Electron and hole mobility in semiconductors

[saad]

Why is electron mobility more than hole mobility in semiconductors?

 

[INS-ANI]

who said so?
which charge carrier depends on kind of doping.
If its N-type doping, there are more electrons wrt. holes(or absence of electrons) in the semiconductor.
In other case if its a P-type doping, then there are more holes wrt. electrons in the semiconductor.

So,the mobility depends on type of doping on the semicnductor.

 

[saad]

who said so?
which charge carrier depends on kind of doping.
If its N-type doping, there are more electrons wrt. holes(or absence of electrons) in the semiconductor.
In other case if its a P-type doping, then there are more holes wrt. electrons in the semiconductor.

So,the mobility depends on type of doping on the semicnductor.

i m talking about mobility values µn and µp (not the charge carrier concentrations)

Regards,
Saad

 

[A.Anand Srinivasan]

the mobility of electrons is more than that of holes because the electrons are moving in conduction band where the obstruction to motion is less while holes move in valence band where there is lot of obstruction due to vibration due to temperature and attraction from the nuclei....

 

[lsimeon]

the free electrons move faster than holes because they are already in the conduction band means they have reached a certain energy for them to be highly excited than of holes which are majority located at the valence band...

 

[saad]

thanks @ Anand Srinivasan

i knew this reason but i was thinking if there could be some quantum mechanical phenomenon that might lead to this behaviour. anyways, thanks for ur reply

 

[teteamigo]

There is a Quantum explanation:

E(k) -->spectrum of Hamiltonian

E in a eigenvalue of Hamiltonian-Shrödinger equation.
k is related with p and kinetic energy.

In crystal, atom, the description of electron motion is made by Quantum Mechanics.

Band diagram where we have parabolic regime of E(K) like in free electron regime (not real, neither quantic).

The efective mass of particle that carries current in valence band is related with E(K) of valence band.

The wavefunction carries momentum, we know that 2nd Law of Newton F=dp/dt=m*a

Knowing p we can calculate dp/dt, and a=dv/dt v=wave group velocity

and so on...

**broken link removed**

 

[ester88]

There is a Quantum explanation:

E(k) -->spectrum of Hamiltonian

E in a eigenvalue of Hamiltonian-Shrödinger equation.
k is related with p and kinetic energy.

In crystal, atom, the description of electron motion is made by Quantum Mechanics.

Band diagram where we have parabolic regime of E(K) like in free electron regime (not real, neither quantic).

The efective mass of particle that carries current in valence band is related with E(K) of valence band.

The wavefunction carries momentum, we know that 2nd Law of Newton F=dp/dt=m*a

Knowing p we can calculate dp/dt, and a=dv/dt v=wave group velocity

and so on...

**broken link removed**

@teteamijo: you mean: because high effective mass of electron in conduction band rather than carriers in valence band, electrons move faster than holes, and there is another question, why is effective mass of carriers in conduction band higher than carriers in valence band?

 

[dimimi]

Conduction in cunduction band is governed by the sommerfeld assumption. An electron in an infinite potential well. The well is defined by the material size. The well limits are the limits of the material as a whole. Inside of it the electron is not affected by the micropotential of the particular lattice atoms. It is almost like free electron inside the material. On the other hand, "conduction" in the valence band is in fact electrons moving from bond to bond. Quantomechanically this can only be described by the tunneling effect! In order for an electron to move to a nearby covallent bond, it has to brake the potential between atoms through tunneling effect. Like drilling a hole in the wall to pass a tennis ball to the next appartment. Conduction through tunnelling effect requires more effort than the semi-free mechanism of of sommerfeld conduction. This is depicted as different effective masses for semi-free electron conduction to tunneling effect conduction mechanism.

 

[ester88]

Conduction in cunduction band is governed by the sommerfeld assumption. An electron in an infinite potential well. The well is defined by the material size. The well limits are the limits of the material as a whole. Inside of it the electron is not affected by the micropotential of the particular lattice atoms. It is almost like free electron inside the material. On the other hand, "conduction" in the valence band is in fact electrons moving from bond to bond. Quantomechanically this can only be described by the tunneling effect! In order for an electron to move to a nearby covallent bond, it has to brake the potential between atoms through tunneling effect. Like drilling a hole in the wall to pass a tennis ball to the next appartment. Conduction through tunnelling effect requires more effort than the semi-free mechanism of of sommerfeld conduction. This is depicted as different effective masses for semi-free electron conduction to tunneling effect conduction mechanism.

i read sth about how to achieve effective mass in infinte potential well problem, i don't get the second part of your word! tunneling efect which describe the reverse current in p-n junction!

