Electrical current in semiconductors

[ZeroFunGame]

TL;DR Summary

When a voltage is applied to a semiconductor at RT, the thermally excited electrons in the conduction band can move freely, similarly the hole that is generated in the valance band. Suppose we drop a voltage across the semiconductor. The electrons in the conduction band moves towards the positive electrode, the holes in the valance band move to the negative electrode. Is the current the sum of the electron current + hole current?

When a voltage is applied to a semiconductor at RT, the thermally excited electrons in the conduction band can move freely, similarly the hole that is generated in the valance band. Suppose we drop a voltage across the semiconductor. The electrons in the conduction band moves towards the positive electrode, the holes in the valance band move to the negative electrode. Is the current the sum of the electron current + hole current?

 

[DaveE]

I think it is easiest to consider the current as the net number of charges that cross a 2-D plane in your 3-D material. Electrons crossing left to right cancel with holes crossing left to right (i.e. in the same direction). Electrons crossing left to right add with holes crossing right to left. An electron hole pair created will have the two charges moving in opposite directions in the applied E-field, so only one will cross the plane you have defined, except perhaps for strange (pathological) geometries.
The important point is to be clear about the surface through which you are defining "current". You can think of it as charge flux across a surface.

 

[QuantumQuest]

Summary: When a voltage is applied to a semiconductor at RT, the thermally excited electrons in the conduction band can move freely, similarly the hole that is generated in the valance band. Suppose we drop a voltage across the semiconductor. The electrons in the conduction band moves towards the positive electrode, the holes in the valance band move to the negative electrode. Is the current the sum of the electron current + hole current?

When a voltage is applied to a semiconductor at RT, the thermally excited electrons in the conduction band can move freely, similarly the hole that is generated in the valance band. Suppose we drop a voltage across the semiconductor. The electrons in the conduction band moves towards the positive electrode, the holes in the valance band move to the negative electrode. Is the current the sum of the electron current + hole current?

First, I have to ask what do you think about it from your readings / study?

So, let me ask you, what about the states in the valence and conduction bands when we have a semiconductor crystal (let's say a silicon one) at zero temperature? Does the increase in temperature have some effect and what if we additionally apply an electric field?

 

[DaveE]

BTW, my cursory look at web links for "electric current definition" was pretty disappointing. Pages like Wikipedia (which is usually great) where just wrong when they said "An electric current is the rate of flow of electric charge past a point...".
"past a point" is at best nonsensical. I suspect they are thinking of schematic diagrams where wires are 1-D. Current flows through surfaces, not past points.

 

[ZeroFunGame]

So, let me ask you, what about the states in the valence and conduction bands when we have a semiconductor crystal (let's say a silicon one) at zero temperature? Does the increase in temperature have some effect and what if we additionally apply an electric field?

At T=0K, the conduction band is empty and electrons are stuck in the filled valance band, thus the material is an insulator. As T increases, the thermally excited electrons leave the valance band to the conduction band, causing free carriers to exist, and current to flow under an external voltage potential. So there’s a steady stream of electrons in one direction (conduction band) and holes in the other direction (valance band).

 

[ZeroFunGame]

I think it is easiest to consider the current as the net number of charges that cross a 2-D plane in your 3-D material. Electrons crossing left to right cancel with holes crossing left to right (i.e. in the same direction). Electrons crossing left to right add with holes crossing right to left. An electron hole pair created will have the two charges moving in opposite directions in the applied E-field, so only one will cross the plane you have defined, except perhaps for strange (pathological) geometries.
The important point is to be clear about the surface through which you are defining "current". You can think of it as charge flux across a surface.

when a hole reaches the negative terminal/electrode, does an electron recombine with the semiconductor to make it charge neutral again?

I imagine that as the electrons in the conduction band are flowing to the positive terminal/electrode, it will just flow into the wire and join the “sea of electrons”

I have a harder time imagining what happens to the holes. I assume an electron from the metal contact fills in the hole?

 

[QuantumQuest]

At T=0K, the conduction band is empty and electrons are stuck in the filled valance band, thus the material is an insulator. As T increases, the thermally excited electrons leave the valance band to the conduction band, causing free carriers to exist, and current to flow under an external voltage potential. So there’s a steady stream of electrons in one direction (conduction band) and holes in the other direction (valance band).

When we apply an electric field at room temperature and as the number of free electrons occupying the states in the conduction band is much lower with reference to the total number of states available in this band, these electrons will move, so there will be a global charge transfer that corresponds to an electric current. Now, in the valence band, there is a number of unoccupied states which allows the electrons in this band to contribute to the aforementioned current. So, this way, the unoccupied states (called holes) move in the opposite direction.

 

[ZeroFunGame]

When we apply an electric field at room temperature and as the number of free electrons occupying the states in the conduction band, is much lower with reference to the total number of states available in this band, these electrons will move, so there will be a global charge transfer that corresponds to an electric current. Now, in the valence band, there is a number of unoccupied states which allows the electrons in this band to contribute to the aforementioned current. So, this way, the unoccupied states (called holes) move in the opposite direction.

Does this mean the number of states available in the conduction band is discrete? If so, if all the states in the conduction band were filled(empty valance band and filled conduction band, hypothetically), would the material still conduct?

At the metal-semiconductor interface (not looking at contact resistance and work function mismatch), would the free electron in the conduction band flow into the “sea of electrons” in the metal, and the hole would collect an electron from the metal to become charge neutral again? Trying to understand what happens when the electron reaches the metal, and the hole pair reaches the metal.

 

[QuantumQuest]

Does there mean the number of states available in the conduction band is discrete?

No, energy bands consist of all the possible energy levels. Due to the very large number of atoms the energy of adjacent levels is so close together that they can be considered as a continuum i.e an energy band.

At the metal-semiconductor interface (not looking at contact resistance and work function mismatch), would the free electron in the conduction band flow into the “sea of electrons” in the metal, and the hole would collect an electron from the metal to become charge neutral again? Trying to understand what happens when the electron reaches the metal, and the hole pair reaches the metal.

Are you asking about the nature of potential barrier between the Fermi level in the metal and the majority carrier's band edge of the semiconductor at the interface? If so, it is beyond my formal education to explain it in detail but I would recommend https://www.researchgate.net/publication/222222764_The_Structure_and_Properties_of_Metal-Semiconductor_Interfaces paper.

 

[Tom.G]

when a hole reaches the negative terminal/electrode, does an electron recombine with the semiconductor to make it charge neutral again?

Yes.

Try this for a mental image:
The thing to remember is that the Holes are just Atoms that are missing an Electron. For instance consider a bucket brigade where you have a line of people transferring buckets along from one end to the other. The buckets (Electrons), will be moving in a 'forward' direction. As a bucket is removed from the end, it creates a Hole, which is then filled from the previous line position.

The difference between this and an electrical circuit is that the bucket brigade would be in a circle rather than a straight line.

Oh, and the energy source in an electrical circuit would be a battery, whereas the energy source for the bucket brigade would be their previous meal.

Hope this help.

Cheers,
Tom