Direct measurement of the band structure of a buried two-dimensional electron gas

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

Two-dimensional dopant layers (δ-layers) in semiconductors provide the high-mobility electron liquids (2DELs) needed for nanoscale quantum-electronic devices. Key parameters such as carrier densities, effective masses, and confinement thicknesses for 2DELs have traditionally been extracted from quantum magnetotransport. In principle, the parameters are immediately readable from the one-electron spectral function that can be measured by angle-resolved photoemission spectroscopy (ARPES). Here, buried 2DEL δ-layers in silicon are measured with soft X-ray (SX) ARPES to obtain detailed information about their filled conduction bands and extract device-relevant properties. This study takes advantage of the larger probing depth and photon energy range of SX-ARPES relative to vacuum ultraviolet (VUV) ARPES to accurately measure the δ-layer electronic confinement. The measurements are made on ambient-exposed samples and yield extremely thin (< 1 nm) and dense (≈1014  cm-2 ) 2DELs. Critically, this method is used to show that δ-layers of arsenic exhibit better electronic confinement than δ-layers of phosphorus fabricated under identical conditions.

Probing the Atomic Arrangement of Subsurface Dopants in a Silicon Quantum Device Platform

High-density structures of subsurface phosphorus dopants in silicon continue to garner interest as a silicon-based quantum computer platform; however, a much-needed confirmation of their dopant arrangement has been lacking. In this work, we take advantage of the chemical specificity of X-ray photoelectron diffraction to obtain the precise structural configuration of P dopants in subsurface Si:P δ-layers. The growth of δ-layer systems with different levels of doping is carefully studied and verified using X-ray photoelectron spectroscopy and low-energy electron diffraction. Subsequent diffraction measurements reveal that in all cases, the subsurface dopants primarily substitute with Si atoms from the host material. Furthermore, no signs of carrier-inhibiting P-P dimerization can be observed. Our observations not only settle a nearly decade-long debate about the dopant arrangement but also demonstrate how X-ray photoelectron diffraction is surprisingly well suited for studying subsurface dopant structure. This work thus provides valuable input for an updated understanding of the behavior of Si:P δ-layers and the modeling of their derived quantum devices.

Metal Sheet of Atomic Thickness Embedded in Silicon

The controlled confinement of the metallic delta-layer to a single atomic plane has so far remained an unsolved problem. In the present study, the delta-type structure with atomic sheet of NiSi₂ silicide embedded into a crystalline Si matrix has been fabricated using room-temperature overgrowth of a Si film onto the Tl/NiSi₂/Si(111) atomic sandwich in ultrahigh vacuum. Tl atoms segregate at the growing Si film surface, and the 1.5-3.0 nm thick epitaxially crystalline Si layer forms atop the NiSi₂ sheet. Confinement of the NiSi₂ layer to a single atomic plane has been directly confirmed by transmission electron microscopy. The NiSi₂ delta-layer demonstrates a p-type conductivity associated with the electronic transport through the two hole-like and one electron-like interface-state bands. The basic structural and electronic properties of the NiSi₂ delta-layer remain after keeping the sample in air for one year.

The occupied electronic structure of ultrathin boron doped diamond

Using angle-resolved photoelectron spectroscopy, we compare the electronic band structure of an ultrathin (1.8 nm) δ-layer of boron-doped diamond with a bulk-like boron doped diamond film (3 μm). Surprisingly, the measurements indicate that except for a small change in the effective mass, there is no significant difference between the electronic structure of these samples, irrespective of their physical dimensionality, except for a small modification of the effective mass. While this suggests that, at the current time, it is not possible to fabricate boron-doped diamond structures with quantum properties, it also means that nanoscale boron doped diamond structures can be fabricated which retain the classical electronic properties of bulk-doped diamond, without a need to consider the influence of quantum confinement.

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

Advanced hydrogen lithography techniques and low-temperature epitaxial overgrowth enable the patterning of highly phosphorus-doped silicon (Si:P) monolayers (ML) with atomic precision. This approach to device fabrication has made Si:P monolayer systems a testbed for multiqubit quantum computing architectures and atomically precise 2-D superlattice designs whose behaviors are directly tied to the deterministic placement of single dopants. However, dopant segregation, diffusion, surface roughening, and defect formation during the encapsulation overgrowth introduce large uncertainties to the exact dopant placement and activation ratio. In this study, we develop a unique method by combining dopant segregation/diffusion models with sputter profiling simulation to monitor and control, at the atomic scale, dopant movement using room-temperature grown locking layers (LLs). We explore the impact of LL growth rate, thickness, rapid thermal annealing, surface accumulation, and growth front roughness on dopant confinement, local crystalline quality, and electrical activation within Si:P 2-D systems. We demonstrate that dopant movement can be more efficiently suppressed by increasing the LL growth rate than by increasing the LL thickness. We find that the dopant segregation length can be suppressed below a single Si lattice constant by increasing the LL growth rates at room temperature while maintaining epitaxy. Although dopant diffusivity within the LL is found to remain high (on the order of 10-17 cm2 s-1) even below the hydrogen desorption temperature, we demonstrate that exceptionally sharp dopant confinement with high electrical quality within Si:P monolayers can be achieved by combining a high LL growth rate with low-temperature LL rapid thermal annealing. The method developed in this study provides a key tool for 2-D fabrication techniques that require precise dopant placement to suppress, quantify, and predict a single dopant's movement at the atomic scale.

