The mobility of holes and electrons is different because electrons are less bounded in an atom than a hole. Actually hole is basically a vacancy of electron thus they are more bounded to the nucleus of an atom which makes it difficult for them to travel as faster as the electron.

well it's more complicated, depends on crystal direction, material, temperature etc. in general band structure, sometimes the hole mobility (rather effective than 0 - or better drift velocity) can be larger than for electrons, thus holes drift faster than electrons, which is the case eg. for diamond in 100 direction.........

Basically holes are due to absence of electrons. In semiconductors excited electron moves from valence band to conduction band. This creates a free electron in conduction band and a hole in valence band. The electrons therefore have better mobility as they have gained excitation energy and are further away from the region of influence of the nucleus. The holes are under the influence of nucleic forces and also have low excitation energy, therefore less mobility. In diamond as well, electron mobility is normally higher (check link). Higher hole mobility across 100 direction may be an exception.

http://www.el.angstrom.uu.se/Seminar/MGabrysch_Lic.pdf

well, I was rather referring to  'it difficult for them to travel as faster as the electron.(' so rather effective mobility than mu0 or better drift velocity), clearly in diamond at RT holes drift faster than electrons, anyhow mobility of both e-h depends on effective mass and that's a tensor so all the mu0 values are an average (depends on population of CB or VB mini/max - there is not too much sense of speaking about mobility of one electron or hole since you must know in which valley min/max it's located ) and this can be influenced by a lot factors (scattering)..

Because the band structure of valence and conduction band are different, and hence also the effective masses. Look in a textbook.

BTW: Conduction electrons are just as 'fictitious' as holes. When 

a semiconductor physicist talks about 'electrons' he is most likely talking 

about conduction electrons. Conduction electrons are not equivalent to 

vacuum electrons. In general, a conduction electron is lighter than a vacuum 

electron and a hole is heavier than a vacuum electron. 

     You want a heuristic answer without any mathematics. I will try. However, you have to understand one thing. The description of conduction electrons and valence holes as pseudo particles is fictitious. They are not true particles, but they act like particles. They can be described with equal validity as atomic states in different atoms that overlap in a crystal. So analysis of  conduction electrons and holes often involves looking closely at the atomic states. 

     Semiconductor bands overlap atomic states. What distinguishes the conduction band from the valence band is the atomic state most closely associated with the electrons in the band. The valence band is associated with the valence band in an atom with the outermost shell filled up. The conduction band is associated with the first excited state of the same atom. 

       The electrons in the conduction band and the electrons in the valence 

band of a semiconductor have wave functions that strongly overlay the 

associated atomic states. Generally, the valence band overlaps the atomic states that are mostly filled with vacuum electrons. The conduction band overlaps atomic states that are mostly empty of vacuum electrons.

   I will distinguish between 'vacuum electrons' and 'conduction electrons.' A vacuum electron is an electron state that would exist in a vacuum far from any nucleus. A conduction electron is a mixed state consisting of different vacuum electrons that are being acted on by a nucleus and is overlapping  an excited states of the atom. A valence electron is a mixture of vacuum electrons acted on by a nucleus and overlapping one of the ground states of the atom.

    The atom is in a crystal matrix. A hole can be considered a gap in the ground state of the atom. It is a mixture of different atomic electron states. However, so is a conduction electron. The conduction electron can be considered an excited atomic state of the same atom.

       The difference between a conduction electron and a hole is mostly caused 

by the fact that they overlap different vacuum electron states. The vacuum electrons in the valence band are closer to the nucleus of the atom than the vacuum electrons in the conduction band. The nucleus of a specific atom pulls at the valence electrons more than the nuclei of distant atoms. The atomic orbit of the valence band electron is closer to the associated nucleus than to nearby atoms. Hence, the weight of the nucleus slows down the valence electron. Hence, the valence hole is heavier than a vacuum electron.

        The orbit of an electron in an excited state is farther from the nucleus than the orbit of an electron in the ground state. Hence, nearby atoms pull at the excited state electron more than the valence band electron. The stronger pull of the distant nuclei from the nucleus makes the conduction band electron lighter. Hence, the conduction electron is lighter than the vacuum electron.

        Blochs theorem helps one connect the atomic states with the semiconductor crystal states. A wave function in a crystal is a product of a Bloch function and a periodic function. The Bloch functions very often approximate the atomic states. The periodic function that follows the Bloch state is responsible for the behavior as a pseudo particle. The periodic function is a momentum state of a collective excitation (hole or conduction electron).

     So one can't completely separate the atomic state behavior from the pseudoparticle behavior. The effective mass is determined by the atomic state behavior. The conservation of psuedomomentum is caused by the pseudo particle behavior. 

      So understanding the crystal states often requires jumping from the atomic states (Bloch functions) to the periodic factor (the momentum states).

