Simulation of boron effects on OISF-ring dynamics for Czochralski silicon growth: a comparative study

Huang, Lei-Ching; Lee, P.C.; Hsieh, C.K.; Shu, Weining; Lan, C.W.

doi:10.1016/j.jcrysgro.2004.02.094

Cited by 4 publications

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Voronkov and Falster 87 on the other hand compared possible influence of doping on the equilibrium concentrations of the charged intrinsic point defects and compared this with other possible reasons like dopant pairing with self-interstitials and vacancies. Huang et al 89 performed simulations comparing both previous models and concluded that the electronic shift model gives the best results and needs also the lowest number of fitting parameters. As was discussed in paragraph IV, the pairing between substitutional B atoms and self-interstitials will increase the total concentration of self-interstitials while the number of free self-interstitials (not bound to a B atom) will hardly decrease.…”

Section: Impact Of Fermi Level and Bandgap On Intrinsic Point Defect mentioning

confidence: 99%

Silicon Single Crystal Growth from a Melt: On the Impact of Dopants on thev/GCriterion

Vanhellemont

Kamiyama

Sueoka

2013

ECS J. Solid State Sci. Technol.

View full text Add to dashboard Cite

The so called v/G criterion defines a critical value 0 crit of the ratio of the pulling rate v over the thermal gradient G at the melt-solid/interface. For a ratio larger than this critical value, the crystal is vacancy-rich while for values below the critical value, the crystal is self-interstitial-rich. When the ratio is equal to the critical value, the crystal would be defect free or made of so called "perfect silicon". The basic analytical expression for the critical ratio is analyzed and it is shown that thermal stress at the melt-solid interface and doping have an important effect on the 0 crit value. Furthermore, DFT calculations suggest that near the melt-solid interface the formation energy of the intrinsic point defects is lower than in the bulk of the crystal. This would lead to thermal equilibrium concentrations of vacancies and self-interstitials at the free surface and most probably also at the melt-solid interface that are considerably different from those in the bulk. It is illustrated how the v/G criterion can be further refined by taking into account these effects.The so called "Voronkov criterion" which allows predicting if a Si single crystal pulled from a melt will be vacancy-or self-interstitialrich, is the basis for defect-free Si crystal and wafer production. In its most simple form it is written as the critical ratio 0 crit of the pulling speed v over the thermal gradient G0 at the melt-solid interface 1-3with C eq and D the intrinsic point defect thermal equilibrium concentration and diffusivity, respectively, both at the melt temperature T m . E f is the intrinsic point defect formation energy and C the actual concentration of the intrinsic point defects at the melt-solid interface. The criterion was later further generalized by including also the possible effect of vacancy and self-interstitial drift which was shown however to be of minor importance. 3 An important question is which values one should use for the thermodynamic parameters of the intrinsic point defects in Eq. 1 as a very wide range of values have been reported in literature. The values for the self-diffusion coefficient D S D Si have however converged during the last years and in the temperature range between 855 and 1388 • C, D S D Si (in cm 2 s −1 ) is accurately described by 4with f I and f V the diffusion-correlation factors for self-interstitials and vacancies, respectively. Also the uncertainty on the transport capacity C eq D of the vacancy and the self-interstitial has decreased significantly. Assuming f I = 0.73, Bracht et al. 5,6 obtained (in cm −1 s −1 ) C eq V D V = 6.2C Si exp − 4.33 eV k B T [3] C eq I D I = 43C Si exp − 4.56 eV k B T . For the diffusivity of the vacancy Watkins recently proposed best estimates (in cm 2 s −1 ) for the double positively charged vacancy V 2+ and for the uncharged vacancy V 0 diffusivities, given by 7 D V 2+ = 6.5 × 10 −5 exp − 0.32 eV k B T [4] D V 0 = 0.0012 exp − 0.45 eV k B T . * Electrochemical Society Active Member. z E-mail: jan.vanhellemont@ugent.be Combining Eqs. 3 an...

show abstract

Section: Impact Of Fermi Level and Bandgap On Intrinsic Point Defect mentioning

confidence: 99%