Effective mass theory of monolayer δ-doping in the high-density limit

Abstract

Monolayer δ-doped structures in silicon have attracted renewed interest with their recent incorporation into atomic-scale device fabrication strategies as source and drain electrodes and in-plane gates. Modeling the physics of δ-doping at this scale proves challenging, however, due to the large computational overhead associated with ab initio and atomistic methods. Here, we develop an analytical theory based on an effective mass approximation. We specifically consider the Si:P materials system, and the limit of high donor density, which has been the subject of recent experiments. In this case, metallic behavior including screening tends to smooth out the local disorder potential associated with random dopant placement. While smooth potentials may be difficult to incorporate into microscopic, single-electron analyses, the problem is easily treated in the effective mass theory by means of a jellium approximation for the ionic charge. We then go beyond the analytic model, incorporating exchange and correlation effects within a simple numerical model. We argue that such an approach is appropriate for describing realistic, high-density, highly disordered devices, providing results comparable to density functional theory, but with greater intuitive appeal, and lower computational effort. We investigate valley coupling in these structures, finding that valley splitting in the low-lying Γband grows much more quickly than the Γ-Δband splitting at high densities. We also find that many-body exchange and correlation corrections affect the valley splitting more strongly than they affect the band splitting.

References in corpus (4)

• Single-shot read-out of an individual electron spin in a quantum dot
• Tunable spin-selective loading of a silicon spin qubit
• Physical mechanisms of interface-mediated intervalley coupling in Si
• Single-electron quantum dot in Si/SiGe with integrated charge-sensing

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• Electronic transport in two dimensional Si:P $\delta$-doped layers
• Observation and origin of the $\Delta$-manifold in Si:P $\delta$-layers
• Conductivity and size quantization effects in semiconductor $\delta$-layer systems
• Fermi level pinning at the Ge(001) surface - A case for non-standard explanation
• Electronic properties of delta-doped phosphorus layers in silicon and germanium
• Atomic-layer doping of SiGe heterostructures for atomic-precision donor devices
• Momentum-space imaging of ultra-thin electron liquids in delta-doped silicon
• Electronic transport in Si:P delta-doped wires
• Electronic structure of boron and aluminum $\delta$-doped layers in silicon
• Probing the Atomic Arrangement of Sub-Surface Dopants in a Silicon Quantum Device Platform
• Extrapolated Elliptic Regularity and Application to the van Roosbroeck system of Semiconductors