- #1
Chiz
- 4
- 0
Hi there,
i've already read some topics in this forum about the fermi-energy/chemical potential. I've also read the article "The chemical potential of an ideal intrinsic semiconductor" from Mark R. A. Shegelski which made the whole thing a little bit more clear to me. but there are some questions left:
The chemical potential ist defined as :
[tex]\mu(N,T,V)=F(N,T,V)-F(N+1,T,V)[/tex]
So it is the change in the free energy by adding one particle to the ensemble. in my interesting case: adding one electron to the semiconductor
By T=0K, the chemical potential must lie (if the valence band is totaly filled) on the bottom edge of the conduction band [tex]E_c[/tex], because by adding one electron, the energy change is [tex]E_c[/tex]. that's what is written in the article of Shegelski and what's wrong in many textbooks. there's often said "at T=0K the chemical potenial lies in the middle of the band gap".
But at higher temperatures, when there are some electrons in the conduction band, the chemical potential lies round about the middle of the gap. but why? for me it doesn't make sense, that by adding one electron the energy changes about a value [tex]\approx E_{gap}/2[/tex] because i can't add an electron whit that energy.
I think I must mix up something here.
On the other side the fermi energy/chemical potential is often defined as the energy where the fermi distribution has the value 1/2. but for me this has nothing to do with the thermodynamic definition
[tex]\mu(N,T,V)=F(N,T,V)-F(N+1,T,V)[/tex]
are both definitions related with each other?
maybe someone can make the whole thing a bit more clear to me!
All this confusion came up to me by thinking about the pn-contact. I've read several times "in contact, the chemical potential must be the same everywhere in the system".
i've already read some topics in this forum about the fermi-energy/chemical potential. I've also read the article "The chemical potential of an ideal intrinsic semiconductor" from Mark R. A. Shegelski which made the whole thing a little bit more clear to me. but there are some questions left:
The chemical potential ist defined as :
[tex]\mu(N,T,V)=F(N,T,V)-F(N+1,T,V)[/tex]
So it is the change in the free energy by adding one particle to the ensemble. in my interesting case: adding one electron to the semiconductor
By T=0K, the chemical potential must lie (if the valence band is totaly filled) on the bottom edge of the conduction band [tex]E_c[/tex], because by adding one electron, the energy change is [tex]E_c[/tex]. that's what is written in the article of Shegelski and what's wrong in many textbooks. there's often said "at T=0K the chemical potenial lies in the middle of the band gap".
But at higher temperatures, when there are some electrons in the conduction band, the chemical potential lies round about the middle of the gap. but why? for me it doesn't make sense, that by adding one electron the energy changes about a value [tex]\approx E_{gap}/2[/tex] because i can't add an electron whit that energy.
I think I must mix up something here.
On the other side the fermi energy/chemical potential is often defined as the energy where the fermi distribution has the value 1/2. but for me this has nothing to do with the thermodynamic definition
[tex]\mu(N,T,V)=F(N,T,V)-F(N+1,T,V)[/tex]
are both definitions related with each other?
maybe someone can make the whole thing a bit more clear to me!
All this confusion came up to me by thinking about the pn-contact. I've read several times "in contact, the chemical potential must be the same everywhere in the system".