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Hubbard Band Formation Observed Directly in Copper-Doped Germanium
Eugene Haller

Researchers at the Center for Advanced Materials Electronic Materials Program have discovered a new form of metal-to-insulator transition (MIT) in copper-doped germanium crystals. The phenomenon, which in these experiments involved the transition from insulator to metal, was observed as an extremely large increase in conductivity induced by the application of uniaxial stress.

Phenomena associated with transitions of electronic states from localized and insulating to extended and metallic-like have been among the most difficult and extensively studied problems in condensed matter physics. In heavily doped semiconductors, for example, as the concentration of the dopant is increased the conduction mechanism changes from charge carrier "hopping" between isolated dopant sites (giving insulating properties) to motion of carriers in a spatially extended energy band giving metal-like properties. Near the transition point, the overlapping dopant orbitals form a "Hubbard band," which has distinct upper and lower components. The detailed study of these band components has been hampered in the past because in most semiconductors at the transition point the upper Hubbard band merges with the crystal's valence bands, leading to a very convoluted series of overlapping energy states.

The Berkeley Lab researchers found that these complications could be eliminated by using copper-doped germanium (Ge) and subjecting it to uniaxial stress. At Cu concentrations below the transition point, both the lower and the upper Hubbard bands are energetically well separated from the Ge valence band. Thermally activated, "hopping" conductivity is observed, indicating that the two Hubbard bands are separated by an energy gap. However, compression of the crystal changes the germanium band structure such that the ground state of the Cu atoms switches from a (1s)3 to a (1s)2(2s) configuration. The latter configuration is much larger in size (see figure) so the orbitals of the copper dopant atoms overlap. The team observed that application of stress reduces the resistivity near 4 K by an unprecedented 12 orders of magnitude (see figure), changing the germanium from practically insulating to metallic. The team also found very high mobilities, exceeding 106 cm2/Vs, for the charge carriers in the upper Hubbard band, indicative of a low effective mass. This observation, combined with a large and positive magnetoresistance effect, proved that the upper Hubbard band was an independent band, well-separated from the Ge valence band. In other words, uniaxially stressed Cu-doped Ge has an independent metal-like band embedded in its semiconductor energy gap.

This newly demonstrated ability to study conduction mechanisms in deep impurity bands without interference from hopping or valence band conduction should allow previously unattainable studies of conductivity in these bands. Cu-doped Ge should also provide a model system to investigate solid-state phenomena that have only been predicted theoretically. An example is "Wigner crystallization," in which the charge carriers assume an ordered, crystalline configuration at room temperature.