I would like to know more about both mechanisms in disorder materials
Hopping is just hopping, of an electron from one site to a neighbouring site (a site may be viewed as a pond of electrons, physically separated from other ponds of electrons). Variable-range hopping is a hopping according to a statistical distribution governed by a specific metric named 'range', determined both by the physical distance of hopping and the difference of the energies of the initial and final states involved in the process of hopping. In general, in a disordered system one speaks of electronic conduction taking place on the basis of the variable-range hopping when the conductivity diminishes exponentially for decreasing temperatures, with the exponent being determined by a power of the inverse of the ambient temperature; in three dimensions this power is equal to 1/4 for non-interacting electrons; when electron-electron interaction is included, this power is increased to 1/2 (according to Efros and Shklovskii - see below), however to observe this power experimentally, it is required to conduct experiments at very low temperatures; at elevated temperatures one observes the former power, namely 1/4.
For details, see Chapter 9 of the book Electronic Properties of Doped Semiconductors, by Shklovskii and Efros (Springer, Berlin, 1984), as well as the book Metal-Insulator Transitions, by NF Mott (Taylor & Francis, 1990). You may also consider to begin by consulting the following rather incomplete Wikipedia entry:
http://en.wikipedia.org/wiki/Variable-range_hopping
Hopping is just hopping, of an electron from one site to a neighbouring site (a site may be viewed as a pond of electrons, physically separated from other ponds of electrons). Variable-range hopping is a hopping according to a statistical distribution governed by a specific metric named 'range', determined both by the physical distance of hopping and the difference of the energies of the initial and final states involved in the process of hopping. In general, in a disordered system one speaks of electronic conduction taking place on the basis of the variable-range hopping when the conductivity diminishes exponentially for decreasing temperatures, with the exponent being determined by a power of the inverse of the ambient temperature; in three dimensions this power is equal to 1/4 for non-interacting electrons; when electron-electron interaction is included, this power is increased to 1/2 (according to Efros and Shklovskii - see below), however to observe this power experimentally, it is required to conduct experiments at very low temperatures; at elevated temperatures one observes the former power, namely 1/4.
For details, see Chapter 9 of the book Electronic Properties of Doped Semiconductors, by Shklovskii and Efros (Springer, Berlin, 1984), as well as the book Metal-Insulator Transitions, by NF Mott (Taylor & Francis, 1990). You may also consider to begin by consulting the following rather incomplete Wikipedia entry:
http://en.wikipedia.org/wiki/Variable-range_hopping
Thank you sir, really I have got good explanation and one more if any article precisely explaining both concepts please let me know
You are welcome! The best two reference books known to me are the ones I introduced above, by Shklovskii & Efros, and Mott.
I totally agree with Benham Farid - these are the best books on electronic properties of disordred semiconductors. If you insist on articles as oppose of books, you may want to search for Shklovski, Efros, or Mott as authors, and you'll find their original articles which served as the foundation for the above mentioned books.
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