Silicon single crystal pulling condition calculation program, silicon single crystal hot zone improvement method, and silicon single crystal growing method

1. A computer-readable medium storing a code of monocrystalline silicon pulling condition calculation program for determining, for growth of a monocrystalline silicon, an optimal value of a solid-liquid interface height h of a solid-liquid interface and an optimal value of a distance Gap between a heat shield plate of a pull-up apparatus for the monocrystalline silicon and a surface of a silicon melt, the program being configured, when being read and run by a computer, to enable the computer to perform the steps of:

setting a plurality of sets of pulling conditions based on a plurality of values of the solid-liquid interface height h and a plurality of values of the distance Gap between the heat shield plate and the surface of the silicon melt;

performing, for each set of the pulling conditions, the steps of: calculating a heat flux q (W/m 2 ) and a crystal surface temperature T(K) in the pull-up apparatus by global heat transfer analysis; defining a reference temperature Tref(K) and a geometry of the solid-liquid interface as boundary conditions, the reference temperature Tref(K) being given by an equation (1) below based on the calculated heat flux q(W/m 2 ) and crystal surface temperature T(K); recalculating an in-crystal temperature distribution in the monocrystalline silicon based on the defined boundary conditions; calculating a mean stress σmean caused in the monocrystalline silicon by structure analysis based on the recalculated in-crystal temperature distribution in the monocrystalline silicon; calculating a defect distribution in a pulling n in the monocrystalline silicon based on the calculated mean stress σmean in the monocrystalline silicon and the recalculated in-crystal temperature distribution in the monocrystalline silicon; and determining a defect-free region in the pulling direction in the monocrystalline silicon based on the calculated defect distribution in the pulling direction in the monocrystalline silicon;

drawing a contour line of the defect-free region on a two-dimensional map based on a dimension of the defect-free region in the pulling direction in the monocrystalline silicon for each set of the pulling conditions, the two-dimensional snap being defined by the distance Gap between the heat shield plate and the surface of the silicon melt and the solid-liquid interface height h; and

selecting, based on the contour line drawn on the two-dimensional map, one of the values of the solid-liquid interface height h and one of the values of the distance Gap between the heat shield plate and the surface of the silicon melt that maximize the dimension of the defect-free region, wherein

the mean stress mean is given by σmean=T+σrr+σ θθ +σzz)/3, where σrr, σ θθ , and σzz represent stress components perpendicular to r-plane, θ-plane, and z-plane, respectively,

Tref

=

T

4

-

q

ɛσ

4

(

1

)

where

ε=0.55: emissivity of the monocrystalline silicon, and

σ=5.67×10 −8 (W/m 2 /K 4 ): Stefan-Boltzmann coefficient.

2. A hot zone improvement method for a monocrystalline silicon, the method comprising:

reading the computer-readable medium storing a code of the monocrystalline silicon pulling condition calculation program according to claim 1 by a computer and running the monocrystalline silicon pulling condition calculation program by the computer to calculate the pulling conditions of the monocrystalline silicon for each of respective geometries of a plurality of hot zones;

calculating the defect-free region corresponding to each of the hot zones; and

selecting optimal one of the hot zones that provides a maximum defect-free region.

3. A monocrystalline silicon growing method for growing a monocrystalline silicon, the method comprising:

reading the computer-readable medium storing a code of the monocrystalline silicon pulling condition calculation program according to claim 1 by a computer and running the monocrystalline silicon pulling condition calculation program by the computer to calculate the pulling conditions of the monocrystalline silicon; and

pulling up the monocrystalline silicon based on the calculated optimal value of the solid-liquid interface height h and optimal value of the distance Gap between the heat shield plate and the surface of the silicon melt.

4. A monocrystalline silicon growing method for growing a monocrystalline silicon, the method comprising:

based on the hot zone improvement method of a monocrystalline silicon according to claim 2 , calculating the pulling conditions of the monocrystalline silicon for each of the respective geometries of the plurality of hot zones; and

pulling up the monocrystalline silicon based on the calculated optimal value of the solid-liquid interface height h and optimal value of the distance Gap between the heat shield plate and the surface of the silicon melt.