Effective distribution coefficient in magnetic Czochralski growth

Boron segregation control in silicon crystal ingots grown in Czochralski process

“…k e can be calculated from the slope or the intercept in the log-log plot of Eq. (5). If k e is close to unity, lnðC=C 0 Þ should be 0 at f ¼ 0 as shown in Eq.…”

“…They found that the magnetic field stabilized the melt convection and k e increased with increasing magnetic strength. These facts were verified in theoretical studies with a simplified model by Hurle and Series [5]. Various types of magnetic fields were discussed by Series and Hurls [6].…”

Thermally induced effects during initial stage of crystal growth from melts

“…Integrated computational models including hydrodynamics, heat and mass transfer [1][2][3][4][5][6][7][8][9][10][11], radiation transport [12][13][14], and electromagnetic field effects [15][16][17][18] allow a detailed parametric analysis of the crystal growth interface, of dopant and impurities distribution in crystals, of the temperature field along the crystal and associated stresses [19,20], of onset of constitutional supercooling and morphological destabilization [21,22], and of the formation of defect structures in the growing crystals [23]. Analytical computational models being less comprehensive nevertheless have several advantages allowing fast and simple order of magnitude estimates that identify the main qualitative trends necessary for practical process optimization.…”

Distribution coefficient of boron in Si crystal ingots grown in cusp-magnetic Czochralski process

“…They found that the magnetic field stabilized the melt convection and k e increased with increasing magnetic strength. These facts were verified in theoretical studies with a simplified model by Hurle and Series [8]. Various types of magnetic field were discussed by Series and Hurle [9].…”

“…In all previous studies [6][7][8][9], the effect of the magnetic field on melt flow and dopant distribution has been investigated experimentally and numerically, and the cusp-magnetic field applied to the silicon melt was symmetric to zero-Gauss plane (ZGP), where ZGP is flat (MR=1 in Fig. 1) due to the same electric-current densities of the upper and lower coils in the configuration of the cusp-magnetic field.…”