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Scaling Analysis of the Variable Range Hopping in p‐Ge at High Compensation
Author(s) -
Rentzsch R.,
Chiatti O.,
Müller M.,
Ionov A.N.
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<237::aid-pssb237>3.0.co;2-s
Subject(s) - condensed matter physics , scaling , dielectric , coulomb , impurity , variable range hopping , magnetoresistance , electrical resistivity and conductivity , materials science , physics , electron , magnetic field , nuclear physics , quantum mechanics , mathematics , geometry
Isotopic mixtures of 70 Ge and 74 Ge (Isotopically Engineered: IE‐Ge) were by a neutron‐transmutation doping (NTD) process provided with a high compensation of K = N As / N Ga ≅ 0.4, 0.6, 0.9. Variable range hopping (vrh) resistivity at T = 0.1–4.2 K shows ϱ ( T ) = ϱ 0 exp( T 0 / T ) 1/2 . At K = 0.4–0.6 a small change of the critical concentration of the metal‐insulator transition, N c and at K = 0.9 a very strong increase of up to N c = (1.2 ± 0.2) × 10 19 cm —3 was found. We calculated the value of the localization length a from measurements of the temperature‐ and low‐field dependencies of the positive magnetoresistance, and by a combination of a with T 0 = 2.8 e 2 / k B a 4 πε 0 κ the dielectric constant κ is estimated. In accordance with the predictions of a disorder‐induced scaling theory, the critical indices ν ≅ 1, ζ ≅ 2, and p ≅ 3 were obtained for a , κ and T 0 , respectively. At medium compensation, K ≤ 0.6, the value of T 0 is much smaller than T ES predicted by Efros and Shklovskii for one‐electron‐transitions, which is interpreted as being due to many‐particle excitations which reduce the width of the Coulomb gap. Only at K = 0.9 and at very low impurity concentration far from the range of validity of the scaling relation many‐particle excitations can be neglected, resulting in a strong increase of T 0 → T ES ≅ 366 K.