What is the Donor-Electron Ionization Energy of Silicon Crystal?

In summary, the donor-electron ionization energy of a silicon crystal with an electron effective mass of .98 times the electron rest mass and a dielectric constant of 12.3 is approximately -1.4138x10-20 Joule. This result is more reasonable than the original calculation of -1.415x10-54 Joule.
  • #1
ee1215
29
0

Homework Statement


Find donor-electron ionziation energy of silicon crystal. Electron effective mass mc=.98mo and dielectric constant ε/εo=12.3

Homework Equations


I use the ED=-(1/4πε)2*[(mc*e4) / (2*(h/2π)2)]


The Attempt at a Solution


My answer of -1.415x10-54 does not seem right. I solved for mc and ε from given equations in the problem and plugged in. Is this correct or have I made a mistake?
 
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  • #2
What you did is correct in principle. You could made same calculation error or plugged in wrong value for m0. Show your data and calculation. And what unit of energy did you use?

ehild
 
  • #3
Well, using the ED formula mentioned above. I solved for mc = .98*9.1094x10-31 = 8.927x10-31kg and solved for ε=12.3*8.854x10-12 = 1.089x10-10F/m. Plugged those two equations into ED, and also h-bar = 1.054x10-34Js and e=1.6022x10-19C, I got the answer I mentioned above in my calculation.
 
  • #4
Your result is impossible. Count the exponents: 4*(-19)+(-31)-(2*(-12)+2*-(34)). It is -15. Multiply the numbers, this gives a magnitude of 10-5. So the result is of magnitude 10-20Joule.

ehild
 
  • #5
You are correct. Even though I thought I double checked me answer before I posted the question, I just did the calculation and got -1.4138x10-20. This is more reasonable?
 
  • #6
ee1215 said:
You are correct. Even though I thought I double checked me answer before I posted the question, I just did the calculation and got -1.4138x10-20. This is more reasonable?

Sure!:smile:If you feel the result impossible try to estimate its magnitude without calculator.

ehild
 

1. What is the "Energy of Donor Electron"?

The energy of donor electron refers to the amount of energy required to remove an electron from a donor atom or molecule. This energy is typically measured in electron volts (eV) and is an important concept in the study of semiconductor materials and electronic devices.

2. How is the energy of donor electron related to conductivity?

The energy of donor electron plays a crucial role in determining the conductivity of a material. In semiconductors, donor electrons can move freely and contribute to the flow of electrical current. The lower the energy of donor electron, the higher the conductivity of the material.

3. What factors affect the energy of donor electron?

The energy of donor electron is affected by various factors such as the type and concentration of dopants in a material, temperature, and external electric fields. The energy level of the donor atom or molecule also plays a role in determining the energy of donor electron.

4. How does the energy of donor electron differ from the energy of acceptor electron?

The energy of donor electron refers to the energy required to remove an electron from a donor atom, while the energy of acceptor electron refers to the energy required to add an electron to an acceptor atom. In semiconductors, these two energy levels are typically close to each other, and the difference between them determines the bandgap energy of the material.

5. Can the energy of donor electron be modified or controlled?

Yes, the energy of donor electron can be modified or controlled through various methods such as doping with different types and concentrations of impurities, applying external electric fields, and changing the temperature of the material. These techniques are commonly used in the fabrication of electronic devices to achieve desired properties and functionality.

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