The Stress and Strength at the Neck of a Large Diameter Silicon Crystal during Growth

Abstract

Temperature, strength, and stress at the Dash thin neck of large diameter silicon crystals during Czochralski growth are analyzed. The combination stress from the crystal weight, the meniscus weight, and the surface tension are calculated for the initial crystal growth stage, including shoulder portion and the first 12.5 cm long of body growth. Two shoulder lengths, 2.5 and 10 cm with three diameter sizes, 200, 250, and 300 mm are calculated. A two-dimensional, axisyrnmetric heat conduction model using a commercially available software, ANSYS"." is used to calculate the temperature distribution in the crystals. The strength of the thin neck is obtained from the relationship between the upper yield strength of silicon and temperature. To maintain a dislocation-free (DH) lattice structure, the strength of the thin neck must be higher than the combination stress acting upon the thin neck. The results indicated that the neck temperature increases with the crystal diameter and decreases with the shoulder length. The minimum neck diameter to maintain a DF structure for a 200 rnrn crystal is 3.7 mm with a 2.5 cm shoulder and 3.06 mm with a 10 cm shoulder. For a 250 mm crystal, the minimum neck diameter is 4.8 mm with a 2.5 cm shoulder and 4.1 mm with a 10 cm shoulder. For a 300 mm diameter crystal, the minimum neck diameter is 6.1 mm with a 2.5 cm shoulder and 5.2 mm with a 10 cm shoulder.) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 128.218.248.200 Downloaded on 2015-04-12 to IP Process and Device Center, Dallas, TX 75243. Present address: National Semiconductor Corporation, Santa microscopy (STM),*." transmission electron microscopy Clara, CA 95052. (TEM),ll-l5 and x-ray diffraction (XRD),'"17 have been Present address: Hitachi, Ltd., Tokyo 185, Japan. employed t o investigate the effect o f thermal oxidation on ) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see 128.218.248.200 Downloaded on 2015-04-12 to IP

Phosphorus Concentration Limitation in Czochralski Silicon Crystals

“…The axial temperature distribution of a crystal decreases from the melting point (1420ЊC) at the solid/melt interface to a much lower temperature at the shoulder depending on the length of the crystal, the crystal diameter, and the hot zone setup. 6,18 The estimated temperature where the center dislocations started to propagate was about 1100ЊC. The yield strength of the silicon crystal decreases as the temperature increases.…”

“…Melt temperature was stabilized again, and the seed was dipped into the melt to start the crystal growth. 6 Part of the phosphorus that was dissolved in the silicon melt evaporated from the melt surface during the crystal growth process. The evaporation rate decreases the P concentration in the melt and is equivalent to reducing the rate of P rejection into the melt.…”

“…The yield strength of the silicon crystal decreases as the temperature increases. 6,18 Due to the axial and radial temperature gradients in a growing crystal, thermal stresses exists. However, the calculated thermal stresses along a crystal are much lower than the corresponding yield stresses of silicon lattice at corresponding temperatures.…”

Constitutional Supercooling in Czochralski Growth οf Heavily Doped Silicon Crystals

“…in [40]. For the transition from the starting cone to the cylindrical body it is concluded from very few experimental data [39,40] that G is about 1050% higher than in the subsequent cylindrical body phase. More precise data could only be obtained by fully time-dependent simulations which are still very challenging [23].…”

“…The temperature gradient G in the crystal during the seeding and necking phase is in the order of 50100 K/cm according to direct measurements performed in a CZ puller for growing silicon crystals with 300 mm diameter [42] and according to experiments [36,40] at pulling rates V of around 1 mm/min [39,40,43]. The temperature gradient can also vary along the length of the cylindrical body as reported e.g.…”