Posted by Roger (22.214.171.124) on January 28, 2008 at 17:50:03:
In Reply to: high resistivity melt with low resistivity silicon posted by Rick Matheson on January 28, 2008 at 04:29:07:
: Single crystal IC silicon is often remelted and cast for use in solar applications; frequently a mix of high res and low res material. Is there a simple calculation method to produce the resistivity of hi and low res Si mixed in a melt, given the high-to-low res ratio and average resistivity reading for both high and low resistivity starting silicon? For example 100kg of .002 ohm cm start silicon with 500kg 18 ohm cm silicon (assuming both are single crystal - high purity, IC grade start silicon) ---- Thank you very much --- your website is fantastic and rich in interesting information. - Rick
You probably know more about this than I do but here is my thought:
Convert to concentration first. (Qualification: this assumes most of the concentration is electrically active.)
Our resistivity to concentration converter may be convenient. The link is on our technical page.
18 ohm-cm = 7.29e14 cm-3 for p-type and 2.43e14 cm-3 for n-type
0.002 ohm-cm = 5.72e19 cm-3 for p-type and 3.43e19 cm-3 for n-type
So, my algebra for p-type would be:
((500 x 7.29e14) + (100 x 5.72e19)) / (500 + 100) = 9.54e18 cm-3
9.54e18 cm-3 = 8.87e-3 ohm-cm (p-type) or about 0.009 ohm-cm.
Comments: The dopant in the 18 ohm-cm material is negligible. Really, you are taking the dopant from the .002 ohm-cm and diluting it to 1/6. But the resistivity didn't go 6 times as high -- only 9/2 (= 4.5) times as high. This is due to the high carrier mobility obtained with lower concentration. Interesting stuff--isn't it?
Thanks for the compliments, Roger