What happens when semiconductor melt?

[opuktun]

Homework Statement

For intrinsic (undoped) silicon with a band gap of 1.1eV at 1500 K, what is the population of conduction electrons (m-3)? Comment on your result. Note that the melting point of silicon is 1687 K, and atom density of silicon is 5 x 10^28 atoms m-3.

Note: My main problem is to "comment"

Homework Equations

http://hyperphysics.phy-astr.gsu.edu/HBASE/solids/fermi3.html#c1 <-- see here for the steps taken
In the end, I got 3.96x10^22 electrons/m3 which is close to the one given by the applet (maybe 'cos I used different values)

The Attempt at a Solution

I was thinking of writing something like:
Although this equation may imply that increase in temperature will lead to increased conductivity (because increased no. of conducting electrons), we have to consider the state of the matter in which it is in. At higher temperature such as 1700 K, melting would have occurred. This may result in lower value of conductivity calculated than the actual. This is because melting would have caused the semiconductor to be in liquid state. Thus, the positive metal ions can carry charges along with the sea of electron.

But I'm not too sure if the bold sentence is correct. I would really appreciate it if you guys can give me some feedback on this answer.

Thanks!

 

[anathema]

Your calculation for the population of conduction electrons in intrinsic silicon at 1500 K is correct. The equation you used takes into account the band gap of silicon, which is an important factor in determining the number of conduction electrons. Your result of 3.96x10^22 electrons/m3 is also in close agreement with the value given by the applet, which suggests that your calculations are accurate.

However, it is important to note that this result is only valid for solid silicon at 1500 K. As you mentioned, at higher temperatures such as 1700 K, silicon would have melted and become a liquid. In this state, the positive metal ions can also carry charges along with the sea of electrons, which would affect the conductivity of the material. Therefore, the calculated value of conduction electrons may be lower than the actual value in a liquid state.

In conclusion, your calculation for the population of conduction electrons in intrinsic silicon at 1500 K is correct and your reasoning for the potential discrepancy at higher temperatures is valid. It is important to consider the state of the material when interpreting conductivity values.

 

[Moetasim]

Your response is on the right track. When a semiconductor melts, it transitions from a solid state to a liquid state. This transition can significantly affect the population of conduction electrons. In the case of intrinsic silicon at 1500 K, the calculated population of conduction electrons may be lower than the actual value due to the presence of positive metal ions that can also carry charges. This highlights the importance of considering the state of the material when analyzing its conductivity. Additionally, it is worth noting that the melting point of silicon (1687 K) is close to the temperature at which the calculation was performed (1500 K). This could also affect the accuracy of the calculated value.