Furthermore, we demonstrate the fabrication of a heterogeneous chemobrionic composite material composed of aligned, high-aspect ratio calcium phosphate channels running through an otherwise dense matrix of poly(2-hydroxyethyl methacrylate) (pHEMA). Given that the principles we derive can be broadly applied to potentially control various chemobrionic systems, this work paves the way for fabricating multifunctional materials that may hold great potential in a variety of application areas, such as regenerative medicine, catalysis and microfluidics.Chemical gardens are an example of a chemobrionic system that typically result in abiotic macro-, micro- and nano- material architectures, with formation driven by complex out-of-equilibrium reaction mechanisms. From a technological perspective, controlling chemobrionic processes may hold great promise for the creation of novel, compositionally diverse and ultimately, useful materials and devices. In this work, we engineer an innovative custom-built liquid exchange unit that enables us to control the formation of tubular chemical garden structures grown from the interface between calcium loaded hydrogel and phosphate solution. We show that systematic displacement of phosphate solution with water (H Chemobrionic materials with applications in tissue engineering can be grown at the interface of calcium and phosphate solutions, however, controlling their dimensions and purity can be difficult. Herein, a flow device allows control of the height and in situ purification of chemical gardens, which can be encased in a photoset hydrogel for subsequent use. These formations are commonly characterised by the spontaneous formation of colourful hollow tubular precipitates following the introduction of metal salt seeds, which provide a broad spectrum of cations , copper (Cu2+), iron (Fe2+/3+), etc.), to reservoirs of anionic solution (e.g. carbonate (CO32−), phosphate (PO43−), silicate (SiO44−), etc.)2. Structures can also be grown from the controlled injection of reactant solutions into one another, as well as from the interface between reactant-loaded hydrogels and solution reservoirs6. Though completely abiotic, the resulting structures often possess striking resemblances to biotic organisms and forms, including plants and fungi.Chemobrionic systems encompass a diverse range of complex self-organisation reactions that typically result in the formation of hierarchical architectures. Chemical gardens are a classical example of a chemobrionic system first reported several centuries ago in 16469. In particular, the study of chemobrionics in relation to hydrothermal vents has helped to shed light on the origins of life12. Investigations simulating hydrothermal conditions have subsequently implicated the role of chemobrionic phenomena in providing energy and catalysing prebiotic chemical reactions, including the formation of energy-rich pyrophosphate species (P2O74−), amino acids and ribonucleic acid (RNA)16.The understanding of fundamental chemobrionic principles has advanced significantly in recent decades, informing potential mechanisms of biomineralisation and pathways responsible for the formation of geological structures and artefacts17, biochemical and therapeutic delivery18, soft bioinspired materials19, catalysis20, electrochemistry21, gas sensors22, luminescent materials24 and microfluidics25. Harnessing control over chemobrionic processes may hold great promise toward the creation of novel, compositionally diverse and ultimately, useful materials and devices27.From a technological perspective, chemobrionic reactions offer a means to build complex structures across nano-, micro- and macroscales from a plethora of organic and/or inorganic, ionic and/or molecular building blocks. Advances have been made in numerous areas of application, including but not limited to regenerative medicineConsidering that thermodynamic disequilibrium drives self-organisation in many chemobrionic systems , tubular chemical garden structures can continue to lengthen until the system either reaches a state of thermodynamic equilibrium or is depleted of reactant. Problematically, the continued deposition of precipitate in these confined reactions can result in the growth of structures that reach the solution–air interface, proceed to agglomerate and eventually, collapse. As such, the retrieval of intact frameworks requires structures to be harvested from the growth environment whilst still actively undergoing formation. Additionally, harvesting of structures can lead to loss of alignment and breakage. Therefore, the growth and acquisition of chemobrionic structures in such a manner that allows for ease of further processing toward technologically relevant materials remains highly challenging.30. Self-assembly of calcium phosphate chemical gardens from the interface between a hydrogel and solution occurs in a mechanistically similar manner to the formation of architectures from cationic salt seeds submerged in anionic reservoirs31. In the hydrogel–solution system, calcium ions are homogeneously diffused throughout the hydrogel. A variety of hydrogel networks can be utilised, including agar, gelatin or carrageenan34. When phosphate solution is introduced on top, a semi-permeable precipitate membrane forms from the interaction of calcium ions at the surface of the hydrogel with phosphate ions in solution. Osmotic pressure differences between the outside and inside of the membrane draws water inward, causing the hydrogel to swell. The membrane also facilitates steep chemical and pH gradients that drive the interaction of reactive species.35 Eventually, the osmotic pressure causes the semi-permeable membrane to rupture, releasing streams of buoyant calcium-rich fluid into the surrounding anionic solution. Precipitation around these streams leads to the formation of calcium phosphate tubes. Repetitive build-ups in osmotic pressure and release maintains the ascension of calcium-rich fluid through established structures. Subsequently, the tips rupture and the emission of calcium-rich fluid leads to further precipitation, continuing the elongation of the tubes. In an uncontrolled set-up, calcium phosphate tubes can reach the solution–air interface and continue to grow along it. Agglomeration of tubes through the continued deposition of calcium phosphate will eventually lead to the collapse of structures, limiting processability.Calcium phosphate chemical gardens grown from hydrogel–solution interfaces have been proposed to hold great potential in the field of tissue engineering as cellular scaffolds and biologically responsive structures2O) could act as a means to control the self-assembly of calcium phosphate chemical gardens. Not only could we halt the growth of calcium phosphate tubes, we were also able to precisely control tube height and purify the structures in situ. Moreover, the integration of calcium phosphate tubes in a matrix of poly(2-hydroxyethyl methacrylate) (pHEMA) is demonstrated, highlighting a viable route for the development of novel chemobrionic materials for biotechnological applications.The aim of this study is to determine a method to control the formation of calcium phosphate chemical gardens and take critical steps toward the development of a new class of biomaterial consisting entirely of, or incorporating, biologically relevant chemobrionic components. We engineered a custom-built liquid exchange unit that enabled us to investigate whether the systematic displacement of phosphate solution with water  to be controllably introduced in place of phosphate solution during self-assembly of chemical garden structures. Initially, the inlet channel was served by a reservoir of H2O, whilst the outlet channel led to an outlet reservoir to collect displaced phosphate solution.To explore the systematic exchange of phosphate solution with H2O  of H2O (ρ = 1.01 ± 0.01 g/cm3 at 25 °C and 1 atm) was found to be measurably less than that of phosphate solution (ρ = 1.08 ± 0.01 g/cm3 at 25 °C and 1 atm). Moreover, phosphate anions in solution can possess attractive intermolecular interactions facilitated by short-range hydrogen bonding, which may further contribute to preventing immediate equilibration38. Only after several hours were the miscible liquids seen to completely equilibrate, suggesting that the separation of H2O and phosphate solution is stable over a period of time sufficient to influence chemical garden formation .We first sought to understand the interaction between phosphate solution and H2O Fig. . To bett2O was performed during the formation of calcium phosphate tubes from a hydrogel–solution interface  values were in the range of approximately 15–160 at the point of liquid entering the liquid exchange unit, indicating laminar flow during exchange 2O, the flow of fluid emitted from the tips may be compressed due to the density of cationic fluid leaving the tip being relatively greater than that of H2O, leading to a downward swirling vortex akin to that seen in examples of Rayleigh-Taylor instability and Richtmyer-Meshkov instability41. Precipitation appears to capture the doming pattern of flow, resulting in the distinct tip morphology.Scanning electron microscopy (SEM) imaging revealed that the typical diameter of structures was between 20 and 50 µm. Interestingly, the diameter of a growth halted structure widens to around 100–150 µm toward a dome shaped apex Fig. . This mi2O provides a means of purifying chemical garden structures in situ. Purification of products prepared by precipitation reactions is generally necessary in order to prevent the crystallisation of otherwise soluble phases on drying. X-ray diffraction (XRD) was used to examine the compositional purity of the calcium phosphate chemical gardens  and diammonium phosphate ((NH4)2HPO4) being apparent over those indicative of poorly crystalline calcium-deficient hydroxyapatite (CDHA) (Ca9HPO4(PO4)5OH). Purification of harvested structures with excess H2O and filtration apparatus eliminated these soluble contaminant phases, as shown by the appearance of peaks