Modeling and in Situ Probing of Surface Reactions in Atomic Layer Deposition (original) (raw)

Supporting Information

Modeling and In-situ Probing of Surface Reactions in Atomic Layer Deposition

Yuanxia Zheng 5,, { }^{5, \text {, }}, Sungwook Hong 2,, { }^{2, \text {, }}, George Psofogiannakis 2{ }^{2}, G. Bruce Rayner, Jr. 5{ }^{5}, Suman Datta 6{ }^{6}, Adri C.T. van Duin 2,∗{ }^{2, *}, and Roman Engel-Herbert 8,∗{ }^{8, *}

Abstract

1{ }^{1} Department of Physics, 2{ }^{2} Department of Mechanical and Nuclear Engineering, 4{ }^{4} Department of Materials Science and Engineering, the Pennsylvania State University, State College, PA16802, USA, 5{ }^{5} Kurt J. Lesker Company, Pittsburgh, PA 15025, USA, and 6{ }^{6} Department of Electrical En-gineering, University of Notre Dame, Notre Dame, IN 46556, USA. 2{ }^{2} These authors contributed equally. ∗{ }^{*} E-mails: acv13@psu.edu, rue2@psu.edu.

SECTION 1. REAXFF REACTIVE FORCE FIELD DEVELOPMENT

In this work, the ReaxFF reactive force field was employed for atomic-scale simulations. The ReaxFF is an empirical reactive force field optimized against quantum mechanics (QM) based training sets. 1{ }^{1} Essentially, the ReaxFF utilizes a bond order/distance relationship, and the bond order is calculated and updated at every step, allowing for each atom’s neighbor list to be corrected accordingly (i.e. no rigid connectivity for all of atoms). As such, the ReaxFF is capable of describing chemical reactions (i.e. bond forming and breaking) for complex materials, especially including gas-surface systems. 2−4{ }^{2-4} The recent review of the ReaxFF potential and its applications can be found in Senftle et al. 5{ }^{5}

In order to develop a ReaxFF reactive force field for Ge/Al/C/H/O\mathrm{Ge} / \mathrm{Al} / \mathrm{C} / \mathrm{H} / \mathrm{O} interactions, quantum mechanics (QM) calculations were carried out for both periodic and non-periodic systems, and ReaxFF reactive force field parameters were optimized against the QM calculations. For the periodic systems, density functional theory (DFT) calculations for 8 atoms of GeO and 9 atoms of GeO2\mathrm{GeO}_{2} unit cells were performed with the Vienna ab initio simulation package (VASP), 6{ }^{6} using the GGA-PBE functional 7{ }^{7} in the projector

augmented-wave (PAW) method, 8{ }^{8} a 500 eV energy cutoff, Gaussian smearing ( σ=0.05\sigma=0.05 ), and a 6×6×6 \times 6 \times 6 Gamma-centered k-point grid. Equations of state were calculated by varying lattice parameters of the fully-optimized unit cell and performing ionic optimizations using the conjugate-gradient algorithm. The formation energies for two structures, GeO , and GeO2\mathrm{GeO}_{2}, are reported in Figure S1 with respect to the respective Ge diamond phases, and O2\mathrm{O}_{2} gas-phase, based on the VASP optimizations of Ge , and O2\mathrm{O}_{2} using the same computational choices. For the non-periodic clusters containing Ge/Al/C/O/H\mathrm{Ge} / \mathrm{Al} / \mathrm{C} / \mathrm{O} / \mathrm{H} interactions, the rapid ab initio electronic structure package of Jaguar 9{ }^{9} (version of 8.3) with the B3LYP functional and LACV3P basis set, was used to calculate bond dissociation and angle distortion energies for Ge/Al/C/H/O\mathrm{Ge} / \mathrm{Al} / \mathrm{C} / \mathrm{H} / \mathrm{O} interactions, potentially allowing for chemical reactions between tri-methyl-aluminum (TMA)/water (H2O)\left(\mathrm{H}_{2} \mathrm{O}\right) precursors and GeOx/Ge\mathrm{GeO}_{\mathrm{x}} / \mathrm{Ge} surfaces.

1.1 ReaxFF Fits to QM Calculations for Periodic Systems

To describe bulk characteristics of GeOx\mathrm{GeO}_{\mathrm{x}} systems by the ReaxFF description correctly, ReaxFF reactive force field parameters were trained against formation energies and equations of state for GeO and GeO2\mathrm{GeO}_{2} crystal structures. Figure S1 shows ReaxFF fits to compression and expansion energies for the GeO and GeO2\mathrm{GeO}_{2} structures. The results indicate that the ReaxFF qualitatively reproduces the bulk charac-

Figure S1. Equations of state for GeO and GeO2\mathrm{GeO}_{2} crystal structures obtained by ReaxFF and DFT calculations. Note that formation energies were calculated with respect to Ge-diamond and O2\mathrm{O}_{2}-gas phases. Green and red spheres represent Ge and O atoms, respectively.

teristics of both GeO and GeO2\mathrm{GeO}_{2} structures.

