Mobility is proportional to the average time between two consecutive scattering events (collisions) and is inversely proportional to the effective mass. Electrons and holes are scattered by different types of crystal imperfections, which include phonons, impurities, defects, etc. In current MOSFETs, the channel electrons and holes are scattered mainly by impurity and interface charges (Coulomb scattering), interface roughness, and phonons. The average time between collisions (also known as the mean free time) is given by the Mathiessen's Rule. 

For most semiconductors (elemental, III-V compounds, II-VI compounds, etc.), the electron mobility is larger than the hole mobility, and in some cases much larger; but there are exceptions. Exceptions are: electron mobility/hole mobility in cm-2V-1s-1:

C (Diamond) - 1800-2200/1600-1800; PbS - 600/700; PbTe - 2500-6000/1000-4000.

Mobility is proportional to the average time between two consecutive scattering events (collisions) and is inversely proportional to the effective mass. Electrons and holes are scattered by different types of crystal imperfections, which include phonons, impurities, defects, etc. In current MOSFETs, the channel electrons and holes are scattered mainly by impurity and interface charges (Coulomb scattering), interface roughness, and phonons. The average time between collisions (also known as the mean free time) is given by the Mathiessen's Rule. 

For most semiconductors (elemental, III-V compounds, II-VI compounds, etc.), the electron mobility is larger than the hole mobility, and in some cases much larger; but there are exceptions. Exceptions are: electron mobility/hole mobility in cm-2V-1s-1:

C (Diamond) - 1800-2200/1600-1800; PbS - 600/700; PbTe - 2500-6000/1000-4000.

I already added a similar question before. 

Anyways, I copy and pasted that answer below:

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.

I think holes do not move , but electrons move with some drift velocity .While moving they collide with next atom and knock out electrons from outer shell or occupy available holes which seems holes move in one direction(-ve of battery)  and electrons in the other (+ve of battery).

It depends on the material.

In a metal, the mobility of electrons and holes is almost the same.

https://staff.aist.go.jp/v.zayets/spin3_38_Holes.html

In a semiconductor, the electron mobility is larger than the hole mobility (except for a few exceptions)

The major reason of different motilities in a semiconductor is different special symmetry for electrons and holes.

The special symmetry of electrons is s-orbital like (spherical).

The special symmetry of holes is p-orbital like.

It takes a longer time for an electron to circle the p-orbital than the s-orbital. It makes a hole slower than an electron.

https://staff.aist.go.jp/v.zayets/spin3_32_SpinOrbit.html

Fig. Movement of a delocalized electron in a metal

Electrons travel in the conduction band between the two materials. Since the conduction band is formed by the uppermost shell, farthest from any of the nucleus, and since proton resides inside nucleus and hence more energy is required to move an proton than an electron 

Explanation given by Joel T. Asubar is absolutely right.

Explanation given by Joel T. Asubar is not correct.

The movement of holes is not movement of electrons to fill up an adjacent hole in the covalent bond. The movement of a hole is as "free" as the movement of an electron. In fact, both the electrons and the holes are the same delocalized electrons. For example, in a metal the electrons and holes can be only distinguished by their energy. The energy of an electron is above the Fermi energy and the energy of a hole is below the Fermi energy. Of cause, an electron and a hole interact differently with electrical field.

The mean-free path of a hole may reach several micrometers (typically in a semiconductor it is 50-200 nm at room temperature). If you see an electron as a wave, the mean-free path of an electron is just the size of the electron. Therefore, the size of a hole may be a micrometer. The distance between covalent bonds is about 0.1 nm. It means that simultaneously an electron or a hole is filling up or interacts with a million of covalent bonds. Surely, the movement of holes is not movement of an electron to fill up adjacent holes in the covalent bonds. Besides, in order to jump from one covalent bond to other covalent bond an electron needs to interact with a phonon. In the case if such jumping between the covalent bonds were the mechanism of the hole transport, the hole mobility would be very small. It would be even smaller than mobility in a material with hopping conduction.

In a metal the electron mobility and the hole mobility is the same. Only reason for a difference in the mobilities in a semiconductor is different spatial symmetry of the envelop function for an electron and a hole.

Vadym Zayets' answer is the more complete and more correct answer to the question because he fully considered the particle and wave nature duality of electrons and holes. My answer is of more classical nature treating the carriers more of particles and therefore is very simplified in the hope of giving a more visual image of a complicated quantum mechanical process. 

Thank you Vadym Zayets for the detailed explanation considering spin-orbit interaction. However, I have a little doubt in my mind. As you pointed out, both are delocalized electrons having only difference in spatial symmetry,how would you explain the effective mass of electrons is smaller than hole in accordance with your explanation?

The mobility of electrons and holes is different, because the electrons and holes have different spatial symmetry. The electrons have s-orbital-like symmetry of the envelop wave function. The holes have p-orbital-like symmetry of the envelop wave function.

There are two reasons why the difference in the spatial symmetry causes the different mobility. They may sound different, but they explain the same fact.

The first reason, why the mobility is different, is that it takes a longer time for an electron to circle around the p-orbital than around the s-orbital.

A delocalized electron simultaneously moves along the crystal lattice and rotates around millions of atomic nuclei . It might sound strange that it is possible to rotate around several objects simultaneously. Since an electron is a wave, it is possible. For example, when light is diffracted by a diffraction grating , each photon is reflected from each of million steps of the grating) simultaneously. Any wave can interact with many objects simultaneously. It is not forbidden.

There are many experimental proofs that delocalized electrons have a non-zero orbital moment. For example, their g-factor is different from 2, they experience the center-symmetrical spin-orbit interaction and the existence of the split-off valence band is other proof. The non-zero orbital moment literally means that the delocalized electron is orbiting around atomic nuclei.

The second reason, why the mobilities (effective masses) are different for holes and electrons in a semiconductor, is that the magnitudes of the s-like and p-like envelope functions are different in the vicinity of the atomic nucleus. The electrons of different symmetry interact differently with the nucleus. Therefore, the amplitude of the lattice periodic potential is different for electrons and holes in a semiconductor. This causes the different effective masses.

Thank you so much Prof. Vadym for a detailed clarification.