corresponding to CDHA only. Though effective for purification, we noted that it was very easy to damage chemical garden structures with this method. Alternatively, in situ purification was performed without compromising the structural integrity of calcium phosphate tubes and was in practice inherently more controllable than filtration. Chemical gardens were purified in situ with a volume displacement (VD) ratio of either 5:1 or 10:1 (H2O to phosphate solution) at a displacement rate of 10 mL/min. Contaminant phases were detectable when structures were purified with a VD of 5:1. Increasing the VD ratio to 10:1 resulted in structures that were comparably pure to those washed by filtration. Therefore, in situ purification employing a VD of 10:1 was effective at eliminating contaminant phases.We next investigated whether the continued displacement of phosphate solution with Hens Fig.  and  S4.2O following purification with either liquid polymers or hydrogels, which upon curing and/or cross-linking, respectively, would harden and encase the self-assembled structures within a surround matrix. In order to demonstrate the preparation of chemobrionic materials in principle, we prepared a chemobrionic composite using 2-hydroxyethyl methacrylate (HEMA), which forms a hydrogel when irradiated with UV light, as the matrix material.We next explored the potential to utilise the liquid exchange unit for fabricating chemobrionic materials. It was envisioned that a chemobrionic composite incorporating highly aligned tubular channels could be engineered by displacing H2O was performed 10 s after the layering phosphate solution over the hydrogel at a rate of 10 mL/min. Displacement was halted when the tips of structures met the interface between phosphate solution and H2O. The calcium phosphate tubes were then purified in situ with a VD of 10:1 (H2O to phosphate solution) at a rate of 10 mL/min  being greater than that of H2O (ρ = 1.01 ± 0.01 g/cm3 at 25 °C and 1 atm), the conventional positions of the inlet and outlet channels were reversed prior to polymer infiltration. Displacement of H2O with HEMA was performed at a rate of 10 mL/min. Phase separation of the HEMA component was not observed during displacement, resulting in partitioning of the liquids, with H2O overlaying the incoming HEMA. Uncured HEMA was of a sufficiently low viscosity to permeate between individual tubes and completely surround the structures whilst maintaining alignment of the array  3D reconstructions revealed the relatively well-persevered vertical orientation of high-aspect-ratio channels throughout the bulk polymer Fig. . Section43. The integration of structured calcium phosphate tubes provides seemingly perfusable channels in an otherwise dense matrix, not entirely dissimilar to Haversian canals enclosed in concentric layers of compact bone44. Tubular structures are inherent features of bone tissue that are vital for the supply of nutrients and oxygen, as well as waste removal45. Regenerative hard tissue scaffolds that possess tubular features that recapitulate microstructures found in bone are highly sought for improving cellular recruitment and tissue regeneration, as well as promoting implant vascularisation, beyond the integration of mineral particles and simple porosity47. In this respect, chemobrionic principles have the potential to significantly influence biomaterials design through the guided formation of heterogeneous systems and devices.In relation to biomedical applications, pHEMA has previously been employed in the fabrication of bone repair composites in combination with calcium phosphate particles composed of hydroxyapatite (HA) and beta-tricalcium phosphate (ß-TCP) phases, which improve biocompatibility and integration with hard tissueIn summary, the principles described herein demonstrate a significant leap toward controlling the formation chemical gardens that may further facilitate the fabrication of technologically relevant materials consisting entirely of, or incorporating, chemobrionic components. Whilst we have focused on controlling the formation of calcium phosphate chemical gardens, our approach could undoubtedly be adapted to influence the formation of structures grown from salt seeds or by injection methods, of which there are many compositionally diverse examples. Thus, as well as regenerative applications, there is also an opportunity to explore the generation of heterogeneous chemobrionic materials for a variety of uses, including catalysis and microfluidics. Future work will focus on refining the methods of composite fabrication, improving our understanding of the effects of  processing on the chemical garden structures and investigating the capacity of chemobrionic composites to direct biological healing processes.The liquid exchange unit was engineered from a transparent 0.14 L “Really Useful Box” with external dimensions of 90 × 65 × 55 (length × width × height) and internal dimensions of 68 × 48 × 42 mm (length × width × height). Using a Dremel 3000 equipped with a 3.2 mm diameter high-speed cutter attachment , a total of two holes measuring 3.2 mm in diameter were introduced, each one centrally aligned on opposing sides of the box, positioned 25 mm and 5 mm from the base, respectively. Each hole was fitted with a small cone shaped piece of tubular plastic with an inward end diameter of 3.0 mm and an outward end diameter of 3.4 mm, which served as an adapter for the installation of flexible rubber tubing with an internal diameter of 3.4 mm and external diameter of 6.2 mm. Both pieces of tubing were fed through a set of Watson-Marlow101U/R peristaltic pumps  to enable the displacement of liquid phases from and to inlet and outlet reservoirs, respectively.3)2.4H2O) , ammonium phosphate dibasic ((NH4)2HPO4)  and agar (for microbiology) were acquired from Sigma-Aldrich . All mixtures and solutions were prepared with H2O with a recorded resistivity of 15–18 MΩ.cm (at 25 °C and 1 atm) from a Milli-Q® Integral 3 water purification system equipped with Q-Gard® and Quantum® cartridges . Calcium-loaded hydrogel was prepared by heating a mixture of Ca(NO3)2.4H2O ( = 1 M).Calcium nitrate tetrahydrate  prior to displacement. Complete displacement of reactant with excess H2O was performed as a means of purifying growth halted chemical garden structures. Reactant VD ratios of 5:1 or 10:1 (H2O to reactant) were employed to purify chemical garden structures . In order to comparatively assess purification efficacy of this method against conventional approaches, structures were also prepared without washing or washing with excess H2O (500 mL) by filtration using Buchner funnel apparatus. Structures were then transferred to an oven and dried in air at 60 °C for 12 h.Displacement of phosphate solution with H2O was added, following which 1 mL of UV initiator (Omnirad 4265) was added whilst stirring at 250–500 rpm. The mixture was then deoxygenated by bubbling through nitrogen gas for 10 min. Following the growth and purification of calcium phosphate tubes, displacement of HEMA solution with H2O was performed and the excess HEMA drained. The liquid exchange unit and its contents were then irradiated at 20% irradiance for 10 min using an S2000 Spot UV Curing System . The contents of the liquid exchange unit were then removed and the composite separated from the underlying hydrogel. A scalpel was then used to section the chemobrionic composite prior to characterisation.HEMA , ethylene glycol dimethacrylate (EGDMA)  and inhibitor removal beads were acquired from Sigma-Aldrich . Omnirad 4265 (mixture of Omnirad-TPO and Omnirad-73) was acquired from IGM Resins . To 60 mL of HEMA, 1 mL of EGDMA was added. To this mixture, 1 g of inhibitor removal beads was added whilst stirring at 250–500 rpm magnetic stirrer hot plate. After several minutes the beads were removed by filtration and 36 mL H2O and HEMA solution were determined by measuring the mass of 1 mL of liquid extruded from a calibrated Sartorius 100–1000 µL pipette  using a Quintix125D-1S microbalance . Measurements were performed in triplicate.The densities of phosphate solution, HDried structures were powdered using a pestle and mortar before being transferred to an appropriate powder specimen holder. XRD was performed using a Diffractometer D8 autosampler instrument equipped with Cu Kα radiation . Diffraction patterns were acquired between 2θ = 5° and 60° with a step size of 2θ = 0.02° and step time of 0.5 s/°. The acquired patterns were then matched to patterns for known crystalline phases within the International Centre for Diffraction Data (ICDD) database using DIFFRAC.SUITE software .2O and excess liquid removed using a pipette before drying in air at 60 °C for 12 h. Sections of the chemobrionic composite were embedded in EpoFix cold-setting embedding resin  using a CitoVac vacuum embedding instrument . To obtain horizontal and vertical cross-sections of the chemobrionic composite, embedded sections were abraded along respective planes, with progressively finer grit discs from FEPA P grade 120 to 4000 using a TechPrep grinder/polisher . Prior to imaging, specimens were mounted onto aluminium stubs using double-sided carbon discs before being gold coated in argon atmosphere with the sputter current at 20 mA and coating time of 20 s using a K550X sputter coater . Embedded samples required the use of copper tape to ensure conductivity between the sample surface and the aluminium stub. SEM images and EDX elemental maps were acquired using a table-top TM 3030 Plus electron microscope coupled with an EDX detector operating with an electron acceleration voltage of 10–15 kV .Growth halted structures were collected on a glass slide, gently washed with Hµ-CT was performed using a Skyscan1172 µ‐CT instrument . A section of chemobrionic composite was scanned with operating parameters of 80 kV source voltage, 100 µA current, 600 ms exposure time, 4 µm pixel size, rotation step of 0.1° and frame averaging of 20. The acquired slice data was reconstructed using NRecon software  and visualised using CTVox software .Supplementary information.