1.2 ReaxFF Fits to QM Calculations for Non-periodic Systems

The ReaxFF reactive force field parameters were also trained against QM calculations of interactions between non-periodic clusters, including the dissociation energies for Al−C,Al−Ge,Ge−C,Ge−H\mathrm{Al}-\mathrm{C}, \mathrm{Al}-\mathrm{Ge}, \mathrm{Ge}-\mathrm{C}, \mathrm{Ge}-\mathrm{H}, single Ge−O\mathrm{Ge}-\mathrm{O}, and double Ge=O\mathrm{Ge}=\mathrm{O} bonds, and angel distortion energies for C−Ge−O,H−Ge−O,O−Ge−O\mathrm{C}-\mathrm{Ge}-\mathrm{O}, \mathrm{H}-\mathrm{Ge}-\mathrm{O}, \mathrm{O}-\mathrm{Ge}-\mathrm{O}, and Al−O−\mathrm{Al}-\mathrm{O}- Ge. The results in Figures S2 and S3 show that the ReaxFF descriptions qualitatively agree with the QM calculations. Furthermore, to give the ReaxFF description the ability to correctly mimic directions of reactions (i.e. endothermic or exothermic reactions) for TMA/Ge-related interactions, the ReaxFF reactive force field parameters were fit to QM calculations for reaction energies of our interests, as summarized in Table S1. In summary, the ReaxFF description, as developed in this work, enables us not only to model GeO and GeO2\mathrm{GeO}_{2} crystal structures, but also to simulate the complex surface chemistry of TMA and H2O\mathrm{H}_{2} \mathrm{O} chemisorption on Ge and GeO2/Ge\mathrm{GeO}_{2} / \mathrm{Ge} surfaces. The full ReaxFF reactive force field parameters

Figure S2. ReaxFF fits to DFT calculations of (a) Al−C\mathrm{Al}-\mathrm{C} and (b) Al−Ge\mathrm{Al}-\mathrm{Ge} full bond dissociation curves. Ge,C,H\mathrm{Ge}, \mathrm{C}, \mathrm{H}, and Al atoms are displayed in green, brown, white, and sky-blue, respectively.
for Ge/Al/C/H/O\mathrm{Ge} / \mathrm{Al} / \mathrm{C} / \mathrm{H} / \mathrm{O} interactions are included in Section 9 of Supporting Information.

Figure S3. ReaxFF fits to DFT calculations of bond dissociation and angle distortion energies for non-periodic clusters containing Ge/Al/C/H/O\mathrm{Ge} / \mathrm{Al} / \mathrm{C} / \mathrm{H} / \mathrm{O} interactions: (a) Ge−C,Ge−H,Ge−O\mathrm{Ge}-\mathrm{C}, \mathrm{Ge}-\mathrm{H}, \mathrm{Ge}-\mathrm{O} (single), and Ge=O\mathrm{Ge}=\mathrm{O} (double) bond; (b) C-Ge-O, H-Ge-O, O-Ge-O, and Al-O-Ge bond angle. The Ge atoms are displayed in green, C in brown, O in red, H in white, and Al in sky-blue.

Table S1. Reaction energies for TMA/Ge clusters interactions, derived by DFT and ReaxFF calculations.

SECTION 2. REAXFF REACTIVE FORCE FIELD VALIDATION

2.1 Hydrogen Migration along Ge-bulk Systems

To check if the developed ReaxFF description is capable of describing H migration along Ge bulk systems, we calculated H diffusion between two tetrahedral interstitial sites of a Ge crystal structure, as reported in DFT literature. 10{ }^{10} The DFT study indicates that a reaction barrier along this path is about 0.3 eV , while ReaxFF-nudged elastic band (ReaxFF-NEB) calculations with 3 intermediate images yield the reaction barrier of 0.45 eV (initial and final positions of H atom for this analysis are shown in Figure S4). These results indicate that the ReaxFF reactive force field, as developed in this study, can be applicable to capture the reaction path for H diffusion along Ge bulk systems with the reaction barrier, which

Figure S4. H diffusion (indicated by circles) between two tetrahedral interstitial sites of a Ge crystal structure, described by ReaxFF-nudged elastic band (ReaxFF-NEB) calculations (Ge: orange; H: white).
is a qualitative agreement with the DFT value.

