The Metal-Insulator Transition in n-Type Silicon in High Magnetic Fields

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The study of the metal-insulator (MI) transition in doped semiconductors in recent years has focused on the scaling behavior of the DC conductivity [1,2], the static dielectric ’constant’ [3,4], and more recently the critical behavior of the spin susceptibility [5] and Mott variable range hopping (VRH) conduction [6]. Unlike the 2d inversion layer systems, where one can continuously vary the carrier density by changing a gate voltage, there is no simple way to continuously vary the impurity or carrier density for a bulk 3d system. For these systems experimentalists have employed uniaxial stress or magnetic fields to tune the critical density Nc and thereby vary (N-Nc) and in many cases to successfully tune a sample completely through the transition. Uniaxial stress experiments have been particularly important and useful for the study of the n-type many-valley semiconductors Ge [7] and Si [2,4] because the stress removes the degeneracy of the conduction band minima, changes the screening, and thereby alters Nc [8]. PAALANEN et.al. [2,4] have utilized uniaxial stress to accurately determine the scaling behavior of the DC conductivity σDC and the ‘static’ dielectric response e’(N) for Si:P as T→OK. Since the classic YAFET, KEYES, and ADAMS [9] calculation demonstrating the donor wave function shrinkage in large static magnetic fields there have been many studies of InSb [10–13] demonstrating the tuning of metallic samples to insulating behavior with some threshold field Hc dependent on (N-Nc).