# mass of electron and holes-why mass of hole is more?

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#### nandinichakrab

##### Newbie level 5
mass of hole and electron

now, holes are created when the electrons are removed from there positions. so the mass of the hole produced and the electron removed should have been same. but it is said that the mass of hole is more than that of an electron.why? from where does this excess mass come from?the empty space created by the removal of electron should not exceed that of an electron. also can u explain the concept of effective mass that is why it is negative for the holes?

effective mass of hole and electron

I'm not sure, but I'd imagine it was due to the differing mobilities of electrons and holes (and also I believe with sub-atomic particles the meanings of things such as mass and energy get a bit fuzzy). Thus, under the same applied force, and electron will have greater acceleration than a hole, which leads to the conclusion that the hole must have more mass, F = ma.

why effective mass of hole greater than electron

A hole is an imaginary particle that is used to make the math work.

• XT.5155

### XT.5155

Points: 2
effective mass of electron

The effective mass of a hole in semiconductors is positive (I should say - mostly positive, because warping of isoenergetic surfaces for holes in k-space (k is a wavevector) in some semiconductors - for example, in silicon - may lead to negative effective mass in certain domains of k-space).

In general, hole effective mass can be either larger or smaller than the electron effective mass - that depends on semiconductor material. In silicon, GaAs, and other materials hole effective mass is larger than electron effective mass, but in Germanium, for example, the opposite is true (m_h < m_e).

The concept of effective mass in semiconductors is an oversimplification of the real physical situation. In general, the behavior of electrons and holes is determined by dispersion relation - dependence of energy on the wavevector k, and only in a simple model of effective mass this dependence looks similar to free electron dispersion relation: E=mp^2/2 = m(hk)^2/2.

In reality, there are different types of electrons and holes in a semiconductor (belonging to different valleys and subbands), and each type of the carriers (electrons or holes) may have complicated shapes of isoenergetic surfaces - ellipsoids (e.g., electrons in Si and Ge) that are characterized by two parameters - longitudinal and transverse effective mass (ml and mt), or warped surfaces (e.g., heavy holes in Si), etc.

(Simplified) effective mass value is determined by quantum mechanical properties of crystal, and there is no an easy explanation as to why this value has some specific numerical value.

Old Nick said:
I'm not sure, but I'd imagine it was due to the differing mobilities of electrons and holes (and also I believe with sub-atomic particles the meanings of things such as mass and energy get a bit fuzzy). Thus, under the same applied force, and electron will have greater acceleration than a hole, which leads to the conclusion that the hole must have more mass, F = ma.

Actually, the effective mass is a more fundamental concept than mobility, and smaller effective mass leads to higher mobility (in general):

mobility=e*tau/m

where e is the electron charge, and tau is momentum relaxation time. Tau also depends on m (the higher the m, the lower the tau), as effective mass impacts teh density of states and the (phonon) scattering rate.

why mobility of electron is more than hole

but here i also want to know, whether the mass (not the effective mass) of the hole is said to be more than that of an electron.why is it so? bcoz holes and electrons should hav same mass. again holes should not be confused with protons, bcoz protons are real particles, but holes are hypothetical. and the mobility of the holes is less because the mass of holes are considered to be more.plz help.

effective mass of electrons and holes

nandinichakrab said:
but here i also want to know, whether the mass (not the effective mass) of the hole is said to be more than that of an electron.why is it so? bcoz holes and electrons should hav same mass. again holes should not be confused with protons, bcoz protons are real particles, but holes are hypothetical. and the mobility of the holes is less because the mass of holes are considered to be more.plz help.

This is something that you should accept as a given fact - that effective mass of hole may be larger or smaller than effective mass of electron in a semiconductor. There is no simple explanation to this phenomenon. This acceptance is more than enough for all practical purposes. If you do not want to accept this - please read one of the textbooks on solid state or semiconductor physics.

I will give you a relevant puzzle from classical physics - why a drop of water falls in the air with a high, while an air bubble (having the same size, and obviously much smaller mass) moves up in the water (under the action of expulsion force) with a much slower speed?

• XT.5155

### XT.5155

Points: 2
effective mass holes

ok, the air bubble while going up experiences both gravitational force and also the viscous force. the drop of water falling under the effect of gravity only experiences the resistance offered by the air. and also we know that the density of water is more than that of air.so the water drop falls faster.

effective mass of holes

Mass of the Hole depends on the Curve of the E-K diagram... An hole is not always heavier than an electron....

electron mass hole silicon

nandinichakrab said:
ok, the air bubble while going up experiences both gravitational force and also the viscous force. the drop of water falling under the effect of gravity only experiences the resistance offered by the air. and also we know that the density of water is more than that of air.so the water drop falls faster.

In a somewhat similar fashion, the crystal lattice has different effect (you can think of friction, but in reality this is a quantum mechanical effect) on electrons in the valence band and in the conduction band, so it's not surprising that effective masses of electrons and holes are different.

value mass of hole and electron

nandinichakrab said:
but here i also want to know, whether the mass (not the effective mass) of the hole is said to be more than that of an electron.why is it so?

Holes are a concept defined as the lack of an electron, and this only is useful within a semiconductor lattice. It is the periodic nature of the lattice which allows for concepts such as effective mass and holes. There is no "hole mass". If you want to understand deeper, you need to understand how effective mass is derived. It is a simplification of quantum physics that allows us to use newtonian physics on particles in a lattice.

Re: electron mass hole silicon

can we assign degree of freedom to a hole ? if yes, what is it? electron is a fermion .. cn a hole be classified on these lines (the properties it is associated with n its degree of freedom in a lattice) ?

timof said:
nandinichakrab said:
ok, the air bubble while going up experiences both gravitational force and also the viscous force. the drop of water falling under the effect of gravity only experiences the resistance offered by the air. and also we know that the density of water is more than that of air.so the water drop falls faster.

In a somewhat similar fashion, the crystal lattice has different effect (you can think of friction, but in reality this is a quantum mechanical effect) on electrons in the valence band and in the conduction band, so it's not surprising that effective masses of electrons and holes are different.

Re: why effective mass of hole greater than electron

A hole is an imaginary particle that is used to make the math work.

I like the wording "imaginary particle"

Re: why effective mass of hole greater than electron

To me, the whole theory is imaginary though necessary for the math work. Actually, the energy (due to electrical, magnetic or gravity field... etc) propagates by waves only. But the particles by which these waves can travel, are surely not the ones of the atomic universe.

World scientists will have to wait many years before introducing the concept (theory) that relates to the universes below and above the two already perceived ones; our universe and the universe which form its masses (the atomic one)

For those who are curious, the particles of the first universe below the atomic one are the particles forming its masses; the masses of electrons, nucleus... etc. Obviously these sub-particles, in turn, are also formed by moving particles in the space of a lower sub-universe... In other words, our existence is made by a universe formed by a huge space and particles (called stars and planets...) which in turn are made by a universe formed by a huge space (relatively speaking) and particles (called electrons...) which in turn are made... to the end of the song

So till this new theory will be born, we have to live with electrons and holes, without forgetting our dear photon which can take the form we like; a particle or wave energy.

Oh... I forgot the universe above ours... I guess most of you now have already imagined it by applying the same concept.

Kerim

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For a hole to move, requires a series of electrons to vacate position ahead of it.
So its "mass" is going to look like all those reluctant valence electrons' mass
that had to be plowed out of the way (time shared).

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