The mobility is inversely proportional to the effective mass,and the effective mass of hole is much higher than that of electron.Thus the electron mobility is higher than that of hole

In a semiconductor the mobility of electrons (referring to ‘conduction electrons’ or ‘free-electrons’) is greater than that of a holes (indirectly referring to ‘valence electrons’) because of different band structure and scattering mechanisms of these two carrier types.

Conduction electrons (free-electrons) travel in the conduction band and valence electrons (holes) travel in the valence band. In an applied electric field, valence electrons cannot move as freely as the free electrons because their movement is restricted. The mobility of a particle in a semiconductor is larger if its effective mass is smaller and the time between scattering events is larger.

Holes are created by the elevation of electrons from innermost shells to higher shells or shells with higher energy levels. Since holes are subjected to the stronger atomic force pulled by the nucleus than the electrons residing in the higher shells or farther shells, holes have a lower mobility.

In an intrinsic silicon, at temperature 300 K:

Electron mobility = 1500 cm2/(V∙s)

Hole mobility = 475 cm2/(V∙s)

because electron effective mass is smaller than holes therefore mobility of electron is higher than holes.

Effective mass of holes are greater than that of electrons. That is why the mobility of of holes is lesser as compare to electrons.

for simplicity let us consider N-type semiconductor, number of electron is greater than hole and those excess electron is found in CB. now let us exert electric field. electrons in the valance band drift to fill the vacancy (hole) in valance band, hear one thing you should clear that vacancy exist in valance band, which is  relatively tightly bound. conduction electrons are really freely and have better drift velocity. therefore, in general, the mobility of electron also higher than hole.

Some (experimental) values for effective masses

Holes are absence of electrons in covalent bond and hole movements are actually movement of electrons to fill up an adjacent hole in the covalent bond. Thus, the electrons moving this way are still under the influence of nuclear forces that scatter them. In contrast, free electrons (or just commonly referred to as electrons) move within the semiconductor material freely, without going from a covalent bond vacancy to another. Meaning, free electrons are less influenced by the scattering due to nuclear forces and hence the higher mobility.

Because the mobility of a hole is the mobility of multiple electrons?

Isn't the bigger mass of the hole rather a result than the reason?

The simplest answer in my opinion is that for a hole to move it must wait for an electron to jump in it. Hence the mobility of holes cannot be higher than mobility of electrons.

I agree completely, when prof Prof.  Nebi Caka wrote:

Holes are created by the elevation of electrons from innermost shells to higher shells or shells with higher energy levels. Since holes are subjected to the stronger atomic force pulled by the nucleus than the electrons residing in the higher shells or farther shells, holes have a lower mobility.

Dear Qamil Kabashi do you think that hole movement is possible with out electron movement? If not we need to consider that e- & h in the same energy level pulled by equal nuclear force and also their mobility is equal, however, as you said if we consider in general, e-s at higher energy level than holes will be relatively free, andtheir mobility will be larger

My book says the same that Abdulla Suhail, and when i learned the subject i don´t remember very well which was the cause of the difference of effective mass, but to understand conduction in Semi Conductors it´s not very important.

I said the same:

The mobility of a particle in a semiconductor is larger if its effective mass is smaller.

Yes, but you didn´t mentioned that that subject is not important to understand the conduction in Semi Conductors, and then the joints, etc.

The question of Raghuram Tr was:

Why is the mobility of holes different from that of electrons?

and the answer is:

The mobility of holes is larger than the mobility of electrons because the effective mass of hole is larger then the effective mass of electron.

Dear Nebi

Thank you for your explanation,but The mobility of holes isnot  larger than the mobility of electrons .

You are right, mr. Yousefi,

It's 'lapsus calami'.

The mobility of electrons is larger than the mobility of holes,

as I wrote early,

In a semiconductor the mobility of electrons (referring to ‘conduction electrons’ or ‘free-electrons’) is greater than that of a holes (indirectly referring to ‘valence electrons’) because of different band structure and scattering mechanisms of these two carrier types.

Why is the mobility of holes different from that of electrons? - ResearchGate. Available from: https://www.researchgate.net/post/Why_is_the_mobility_of_holes_different_from_that_of_electrons [accessed Sep 10, 2015].

why the mobility of holes is more then electrons in case of  organic semiconductors?

In most organic semiconductors, the hole mobility is at least 10-100 times greater than electron mobility.