O and VZn defects without any significant effect on the crystal or electronic structure of Wurtzite ZnO. The combined effects of grain boundaries and voids are considered responsible for the apparent colossal dielectric constant (ε′) > 104 at low frequency (∼102 Hz) for all the sintered ZnO ceramics. The superior contact among grains of the ZnO-1200 sample enhances both the interfacial and orientational polarization of the Zn2+–VO dipoles, which results in the increase of low and high frequency dielectric constants (ε′) and the corresponding dielectric loss (tan δ) also increases. On the other hand, high temperature sintering of ZnO at 1300 °C and 1400 °C introduces voids at the expense of reduced grain and grain boundary contact areas, thus affecting both the interfacial and orientational polarization with corresponding reduction of dielectric constant (ε′) and dielectric loss. Orientational polarizations due to Zn2+–VO dipoles are suggested to remain fixed and it is the microstructure which controls the dielectric properties of high temperature sintered ZnO ceramics.High temperature sintering (1200–1400 °C) has been performed on ZnO ceramics. An X-ray Absorption Fine Structure (XAFS) study shows that high sintering temperature introduces a constant amount of V ε′) and dielectric loss (tan δ).Superior grain contacts of ZnO-1200 samples enhance low and high frequency dielectric constants ( Extensive studies have been carried out on high dielectric constant materials (ε′ > 104) including ferroelectric and non-ferroelectric like CaCu3Ti4O12 (CCTO). Despite substantial efforts, these materials have not been fully realized towards straightforward device applications operating at frequencies of MHz and GHz. The problems of the temperature and frequency dependence of ε′, high magnitude of dielectric loss (tan δ) and difficulty in synthesizing pure phases are the main obstacles.1–4 Therefore, further developments towards high ε′ with low tan δ and easy to prepare materials are still essential.Colossal dielectric constant  semiconductor and has attracted considerable attention due to its applications in piezotronics,5 super-capacitors,6,7 and resistive switching.8 Although wide range of temperature and frequency dependent dielectric behaviors of various types of ZnO nano-structures,9 films,10 and ceramics11 have been studied, the relative dielectric constant of pure ZnO is still quite low (<1500 at 100 Hz). The dielectric properties of ceramics are significantly influenced by the amount of porosity, its geometrical morphology and the grain boundaries.12–14 Controlled porosity can produce low-frequency dielectric constant ∼106 in porous ceramics.14Compared to the multi-component high dielectric constant materials, low cost ZnO is easier to synthesize in the pure form and is commercially available in large scale. ZnO is an academically curious direct wide band gap  of pure ZnO has been associated with porosity, low-density and low grain boundary resistance. On the other hand, in a recent publication Ndayishimiye et al.,16 reported fabrication of high density pure ZnO and ZnO–polydimethylsiloxane composites via cold sintering process. In cold sintered pristine ZnO ceramic, dielectric constants at high frequency (ε′ ∼140 at 105 Hz) and low frequency have been associated to the dense isotropic grains and charge accumulation at grain boundaries, respectively. However, role of the porosity was totally ignored. In these reports, generally the apparent high dielectric constant of pristine ZnO was associated to Maxwell–Wagner polarization effects but the results lack proper justifications from the view point of realistic origin of the observed dielectric constant at low and high frequency sides.In case of ZnO, role of porosity in tuning dielectric properties has been illustrated but the picture is still unclear. Li i.e., grain boundary regions) on a mesoscopic scale, or at the external electrode-sample interfaces on a macroscopic scale and normally considered as extrinsic effect.17 In the observed dielectric phenomena, the successful detachment of Maxwell–Wagner polarization from that of intrinsic grains is mandatory to consider realistic dielectric constant of the material. Therefore, present study is designed to explore the effects of microstructure  and point defects on the dielectric properties of high temperatures sintered ZnO. Impedance Spectroscopy (IS) can separate the transport characteristics in grains, grain boundaries and at the interface.18 Different formalisms in IS can provide supportive information about the localized/mobile charge carriers present at different electro-active regions of sintered ZnO samples, which can be helpful in the extension of the spectrum of their applications. Therefore, a battery of characterization techniques including lab and synchrotron base X-ray diffraction (SXRD), X-ray Absorption Fine Structure (XAFS) spectroscopy, Scanning Electron Microscopy (SEM) and impedance spectroscopy have been employed to explore the possible role of sintering temperatures on the microstructure and dielectric properties of sintered ZnO ceramics. The origin of the observed dielectric constant has been explained according to the comprehensive information collected from several characterization techniques. The outcome of the present investigation might be useful to understand the nature of local structural environment and its correlation if any to the structural and dielectric properties of wide band gap semiconductors such as ZnO.The Maxwell–Wagner polarization leads to separation of charges either through inner dielectric boundary layers (2.2.1High purity ZnO powder (purity 99.99% by Alfa Aesar) was used for the present study. ZnO powder was initially grounded for 45 minutes by using mortar and pastel. Subsequently, the powder was heat treated at 400 °C, 600 °C, 700 °C, 800 °C and 900 °C for 6 hours at each temperature with 30 minutes intermediate grinding. After heating at 900 °C, the powder was pressed into pellets of 10 mm diameter and thickness of 2 mm without using any binder. We further sintered ZnO pellets at 1000 °C, 1100 °C, 1200 °C, 1300 °C and 1400 °C for 10 hours. The ZnO pellets sintered at 1200 °C (ZnO-1200), 1300 °C (ZnO-1300) and 1400 °C (ZnO-1400) were finally selected for detailed analysis.2.2θ ≤ 80. High resolution Synchrotron X-ray Powder Diffraction (SXRD) data were collected at the MSPD beamline at the ALBA Synchrotron Light Source . The powdered samples were sealed in a 0.7 mm diameter capillary and SXRD data were collected using a continuous scanning of the MAD26 high resolution detector setup comprised of 13 Si analyzer crystals (Si 111 reflection) and scintillator/PMT detectors separated by angular offsets of ∼1.5°. Data for each pattern was collected in a 2θ angular range of 2–49° at a wavelength of 0.619 Å.Lab base powder X-ray diffraction (XRD) measurements were performed on the sintered samples using DMAX-III diffractometer  operating with CuKα radiation (1.54 Å) over the angular range of 20° ≤ 219 at the ELETTRA Synchrotron  with the storage ring running at 2 GeV and a typical current of 300 mA. These data were collected at room temperature in transmission mode using a double crystal Si(111) monochromator. The data for Zn metal foil placed in a second experimental chamber after the sample was collected simultaneously with each sample and used for energy calibration and to check the stability of the beamline and optics system. Multiple spectra were collected for each sample (2–5 scans) and merged together to get better statics and sufficiently high signal-to-noise ratio. All the transmission spectra were collected with an integration time of 3 s per point with a variable energy step: large step (5 eV) in the first 200 eV of the spectrum, smaller step (0.2 eV) in the XANES region and a constant k step of 0.03 Å−1 in the EXAFS region.XAFS data at the K-edge of Zn (9659 eV) were collected at beamline 11.1 (XAFS)Field Emission Scanning Electron Microscope  was used to study the surface morphology and for Energy Dispersive X-ray (EDX) analysis of the samples. Room temperature impedance spectroscopy (IS) measurements were performed on samples sintered at 1000–1400 °C in a wide frequency range (01 Hz to 10 MHz) using an Alpha-N analyzer . However, temperature dependent (20 °C to 90 °C) IS measurements were performed on ZnO-1200, ZnO-1300 and ZnO-1400 ceramic pellets. To perturb the system, an AC signal of 0.2 V was used. Contacts were made on opposite sides of pellets in capacitor mode using silver paste, and cured under a tungsten lamp for 3 h. Leads were carefully checked to ensure the absence of any irrelevant resistive or capacitive coupling in measured frequency range. Fully automated WINDETA software was used for interfacing the experimental setup of the analyzer to the computer and for data acquisition. Zview software  was used for fitting the equivalent circuits to the impedance data. Reduced chi-squared value below 0.0006 was used as fitting criterion.3.3.120,21 A simple fifth order polynomial background in 2θ along with other profile and structural parameters were refined simultaneously. Peak profile was modeled by a pseudo-Voigt peak shape function. Three parameters function described by Caglioti et al.22 was employed for the refinement of peak full width at half maximum. Instrumental peak asymmetry was modeled using a single asymmetry parameter after Howard,23 while preferred orientation was described by one parameter March model.24,25P63mc.26 The cell parameters, atomic positions and fractional site occupancy of oxygen were used as refinement parameters. The results of the refinement are presented in χ2) is obtained for both ZnO-1300 and ZnO-1400 samples  peak without any extra peak from impurity. Due to lower resolution of lab base XRD, the tiny peaks belonging to any secondary phase or impurity when they are present in small quantities are difficult to observe. However, synchrotron based XRD due to very high intensity and resolution can reveal very minor impurities. Therefore, SXRD measurements were performed on ZnO-1300 and ZnO-1400 samples and data have been analyzed by full profile Rietveld analysis method by employing Rietica software package.via ordinary analysis. Therefore, we need more sophisticated tools like Extended X-ray Absorption Fine Structure (EXAFS) and X-ray Absorption Near Edge Structure (XANES) to analyze local structure around the metal centers, which may contain either undistorted or orientationally disordered ZnO4 tetrahedra. In the present study, the extraction of the χ(k) function was performed using the Athena program29 in the k: 2–13 Å−1 interval and the corresponding k3-weighted χ(k) functions were averaged.30 EXAFS data analysis has been performed using the Artemis software.30 Phase and amplitude functions were calculated by the FEFF6 code.31 For each spectrum, a theoretical model was designed by adding shells around the central excited atom and least-squares iterating the absorption edge energy (E0), the radial distances (R) and the Debye–Waller Factors (DWFs) σ2 (Å2). The DWFs consider both dynamic and static disorder, however dynamic disorder can be excluded as all the measurements were done at room temperature. The lattice parameters obtained from the Rietveld refinement  and the most relevant multiple scattering (MS) paths involving the oxygen atoms of the first shell and the zinc atoms of the second shell, were included.In ZnO system, structural and point defects play key role in determining the crystallinity, compositional purity and dielectric properties. Although these defects do subsidize to the broadening of the XRD peaks, their accurate identification cannot be achieved finement  were emp35,36 A preliminary investigation of the In order to understand if sintering temperatures can have any influence on the Zn local environment, detailed investigation of the Zn K-edge EXAFS signal was performed. 