Two- to three-dimensional crossover in a dense electron liquid in silicon

Abstract

Doping of silicon via phosphine exposures alternating with molecular beam epitaxy overgrowth is a path to Si:P substrates for conventional microelectronics and quantum information technologies. The technique also provides a well-controlled material for systematic studies of two-dimensional lattices with a half-filled band. We show here that for a dense (n s = 2.8 × 10 14 cm −2 ) disordered two-dimensional array of P atoms, the full field magnitude and angle-dependent magnetotransport is remarkably well described by classic weak localization theory with no corrections due to interaction. The two-to three-dimensional crossover seen upon warming can also be interpreted using scaling concepts developed for anistropic three-dimensional materials, which work remarkably except when the applied fields are nearly parallel to the conducting planes.

Non‐Destructive X‐Ray Imaging of Patterned Delta‐Layer Devices in Silicon

“…where n is the free carrier density as measured by the Hall effect. Finally, for tilted magnetic fields the change in conductance can be described by the phenomenological expression [36] ( )…”

“…By fitting Δσ( B ⊥ ) and Δσ( B || ) we can derive this thickness as [ 35 ] $$\[t = {\left( {\frac{1}{{4\pi }}} \right)^{1/4}}{\left[ {{{\left( {\frac{\hbar }{{e{L_\phi }}}} \right)}^2}(\sqrt n L\gamma )} \right]^{1/2}}\]$$where n is the free carrier density as measured by the Hall effect. Finally, for tilted magnetic fields the change in conductance can be described by the phenomenological expression [ 36 ] $$\[\Delta \sigma {(B)^p} = \Delta \sigma {({B_ \bot })^p} + \Delta \sigma {({B_\parallel })^p}\]$$where p is obtained by fitting the data and is sample and temperature‐dependent.…”

Momentum‐Space Imaging of Ultra‐Thin Electron Liquids in δ‐Doped Silicon

“…[ 14 , 15 , 16 , 17 ] The electronic thicknesses of these layers have also been estimated using quantum magnetoresistance, [ 18 ] with similar results. [ 19 ] Such thicknesses are comparable to the wavelength of the conduction electrons, and the corresponding energy level quantization was observed in planar junction tunneling spectroscopy more than three decades ago. [ 9 , 20 , 21 ] Vacuum ultraviolet angle‐resolved photoemission spectroscopy (VUV‐ARPES) measurements of phosphorous δ‐layers in silicon have also revealed quantized states, yet the origin of these quantized states was incorrectly attributed to the more exotic degeneracy lifting mechanism, valley interference.…”