Potential of MRI in radiotherapy mediated by small conjugates and nanosystems

We investigate the structural and quantum transport properties of isotopically enriched 28 Si / 28 SiO 2 stacks deposited on 300-mm Si wafers in an industrial CMOS fab. Highly uniform ﬁlms are obtained with an isotopic purity greater than 99.92%. Hall-bar transistors with an oxide stack comprising 10 nm of 28 SiO 2 and 17 nm of Al 2 O 3 (equivalent oxide thickness of 17 nm) are fabricated in an academic cleanroom. A critical density for conduction of 1.75 × 10 11 cm − 2 and a peak mobility of 9800 cm 2 / Vs are measured at a temperature of 1.7 K. The 28 Si / 28 SiO 2 interface is characterized by a roughness of (cid:2) = 0.4 nm and a correlation length of (cid:3) = 3.4 nm. An upper bound for valley splitting energy of 480 μ eV is estimated at an eﬀective electric ﬁeld of 9.5 MV/m. These results support the use of wafer-scale 28 Si / 28 SiO 2 as a promising material platform to manufacture industrial spin qubits.


I. INTRODUCTION
Enrichment of the spin-zero 28 Si isotope drastically reduces spin-bath decoherence in silicon [1,2] and has enabled solid-state spin qubits with extremely long coherence [3,4] and high control fidelity [5][6][7]. The limited availability of isotopically enriched 28 Si in industrially adopted forms [8], however, was previously thought to be a major bottleneck to leverage CMOS technology for manufacturing qubits with the quality and in the large numbers required for fault-tolerant quantum computation [9,10]. Recently, isotopically enriched silane ( 28 SiH 4 ) has been employed in a preindustrial CMOS facility to deposit highquality 28 Si epiwafers [11]. Crucially, an industrial supply of 28 SiH 4 has been established and silicon quantum dots were fabricated on a wafer-scale 28 Si/ 28 SiO 2 stack grown in an industrial manufacturing CMOS fab [12]. In these quantum dots, a single-electron spin lifetime of 2.8 ms was obtained at a temperature of 1.1 K and weak charge noise was measured, pointing to a promising material platform for qubit operation at elevated temperatures.
Studies devoted to 28 Si quantum dots, however, tend to discuss only marginally the structural properties of the originating 28 Si/ 28 SiO 2 material stack and the electrical * g.scappucci@tudelft.nl transport in the associated 2DEG. In this paper we provide structural characterization of the same industrial 28 Si wafer used for quantum dots in Ref. [12] and assess the disorder properties of the critical 28 Si/ 28 SiO 2 interface. By investigating the quantum transport properties of Hall-bar transistors, we extract key material metrics such as carrier mobility, critical density, interface roughness, interface correlation length, and valley splitting energy. Electron mobility is typically used as a figure of merit to assess the quality of the semiconductor-oxide interface. However, peak mobility is measured at high electron density, where screening effects are relevant [13,14]. The critical density, instead, indicates the minimum density required to establish metallic conduction by overcoming electron trapping at the oxide interface. As such, the critical density is a complementary metric to the mobility and characterizes the interface disorder at low densities, where quantum devices typically operate. Overall, large mobility and small critical density indicate material uniformity and low disorder at the confining interfaces. These properties are beneficial for obtaining reproducible quantum dots at intended locations on the substrate. Valley splitting quantifies the energetic separation between the ground state used for computation and the lowest excited state. A sharp flat interface is required to achieve large splitting energy, which is beneficial for qubit operation [15,16]. The results reported in this work indicate a low disorder environment at the 28 Si/ 28 SiO 2 interface and potential to achieve large valley splitting, supporting the industrial integration of spin qubits on wafer-scale 28 Si.

