Why do energy bands bend in semiconductors?

[mzh]

Dear Physics forum users
The below figure is from

http://pubs.acs.org/doi/full/10.1021/jp0009305

In Fig. 3, energy band diagrams are shown for a semiconducting material inbetween two metal electrodes.

The figure caption is: "Figure 3 Energy band diagrams for (a) p-type SiNW (b) n-type SiNW devices. The diagrams show schematically the effect of Vg on the electrostatic potential for both types of nanowires."

Why do the bands bend in the way they do when applying a gate voltage V_g? Where can I find an explanation of this?

Thanks for hints or pointing me out to references on this.

 

[Simon Bridge]

http://en.wikipedia.org/wiki/Band_bending
... bands bend in response to the charge distributions in the materials. Makes it look like the band boundaries are trying to be continuous across the interface.

 

[mzh]

what I'm just not getting is why the, say, p-type carriers get lower in energy, when applying positive gate voltage. how can i picture this to me?

 

[Simon Bridge]

Are these electron or hole potentials?
Where is the gate voltage applied?
What happens to the charge carriers under the potential difference?

 

[mzh]

Are these electron or hole potentials?
Where is the gate voltage applied?
What happens to the charge carriers under the potential difference?

i'm not sure i understand your 1. question.. by "potentials" do you mean "bands"? in the figure, the top(bottom) schematic is for p(n)-type carriers, so it is hole(electron) potentials. do you mean this?

The gate voltage is applied to the semiconducting material.

it doesn't make sense to me that a positive voltage should lower the energy of a positive charge carrier. or why does it?

would be great to understand this.

 

[Simon Bridge]

The band edges are potential functions.

If it is concave down, then the middle is repulsive to holes and attractive to electrons.
(for hole potentials, but the other way for electron potentials.)

The band bending though is due to a distribution of mobile charge carriers as well as the applied potential.

What is the gate voltage positive or negative with respect to?
There are usually two other voltages important to these things.

What happens to the mobile charge carriers if you increase the applied gate voltage?

 

[funiverse]

It seems both M-S.C. junctions are in reverse bias. In case of n-type of S.C., without any applied potential, with higher work function of metal & smaller workfunction of S.C. The electrons transfer from S.C. to metal creating a depletion region ( i.e. a space charge region that is depleted of electrons and has positive space charge) in S.C. This continues till the system reaches equilibrium i.e. both the fermi levels of metal & S.C. allign themselves & forming a schottky barrier height. The electrons flowing into the metal form a surface density of negative charges. As a result, the energy an electron at the conduction band edge is higher at the S.C. surface than it is in the bulk of the S.C. outside the depletion region.

What I wrote above is the system in equilibrium. Now, when you apply a +ve potential to metal & -ve potential to n-type S.C, the barrier height between S.C. & metal decreases. This system is called as forward bias.

Its somewhat similar in the case of P-type S.C. Hope I didn't confuse you more.