Understanding Holes in Atomic Structure and Their Impact on Mass Distribution

[cooper607]

Well i have a conceptual problem with the atomic structure and mass distribution. See we call holes as absence of electrons. So holes are actually nothing but emptiness. As shadow is nothing but the absence of light. However while calculating mass we do include the number of holes too along with the electrons. But why is this. We are once considering the mass of electrons. Why do we need to again consider the mass for the absence of it too? I tried to find out the reason but none of them could satisfy. Someplaces I even found that they wrote that mass of a hole is even grater than that of an electron. Isn't it a bit fishy??

 

[DrDu]

The mass you are referring to is effective mass of a quasi-particle. In solid state physics you consider e.g. the equilibrium Fermi distribution as the vacuum state relative to which energies and (via $m=\frac{\partial^2 E}{\partial k^2}$) also effective mass is calculated. I.e. a filled band has E=m=0 and when an electron is missing, it has a nonzero mass relative to the full band.

 

[Claude Bile]

Well, to move a hole, you need to move electrons.

To move a hole right, you need to move electrons left.

Claude.

 

[cooper607]

so, does that mean that as i m moving the hole to accommodate the electron, that's why i m to take the mass of the hole? or in other sense, the mass of the electron itself?

then what happens the hole mass being higher than the electron? is it true anyway? or is it the momentum actually not the mass?
please clarify

 

[mfb]

The hole can have an effective mass different from the electron mass, if I remember correctly.
Even more: The electrons can have an effective mass which is not equal to 511keV. In both cases, the reason is the interaction of the particles inside. Instead of the movement of a free particle, a lot of particles are influenced in some way. Quasiparticles are a natural way to describe this, and their mass depends on the material.

 

[Darwin123]

Well i have a conceptual problem with the atomic structure and mass distribution. See we call holes as absence of electrons. So holes are actually nothing but emptiness. As shadow is nothing but the absence of light. However while calculating mass we do include the number of holes too along with the electrons. But why is this. We are once considering the mass of electrons. Why do we need to again consider the mass for the absence of it too? I tried to find out the reason but none of them could satisfy. Someplaces I even found that they wrote that mass of a hole is even grater than that of an electron. Isn't it a bit fishy??

The valence band electrons are forced to move in coherently. So the electrons in the valence band are like an incompressible fluid with surface tension. So the "hole" in the valence band is a vacancy in the electrons. It is like a bubble in a fluid. If an electric field moves the electrons forward, the hole has to hop backward.
Pauli's exclusion principle provides the hole with a type of "surface tension." The hole acts like a bubble in water.

I can give a classical analog. You can even test this analog out on a bus.
A helium balloon in a bus floats because it has a density less than the density of air. In fact, the balloon will behave as though it is an object with an effectively negative mass in a vacuum.
If the bus stops suddenly, all the dense object seem to be thrown forward. However, the balloon will be "thrown" backward. The dense air piles up in front, pushing the helium balloon backward.
The effect mass, both inertial and gravitational, of a helium balloon on a bus is negative. If you didn't know that the bus had air in it, then you might think that gravity was pulling the balloon up and inertial was pushing it in the opposite direction as the people in the bus.
Another classical analog would be the hole in traffic caused by a traffic jam. Suppose that at an intersection there is a red light that has been there for many minutes. There will be a traffic jam from the intersection backward. When the light turns green, the cars move forward. However, you will see a gap in the traffic move backward from the intersection. Again, you can watch while driving or as a passenger.
The cars are like valence electrons and the gap is like a hole.
There are some mathematical transformations that relate the behavior of valence electrons to holes. These are rather complex. However, the physical idea is simple. Because of the Pauli exclusion principle, the valence electrons are behaving like an incompressible fluid of fixed volume. If there is a bubble (i.e., hole) in this incompressible fluid, it moves in a direction opposite that of the incompressible fluid.

 

[jikim]

Holes are not just emptiness of electrons.
They have their own physical properties.
Effective mass of hole or electrons is determined by second derivative of energy band in k-space by definition.
So the effective masses of holes or electrons depends on its energy and momentum.