37,38 It seems that high temperature sintering does not influence the oxygen radial distances in a significant way. On the other hand, for all the sintered samples of the ZnO, the second shell radial distance is slightly larger than the reported values of undoped ZnO ceramic.37,38 The observed DWFs of second shells are also higher compared to other shells but remain almost same for temperatures of 1300 °C and 1400 °C. High DWFs generally indicates a high degree of local disorder around the absorbing atoms and suggest introduction of atomic vacancies.39 Present study suggests that high temperature sintering of ZnO at 1200 °C introduces local disorder that remains unchanged on further sintering temperatures of 1300 °C and 1400 °C. In ZnO, oxygen vacancy (VO) and zinc vacancy (VZn) are respectively considered to introduce shrinkage and expansion in the lattice parameters40 and presence of VZn is also reported in the second coordination shell.41 Therefore, observed increase in the DWFs and radial distances of the second shell Zn–Zn atoms suggests introduction of local disorder around Zn absorbing atoms due to possible creation of VZn. Further, the second shell DWFs remain unchanged for all the samples of ZnO sintered from 1200 °C to 1400 °C signifying that the amount of VZn concentration remains unchanged and high sintering temperature has very little effect on the overall electronic structure.Fourier transforms  of the Zn K-edge spectra of the sintered ZnO samples are shown in Fig. S1 in ESI3.2In order to investigate morphology and grain growth of the ZnO samples sintered at different temperatures, detailed SEM analysis has been performed as shown in During 1300 °C heating process, relatively bigger ZnO crystallites easily form large structure due to diffusion of small crystallite around them, while the voids between ZnO crystallites are difficult to remove thereby forming open void structure around the grain boundaries. The increased amount of open voids seems to be associated to the decreasing grain-to-grain connections due to steady decrease in grain boundary contact area. Further ZnO sintering at 1400 °C temperature considerably changes microstructure and produce crystallite size in the range of 3–20 μm as shown in 3.342 Furthermore, electrode contact impedances have much higher capacitances ∼10−7 to 10−5 F compared with ∼10−10 to 10−8 F and ∼10−12 F capacitances of grain boundaries and bulk, respectively.43,44 AC electrical response in polycrystalline materials usually relates the effects of electrode contact, inter-grain (grain boundaries) and intra-grain (bulk) effects at low, intermediate and high frequencies, respectively.18,43 This makes the visualization and representation of the properties of a sample an easy process without the need to exclude sample-electrode contact impedances; however, complete analysis of the sample-electrode impedances is mandatory to fully filter intrinsic and extrinsic behaviors of the material.In most of the oxide ceramics, grain boundaries are more resistive than grains due to non-stoichiometric distribution of oxygen and dangling bonds, which act as the carrier's traps and produce a barrier layer.Z′ vs. Z′′ as a parametric function of frequency for ZnO ceramics sintered at different temperatures. The solid symbols represent the experimental data and the frequency increases from right to left as shown by the right hand side arrow. The diameter of semicircular arc on Z′-axis is the resistance of involved micro-structural component, whereas total resistance of a system under investigation is the sum of diameters of all the arcs appear in impedance plane plots.18,43 The ZnO-1200 sample shows the smallest diameter of the semicircular arc, hence lowest resistance. A remarkable increase in the diameters of the semicircular arcs is observed when sintering temperature of the ZnO is increased to 1300 °C and 1400 °C. Increase in the overall resistance upon sintering suggests breaking of the intimate contact between ZnO grains due to introduction of the voids, which is in agreement with the SEM analysis discussed previously. Subsequent sintering at 1400 °C displays a slight decrease in resistance possibly due to grain growth.The prime objective of the impedance analysis is to explore the most suitable equivalent circuit to characterize the data sets. , where  and  are the intercepts of the arc with the real axis at low and high frequencies, respectively.18,43 Due to the presence of defects, structural stresses and distributed elements in the system, the center of the semi-circle is displaced below the real axis. This compression in the semicircular arcs is addressed by depression angel and is related to the deviation of the center of the semicircular arc below the real axis. By employing Zview software, depression angles of the small semicircular arc at higher frequency side worked out to be ∼49°, 28° and 38° for ZnO-1200, ZnO-1300 and ZnO-1400 samples, respectively. Second common feature in the impedance plane plots is the larger semicircular arc at low frequency side. The values of the depression angles of large low frequency semicircular arcs are 13°, 25° and 29° for the ZnO-1200, ZnO-1300 and ZnO-1400 samples, respectively.Collection of typical impedance data for three samples reveals two similar characteristics. The first common feature in all three samples is the depressed semicircular arc at high frequency side whose width is larger than its height 18 To address the heterogeneity of the samples, the constant phase element ‘CPE’ is generally used instead of capacitance to account the non-ideal behavior  to fit the impedance plane plot data. The CPE can be deconvoluted into resistive and capacitive components, whose relative contribution is given by the parameter “n”, which is a measure of deviation from the ideal behavior having a value of 0 for pure resistive and 1 for pure capacitive behavior. The capacitance of a CPE is given by the relation C = Rn)/n(1−(CPE)n1/; where C and R are capacitance and resistance of the associated component.18 A specific feature of a CPE is that it provides a power law dependence on frequency scale to both the resistive and capacitive components. The CPE is frequently added subsequently with (i) a resistance R, which relates to the limiting low frequency or DC resistance of the sample and (ii) a capacitance C that links to the limiting high frequency permittivity.45,46Relatively higher values of the depression angles show the presence of more distributed elements with diverse relaxation times due to the existence of micro-structural heterogeneities and defects.i.e., oxygen vacancies, zinc interstitial and zinc vacancies) at grain boundaries.47–49 In addition, voids exist in the form of three-dimensional pockets around the grain boundaries. The high surface area of the voids provides chance for the defects to be distributed and creates obstruction to the flow of charge carriers by reducing the conduction path and compressing current lines, analogous to the effect of impurities at grain boundaries.48,50 A relationship of the two commonly observed features  has been made based on the magnitudes of the associated capacitances. Thus; the high frequency arc is endorsed to the bulk response and the low frequency arc to grain boundary impedance. In the view of discussion above, an equivalent circuit model along with least square fitting data provides a reasonable fit to the impedance data set of ZnO-1200 sample as shown in R1(R2CPE2) connected in series best fit to the high frequency arc and deviation from the ideality of the distorted semicircle is the signature of the element CPE. The non-ideality is apparent by the relatively higher value of the depression angel (49°) and it has also been observed that high frequency arc does not pass though the origin for ZnO-1200 sample.Physical characteristics of the sample have been evaluated by circuit analysis to make assignments of the several circuit elements to electrical features of the sample. In ZnO and other ceramic oxides, the grain boundary resistance is generally higher in comparison to the grains due to segregation of point defects  for ZnO-1200, ZnO-1300 and ZnO-1400 samples. The resistance R2 is associated to the grains (RG). Relatively distorted semicircle at lower frequency side shows at least two different relaxation frequencies during fitting procedure. Moreover, from the SEM analysis, we also observe inhomogeneous distribution of crystallite sizes and voids in all the ZnO ceramic samples. Therefore, resistances R3 and R4 of the semicircular arcs at intermediate and lower frequencies are assigned to the resistances of conventional (intrinsic) grain boundaries (RGB1) and un-conventional (extrinsic) grain boundaries (RGB2), respectively. Unconventional grain boundaries (RGB2) are referred here as a combination of grain boundaries and voids that are present very close to each other. Final equivalent circuit for ZnO-1200 sample turns out to be (RS)(RGCPEG)(RGB1CPEGB1)(RGB2CPEGB2). The parameters RS, RG, RGB1, RGB2, CPEG, CPEGB1, and CPEGB2 were obtained for each ZnO sample sintered at different temperatures by fitting the impedance plane plots (∼5% fitting error) and are presented in In the impedance plane plots, sometimes the semicircular arc does not pass through the origin due to other arcs having higher relaxation frequencies beyond the measurement limit,R1)(R2C2)(R3CPE3)(R4CPE4) along with least square fitting data shown in the corresponding Fig. S2 and S3 in ESIR1, R2, R3 and R4 discussed above, final circuit becomes (RS)(RGCG)(RGB1CPEGB1)(RGB2CPEGB2). In all the cases, excellent agreement is seen between experimental data and fitting model over the entire frequency range. The alternative methodology to check quality of the fit is to plot the residuals between experimental and fitted data as a function of frequency. The upper right insets of 52 Moreover, for all the ZnO samples, our attempt to fit the data with three components by dropping R1 (i.e. RS) from the master circuit resulted in significantly inferior chi-squares values than those obtained by the four components fitting including R1.Similarly, an equivalent circuit  and grain boundary resistance (RGB1) adjacent to the grains.53 Similarly unconventional grain boundary resistance (RGB2) also increases due to introduction of voids at the expense of reduced grain boundary contact area around the voids. Three-dimensional pockets of the voids around the grain boundaries offer high surface area to the defects to be distributed and damage the conduction path of the charge carriers thereby increasing resistance to the transport of charge carriers.48,50 For ZnO-1400 sample, we observe reduction in the values of RGB2, which is suggested due to conversion of open voids to close voids due to grain growth as shown by The result presented in Z*  is a good method to distinguish bulk and grain boundary resistances. However, Z* plot on linear scale offers unnecessary weighting to the largest resistances in a sample and effectively ignores from view the conductive grain cores surrounded by resistive grain boundaries.54 A comprehensive analysis of impedance data that sidesteps such weighting is presented by demonstrating the same impedance data in at least two of the four formalisms: impedance Z*, admittance Y*, electric modulus M* and permittivity ε*.Up till now, we have discussed impedance plane plots and established the link among possible electroactive regions and best fitted capacitances and resistances. Impedance complex plane plot Y′ vs. log f plot provides an equivalent credit to the different conducting elements and in particular emphasizes the existence of a high frequency dispersion modeled by the bulk constant phase element (CPE).54Y′ vs. log f) for