When an electric field E is applied across a piece of material, the electrons respond by moving with an average velocity called the drift velocity , where the electron repeatedly scatters off crystal defects, phonons, impurities, etc. Therefore, it does not accelerate faster, instead it moves with a finite average velocity, called the drift velocity. Then, the electron mobility μ is defined as

Drift velocity = μ * E

Electron mobility is specified in units of cm2/(V·s).

Furthermore, conductivity is proportional to the product of mobility and carrier concentration, n such that:

conductivity = n*e*μ

For example, the same conductivity could come from a small number of electrons with high mobility, or a large number of electrons with a small mobility. The mobility is relatively unimportant in metal physics.

On the other hand, for semiconductors, the behavior of transistors and other devices can be very different depending on whether there are many electrons with low mobility or few electrons with high mobility. Therefore, mobility is a very important parameter for semiconductor materials. Higher mobility usually leads to better device performance.

In summary, typical electron mobility for Si at room temperature (300 K) is 1400 cm2/ (V·s) and the hole mobility is around 450 cm2/ (V·s).[2]

Very high mobility has been found in several low-dimensional systems, such as two-dimensional electron gases (35,000,000 cm2/(V·s) at low temperature), carbon nanotubes (100,000 cm2/(V·s) at room temperature) and more recently, graphene (200,000 cm2/ V·s at low temperature). Organic semiconductors (polymer, oligomer) have been developed with carrier mobilities below 10 cm2/(V·s).

Ref: Wikipedia

Dear sir,

Pi-electrons in Graphene have low dependency on their nuclei. Linear E-k diagram at points which valence band and conductance band reach together (we called them Dirac points), is one of its results. At this points if we apply old effective mass formula to these electrons, second order derivative make effective mass infinity (so this is false). In order to solve, we use quantum-relativistic Schrodinger wave equation. By that, we reach formulas for its mass, mobility and of course its conductivity. Graphene has zero effective mass for both electron and hole. The mentioned properties depends on doping profile which can be alter with potential voltage. Electrons in such this 2D materials called Dirac fermions. Another approach to understand better is to suppose Graphene sheet as a positive ions sea which electron cloud move above it. So we can assume that electrons are in plasma mode (high mobility).

Recently we have published an article in “Laser Physics Letters” journal entitled “Fabrication of graphene based on Q-switched Nd:YAG laser ablation of graphite target in liquid nitrogen” (doi:10.7452/lapl.201210033 & Link: http://iopscience.iop.org/1612-202X/9/7/014?fromSearchPage=true). In this work, a novel technique is presented for the graphene fabrication based on the pulsed laser ablation of graphite target inside the cryogenic liquid using the pulsed nanosecond Q-switched Nd:YAG laser at 1064 nm. Single-stage fabrication process is taken into account as a remarkable advantage without need to high vacuum devices and additional chemical components. The synthesis process is controllable by changing the laser properties and the irradiation conditions accompanying easy collection of the products. Moreover, the suspension graphene generated by this method exhibit good mobility, magnetic and optoelectronic properties in comparison to the other fabrication techniques.

Dispersion law E(k) for electrons in graphene is linear, E(k)=v_F. k , electron is a massless relativistic Dirac particle and the Fermi velocity is v_F~( 1/300) c, c being the light velocity. These properties imply the high mobility

When an electric field E is applied across a piece of material, the electrons respond by moving with an average velocity called the drift velocity , where the electron repeatedly scatters off crystal defects, phonons, impurities, etc. Therefore, it does not accelerate faster, instead it moves with a finite average velocity, called the drift velocity. Then, the electron mobility μ is defined as

Drift velocity = μ * E

Electron mobility is specified in units of cm2/(V·s).

Furthermore, conductivity is proportional to the product of mobility and carrier concentration, n such that:

conductivity = n*e*μ

For example, the same conductivity could come from a small number of electrons with high mobility, or a large number of electrons with a small mobility. The mobility is relatively unimportant in metal physics.

On the other hand, for semiconductors, the behavior of transistors and other devices can be very different depending on whether there are many electrons with low mobility or few electrons with high mobility. Therefore, mobility is a very important parameter for semiconductor materials. Higher mobility usually leads to better device performance.

In summary, typical electron mobility for Si at room temperature (300 K) is 1400 cm2/ (V·s) and the hole mobility is around 450 cm2/ (V·s).[2]

Very high mobility has been found in several low-dimensional systems, such as two-dimensional electron gases (35,000,000 cm2/(V·s) at low temperature), carbon nanotubes (100,000 cm2/(V·s) at room temperature) and more recently, graphene (200,000 cm2/ V·s at low temperature). Organic semiconductors (polymer, oligomer) have been developed with carrier mobilities below 10 cm2/(V·s).

Ref: Wikipedia

     Dear Parviz,

      I am very sorry to have to contradict you. Actually the mobility to the electrons in the graphene is very low if you compare it with the 2D electrons of the in semiconductor heterostructures. The highest mobility is for Ga As/Al Ga As where the fractional quantum Hall effect can be observed due to this feature.