Crystal Growth - Czochralski technique, finding concen. of dopant after growth

In summary, the conversation discusses how to determine the concentration of boron atoms in a silicon ingot grown by the Czochralski technique with a dopant concentration of 1016 boron atoms/cm3. The equations Cs/C0 = k0 (1 - m/m0) k0-1 and k0 = Cs/Cl are mentioned, and there is confusion about the values of m and m0. The question is also clarified to be from an Engineering class.
  • #1
bmarson123
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0

Homework Statement


A doped silicon ingot is to be grown by the Czochralski technique with a dopant concentration of 1016boron atoms/cm3. If k0 = 0.9 for boron/Si, what concentration of boron atoms should be in the melt?

Homework Equations


Cs/C0 = k0 (1 - m/m0) k0-1

k0 = Cs / Cl

The Attempt at a Solution


I think it's just a case of subbing in the numbers to establish Cs and then using this in the second equation to find Cl, but I'm really confused about what the values of M and M0 should be in this scenario.
 
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  • #2
To be honest, I'm not familiar with this topic but I see that your question has gone unanswered for nearly 1-1/2 days so I'll see what I can do to help.

What do the m and m0 in the equation represent? Wherever you got that equation from, there should be definitions of all the terms in it.

Also, is this question from a Physics class or an Engineering class? If it belongs in the Engineering homework area, I could move your post there where people more knowledgeable about it are more likely to see it.
 

1. What is the Czochralski technique for crystal growth?

The Czochralski technique is a method for growing single crystal materials using a high-temperature melt of the desired crystal material. A seed crystal is dipped into the melt and slowly pulled out, causing the crystal to grow in a controlled manner.

2. How does the Czochralski technique achieve high purity in crystal growth?

The high-temperature melt used in the Czochralski technique allows for impurities to be easily dissolved and removed, resulting in a high-purity crystal. Additionally, the controlled pulling of the crystal seed ensures the growth of a single, uniform crystal with minimal defects.

3. How is the concentration of dopants determined after crystal growth using the Czochralski technique?

The concentration of dopants in a crystal grown using the Czochralski technique can be determined through various analytical techniques such as energy-dispersive X-ray spectroscopy (EDS) or secondary ion mass spectrometry (SIMS). These techniques measure the elemental composition of the crystal, allowing for the determination of dopant concentration.

4. Can the Czochralski technique be used to grow crystals with a specific dopant concentration?

Yes, the amount of dopant in a crystal grown using the Czochralski technique can be controlled by adjusting the amount of dopant added to the melt. This allows for the precise tuning of the dopant concentration in the final crystal product.

5. What are the advantages of using the Czochralski technique for crystal growth?

The Czochralski technique allows for the growth of large, high-quality single crystals with a high degree of control over their dopant concentration and purity. It is also a relatively simple and cost-effective method compared to other crystal growth techniques.

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