Simultaneous Conduction and Valence Band Quantization in Ultrashallow High-Density Doping Profiles in Semiconductors

We demonstrate simultaneous quantization of conduction band (CB) and valence band (VB) states in silicon using ultrashallow, high-density, phosphorus doping profiles (so-called Si:P δ layers). We show that, in addition to the well-known quantization of CB states within the dopant plane, the confinement of VB-derived states between the subsurface P dopant layer and the Si surface gives rise to a simultaneous quantization of VB states in this narrow region. We also show that the VB quantization can be explained using a simple particle-in-a-box model, and that the number and energy separation of the quantized VB states depend on the depth of the P dopant layer beneath the Si surface. Since the quantized CB states do not show a strong dependence on the dopant depth (but rather on the dopant density), it is straightforward to exhibit control over the properties of the quantized CB and VB states independently of each other by choosing the dopant density and depth accordingly, thus offering new possibilities for engineering quantum matter.

Fragility of the Dirac Cone Splitting in Topological Crystalline Insulator Heterostructures

The "double Dirac cone" 2D topological interface states found on the (001) faces of topological crystalline insulators such as Pb_1-xSn_xSe feature degeneracies located away from time reversal invariant momenta and are a manifestation of both mirror symmetry protection and valley interactions. Similar shifted degeneracies in 1D interface states have been highlighted as a potential basis for a topological transistor, but realizing such a device will require a detailed understanding of the intervalley physics involved. In addition, the operation of this or similar devices outside of ultrahigh vacuum will require encapsulation, and the consequences of this for the topological interface state must be understood. Here we address both topics for the case of 2D surface states using angle-resolved photoemission spectroscopy. We examine bulk Pb_1-xSn_xSe(001) crystals overgrown with PbSe, realizing trivial/topological heterostructures. We demonstrate that the valley interaction that splits the two Dirac cones at each X̅ is extremely sensitive to atomic-scale details of the surface, exhibiting non-monotonic changes as PbSe deposition proceeds. This includes an apparent total collapse of the splitting for sub-monolayer coverage, eliminating the Lifshitz transition. For a large overlayer thickness we observe quantized PbSe states, possibly reflecting a symmetry confinement mechanism at the buried topological interface.

In Situ Patterning of Ultrasharp Dopant Profiles in Silicon

We develop a method for patterning a buried two-dimensional electron gas (2DEG) in silicon using low kinetic energy electron stimulated desorption (LEESD) of a monohydride resist mask. A buried 2DEG forms as a result of placing a dense and narrow profile of phosphorus dopants beneath the silicon surface; a so-called δ-layer. Such 2D dopant profiles have previously been studied theoretically, and by angle-resolved photoemission spectroscopy, and have been shown to host a 2DEG with properties desirable for atomic-scale devices and quantum computation applications. Here we outline a patterning method based on low kinetic energy electron beam lithography, combined with in situ characterization, and demonstrate the formation of patterned features with dopant concentrations sufficient to create localized 2DEG states.

Determining the electronic confinement of a subsurface metallic state

Dopant profiles in semiconductors are important for understanding nanoscale electronics. Highly conductive and extremely confined phosphorus doping profiles in silicon, known as Si:P δ-layers, are of particular interest for quantum computer applications, yet a quantitative measure of their electronic profile has been lacking. Using resonantly enhanced photoemission spectroscopy, we reveal the real-space breadth of the Si:P δ-layer occupied states and gain a rare view into the nature of the confined orbitals. We find that the occupied valley-split states of the δ-layer, the so-called 1Γ and 2Γ, are exceptionally confined with an electronic profile of a mere 0.40 to 0.52 nm at full width at half-maximum, a result that is in excellent agreement with density functional theory calculations. Furthermore, the bulk-like Si 3pz orbital from which the occupied states are derived is sufficiently confined to lose most of its pz-like character, explaining the strikingly large valley splitting observed for the 1Γ and 2Γ states.

Valley splitting in a silicon quantum device platform

By suppressing an undesirable surface Umklapp process, it is possible to resolve the two most occupied states (1Γ and 2Γ) in a buried two-dimensional electron gas (2DEG) in silicon. The 2DEG exists because of an atomically sharp profile of phosphorus dopants which have been formed beneath the Si(001) surface (a δ-layer). The energy separation, or valley splitting, of the two most occupied bands has critical implications for the properties of δ-layer derived devices, yet until now, has not been directly measurable. Density functional theory (DFT) allows the 2DEG band structure to be calculated, but without experimental verification the size of the valley splitting has been unclear. Using a combination of direct spectroscopic measurements and DFT we show that the measured band structure is in good qualitative agreement with calculations and reveal a valley splitting of 132 ± 5 meV. We also report the effective mass and occupation of the 2DEG states and compare the dispersions and Fermi surface with DFT.

Exploring the limits of N-type ultra-shallow junction formation

Low resistivity, near-surface doping in silicon represents a formidable challenge for both the microelectronics industry and future quantum electronic devices. Here we employ an ultra-high vacuum strategy to create highly abrupt doping profiles in silicon, which we characterize in situ using a four point probe scanning tunnelling microscope. Using a small molecule gaseous dopant source (PH3) which densely packs on a reconstructed silicon surface, followed by encapsulation in epitaxial silicon, we form highly conductive dopant sheets with subnanometer control of the depth profiles. This approach allows us to test the limits of ultra-shallow junction formation, with room temperature resistivities of 780 Ω/□ at an encapsulation depth of 4.3 nm, increasing to 23 kΩ/□ at an encapsulation depth of only 0.5 nm. We show that this depth-dependent resistivity can be accounted for by a combination of dopant segregation and surface scattering.