II. MATERIAL CHARACTERIZATION
The schematics in Fig. 1 illustrate the key steps in the supply chain of isotopically enriched precursors for wafer-scale epitaxial growth of 28 Si. A silicon-tetrafluoride gas (SiF 4 ) with natural abundance of 28 Si of 92.23% is isotopically enriched in 28 Si to a concentration greater than 99.92% by centrifuge separation. The 28 SiF 4 , with a residual 29 Si concentration of 0.08%, is then reduced to obtain high purity 28 SiH 4 . 28 SiH 4 gas cylinders (1% dilution in H 2 ) have been installed for use in a state-of-the-art chemical-vapor deposition tool of a 300-mm fabrication line to deposit 28 Si epilayers. Maintaining the chemical purity of gas precursors throughout the supply chain is crucial to obtain a low disorder 28 Si/ 28 SiO 2 stack. The growth process starts with the deposition of 1 μm of intrinsic natural Si on a high-resistivity 300-mm Si(100) wafer followed by a 100-nm-thick intrinsic 28 Si epilayer. The wafer is then thermally processed at high temperature for the formation of a high-quality 10-nm-thick 28 SiO 2 layer. The oxidation process is based on prior Intel transistor technology [17][18][19]. In this work, the allowed thermal budget for oxidation is optimized [20] to minimize Si self-diffusion and obtain sharp isotopic profiles, as evident in the secondary ion mass spectroscopy profiles in Fig. 1.
In Fig. 1 we compare morphology and composition of the grown stack at the center and the edge of the 300-mm wafer. No difference in surface or interface roughness, composition, and purity can be observed across the wafer, indicating a uniform film deposition. Atomic force microscopy shows a uniform and near defect-free surface with a root-mean-square surface roughness of 0.2 nm measured over an area of 1 μm × 1 μm. Secondary ion mass spectroscopy of isotopes 28 Si, 29 Si, and 30 Si shows a high-purity film with a residual concentration of nonzerospin nuclei 29 Si reduced from 4.76% in the Si buffer to 0.08% in the purified epilayer, demonstrating that the precursor purity is preserved during the deposition process. The concentration of common background contaminants C and O is below the detection limit of 4 × 10 17 cm −3 and 1 × 10 18 cm −3 , respectively. Background doping from P and B is also below the detection limit of 3 × 10 15 cm −3 and 1 × 10 14 cm −3 , respectively. High-resolution transmission electron microscopy shows that no dislocations or stacking faults are visible in the epilayer. Moreover, the 28  typical size of Si quantum-dot spin qubits (≤50 nm). This increases the chance of defining a quantum dot in a stepfree area, which is beneficial for obtaining large valley splitting [15,16]. The sharpness of the interface, the negligible density of defects in the lattice, and the associated electron diffraction pattern highlight the film quality and the good control over the growth process despite the introduction of a new Si precursor in the manufacturing CMOS fab.

