What Is the Current Density in a Semiconductor at T>0 K?

[Niles]

Homework Statement

Hi all.

Say we are looking at a (pure) semiconductor at T=0 K. Now we turn on the heat, so only 1 electron jumps up to the conduction band per cm³, and likewise 1 hole is created in the valence band per cm³. Does this mean that the current density of this semiconductor is equal to qv per cm³, or 2qe per cm³?

 

[Troels]

Homework Statement

Hi all.

Say we are looking at a (pure) semiconductor at T=0 K. Now we turn on the heat, so only 1 electron jumps up to the conduction band per cm³, and likewise 1 hole is created in the valence band per cm³. Does this mean that the current density of this semiconductor is equal to qv per cm³, or 2qe per cm³?

Total nonsense. Where in the preperation of your experiment did you specify an electric field to give rise to a directed current density? Also, you might want to check the units of current density.

 

[Niles]

Yes, I should have specified that we subject the solid to an electric field. My book says that electric current density is j=nqv. Is it wrong?

 

[Troels]

Yes, I should have specified that we subject the solid to an electric field. My book says that electric current density is j=nqv. Is it wrong?

No, it's the general definition of current density, and is not wrong, but rather useless in the present context, as the drift-velocity depends on the electric field in a very subtle way in a semi conductor. It is actualy a quantum mechanical argument and often subject of several chapters in your average solid state textbook. You may have to be more specific in your question as to where you get lost :)

 

[Niles]

I see. But my question is more so I can get an intuitive feeling of the electron-hole connection in semiconductors. Because I can understand from the math, that holes can conduct current just like electrons can. But I am just wondering what this means: I.e., if one electron goes up to the conduction band (and thus a hole to the valence band), does this mean that there are now extra 2 carriers that can contribute to the current, or only 1?

 

[Troels]

I.e., if one electron goes up to the conduction band (and thus a hole to the valence band), does this mean that there are now extra 2 carriers that can contribute to the current*snip*

Indeed so - a hole in a "sea" of negative charges behaves just like a positive charge, and conduct current in the same manner

 

[Niles]

I see, very interesting. Thank you.I need to find out if I have understood some basic concepts correctly, and you seem very good at these things, so you can help me. Please correct me, if I am wrong in the following statement:

The valence band is the band, where electrons are at T=0K, i.e. they are bound to the atoms. When the temperature rises, they are thermally excited (i.e. the atoms in the lattice are ionized) and the electrons are free to move in the lattice - they are now in the conduction band.

Btw, can I ask you what you wrote your B.Sc.-thesis about?

 

[Troels]

The valence band is the band, where electrons are at T=0K, i.e. they are bound to the atoms.

Not exactly. There are materials that have electrons in the conduction band at T = 0 as well, that is, normal metals. It all depends on the position of the Fermi level, which by the very definition of a semi conductor lies in the small gab between valence and conduction band.

But otherwise correct, electrons in the valence band are bound to individual atoms whereas electrons in the conduction band are free to move in the crystal lattice.

When the temperature rises, they are thermally excited (i.e. the atoms in the lattice are ionized) and the electrons are free to move in the lattice - they are now in the conduction band.

I dislike the term "ionized" here because that implies that the atom and the electron are completely separated, which is not the case for electrons in the conduction band - the crystal as a whole is still neutral.

Btw, can I ask you what you wrote your B.Sc.-thesis about?

That you can, but I'm affraid the only answer I'm entitled to give is "magnetic microsensors" as my work is currently in peer review :)