“Organic semiconductors can be broadly classified into two categories: small molecules or oligomers (usually processed in vacuum) and polymers (usually processed by wet chemical techniques). In each case, various materials have been designed over the years that preferentially transport holes or electrons. In most instances, this distinction does not rely on the actual ability of the materials to transport charges (i.e., on the actual values of charge mobilities) but rather reflects the ease of charge injection from electrodes traditionally used in devices. In that context, a material is often referred to as a hole [electron] transporter when its ionization energy [electron affinity] closely matches the Fermi level of the electrode material.“ (http://inside.mines.edu/~Zhiwu/research/papers/G02_charge_transfer.pdf)

“Organic semiconductors based on π-conjugated oligomers and polymers constitute the active elements in new generations of plastic (opto)electronic devices.”

“The charge-transport properties critically depend on the degree of ordering of the chains in the solid state as well as on the density of chemical and/or structural defects.”

“Because in isolated π-conjugated chains, the LUMO (Lowest Unoccupied Molecular orbital) wave function has usually one more node than the HOMO (Highest Occupied Molecular Orbital) wave function, the LUMO splitting is expected to be smaller than the HOMO splitting. Qualitatively, for large clusters, this difference will translate into larger HOMO bandwidths. This feature is what has given rise to the conventional wisdom that in crystals or crystalline films of π-conjugated chains, the hole mobility is expected to be higher than the electron mobility. (http://www.pnas.org/content/99/9/5804.full)

In crystalline materials the mobility is inversely proportional to the the effective mass of the drifting charge either electrons or holes.

The electrons move in the conduction band which is a a partially filled band while the holes moves on the top of the valence band which is partially empty band. The electrons and holes move under the effect of the electric field with an effective mass m* because of the the periodic interaction with lattice atoms. The concept of the effective mass is introduced to take into consideration this internal periodic forces on the motion of electrons and holes. The effective mass itself is determined from the energy band structure determined by solving the wave mechanical equations where one gets E= f(p), the energy E as a function of momentum p. The easiest way to get the effective mass is to fit the conduction band minimum and the valence band maximum by a parabola:

E= p^2/2 m*. Normally the effective mass of electrons is smaller than the effective mass of holes. This why the hole mobility is normally smaller than the electron mobility in crystalline materials.

The mobility depends also on the the presence of crystallographic defects

with the most effective in reducing the mobility is the grain boundaries.

To get more information please refer to the link: Book Electronic Devices

Best wishes

Besides all physical/technical explanations from the respectable researchers, the students may also like to know of a rather simplified explanation (though cannot represent some details of the actual behavior), which is based on the fact that movement of a hole through the semiconductor structure relies on movement of multiple neighbor valence electrons.

A very simple and short animation example is as follows:

https://www.youtube.com/watch?v=oSCX78-8-q0

However, when teaching the 2nd year engineering students, I prefer to use the analogy of an empty seat ("hole") in a theater hall, to which a late-comer person finds difficult to proceed to from the aisle and asks several seated persons ("valence electrons") to move by one seat (to the next/empty seat) successively, which eventually "moves" the empty seat ("hole") in the opposite direction, to the aisle. Such a movement is relatively slower than the movement of an un-seated person ("free electron": e.g. the late-comer, who walked from the door to the aisle until her/his seat row).

Best regards...

Abdelhalim abdelnaby Zekry Nebi Caka

What are the electron mobility, hole mobility values, Nc and Nv values for SiO2????

I need to assign these values to SiO2 in COMSOL urgently.

Thanks & Regards

the holes have a higher effective mass since they are close to each other. and the electrons have a low effective mass due to the loosely held. and electrons which are loosely held have a low effective mass. This is the reason why the mobility of a hole is less compared to an electron.

Dear Sherif Tawfik

Silicon dioxide is not a semiconductor material. It is an insulator which is described by a dielectric constant and a dielectric loss factor. It can be also described by a refractive index and extinction coefficient. The energy gao of the SiO2 is too high to be a semiconductor. It is about 7-9 eV.

Best wishes

Abdelhalim abdelnaby Zekry

Dear Doctor,

Thanks a lot for your help.

But what do you suggest to assign these values in COMSOL to just run the module.

A zero value e.g.?

Thanks & Best Regards

Dear Amir Sharfuddin ,

The hole has an identity as a defect electron in the valence structure of the semiconductor. It is observed experimentally that these defect electrons moves in the direction of the electric field which means it has a positive charge equals that of the electrons because the material is locally neutral then when we take away an electron to create a hole the whole must have a positive charge equals that of the electron. It is found that it has an effective mass when moving in the crystal. It effective mass could be measures and estimated.

In fact the main difference between the conduction in metal and in semiconductors is the presence of two types of mobile charge carrier: the electrons in the conduction band and the defect electrons(holes) in the valence band. That is conduction in to bands.

Practically there are the two types of conductions:

the n-type semiconductors

and the p-type semiconductors

This is one of main properties of semiconductors that make possible to make new electronic devices.

I would like that you refer to the book in the link:

Book Electronic devices with physical insight

The concept of hole is discussed in detail in this book.

Please tell us about your experience with thebook

Best wishes