Binding Energy of the hydrogenic acceptor state in Silicon?

In summary, the equation for the binding energy in a medium with permittivity ε is E_b = \frac{k_c e^2}{2a_0} and the equation for the energy in a medium with permittivity ε is ehildke = 1/(4∏ε).
  • #1
HunterDX77M
43
0

Homework Statement


Find the theoretical binding energy of the hydrogenic acceptor state in Si (eg, as produced by Aluminum impurities), using hole mass 0.39 and permittivity 11.8.


Homework Equations


[itex]
E_b = \frac{k_c e^2}{2a_0} \\
a_0 = \frac{\hbar ^2}{mk_c e^2}
[/itex]


The Attempt at a Solution


When we discussed binding energy in my class, these were the two equations that my professor gave. But looking at them now, I don't think they are right. For one thing, they don't take the permittivity into account and for another, a0 seems to cancel out several variables in Eb. I've searched around for some time trying to find the equation(s) that would make more sense for this type of problem, but have so far had nothing but dead ends. Is anyone familiar with the equations for a problem like this?
 
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  • #2
HunterDX77M said:

Homework Statement


Find the theoretical binding energy of the hydrogenic acceptor state in Si (eg, as produced by Aluminum impurities), using hole mass 0.39 and permittivity 11.8.


Homework Equations


[itex]
E_b = \frac{k_c e^2}{2a_0} \\
a_0 = \frac{\hbar ^2}{mk_c e^2}
[/itex]


The Attempt at a Solution


When we discussed binding energy in my class, these were the two equations that my professor gave. But looking at them now, I don't think they are right. For one thing, they don't take the permittivity into account and for another, a0 seems to cancel out several variables in Eb. I've searched around for some time trying to find the equation(s) that would make more sense for this type of problem, but have so far had nothing but dead ends. Is anyone familiar with the equations for a problem like this?

ke means 1/(4∏ε) in a medium of permittivity ε.

No variables cancel if you plug in the expression for ao into the formula for the energy.

ehild
 
  • #3
ehild said:
ke means 1/(4∏ε) in a medium of permittivity ε.

Oh, yeah. How could I forget about that? That's pretty basic. :-/

No variables cancel if you plug in the expression for ao into the formula for the energy.

This is probably why it's a bad idea for me to do homework without sleeping for the majority of the day.

Thanks for your help! :)
 

1. What is binding energy?

Binding energy is the amount of energy required to break apart a nucleus into its component parts or to separate an electron from an atom.

2. How is binding energy measured?

Binding energy is typically measured in units of electron volts (eV) or joules (J).

3. What is the hydrogenic acceptor state in Silicon?

The hydrogenic acceptor state in Silicon refers to a specific energy state in which a hydrogen atom has been incorporated into a silicon lattice, resulting in an excess positive charge that can act as an acceptor for electrons.

4. Why is the binding energy of the hydrogenic acceptor state in Silicon important?

The binding energy of the hydrogenic acceptor state in Silicon is important because it affects the electrical and optical properties of silicon, which is a key material in many electronic devices.

5. How does the binding energy of the hydrogenic acceptor state in Silicon relate to its conductivity?

The binding energy of the hydrogenic acceptor state in Silicon affects its conductivity by determining the amount of energy required to free electrons from the acceptor atoms and allow them to contribute to the flow of electricity.

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