 

[dimimi]

No. when a valence electron is moving from atom to atom it finds a barrier potential which has to pass through. The only way a valence electron can move from atom to atom is via tunnel effect. As far as i know at least. I was not reffering to p-n junction.

--- potential--------potential
------well--------------well
--- of atom1-------of atom2

|---------------|\|------------|
|------ e->---|\\|------------|
|-------------|\\\|------------|
|------------|\\\\|------------|
|------------|\\\\\|-----------|
|-----------|\\\\\\\|-----------|
|(atom1)-|\barrier\|-(atom2)---|
|----------|\potential\|---------|

 

[biank88]

No. when a valence electron is moving from atom to atom it finds a barrier potential which has to pass through. The only way a valence electron can move from atom to atom is via tunnel effect. As far as i know at least. I was not reffering to p-n junction.

--- potential--------potential
------well--------------well
--- of atom1-------of atom2

|---------------|\|------------|
|------ e->---|\\|------------|
|-------------|\\\|------------|
|------------|\\\\|------------|
|------------|\\\\\|-----------|
|-----------|\\\\\\\|-----------|
|(atom1)-|\barrier\|-(atom2)---|
|----------|\potential\|---------|

image from Pierret-advanced semiconductor foundamentals

Hi, i've the same problem in understanding how we can move from the Kroenig-Penny periodic-potential model to the simplified Sommerfeld model;
in particular i don't understand why the valence electrons are said to be strictly bounded (so they necessary need tunnel effect to move) if, in the Kronigh-Penny model, they "live" in an energy valence band that is "above" the periodic lattice potential...
sorry for my english

 

[aussiewhite]

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[dimimi]

Well... i was expecting the valence band to be lower in comparison to the diagram you have uploaded.. In that case the tunneling effect would make sense for explaining conductivity. I was imagining the Kroenig-Penny periodic-potential model to be inside the valenve band. Where did you get this scanning from? The book title i mean.

 

[biank88]

Well... i was expecting the valence band to be lower in comparison to the diagram you have uploaded.. In that case the tunneling effect would make sense for explaining conductivity. I was imagining the Kroenig-Penny periodic-potential model to be inside the valenve band. Where did you get this scanning from? The book title i mean.

Thanks for the the reply... i'm studing Pierret-advanced semiconductor foundamentals

 

[dick_freebird]

Look at it this way. A freed electron just goes where it's
pushed / pulled by the field, with fairly sparse interaction.
A hole, however, is really the -absence- of an electron
and for that "bubble" to move, electron after electron
has to "get out of its way". That's always going to be a
slower process.

 

[biank88]

Look at it this way. A freed electron just goes where it's
pushed / pulled by the field, with fairly sparse interaction.
A hole, however, is really the -absence- of an electron
and for that "bubble" to move, electron after electron
has to "get out of its way". That's always going to be a
slower process.

Maybe the real problem is due to the desperate effort
to "intuitively" understand results (such as mobility or effective mass)
that have been deduced by absolutely "non intuitive" quantum/mechanics postulates.

 

[mrarslanahmed]

I think mass difference in mass is the only reason for difference in mobility

 

[dick_freebird]

Maybe the real problem is due to the desperate effort
to "intuitively" understand results (such as mobility or effective mass)
that have been deduced by absolutely "non intuitive" quantum/mechanics postulates.

People deduced, or intuited, those postulates at one point.

Now people think they're the only valid way to understand
what goes on. Especially ones with too much book time and
not enough grit under their fingernails.

If you're feeling all proud about your mathematics, good for
you. But sometimes a simple answer has all the truth a
simple question needs. And I doubt your postulate of choice
has any better explanatory power. Though it's likelier to
please a professor.

 

[biank88]

People deduced, or intuited, those postulates at one point.

Now people think they're the only valid way to understand
what goes on. Especially ones with too much book time and
not enough grit under their fingernails.

If you're feeling all proud about your mathematics, good for
you. But sometimes a simple answer has all the truth a
simple question needs. And I doubt your postulate of choice
has any better explanatory power. Though it's likelier to
please a professor.

Maybe, my observation was ambiguous... I only think that, in order to
define quantum postulates as "intuitive" and not only "workable", we need,
or better, our Minds need to completely rearrange all their circuits... and unfortunately it's a slow process...
It's like Galileo's revolutionary studies about the falling body from Pisa' tower...
thanks to him and other genius, now we have an intuition completely different from
that in XIV century but, surely, not suitable for microscopic phisics.
Maybe Schrodinger' equation will be a new powerful intuitive concept for my granddaughter,
but now, for me and my classical intuition, it is only a mathematical relation that "works" in some contents;
it gives me the possibility to introduce important new ideas (ex. effective mass, scattering etc.) but,
I think I'd only waste energy and time if I tried to intuitively understand these "new" results in terms of "simple" classical concepts...