ZnO sintered samples. Typical admittance spectra for all the samples show two different regions i.e. plateau region and the frequency dependent region ∼103 Hz. The plateau region is frequency independent and is referred as DC conductivity, which arises from the hopping of carriers between strictly localized states. The two frequency dependent regions at higher frequencies include the conductivity of the easier hops. For all the sintered samples, there is an evidence of second and third series CPE components in the equivalent circuit models corresponding to the two frequency dependent regions of log Y′ vs. log f spectra. The presence of a CPE in the equivalent circuit represents the power law dispersion. Comparatively, ZnO-1200 sample indicates higher magnitude of conductivity with a well-defined DC limit signifying the formation of an electronically conducting path in agreement with SEM results where we found excellent intimate contact among grains. For ZnO-1300 and ZnO-1400 samples, the region of low frequency DC limit shrinks due to expansion in frequency dependent region, which might be related to the combined effects of dissipative process of dipole reorientation and geometrical heterogeneity around the dipoles .Log Z′′ vs. log f and M′′ vs. log f is helpful to see whether the main resistance shown by the largest arc in Z′′ vs. Z′ plots or the largest peak in Z′′ vs. log f plots specifies the sample bulk. Occurrence of relaxation peak in the loss spectrum (Z′′ vs. log f) is the indication of the current dissipation and is related to the most resistive part of the material. Similarly, modulus formalism (M′′ vs. log f) is associated with the bulk properties of the material and demonstrates a maximum at a characteristic frequency in the conduction process of the relevant phase.18 Therefore, to have an insight into the relaxation process and conduction mechanism, we have studied both impedance (Z′′ vs. log(f)) and modulus (M′′ vs. log(f)) formalisms as presented in Generally, together with the impedance, modulus formalism is used to separate grain and grain-boundary effects to distinguish the microscopic processes responsible for localized and long-range conductions. The simultaneous presentation of Z′′ vs. log(f) spectra as presented in 3 Hz for ZnO-1200 sample gradually shifts towards lower frequency at and down to 102 Hz for ZnO-1300 and ZnO-1400 samples, respectively. This shift in relaxation peak towards lower frequency side is related to the introduction of micro-structural heterogeneities (i.e. grain boundaries and voids) upon sintering. The associated dipoles present at the micro-structural heterogeneities face difficulty in flipping their poles and therefore, show their relaxation at much lower frequency side. The relaxation frequency (fRex) of the charge carries present at micro-structural heterogeneities were estimated by fRex = 1/2πRC, where R and C are the resistance and capacitance of individual components, respectively and results are presented in i.e., fRex-GB1 and fRex-GB2) is only of an order of magnitude for all the sintered samples of ZnO. This close proximity of values of relaxation frequencies of fRex-GB1 and fRex-GB2 makes it hard to spread the competing phases and results in the occurrence of a broad loss peak at low frequency side in the Z′′ vs. log(f) formalism.42,51 On the other hand, absence of loss peak in the high frequency region may be related to the dominancy of dipoles in the conduction process whose relaxation may occur out of available experimental frequency range. The M′′ vs. log(f) spectra presented in Z′′ vs. log(f)) and modulus (Z′′ vs. log(f)) formalisms. However, for all three samples, high frequency dipolar relaxation peak is well resolved in the dielectric loss (tan δ) spectrum and will be discussed in the upcoming section.All the sintered samples of ZnO show only one broad relaxation peak in the ε′) against frequency for all three samples sintered at different temperatures. The dielectric response for all the samples clearly reveals at least one dispersion region. Different surrounding environments for carriers present at grain boundaries and close to the voids may produce more than one relaxation process. Those electroactive regions having alike or comparable relaxation frequencies for charge carriers involved in conduction and are difficult to resolve; therefore, dispersion in dielectric constant at low frequency (<104 Hz) is not resolved in spectrum due to very close relaxation times of the charge carries present at their related heterogeneity.55 Interfacial polarization has a significant role in tuning the dielectric characteristics of materials below 102 Hz where grain boundaries are more dominant.42,56 In the present study, at lower frequency (∼102 Hz), the magnitude of ε′ > 104 for all the sintered samples fulfills the definition of colossal dielectric constant materials.3 ZnO-1200 sample shows larger value of ε′ at both low and higher frequencies than that of ZnO-1300 and ZnO-1400 samples. The observed dielectric response below 102 Hz and above 105 Hz can be attributed to the extrinsic  and intrinsic (grain interior) effects, respectively. In the pristine ZnO, polarization is generally governed by orientational polarization due to association of the Zn2+ with oxygen vacancies, which have limited dipole moment.57,58 In the present study, all the samples were heat treated at very high temperatures (1200–1400 °C) and XAFS study shows that amount of VO and VZn concentrations more or less remains the same in all the samples. Therefore, orientational polarization due to the Zn2+–VO dipoles remains fix and it is the microstructure, which controls the overall dielectric constant in the whole frequency range of all the sintered ZnO ceramics.Fundamentally, four kinds of polarization are described, namely interfacial, dipolar, atomic and electronic.5 Hz) dielectric constant may arises mainly due to the orientational polarization of the Zn2+–VO dipoles present at the grain interior and can be considered as an intrinsic effect. As sintering temperature increases to 1300 °C and 1400 °C, dispersion in dielectric constant extends and shifts towards higher frequencies thereby suggesting good grain growth, which is in agreement with SEM results. Increased grain growth provides more defect free grain interiors by removing trapped charges and therefore Zn2+–VO related dipoles relax more freely at high frequency side.High magnification SEM micrograph of the ZnO-1200 sample depicts very dense microstructure and good grain to grain contacts with minimum number of voids as shown in Fig. S4 in ESI.δ) with respect to frequency for all the ZnO sintered samples are presented in δ values compared to other samples in the measured frequency range. Furthermore, each spectrum possesses at least one dielectric loss peak showing at least one relaxation process in the system. The tan δ peak in high frequency region >105 Hz is ascribed to the relaxation process associated with Zn2+–VO dipole present in grains. It has also been observed that as sintering temperature increases from 1200 °C to 1400 °C, the tan δ peak shifts towards higher frequency side due to introduction of grain growth. Grain growth promotes a defect-free structure inside the grains and associated dipoles involved in the polarization show their tan δ peak at high frequency region. Therefore, in sintered ZnO samples, tan δ peak above 105 Hz is credited to relaxation of dipoles present in grain interior and can be considered as an intrinsic loss effect. The extracted dielectric constant (ε′) and dielectric loss (tan δ) values at different frequencies for all the sintered samples of ZnO are presented in Alteration in the tangent loss (tan 2 Hz), the observed dielectric constant ε′ ∼1.9 × 104 for ZnO-1200 sample presented in ε′ ∼1.8 × 104 at 102 Hz by Li et al.,15 for the pristine porous ZnO ceramic sintered at 1050 °C under high pressure. However, at high frequency side (above 105 Hz), the interesting feature of ZnO-1200 sample is its comparable dielectric constant (ε′) with low dielectric loss (tan δ) than the reported ones15,16 along with good temperature stability as shown in Fig. S5(a and b) in ESI.15,16 present study shows that at high frequency, improved, stable and realistic dielectric constant with low dielectric loss values of ZnO-1200 ceramic excludes the role of voids; instead, defect free grain interiors with excellent intimate contacts among them promote enhanced orientational polarization of the Zn2+–VO dipoles. The superior contact among grains boost both the interfacial and orientational polarization, which result in the increase in low and high frequency dielectric constant (ε′) and corresponding dielectric loss also increases. On the other hand, high temperature sintering of ZnO at 1300 °C and 1400 introduces voids at the expense of reduced grain and grain boundary contact areas, thus damage to the both interfacial and orientational polarization resulting in the corresponding reduction of dielectric constant (ε′) and dielectric loss.59–61At low frequency (102 Hz) all the sintered ZnO ceramics show colossal ε′ > 104, the observed dielectric response is unrealistic and related to combined effects of grain boundaries and voids. This phenomenon is also evident by the unstable temperature dependent dielectric constant (ε′) and dielectric loss (tan δ) at lower frequency side, which becomes stable at higher frequencies of ≥105 Hz for the same ZnO-1200 ceramic as presented in Fig. S5(a and b) in ESI.ε′ and tan δ values. The ε′ and tan δ data for ZnO sintered at 1000–1400 °C  in ESIδ values at higher frequencies of 105 Hz, corresponding ε′ is quite low. Compared to 1200 °C sintering temperature, it is expected that at lower sintering temperatures of 1000 °C and 1100 °C, ZnO grains are not fully developed and are more coarsed, which cannot enhance both the interfacial and orientational polarizations and result in the lower dielectric constant (ε′) and dielectric loss in the entire measured frequency region. This implies that among different sintered samples, pristine ZnO ceramic sintered at 1200 °C still produces high ε′ with low tan δ values.Although at lower frequency  and intrinsic (grain interior) effects, respectively. From the microscopic view point, interfacial and orientational polarization of the Zn2+–VO dipole tune both dielectric constant (ε′) and dielectric loss ability (tan δ) at low and high frequency sides respectively. These microscopic entities are highly correlated with microstructure of the sintered samples. Unrealistic colossal dielectric constant ε′ > 104 at low frequency (∼102 Hz) has been associated to the combined effects of grain boundaries and voids. While at high frequency (>105 Hz), stable and realistic dielectric constant with low dielectric loss value of pristine ZnO-1200 sample is originated by excellent intimate contacts of the defect free grain interiors. The combined microscopic and spectroscopic approach towards realistic dielectric response will open up new avenues from the fundamental understanding and practical viewpoints.We have performed systematic SXRD, XAFS, SEM and detailed impedance spectroscopy on high temperatures sintered (1200–1400 °C) ZnO ceramics to understand the possible role of sintering temperatures on the crystal structure, microstructure and dielectric properties of sintered ZnO ceramics. High sintering temperature creates constant amount of VThere are no conflicts to declare.RA-010-D0RA04273K-s001


