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Variable‐Range Hopping in Si : B: A Temperature‐Independent Prefactor in Three Dimensions
Author(s) -
Sarachik M.P.,
Dai P.
Publication year - 2002
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/1521-3951(200203)230:1<205::aid-pssb205>3.0.co;2-b
Subject(s) - variable range hopping , condensed matter physics , dopant , exponent , atmospheric temperature range , doping , mott transition , metal–insulator transition , electrical resistivity and conductivity , physics , materials science , quantum mechanics , thermodynamics , hubbard model , superconductivity , linguistics , philosophy
For Si : B with dopant concentrations ranging from 0.75 n c to the critical concentration for the metal–insulator transition, the conductivity ranging over five orders of magnitude is shown to collapse onto a single universal curve of the form σ ( T ) = σ 0 f ( T */ T ) with a prefactor σ 0 that is independent of temperature and dopant concentration. The function f ( T */ T ) = exp [—( T */ T ) β ] with β = 1/2 when T * < 10T, corresponding to Efros‐Shklovskii variable‐range hopping. For T * ≤ 8 T the exponent β is 1/3, the value expected for Mott variable‐range hopping in two rather than three dimensions. The temperature‐independent prefactor implies hopping that is not mediated by phonons.