Complete scaling analysis of the metal-insulator transition in Ge : Ga: Effects of doping-compensation and magnetic field

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) Ge-70:Ga samples with the technological compensation ratio K < 0.001, and ii) intentionally compensated NTD Ge-nat:Ga,As samples with K = 0.32. For the case of the uncompensated series in zero magnetic field, the critical exponents mu, v, and zeta determined for the electrical conductivity (sigma), localization length (xi), and impurity dielectric susceptability (chi(imp)), respectively, change at the very vicinity of the critical Ga concentration (N similar to N-c) Namely, the anomalous critical exponents, e.g. mu approximate to 0.5, change to mu approximate to 1 only within the region 0.99N(c) < N < 1.01N(c). On the other hand, the same critical behavior, mu approximate to 1, was found for the K = 0.32 series in much larger region 0.25N(c) < N < 2.4N(c) This finding suggests that the it mu approximate to 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 mu approximate to 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 mu approximate to 0.5 remains for the case of K = 0. An externally applied magnetic field to nominally uncompensated samples also broadens the width of mu approximate to 1 around N-c, 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 mu, v, zeta and for doped semiconductors with and without compensation and magnetic field.