Electronic properties of multiple adjacentδ-doped Si:P layers: The approach to monolayer confinement

Abstract

Recent breakthroughs in single-atom fabrication in silicon have brought the exciting prospect of monolayerbased nanoelectronics and theoretical understanding of such systems into sharp focus. Of particular interest is the effect of such sharp two-dimensional Coulomb array confinement on electronic properties of these donor-based semiconducting systems such as valley splitting, which is critical to quantum electronic applications. In this paper we apply ab initio techniques to these high-density donor systems specifically in order to investigate the approach to monolayer confinement. An optimized basis set is developed for Si:P and validated against our previous work on single δ-doped layers. A systematic study is then conducted wherein the effect of multiple adjacent phosphorus δ layers on the electronic properties of the material is explored. We find nonmonotonic electronic behavior as we approach the monolayer confinement limit, with potentially far-reaching implications for large-scale fabrication techniques.

Electronic properties ofδ-doped Si:P and Ge:P layers in the high-density limit using a Thomas-Fermi method

“…33,38 The valley splitting is inversely proportional to the spatial extent of the donors perpendicular to the doping plane. 35 There are two characterisitcs of the donor potential that affect the confinement of the donor electrons. These are the rate of decay of the gradient of the potential in the z direction and the depth of the potential well.…”

“…These studies used the nemo -d package, 30 which has also been applied to δ-doped Si:P quantum wires. 10,31 Complimentary DFT models of Si:P δ-layers and quantum wires have been proposed using the siesta and vasp packages, with localised atomic orbital (LAO) bases [32][33][34][35] and a planewave basis. 36 However, the applicability of these models to realistic device architectures is restricted by the N 3 scaling in calculation time associated with DFT.…”

Electronic structure of phosphorus and arsenicδ-doped germanium

“…Density functional theory (DFT) calculations on δ-doped germanium are conducted by adapting the general approach previously applied to Si:P by ourselves [16][17][18] and others [19][20][21] to the specific requirements of Ge:P and Ge:As. All calculations are performed using the SIESTA software.…”

Quantifying atom-scale dopant movement and electrical activation in Si:P monolayers

“…13 In Si:P planar contact and gate regions, deviation of the 2-D dopant confinement from an ideal Si:P monolayer has profound effects on 2-D electrical properties . 14 Atomically sharp dopant confinement, high dopant activation ratios, and a defectfree epitaxial environment are essential attributes of proposed donor-based Si:P quantum computer architectures, 6,11,15 necessitating the development of precision metrological and fabrication methodologies to control dopant confinement and epitaxial quality at the atomic scale. 16 In this study, we develop a robust quantification method to monitor and control, at the ultimate monoatomic layer scale, unintentional dopant movement and formation of lattice defects to enable characterization and optimization of Si:P monolayer fabrication, fundamental to donor-based Si quantum computing and atomically precise 2-D superlattice design.…”

“…19 A key development to address the well-known trade-off between low-temperature encapsulation for sharp dopant confinement and high-temperature encapsulation for optimum epitaxial quality [20][21][22] has been the recent application of thin room-temperature grown layers, commonly referred to as locking layers (LL), followed by encapsulation overgrowth at elevated temperatures. [23][24][25] While theoretical calculations have been carried out on the effects of various levels of dopant confinement on Si:P 2-D properties, 1,14 experimental quantification of dopant confinement and redistribution within room-temperature grown LLs remains challenging with little success at the monoatomic layer scale. The importance of this challenge is paramount to the development and performance of atomically precise 2-D superlattice designs and donor-based quantum computing.…”