The seed crystal used for Czocliralski crystal growth is necked down to about 3
ID: 1717712 • Letter: T
Question
The seed crystal used for Czocliralski crystal growth is necked down to about 3 111111 diameter to help produce a dislocation-free ciystal. Use 2 times 10^6 g/cm^2 as the yield strength of silicon at the growth temperature (the units are strange but correct assuming the gravitational constant of earth, etc.) and determine the maximum length of each ingot that can be supported by this neck if the ingots are 150, 200 and 300 111111 diameter. For the 200 111111 diameter case, how many wafers can be produced (if the final wafer thickness is 725 mum).Explanation / Answer
The cross sectional area of the seed = A = pi ( D / 2)2 = pi ( 0.003 / 2) = 0.000007 m2
The maximum mass that can be supported by the seed equals to the product of the critical yeild strength and the seed cross sectioanl area.
M = 0.000007 m2( 2 * 106 g / cm2)
M= 141300g
M = 141.3kg
The mass of ingot having diameter 200mm and length L will be
( 2.33g / cm3) (3.14)(20/2)2 L = 141300g
L = 141300 / 731.62
L = 193.13cm
L = 1.93m
Maximum length of 150m diameter ingot would be
L = 4(141300 ) / ( 2.33g / cm3) (3.14)152
L = 343.34cm
L = 3.43m
The maximum length of 300mm diameter
L = 4(141300 ) / ( 2.33g / cm3) (3.14)302
L = 85.83cm
L = 0.85m