III. DEVICE FABRICATION AND TRANSPORT PROPERTIES
Moving on to device fabrication, Fig. 2(a) shows schematics and optical micrograph of a MOS transistor shaped in a Hall-bar geometry to investigate the magnetotransport properties of the 2DEG at the 28 Si/ 28 SiO 2 interface. The device was fabricated in an academic cleanroom environment, starting from coupon-sized samples diced from the original 28 Si/ 28 SiO 2 300-mm wafer. We employ e-beam lithography and lift-off additive techniques to resemble the process flow used to fabricate quantum dots as in Ref. [12]. Highly doped n ++ regions are obtained by P-ion implantation followed by 30 s of activation anneal at 1000 • C in N 2 environment. Multiple ohmic contacts are deposited on the implant regions by e-beam evaporation of Al. An additional Al 2 O 3 layer of 17 nm is deposited by atomic layer deposition at 300 • C, so that the 28 Si/ 28 SiO 2 interface undergoes similar processing as in the fabrication of multilayer gate-defined qubits [12]. The resulting dielectric stack has an equivalent oxide thickness of 17 nm. A Ti/Pd top gate is deposited to define a Hall-bar geometry with a 100-μm-wide and 500-μm-long central region. The last processing step is a forming gas anneal at 400 • C to reduce the damage induced by e-beam lithography [14,21]. The electrical characterization of the device is performed at a temperature of 1.7 K using standard fourterminal low-frequency lock-in techniques with a constant source-drain excitation voltage of 1 mV. Longitudinal (ρ xx ) and transverse (R xy ) resistivity are measured as a function of carrier density-controlled by the top gate-and external perpendicular magnetic field B. The Hall carrier density n and the electron mobility μ are calculated using the relationships R xy = (ne) −1 B and μ = (neρ 0 ) −1 , respectively, where e is the elementary charge and ρ 0 = ρ xx (B = 0 T).
A dc voltage applied to the top gate (V g ) accumulates a 2DEG at the 28 Si/ 28 SiO 2 interface, which conducts above a turn-on voltage of V TO = 1.22 V [22], as shown in Fig. 2(b). For values below V TO no current flow is observed in the device up to a temperature of T = 23 K, confirming the insulating behavior of the intrinsic 28 Si film at low temperature. For V g > V TO [ Fig. 2(c)] we measure a linear increase in the Hall density n as a function of V g . The experimental capacitance C = e dn/dV g = 0.19 μF/cm 2 matches within 5% of the expected value for the given dielectric stack. Upon multiple sweeps of V g no hysteresis is observed and the same values of V TO and C are measured, indicating a stable potential landscape at the oxide interface.
The experimental and theoretically calculated densitydependent mobility curves are shown in Fig. 2(d). Above a critical density, required to establish metallic conduction in the 2DEG, the mobility rises sharply due to screening from charged impurity Coulomb scattering [23][24][25][26]. A peak mobility of 9800 cm 2 /Vs is reached at n = 1.13 × 10 12 cm −2 , corresponding to a mean free path of 120 nm. Beyond, the mobility drops due to surface-roughness scattering at the 28 Si/ 28 SiO 2 interface [23,25,26]. The calculated scattering-limited mobility takes into account a scattering charge density at the semiconductor-oxide 014013-3 interface and an exponential autocorrelation function form of the interface roughness [13,25,26]. A good match is obtained for a scattering charge density of 4.65 × 10 10 cm −2 , an interface roughness of = 0.4 nm, and an interface correlation length of = 3.4 nm (see Appendix). describes the interface root-mean-square height fluctuations, is the lateral distance over which the fluctuations are correlated. The interface roughness is compatible with the morphology investigation by transmission electron microscopy reported in Fig. 1.
The critical density is extracted from a percolation fit of the density-dependent conductivity [ Fig. 2(e)] σ xx ∼ (n − n p ) p [13,14], where n p , p are the percolation transition density and exponent, respectively. By fixing p = 1.31, as expected in a two-dimensional system, we estimate n p = 1.75 ± 0.02 × 10 11 cm −2 at T = 1.7 K. The fit used to estimate n p is performed over the density range 2.0-7.3 × 10 11 cm −2 (see Appendix). Previous studies have shown that n p decreases with decreasing temperature [13,14], therefore the obtained value of 1.75 × 10 11 cm −2 sets an upper bound for the critical density in the temperature regime at which qubits are typically operated (T ≤ 100 mK).
Both the mobility and critical density obtained in the wafer-scale isotopically enriched 28 Si/ 28 SiO 2 stack are qualitatively comparable to the values previously reported for high-mobility Si MOSFETs at low temperatures [13,14,21,27,28,30,31] (see Table I). In drawing a meaningful comparison with the data reported in the literature, the reader should consider material stacks that have produced quantum-dot devices using a similar process flow. For example, peak mobility is known to be higher in devices with thicker oxide [23,32] and degrades upon device exposure to e-beam [14,21].
Transport characterization at high magnetic field (Fig. 3) allows the measurement of effective mass m * and quantum lifetime τ q , from which we estimate an upper bound for the valley splitting energy and the g factor. In Fig. 3(a) we report the longitudinal magnetoresistivity at a density n = 1.05 × 10 12 cm −2 , which corresponds to an effective electric field of 9.5 MV/m. Shubnikov-de Haas (SdH) oscillations are observed, with minima aligned to quantum Hall plateaus in R xy . SdH oscillations start at B eff = 1 T and spin degeneracy is resolved at B S = 4.3 T, corresponding to the even filling factor ν = 10. Figure 3(b) shows the filling factor progression against 1/B. High mobility and density allow filling factors to be resolved up to ν = 36, with fourfold periodicity at low magnetic field due to spin and valley degeneracy and twofold periodicity beyond B S . We do not observe odd filling factors, indicating that the twofold valley degeneracy is not resolved under these measurement conditions. From the linear filling factor progression we extract a density n SdH = 1.06 × 10 12 cm −2 . The agreement between the Hall density n and n SdH indicates that only one high-mobility subband contributes to electrical transport, confirming the high-quality 28 Si epitaxy.
The transverse effective mass m * of the high-mobility carriers is calculated from the damping of the SdH oscillations with increasing temperature, described by the relation [33][34][35][36] where ρ xx is the SdH oscillation amplitude after polynomial background subtraction, χ = 2π 2 k B T/ ω c , χ 0 = χ(T 0 =1.7 K), ω c = eB/m * is the cyclotron frequency, is the Planck constant, and k B the Boltzmann constant. where m e is the free-electron mass, and a transport lifetime τ t = μm * /e = 1.06 ps. The m * value is in agreement with measurements performed on natural Si [37] and corresponds to the expected value obtained from band-structure calculations neglecting many-body effects [23].
Once the effective mass is measured, the quantum lifetime τ q can be determined from the SdH oscillation envelope at T 0 , using the relation [33,36] The Dingle plot of Fig. 3(e) reports the fit from which we extract τ q = 0.69 ps. This value implies a small Dingle ratio of τ t /τ q = 1.54, indicating that large-angle scattering events are dominant since most sources of scattering are located near the semiconductor-oxide interface. This result confirms the validity of the model used for the theoretically calculated mobility curve of Fig. 2(d) and suggests that scattering associated with the Al 2 O 3 deposition is minimal, which is beneficial for quantum-dot fabrication. From the obtained τ q we calculate a Landau-level broadening of ≈ /2τ q = 480 μeV, which sets an upper bound to valley splitting at the investigated density (electric field) and magnetic field. For comparison, a valley splitting energy of 275 μeV is measured in 28 Si quantum dots fabricated on the same wafer in an academic environment [12] and a valley splitting of 200 μeV is reported for electric fields of 10 MV/m in other quantum dots [38]. The electron g factor is evaluated by considering that the onset of spin splitting at B S implies a Zeeman energy gμ B B S , where μ B is the Bohr magneton. From this, a g factor of g = 1.92 ± 0.07 is estimated, which is close to the expected single-particle value of g = 2.