Electron spins in Si/SiGe quantum wells suffer from nearly degenerate conduction band valleys, which compete with the spin degree of freedom in the formation of qubits. Despite attempts to enhance the valley energy splitting deterministically, by engineering a sharp interface, valley splitting fluctuations remain a serious problem for qubit uniformity, needed to scale up to large quantum processors. Here, we elucidate and statistically predict the valley splitting by the holistic integration of 3D atomic-level properties, theory and transport. We find that the concentration fluctuations of Si and Ge atoms within the 3D landscape of Si/SiGe interfaces can explain the observed large spread of valley splitting from measurements on many quantum dot devices. Against the prevailing belief, we propose to boost these random alloy composition fluctuations by incorporating Ge atoms in the Si quantum well to statistically enhance valley splitting. Spin qubits in Si/SiGe quantum dots suffer from variability in the valley splitting which will hinder device scalability. Here, by using 3D atomic characterization, the authors explain this variability by random Si and Ge atomic fluctuations and propose a strategy to statistically enhance the valley splitting Although these devices bear many similarities to transistors2, qubits operate in the single electron regime3, making them more sensitive to electrostatic disorder and noise arising from the surrounding environment. In strained silicon quantum wells, the electronically active part of the device is separated by an epitaxial SiGe barrier from the electronically noisy interface at the gate-stack, offering a quiet system with high mobility and low leakage between the gate and the quantum dots4. These properties make strained Si/SiGe heterostructures promising for scalable qubit tiles6 and have made it possible to define nine quantum dot arrays7, run quantum algorithms8 and entangle three-spin states9 in natural silicon structures, and achieve two-qubit gate fidelity above 99%11 in isotopically purified silicon structures.Advanced semiconductor manufacturing is capable of integrating billions of transistors onto a single silicon chip. The promise of leveraging the same technology for large-scale integration of qubits into a fault-tolerant quantum processing unit is a key driver for developing electron spin qubits in silicon quantum dots12. These leakage channels increase exponentially with the qubit count13, complicating qubit operation and inducing errors during spin transfers. Despite attempts to enhance the valley energy splitting, the resulting valley splittings are modest in Si/SiGe heterostructures, with typical values in the range of 20 to 100 μeV20 and only in a few instances in the range of 100 to 300 μeV23. Such variability in realistic silicon quantum dots remains an open challenge for scaling to large qubit systems. In particular, the probability of thermally occupying the excited valley state presents a challenge for spin initialization, and, in some cases, intervalley scattering may limit the spin coherence24. Furthermore, small valley splitting may affect Pauli spin blockade readout25, which is considered in large-scale quantum computing proposals6. Therefore, scaling up to larger systems of single-electron spin qubits requires that the valley splitting of all qubits in the system should be much larger than the typical operation temperatures (20−100 mK).However, spin-qubits in silicon suffer from a two-fold degeneracy of the conduction band minima  that creates several non-computational states that act as leakage channels for quantum information26. Past theoretical studies have considered disorder arising from the quantum well miscut angle27 and steps in the interface32 demonstrating that disorder of this kind can greatly decrease valley splitting in quantum dots. However, a definitive connection to experiments has proven challenging for a number of reasons. At the device level, a systematic characterisation of valley splitting in Si/SiGe quantum dots has been limited because of poor device yield associated with heterostructure quality and/or device processing. At the materials level, atomic-scale disorder in buried interfaces33 may be revealed by atom-probe tomography (APT) in three-dimensions (3D) over the nanoscale dimensions comparable to electrically defined quantum dots. However, the current models employed to reconstruct in 3D the APT data can be fraught with large uncertainties due to the assumptions made to generate the three-dimensional representation of the tomographic data34. This results in limited accuracy when mapping heterointerfaces35 and quantum wells38. These limitations prevent linking the valley splitting in quantum dots to the relevant atomic-scale material properties and hinder the development of accurate and predictive theoretical models.It has been known for some time that valley splitting depends sensitively on the interface between the quantum well and the SiGe barrierHerein we solve this outstanding challenge and establish comprehensive insights into the atomic-level origin of valley splitting in realistic silicon quantum dots. Firstly, we measure valley splitting systematically across many quantum dots, enabled by high-quality heterostructures with a low disorder potential landscape and by improved fabrication processes. Secondly, we establish a new method to analyse APT data leading to accurate 3D evaluation of the atomic-level properties of the Si/SiGe buried interfaces. Thirdly, incorporating the 3D atomic-level details obtained from APT, we simulate valley splitting distributions that consider the role of random fluctuations in the concentration of Si and Ge atoms at each layer of the Si/SiGe interfaces. By comparing theory with experiments, we find that the measured random distribution of Si and Ge atoms at the Si/SiGe interface is enough to account for the measured valley splitting spread in real quantum dots. Based on these atomistic insights, we conclude by proposing a practical strategy to statistically enhance valley splitting above a specified threshold as a route to making spin-qubit quantum processors more reliable—and consequently—more scalable.28Si/Si0.7Ge0.3 heterostructures (quantum wells A and B) designed with the same quantum well width and top-interface sharpness (Methods), which are important parameters determining valley splitting26. As shown in high angle annular dark field scanning transmission electron microscopy (HAADF-STEM), quantum well A . A positive gate voltage applied to plunger gates P1 and P2 . Figure EST) by measuring the gate-voltage dependence as a function of parallel magnetic field B along the  →  transition  along the theoretical fit (red line) and the relation EST = gμBBST, where g = 2 is the electron gyromagnetic ratio and μB is the Bohr magneton, we determine EST = 182.3 μeV for this quantum dot. EST sets a lower bound on the valley splitting, Ev ≥ EST40. Due to small size, our dots are strongly confined with lowest orbital energy much larger than EST . First, we show how to reliably reconstruct the buried quantum well interfaces, then we use this methodology to characterise their broadening and roughness.34. Qualitatively, we observe an isotopically enriched 28Si quantum well, essentially free of 29Si, cladded in a SiGe alloy. To probe the interface properties with the highest possible resolution allowed by APT and differently from previous APT studies on Si/SiGe38, we represent the atom positions in the acquired data sets in form of a Voronoi tessellation42 and generate profiles on an x − y grid of the tessellated data, as described in Supplementary Note 38 is used to fit the profiles of each tile in the x − y grid. Here, z0 is the inflection point of the interface and 4τ is the interface width. As the Voronoi tessellation of the data set does not sacrifice any spatial information, the tiling in the x − y plane represents the smallest lateral length scale over which we characterise the measured disorder at the interface. Note that we do not average at all over the z axis and hence maintain the inherent depth resolution of APT. We find that for tiles as small as 3 nm × 3 nm the numerical fitting of sigmoid functions to the profiles converges reliably. Although each tile contains many atoms, their size is still much smaller than the quantum dot diameter, and may therefore be considered to be microscopic. We use the sigmoid fits for each tile stack to visualise and further characterise the interfaces . However, the two-standard-deviation errors (2σ) of each data point can be up to 30% of the mean value In Fig. To pinpoint the root cause of atomic-scale fluctuations at the interface, in Fig. l by l by averaging the random alloy distribution weighted by the lateral charge density in the quantum dot, giving We begin by considering an ideal laterally infinite heterostructure with no concentration fluctuations, and we denote the average Si concentration at layer ℏω = 4.18 meV and corresponding radius m* is the effective mass of Si. Together, 43. The envelope of the effective mass wavefunction ψenv(z) is shown in Fig. 3d5s* NEMO tight-binding model44  is a 1D envelope function, and U(z) is the quantum well confinement potential. The intervalley coupling Δ describes how sharp features in the confinement potential couple the two valley states, which would otherwise be degenerate. In general, Δ is a complex number that can be viewed as the sum of two distinct components: a deterministic piece Δ0, arising from the average interface concentration profile, and a random piece δΔ, arising from concentration fluctuations. The latter can be expressed as a sum of contributions from individual atomic layers: δΔ = ∑lδΔl, where δΔl is proportional to δΔl using the randomized density profile of Fig. ψenv(zl)∣ and the Ge content of the quantum well are both large. In Fig. 0 (black dot) is seen to be located near the center of the distribution in the complex plane, as expected. However, the vast majority of Δ values are much larger than Δ0, demonstrating that concentration fluctuations typically provide the dominant contribution to intervalley coupling.Analytical methods using effective mass theory may also be used to characterise the distribution of valley splittings. First, we model the intervalley coupling matrix elementEv = 2∣Δ∣, and therefore exhibits the same statistical behavior. In Fig. The total valley splitting is closely related to the intervalley coupling via τ) as shown in Fig. Based on the results obtained above, we now propose two related methods for achieving large valley splittings (on average), with high yields. Both methods are derived from the key insight of Fig. 25. This would represent a significant improvement in qubit yield for Si quantum dots. A recent report of SiGe quantum wells with oscillating Ge concentrations provides the first experimental evidence that intentionally placing Ge in the quantum well leads to significant variability and some of the highest recorded values of valley splitting45.We test these predictions using simulations, as reported in Fig. 28Si → Si-Ge heterointerface are enough to account for the valley splitting spread and that these fluctuations are largest when the envelope of the wavefunction overlaps with more Ge atoms. Moreover, while we have only incorporated random alloy disorder into our theoretical framework so far, we foresee that APT datasets including correlated disorder, such as steps, will be used to further refine our theoretical understanding of valley splitting statistics. Since atomic concentration fluctuations are always present in Si/SiGe devices due to the intrinsic random nature of the SiGe alloy, we propose to boost these fluctuations to achieve on average large valley splittings in realistic silicon quantum dots, as required for scaling the size of quantum processors.In conclusion, we argue for the atomic-level origin of valley splitting distributions in realistic Si/SiGe quantum dots, providing key insights on the inherent variability of Si/SiGe qubits and thereby solving a longstanding problem facing their scaling. We relate 3D atom-by-atom measurements of the heterointerfaces