Disentangling phonon and impurity interactions in δ-doped Si(001)

We present a study of the phonon and impurity interactions in a shallow two dimensional electron gas formed in Si(001). A highly conductive ultra-narrow n-type dopant δ-layer, which serves as a platform for quantum computation architecture, is formed and studied by angle resolved photoemission spectroscopy (ARPES) and temperature dependent nanoscale 4-point probe (4PP). The bandstructure of the δ-layer state is both measured and simulated. At 100 K, good agreement is only achieved by including interactions; electron-impurity scattering (W₀ = 56 to 61 meV); and electron-phonon coupling (λ = 0.14 ± 0.04). These results are shown to be consistent with temperature dependent 4PP resistance measurements which indicate that at 100 K, ≈7∕8 of the measured resistance is due to impurity scattering with the remaining 1/8 coming from phonon interactions. In both resistance and bandstructure measurements, the impurity contribution exhibits a variability of ≈9% for nominally identical samples. The combination of ARPES and 4PP affords a thorough insight into the relevant contributions to electrical resistance in reduced dimensionality electronic platforms.