Binding Energy of the hydrogenic acceptor state in Silicon?

  • #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?
 

Answers and Replies

  • #2
ehild
Homework Helper
15,543
1,915

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
HunterDX77M
43
0
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! :)
 

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