IV. CONCLUSION
In conclusion, we investigate the structural and quantum transport properties of isotopically enriched 28 Si/ 28 SiO 2 stacks deposited on 300-mm wafers in an industrial CMOS fab. The material characterization shows that the level of control achieved in the growth process results in a uniform deposition with high-purity epilayers and a sharp semiconductor-oxide interface. Detailed quantum transport characterization of Hall-bar devices fabricated in an academic cleanroom points to a high-quality 28 Si/ 28 SiO 2 interface, promising for hosting spin qubits. Mobility and critical density for these stacks are among the best reported for gate stacks used for quantum-dot fabrication, with the potential to achieve large valley splitting. Disorder at the critical semiconductor-oxide interface is expected to further decrease by processing the entire gate stack in the high-volume manufacturing environment, because an advanced process control is attainable and e-beam-induced damage is avoided.

Mobility-density curve
To assess how sensitive the calculated mobility curve is to the input parameters (i.e., interface roughness , interface correlation length , and scattering charge density n i ), in Fig. 4 we show the mobility curve calculated by varying the parameters one at a time, starting from the best values that generated the theoretical curve reported in Fig. 2(d).
The theoretical curve is more sensitive to variations in and n i , compared to . In fact, a variation of 5% in 014013-5 , and (c) by 5% with respect to the values that generated the theoretical mobility curve in Fig. 2(d), here displayed in black. Upper panels: relative difference between the mobility curve in Fig. 2(d) and the curves obtained by increasing (red curve) and decreasing (blue curve) the parameters by 5%.
or n i results in a maximum variation in the mobility up to approximately 10% and approximately 5%, respectively. A variation of 5% in results, instead, in a negligible variation in the mobility (0.1%). We note that variations of up to 15% are necessary to induce a mobility variation of only 4%.

Percolation transition density
The percolation theory considered to evaluate the percolation transition density n p is valid only in a density range n close to n p and for n > n p . For this reason, the fit reported in Fig. 2(e) of the main text is performed considering a density range of 2.0-7.3 × 10 11 cm −2 , resulting in n p = 1.75 ± 0.02 × 10 11 cm −2 .
To clarify how the density range is chosen to fit the data, in Fig. 5 we show n p as a function of the range over which the fit is performed. The density range n is increased by fixing the lowest density at 2.0 × 10 11 cm −2 and increasing the highest density value. While the error intervals increase for smaller density ranges, the extracted value of n p shows a weak dependency on the density range used for the fit, with all the values between 1.70 × 10 11 cm −2 and 1.75 × 10 11 cm −2 . The chosen value of n p = 1.75 × 10 11 cm −2 is therefore a valid estimate since it is extracted considering a significant density range and further extending this range does not result in improvements in the error intervals.