We report on the complete scaling analysis of low temperature electron transport properties with and without magnetic field in the critical regime for the metal-insulator transition in two series of homogeneously doped p-type Ge samples: i) nominally uncompensated neutron-transmutation-doped (NTD) 70Ge:Ga samples with the technological compensation ratio K < 0.001, and ii) intentionally compensated NTD natGe:Ga,As samples with K = 0.32. For the case of the uncompensated series in zero magnetic field, the critical exponents μ, ν, and ζ determined for the electrical conductivity (σ), localization length (ξ), and impurity dielectric susceptability (χimp), respectively, change at the very vicinity of the critical Ga concentration (N ∼ Nc). Namely, the anomalous critical exponents, e.g. μ ≈ 0.5, change to μ ≈ 1 only within the region 0.99Nc < N < 1.01Nc. On the other hand, the same critical behavior, μ ≈ 1, was found for the K = 0.32 series in much larger region 0.25Nc < N < 2ANc. This finding suggests that the μ ≈ 1 critical behavior observed for the nominally uncompensated series in the extremely narrow region is due to the presence of the self-compensation of acceptors by native defects and/or technologically unavoidable very small amount of doping compensation (K < 0.001). Therefore, the width of the concentration that can be fitted with μ ≈ 1 around N c is likely to scale with the degree of compensation (K), and disappears in the limit K → 0, i.e., only the region with the anomalous exponent μ ≈ 0.5 remains for the case of K = 0. An externally applied magnetic field to nominally uncompensated samples also broadens the width of μ ≈ 1 around Nc, but with a mechanism clearly different from that of compensation. The unified description of our experimental results unambiguously establishes the values of the critical exponents μ, ν, and ζ for doped semiconductors with and without compensation and magnetic field.
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