to the statistical electrical characterisation of devices, and ultimately to underlying theoretical models. We observe qualitative and quantitative agreement between simulated valley splitting distributions and measurements from several quantum dots, supporting our theoretical framework. Crucially, we learn that atomic concentration fluctuations of the 46 suggest that the added scattering from random alloy disorder will not be the limiting factor for mobility in current 28Si/SiGe heterostructures. However, an approximate two-fold reduction in electron mobility was recently reported when an oscillating Ge concentration of about 5% on average is incorporated in the Si quantum well45. We speculate that fine-tuning of the Ge concentration in the quantum well will be required for enhancing the average valley splitting while not compromising the low-disorder potential environment, which is important for scaling to large qubit systems. We believe that our results will inspire a new generation of Si/SiGe material stacks that rely on atomic-scale randomness of the SiGe as a new dimension for the heterostructure design.Our proposed approaches are counter-intuitive yet very pragmatic. The interface broadening approach seems viable for hybrid qubits, which require valley splitting to be large enough to be usable but not so large as to be inaccessible. For single-electron spin qubits, which don’t use the valley degree of freedom, the direct introduction of Ge in the quantum well appears better suited for targeting the largest possible valley splitting. By adding Ge to the Si quantum well in small concentrations we expect to achieve on average valley splitting in excess of 100 μeV. Early calculations from scattering theories28Si/SiGe heterostructures are grown on a 100-mm n-type Si(001) substrate using an Epsilon 2000 (ASMI) reduced pressure chemical vapor deposition reactor equipped with a 28SiH4 gas cylinder (1% dilution in H2) for the growth of isotopically enriched 28Si. The 28SiH4 gas was obtained by reducing 28SiF4 with a residual 29Si concentration of 0.08%47. Starting from the Si substrate, the layer sequence for quantum well A comprises a 900 nm layer of Six1−Gex graded linearly from x = 0 to 0.3, followed by a 300 nm Si0.7Ge0.3 strain-relaxed buffer, an 8 nm tensily strained 28Si quantum well, a 30 nm Si0.7Ge0.3 barrier, and a sacrificial Si cap. The layer sequence for quantum well B comprises a 1.4 μm step-graded Six), followed by a 0.45 μm Si0.7Ge0.3 strain-relaxed buffer, an 8 nm tensily strained 28Si quantum well, a 30 nm Si0.7Ge0.3 barrier, and a sacrificial Si cap. In quantum well A, the Si0.7Ge0.3 strain-relaxed buffer and the Si quantum well are grown at 750 °C without growth interruption. In quantum well B the Si0.7Ge0.3 strain-relaxed buffer below the quantum well is grown at a temperature of 625 °C, followed by growth interruption and quantum well growth at 750 °C. This modified temperature profile yields a sharper bottom interface for quantum well B as compared to quantum well A.The Samples for APT were prepared in a FEI Helios Nanolab 660 dual-beam scanning electron microscope using a gallium focused ion beam at 30, 16, and 5 kV and using a procedure described in detail in ref. 2O3 gate oxide; deposition of thick dielectric pads to protect gate oxide during subsequent wire bonding step; sputtering of Al gates; electron beam evaporation of Ti:Pt to create ohmic contacts to the 2DEG via doped areas. All patterning is done by optical lithography. Quantum dot devices are fabricated on wafer coupons from the same H-FET fabrication run and share the process steps listed above. Double-quantum dot devices feature a single layer gate metallization and further require electron beam lithography, evaporation of Al (27 nm) or Ti:Pd (3:27 nm) thin film metal gates, and lift-off. For linear quantum dot arrays the gate stack consists of 3 layers of Ti:Pd metallic gates  isolated from each other by 5 nm Al2O3 dielectric interlayers. The fabrication processes for quantum dot devices are further detailed in ref. The fabrication process for Hall-bar shaped heterostructure field effect transistors (H-FETs) involves: reactive ion etching of mesa-trench to isolate the two-dimensional electron gas (2DEG); P-ion implantation and activation by rapid thermal annealing at 700 °C; atomic layer deposition of a 10-nm-thick AlTMC = 50 mK50. We apply a source-drain bias of 100 μV and measure the source-drain current ISD, the longitudinal voltage Vxx, and the transverse Hall voltage Vxy as function of the top gate voltage Vg and the external perpendicular magnetic field B. From here we calculate the longitudinal resistivity ρxx and transverse Hall resistivity ρxy. The Hall electron density n is obtained from the linear relationship ρxy = B/en at low magnetic fields. The carrier mobility μ is extracted from the relationship σxx = neμ, where e is the electron charge. The percolation density np is extracted by fitting the longitudinal conductivity σxx to the relation σxx is obtained via tensor inversion of ρxx at B = 0. Quantum dot measurements are performed in Oxford and Leiden cryogenic refrigerators with base temperatures ranging from 10 to 50 mK. Quantum dot devices are operated in the few-electron regime. Further details of the 2DEG and quantum dot measurements are provided in the Supplementary Note Hall-bar measurements are performed in a Leiden cryogenic dilution refrigerator with a mixing chamber base temperature zl is simply defined here as a linear interpolation of the conduction-band offset at the quantum-well interface: l, xs is the average Si concentration in the strain-relaxed SiGe barriers, xw is the average Si concentration in the strained quantum well, and ΔEc is the conduction band offset in the absence of fluctuations. In the effective-mass theory, the intervalley coupling matrix element can then be approximated by the sum0 + δΔ, where the fluctuating term δΔ contains all dependence on 0 represents the matrix element of the ideal, smooth concentration profile, while δΔ describes the fluctuations about this value. For concentration fluctuations Ev = 2∣Δ0 + δΔ∣ corresponds to a Rice distribution with parameters ν = 2∣Δ0∣ and 51. For additional details, see Supplementary Note The quantum-well potential at vertical position Supplementary InformationDescription of Additional Supplementary FilesSupplementary Movie 1Peer Review File


RNA phage virus-like particles (VLPs) packaged with exogenous RNA have been used in clinical diagnostics as workflow controls, serving as surrogates for infectious viral particles. Comparable controls for DNA viruses are more challenging to produce, with analogous DNA phages being infectious and packaging of DNA within RNA phages requiring complex purification procedures and expensive chemical linkers. We present a simple and inexpensive method to produce Emesvirus zinderi (MS2) VLPs, packaged with DNA, that makes use of affinity chromatography for purification and enzymatic production of exogenous DNA suitable for packaging. The produced VLPs were packaged with hepatitis B virus DNA and were then quantified using droplet digital PCR and calibrated against the WHO international standard using a commercial assay in an accredited clinical laboratory.Suitable controls are integral for the validation and continued quality assurance of diagnostic workflows. Plasmids, DNA, or  The assessment of specificity, sensitivity, accuracy, precision, and, particularly, limit of detection requires materials that are accurately quantified and representative of the infectious agent. When available, World Health Organization international standards serve as the primary reference material2 or limited access, there is often a lag where a diagnostic assay is urgently needed and no traceable metrological standards are available. To fill this gap, interim working standards are often produced by laboratories or companies to enable proficiency testing and expedite assay development3 and are later calibrated against the international standard.However, due to delays in availability, safety concerns,in vitro transcribed RNA,4 heat-inactivated virus particles (sold by Zeptometrix and Qnostics), or other viral particles packaged with exogenous RNA6 have all been utilized as working standards. For DNA viruses, plasmids,7 PCR products,8 and viral particles packaged with exogenous DNA9–11 have been utilized.Working standards can be derived from a variety of different materials. For RNA viruses, 13 This is because unprotected nucleic acids are degraded by nucleases when spiked into sample matrices (such as plasma or sputum) and do not serve as processing controls as they do not require extraction.9Although unprotected nucleic acids are popular as a part of the initial validation of diagnostic assays, alternative controls are often recommended when performing assay validation and proficiency testing within clinical laboratories.12 The Emesvirus zinderi (MS2) bacteriophage, a nonenveloped virus, is widely accepted as an RNA virus surrogate and has been described for veterinary applications14 and as a surrogate for influenza A,15 SARS-CoV,15 HIV,16 and SARS-CoV-2.18 Optimized affinity chromatography protocols have also been described, simplifying production and enabling preparation without expensive equipment.19 Analogous DNA phages have been suggested for the preparation of “armored DNA,” but these phages can infect other bacteria,9 suffer from low packaging efficiency,20 are complicated to produce,11 or are less stable in sample matrices than their RNA counterparts.13Within diagnostic laboratories, the use of phages as validation and proficiency controls has become increasingly popular.21 but the process is expensive and complex, making it unlikely to be widely adopted. In this study, we describe a simplified protocol to produce MS2 virus-like particles (VLPs), making use of affinity chromatography and enzymatic digestion of exogenous DNA, to enable the inexpensive manufacturing of DNA-encapsulated particles. We characterize the produced particles using dynamic light scattering (DLS), quantitative PCR (qPCR), droplet digital PCR (ddPCR), and, finally, validate them using a commercial hepatitis B virus (HBV) assay within an accredited clinical laboratory.In an attempt to create more stable surrogates for DNA viral particles, the MS2 RNA phage system has been successfully adapted for the packaging of exogenous DNA,pac site21–23 to be spontaneously packaged within disassembled MS2 phages. Zhang et al have previously shown that this single-stranded portion, called a translational operator DNA (TR-DNA), can be conjugated to a PCR product using chemically modified primers,22 but their approach is complicated and expensive  could then be annealed successfully to generate the required DNA product. The two enzymes contrast in their digestion mechanisms, with λ exonuclease preferentially digesting phosphorylated strands, a form of negative selection, and T7 exonuclease preferentially digesting unprotected strands (strands that have not been phosphorothioated), a form of positive selection (It has been previously reported that there are multiple enzymatic methods for the production of single-stranded DNA.election .24 the enzyme did in fact digest a double-stranded PCR product to a single-stranded product (We benchmarked λ exonuclease and T7 exonuclease using two criteria: (1) the extent to which the double-stranded product is digested to its single-stranded form and (2) the total yield of the final annealed product of the digested X and Y products. We showed that although it was reported that λ exonuclease did not have activity when directly added to an unpurified PCR product, product .24 phosphorylated oligonucleotides ordered from DNA synthesis companies are not all successfully phosphorylated, leading to only partially