US 12,258,675 B2
Method of producing a silicon single crystal based on concentration profiles of vacancies and interstitial silicon atoms during pulling of a silicon single crystal by the Czochralski process
Ryota Suewaka, Tokyo (JP)
Assigned to SUMCO CORPORATION, Tokyo (JP)
Appl. No. 17/772,895
Filed by SUMCO CORPORATION, Tokyo (JP)
PCT Filed Aug. 12, 2020, PCT No. PCT/JP2020/030726
§ 371(c)(1), (2) Date Apr. 28, 2022,
PCT Pub. No. WO2021/084843, PCT Pub. Date May 6, 2021.
Claims priority of application No. 2019-196678 (JP), filed on Oct. 29, 2019.
Prior Publication US 2022/0364260 A1, Nov. 17, 2022
Int. Cl. C30B 15/20 (2006.01); C30B 29/06 (2006.01); G06F 30/20 (2020.01); G06F 111/10 (2020.01)
CPC C30B 15/20 (2013.01) [C30B 29/06 (2013.01); G06F 30/20 (2020.01); G06F 2111/10 (2020.01)] 6 Claims
OG exemplary drawing
 
1. A method of producing a silicon single crystal based on concentration profiles of vacancies and interstitial silicon atoms during pulling of a silicon single crystal by a Czochralski process, the concentration profiles being calculated using a convection-diffusion equation, the method comprising:
determining a concentration Cveq of vacancies in thermal equilibrium represented by an equation (A) shown below and a concentration CIeq of interstitial silicon atoms in thermal equilibrium represented by an equation (B) shown below in the convection-diffusion equation by fitting calculation results to experimental results by using as a fitting parameter, one of a first stress coefficient avf in the equation (A) and a second stress coefficient aIf in the equation (B) and setting the other to be a fixed value obtained by a calculation approach,

OG Complex Work Unit Math
wherein in the equations (A) and (B), T is a temperature, P is a stress, C0,V and C0,I are constants, kB is the Boltzmann constant, Evf is a formation energy of a vacancy, and EIf is a formation energy of an interstitial silicon atom;
calculating the concentration profiles of each of the vacancies and the interstitial silicon atoms during the pulling of the silicon single crystal by the Czochralski process using the convection-diffusion equation for a design of a single crystal pulling apparatus;
repeating changing the design and calculating the concentration profiles of each of the vacancies and the interstitial silicon atoms for the changed design until a condition under which a defect-free silicon single crystal can be obtained is found;
manufacturing the single crystal pulling apparatus in accordance with the design which can produce a defect-free silicon single crystal; and
producing a defect-free silicon single crystal using the manufactured single crystal pulling apparatus under the condition under which a defect-free silicon single crystal can be obtained.