Variable-Range Hopping Conduction

This chapter deals with hopping conduction at temperatures which are so low that typical resistances between neighboring impurities become larger than those connecting some remote impurities whose energy levels happen to be very close to the Fermi level. In this case the characteristic hopping length increases with lowering temperature (hence the name variable-range hopping, or VRH), and for a constant density of states one obtains the celebrated Mott’s law. Derivation of this law is given in Sect. 9.1. In that section it is also discussed how Mott’s law should be modified in the presence of a Coulomb gap. Section 9.2 studies the effect of a magnetic field on hopping conduction in the VRH regime. Section 9.3 describes a peculiar size effect which occurs in thin films of amorphous semiconductors with VRH conduction, and arises due to the finite volume accessible to current. Finally, in Sect. 9.4 we discuss theory of the pre-exponential factor in hopping conductivity, and compare results of different authors and their approaches to this problem.

[1]  J. J. Hauser,et al.  Electrical and Structural Properties of Amorphous Germanium , 1973 .

[2]  M. Knotek.  Temperature and thickness dependence of low temperature transport in amorphous silicon thin films: A comparison to amorphous germanium , 1975 .

[3]  Random walk in disordered hopping systems , 1980 .

[4]  W. Schaich,et al.  Theory of impurity band hopping conduction , 1972 .

[5]  J. J. Hauser.  Electrical, structural and optical properties of amorphous carbon , 1977 .

[6]  F. R. Allen,et al.  Electrical conduction in heavily doped germanium , 1972 .

[7]  B. Shklovskii.  Hopping conduction in semiconductor films , 1975 .

[8]  G. Döhler,et al.  T−13-hopping in organic charge transfer crystals? , 1972 .

[9]  B. Movaghar,et al.  Theory of hopping conduction in disordered systems: Application to the magnetoresistance in impurity conduction , 1980 .

[10]  Nevill Mott,et al.  Conduction in glasses containing transition metal ions , 1968 .

[11]  Numerical calculations of a.c. hopping conductivity , 1979 .

[12]  J. Chalupa.  Percolation in bounded geometries , 1979 .

[13]  M. Pollak,et al.  A Note on the Anisotropy of the Conductivity in Thin Amorphous Films , 1973 .

[14]  R. Hill.  Variable‐range hopping , 1976 .

[15]  P. N. Butcher,et al.  Analytical formulae for d.c. hopping conductivity: r-percolation in 3D , 1978 .

[16]  E. Guyon,et al.  Conductivity of a mixture of conducting and insulating grains: Dimensionality effects , 1980 .

[17]  D. Redfield.  Observation of log σ ∼ T − 1 2 in Three-Dimensional Energy-Band Tails , 1973 .

[18]  B. Movaghar,et al.  Theory of AC and DC Conductivity in Disordered Hopping Systems , 1980 .

[19]  C. H. Seager,et al.  Percolation and conductivity: A computer study. II , 1974 .

[20]  T. M. Donovan,et al.  Thickness Dependence of Hopping Transport in Amorphous-Ge Films , 1973 .

[21]  F. H. Schmitz,et al.  Experiment versus theory , 1982 .

[22]  Walter Schirmacher,et al.  Theory of electronic hopping transport in disordered materials , 1980 .

[23]  J. Kurkijärvi.  Hopping Conductivity in One Dimension , 1973 .

[24]  R. Hill.  On the observation of variable range hopping , 1976 .

[25]  V. Shante.  Variable-range hopping conduction in thin films , 1973 .

[26]  Vinay Ambegaokar,et al.  Hopping Conductivity in Disordered Systems , 1971 .

[27]  D. Redfield.  Transport properties of electrons in energy band tails , 1975 .

[28]  J. J. Hauser.  Hopping conductivity in amorphous carbon films , 1975 .

[29]  G. Döhler,et al.  Hopping conductivity in highly anisotropic systems , 1973 .

[30]  C. Varma,et al.  Hopping Conductivity in "One-Dimensional" Disordered Compounds , 1973 .

[31]  B. Movaghar,et al.  On the theory of hopping conductivity in disordered systems , 1981 .

[32]  G. Sadasiv.  Magnetoresistance in Germanium in the Impurity Conduction Range , 1962 .

[33]  B. Shklovskii.  Thickness dependence of the hopping conduction in amorphous films. Experiment versus theory , 1977 .