digested products. Since our yield of final exogenous DNA product relies on near or total digestion of the generated PCR product to its single-stranded form, λ exonuclease does not perform well using our benchmark criteria.However, as reported previously,In contrast, since T7 exonuclease digests all unprotected DNA (positive selection), there is no requirement for all oligonucleotides to have the required phosphorothioate bonds to ensure complete digestion to a single-stranded product as all oligonucleotides that do not have the required bonds will be digested anyway. We show that T7 exonuclease displays activity when added directly to unpurified PCR products both with and without addition of its requisite reaction buffer .We further demonstrated that X and Y PCRs can be combined with T7 exonuclease, digested, and subsequently annealed successfully in a one-pot format workflow . The addX, C, and S genes . The majority of the qPCR signal is, therefore, generated by our VLPs. Total concentration was 1931 ± 133 copies per microliter for Set A and 1658 ± 106 copies per microliter for Set B.28 and we showed consistent results over four biological replicates. Furthermore, we calibrated our developed standard against the 4th WHO international standard for HBV DNA for NAT using the commercial assay. Our working standard had a calibrated concentration of 832 IU/mL   .Here we describe the development of a novel approach for the generation of dsDNA with a single-stranded TR-DNA for packaging within MS2 VLPs. We combine this novel approach with affinity chromatography to demonstrate a simple low-cost method for the production of DNA MS2 VLPs. We then validate the use of these particles as viral diagnostic controls, using a previously described duplex assay, as well as a commercial assay within a clinical laboratory. As a part of this validation, we calibrate our developed standard against the 4th WHO international standard for HBV for nucleic acid testing (NAT).Suitable controls for DNA viruses are not readily available, with many companies focused on providing either diluted infectious particles or, alternatively, unpackaged DNA in the form of plasmids or chemically synthesized DNA. Furthermore, these controls are expensive and international distribution is made complicated by shipping requirements for infectious samples.29 that has been diluted with HBV-negative plasma and subsequently aliquoted and assigned an international unit (IU) equivalent.30 The infectious nature of the standard means that it needs to be handled under very specific biosafety conditions and there are shipping restrictions that preclude its use in many settings.For example, the WHO international standard for HBV DNA for NAT is formulated from plasma from an HBV carrier with a high viral load18 Our developed SARS-CoV-2 workflow is still making a significant contribution in diagnostic laboratories in London, with >1,500,000 tests performed by October 2022. Our previously developed SARS-CoV-2 VLPs have also been included in a Coronavirus Standards Harmonization Study as a part of the Coronavirus Standards Working Group. The only standard produced at an academic institution in the study, it performed robustly against its commercial counterparts.We have previously shown how locally manufactured, robust, and reliable diagnostic standards can play a critical role in diagnostic workflow development.Adequate pandemic preparedness and resilience within diagnostic laboratories requires ease of access to materials, not only for large commercial enterprises producing their own diagnostics for Emergency Use Authorization or conformité européenne marking, but also for diagnostic laboratories that are developing and maintaining their own in-house assays, also known as laboratory-developed tests, especially those in low- and middle-income countries (LMICs). The reliance on commercial standards alone creates inequity in the development of clinical diagnostics.31 academic institutions can provide the necessary materials and expertise, facilitating technology transfer and allowing for the decentralized production of biosafe “open source” standards, such as VLPs, that rely only on the availability of low-cost protein purification equipment.17Empowering regional centers to manufacture their own standards would provide a means to democratize diagnostic assay development. By leveraging the OpenMTA,The poor availability of clinical samples for diagnostic development inspired us to develop accessible molecular diagnostic standards for both RNA and DNA viruses. Diagnostic standards for RNA and DNA viruses are sometimes commercially available, but there are inevitable delays when new standards for new diseases are needed, and they are often expensive with restrictions on shipping that precludes their use in many LMICs. Furthermore, the availability of commercial standards is dictated by the needs of laboratories in high-income countries.Having already demonstrated that rapidly deployable RNA standards can play a pivotal role in diagnostic workflow development during a pandemic, we wanted to expand our work to include standards for DNA viruses. Our addition of the DNA VLP strengthens our open-source diagnostic standard toolkit. We foresee this toolkit empowering regional health agencies around the world to manufacture their own standards and, thereby, provide a means to democratize diagnostic assay development. Our hope is that this will be the first step in ending the dependence of diagnostic laboratories and health agencies in LMICs on large multinational diagnostics manufacturers.We believe that by providing a toolkit for the development of reliable, robust, and quantitative standards for RNA and DNA viruses and making it available under the OpenMTA, we can begin to enable laboratories around the world to develop their own diagnostic assays. Here we add the DNA MS2 VLP to this toolkit to complement our previously developed method for making low-cost RNA MS2 VLPs. We have made all required materials available under the OpenMTA to enable both commercial and academic institutions to work with the materials without limitations.32) was ordered from GeneArt (ThermoFisher Scientific) and is available from Addgene (Addgene No. 179155).Primers and probes were ordered from Integrated DNA Technologies and are given in ® High-Fidelity 2X Master Mix (NEB). Equal volumes of X and Y PCRs were then combined, supplemented with 0.2 U/μL of T7 exonuclease (NEB) and incubated at 25°C overnight before being heated to 95°C and slowly annealed (−0.1°C/s) in a thermocycler.Two sets of PCRs were set up to create the exogenous DNA for packaging. The X PCR was performed using a phosphorothiated forward primer and unprotected reverse primer and the Y PCR was performed with an unprotected forward primer and phosphorothiated reverse primer. PCRs were performed with a final primer concentration of 1 mM using Q5® Ultra 0.5 mL 30K Centrifugal Filter (Merck Millipore) and two washes were performed with Invitrogen TE Buffer (ThermoFisher Scientific). The final concentrated product was made up to 100 μL with Invitrogen TE Buffer (ThermoFisher Scientific), and 0.7 × AMPure XP beads (Beckman Coulter) were added and the product was purified according to the manufacturer's instructions . Eluted DNA was diluted and quantified using the Qubit™ dsDNA HS kit (ThermoFisher Scientific) on a Qubit 3 Fluorometer (ThermoFisher Scientific).Digested annealed exogenous DNA was concentrated in an Amicong at 4°C and stored at −20°C for later purification.A plasmid construct containing only the maturation protein and his-tagged coat protein dimer (Addgene No. 179156) was transformed into Rosetta2™ (DE3) pLysS cells (Merck). An overnight culture was used to inoculate 200 mL of Terrific Broth (Merck) supplemented with 50 mg/mL of Kanamycin (Merck), and grown at 30°C, 200 rpm until an OD of 0.8. The culture was induced by supplementing with 0.5 mM IPTG (Merck) and grown at 30°C for a further 16 h. Cells were collected at 3220 2, 5 mM CaCl2, and 100 mM NaCl) with 700 U RNase A (Qiagen), 2500 U BaseMuncher Endonuclease (Abcam), and 200 U TURBO DNase (ThermoFisher Scientific). The cells were sonicated for a total of 2 min  on wet ice. The lysate was then incubated for 3 h at 37°C. The lysate was centrifuged at 10,000 g for 10 min at room temperature in a microcentrifuge. The supernatant was then filtered with a Minisart® 5 μm cellulose acetate (SFCA) filter (Sartorius) before being mixed 1:1 with 2 × binding buffer .All protein purification steps were performed at 4°C. The cell pellet was resuspended in 4 mL sonication buffer  on an ÄKTA pure (Cytiva) primed with binding buffer . The protein was eluted with elution buffer  and then desalted and buffer exchanged into STE buffer  using an Amicon Ultra-15 10K Centrifuge Filter (Merck Millipore). The protein concentration was measured using the Qubit Protein Assay Kit and Qubit 3 Fluorometer (Thermo Fisher Scientific).Supernatant was applied to a 5 mL HiTrapg for 20 min at 4°C. The protein sample was then buffer exchanged into sonication buffer  and concentrated down to 500 μL using an Amicon Ultra-15 10K Centrifuge Filter (Merck Millipore).The purified protein was incubated with cold glacial acetic acid  for 30 min on ice before being centrifuged at 6600 Purified exogenous DNA was incubated in a Protein LoBind tube (Eppendorf) with a 10-fold molar excess of disassembled MS2 coat protein dimers for 3 h at room temperature before being incubated for 36 h at 4°C. Sonication buffer was added up to 1.5 mL, supplemented with 100 U of TURBO DNase (ThermoFisher Scientific) and incubated for 90 min at 37°C.The sample was then mixed 1:1 with 2 × binding buffer  and was applied to a 5 mL HiTrap TALON Crude column (Cytiva) on an ÄKTA pure (Cytiva) primed with binding buffer . The protein was eluted with elution buffer  and then desalted and buffer exchanged into STE buffer  using an Amicon Ultra-15 30K Centrifuge Filter (Merck Millipore). All DNA MS2 aliquots were stored at −80°C.DLS was performed using a Zetasizer Nano  according to the manufacturer's instructions.The gel shift assay was run as a 1% agarose gel and poststained with SYBR Gold nucleic acid stain (ThermoFisher Scientific).25 with the primers and probes given in qPCR was performed using a previously described duplex assay25 with the primers and probes given in ddPCR was performed using a previously described duplex assayhttps://github.com/mcrone/plotlydefinerain) of an online tool called Defining The Rain (https://definetherain.org.uk/) with added support for two color channels.The reaction mixture was then thermocycled  on a BioRad C1000 touch PCR machine. Finally, droplets were read using the QX200 Droplet Reader (Bio Rad). Data were then analyzed using a Python implementation (® 6800 system (Roche) and cobas HBV test (Roche) according to the manufacturer's instructions.The 4th WHO international standard for HBV DNA for NAT was ordered from NIBSC. The standard was resuspended according to the instructions for use. Calibration curve samples were generated by diluting the international standard with human plasma (Merck) to create a standard curve ranging from 955,000 to 95.5 IU/mL with three technical replicates of each concentration. Aliquots of our working standard were generated by spiking 50 μL of our generated VLPs into 950 μL of human plasma (Merck). The calibration curve samples and the aliquots of working standard were then tested using a cobas33 based on Fieller's theorem.34 Further details are available in the Supplementary Methods. Residuals of the linear regression are shown in https://github.com/mcrone/qpcr_abs_calibration). All results are available in The working standard calibration was performed by fitting of the standard curve using linear regression, and the error was calculated using a statistical tool