Spatial metrology of dopants in silicon with exact lattice site precision

Abstract

The aggressive scaling of silicon-based nanoelectronics has reached the regime where device function is affected not only by the presence of individual dopants, but more critically their position in the structure. The quantitative determination of the positions of subsurface dopant atoms is an important issue in a range of applications from channel doping in ultra-scaled transistors to quantum information processing, and hence poses a significant challenge. Here, we establish a metrology combining low-temperature scanning tunnelling microscopy (STM) imaging and a comprehensive quantum treatment of the dopant-STM system to pin-point the exact lattice-site location of sub-surface dopants in silicon. The technique is underpinned by the observation that STM images of sub-surface dopants typically contain many atomic-sized features in ordered patterns, which are highly sensitive to the details of the STM tip orbital and the absolute lattice-site position of the dopant atom itself. We demonstrate the technique on two types of dopant samples in silicon -the first where phosphorus dopants are placed with high precision, and a second containing randomly placed arsenic dopants. Based on the quantitative agreement between STM measurements and multi-million-atom calculations, the precise lattice site of these dopants is determined, demonstrating that the metrology works to depths of about 36 lattice planes. The ability to uniquely determine the exact positions of subsurface dopants down to depths of 5 nm will provide critical knowledge in the design and optimisation of nanoscale devices for both classical and quantum computing applications.As we approach the ultimate regime of Feynman's vision 1 of nanotechnology based on atom-by-atom fabrication 2-5 , there is a critical need to match advances in miniaturisation with atomically precise metrology. In conventional CMOS 6 and tunnelling field effect 7,8 transistors the key relationship between doping profile and performance is now dominated by the positions of just a few dopant atoms, and currently cannot be quantitatively determined. Beyond conventional nanoelectronic devices, in quantum processors based on phosphorus dopants in silicon 9 the precise locations of the individual dopants is critical to the design and operation of spin-based quantum logic gates. Previous studies on locating subsurface dopant positions in semiconductors either provide donor depths based on statistical evidence 10 , or only qualitatively locate dopants within a few nanometers region (of the order of 2.5 nm or more)11 . The key metrological challenge in all of the ultra-scaled applications is the ability to determine the position of dopant atoms in the silicon crystal substrate with lattice-site precision, which will drastically transform our understanding at the most fundamental scale leading to devices with optimised functionalities.In this work, we present an atomically precise metrology and demonstrate the pinpointing of the position of subsurface phosphorous (P) and arsenic (As) dopants in si...

Exact location of dopants below the Si(001):H surface from scanning tunneling microscopy and density functional theory

“…We observe highly anisotropic features superimposed on the surface atomic lattice that we have interpreted as arising from the ground state wave function of neutral donors in analogy with previous reports of dopant wave function mapping in GaAs [22,23]. For donor depths beyond 12 layers we find even more diffuse surface features in agreement with a recent report where such features were assigned to As donors approximately 20 atomic layers beneath the surface based on bulk k · p and tight-binding calculations [24,25]; more recent reports [26,27] show that both these approaches give excellent agreement with experiment. This type of semiempirical approach allows for large-scale calculations and will correctly capture the long-range behavior of the dopant wave function, which is particularly important for dopants far from the surface.…”

Excited states of defect linear arrays in silicon: A first-principles study based on hydrogen cluster analogs

“…Impurities in silicon play a vital role in its transport, magnetic, and optical properties [1]. The recent encouraging progress in deterministic positioning of dopants in silicon [2][3][4] promises atom-by-atom design and bottom-up fabrication of silicon-based nanodevices; such nanostructures can offer not only an ultimate limit for conventional electronic components such as wires [5] and tunnel structures [6], but also a potential platform for many applications in silicon quantum electronics [1], and ultimately for new technologies that exploit the quantum properties of electron spin and orbital motion [7][8][9][10][11][12]. An obvious candidate for a quantum bit (qubit) is a donor electron spin: the spin-lattice relaxation time (T 1 ) of donor electron spins in silicon has been measured to be up to a few thousand seconds [13,14], and the coherence time (T 2 ) is up to milliseconds, limited only by interactions with neighboring electron or nuclear spins.…”

Implementation of Multivariable Logic Functions in Parallel by Electrically Addressing a Molecule of Three Dopants in Silicon

“…At present, single dopant atom placement has only been developed at the device level for P:Si . In the future, one can envision building heteronuclear structures by deterministically implanting dopants of different chemical nature.…”

“…The imaging of the electron density of the electronic states of a dopant atom was recently reported using spatially resolved scanning tunnelling spectroscopy (STS). The spatially resolved tunnelling current was shown to be a function | F (Ψ D ( r ))| 2 of the wave function of the donor system, Ψ( r ), as probed by the STM tip orbital at the position r ,. A one phosphorus, 1 and 2e (1P‐1e, 1P‐2e) system embedded in Si was recently characterized and used for implementing a probabilistic finite state machine .…”