single crystal according to claim 1 , wherein in the second step, the diameter value D [mm] is calculated by the formula (1) below, and in the fifth step, the coefficients A are updated by the formula (2) below:
D=N×A×B (1); and
A=A′×{ 1·( D 1 ·D 2)/ D 2} (2)
where in the formula (1), N represents the number of pixels included in between brightness peaks in image data captured by the optical sensor [number of pixels], A represents the weighted coefficient, and B represents the diameter conversion coefficient [mm/number of pixels], and in the formula (2), A represents the weighted coefficient after updating, N represents the weighted coefficient before updating, D 1 represents the average value, within a predetermined period, of the accumulated first measured values pursuant to the diameter measurement by the optical system, and D 2 represents the average value, within a predetermined period, of the accumulated second measured values pursuant to the diameter measurement by the weight system.