2.2 Reaction Profiles for TMA and H2O\mathrm{H}_{2} \mathrm{O} Half Reactions on Hydrogenated Ge Clusters.

Essentially, the ReaxFF description for Ge/Al/C/H/O\mathrm{Ge} / \mathrm{Al} / \mathrm{C} / \mathrm{H} / \mathrm{O} interactions was developed to model and simulate Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ALD on Ge surfaces using TMA and H2O\mathrm{H}_{2} \mathrm{O} cycles. Thus, the ReaxFF should correctly describe kinetics associated with TMA/H2 O/Ge-related systems. For this reason, we performed ReaxFF calculations for TMA and H2O\mathrm{H}_{2} \mathrm{O} half reactions on hydrogenated Ge clusters, previously conducted in DFT litera-

tures. 11{ }^{11} As shown in Figure S5, the results confirm that the ReaxFF has the ability to describe reaction paths for TMA and H2O\mathrm{H}_{2} \mathrm{O} half reactions, qualitatively consistent with the DFT calculations.

Figure S5. Comparison of (a) TMA and (b) H2O\mathrm{H}_{2} \mathrm{O} half reaction pathways on hydrogenated Ge clusters between DFT and ReaxFF calculations (Ge: orange, Al: blue, C: green, H: white, and O: red). The reaction stages are represented by IS (initial state), chemisorption state (CS), transition state (TS), and desorption state (DS), respectively.

SECTION 3. SYSTEM DESCRIPTION FOR REAXFF CALCULATIONS

In this work, four Ge slab models were prepared for ReaxFF- NEB and molecular dynamics (MD) simulations as follows: a hydrogenated Ge(100)\mathrm{Ge}(100) surface [Ge(100):H][\mathrm{Ge}(100): \mathrm{H}], oxidized Ge(100)\mathrm{Ge}(100) surface [Ge−[\mathrm{Ge}- Ox/Ge(100)],GeOx/Ge(100)\mathrm{O}_{\mathrm{x}} / \mathrm{Ge}(100)], \mathrm{GeO}_{\mathrm{x}} / \mathrm{Ge}(100) interface, and [Al2O3/GeOx]/Ge(100)\left[\mathrm{Al}_{2} \mathrm{O}_{3} / \mathrm{GeO}_{\mathrm{x}}\right] / \mathrm{Ge}(100) interface. All of the systems ware obtained by performing the NVT-MD simulations with the Berensen thermostat (a damping constant of 0.25 fs ) in the ReaxFF-ADF code. 12{ }^{12} A time step of 0.25 fs was used for all of the NVT-MD simulations.

3.1 Ge(100):H Surface

A Ge(100)\mathrm{Ge}(100) surface (20A˚×20A˚×10A˚)\left(20 \AA \times 20 \AA \times 10 \AA\right) was obtained by cleaving a Ge-diamond structure. The periodic boundary condition was used in the x - and the y - directions and a vacuum layer of 30A˚30 \AA was applied to the z-direction. The surface model was annealed ( 300 K−500 K−300 K300 \mathrm{~K}-500 \mathrm{~K}-300 \mathrm{~K} ) for 25 ps . After the annealing process, H atoms were attached to the top and bottom of the Ge(100)\mathrm{Ge}(100) surface where Ge atoms were not fully coordinated. Then, the surface model was fully relaxed and re-annealed ( 300 K−500 K300 \mathrm{~K}-500 \mathrm{~K} 300 K ) for 25 ps to generate a Ge(100)\mathrm{Ge}(100) :H surface. The Ge(100)\mathrm{Ge}(100) :H surface is shown in Figure S6a. Finally, the Ge(100)\mathrm{Ge}(100) :H surface was expanded by a factor of 2 in the x - and y - directions (i.e. a size of 40A˚×40 \AA \times 40A˚×10A˚40 \AA \times 10 \AA ). To elucidate effects of a Ge-dangling bond on TMA and H2O\mathrm{H}_{2} \mathrm{O} adsorption, we manually removed one H atom on top of the Ge(100):H\mathrm{Ge}(100): \mathrm{H} surface.

3.2 GeO Ox/Ge(100)\mathrm{O}_{\mathrm{x}} / \mathrm{Ge}(100) Surface

To model GeOx/Ge(100)\mathrm{GeO}_{\mathrm{x}} / \mathrm{Ge}(100) surface, a Ge(100)\mathrm{Ge}(100) surface (20A˚×20A˚×10A˚)\left(20 \AA \times 20 \AA \times 10 \AA\right) was sandwiched by a 20A˚20 \AA ×20A˚×10A˚\times 20 \AA \times 10 \AA of GeO2\mathrm{GeO}_{2} layer. The Ge(100)\mathrm{Ge}(100) surface and GeO2\mathrm{GeO}_{2} layer were initially separated by 2A˚2 \AA. Subsequently, the entire surface model was annealed ( 300 K−500 K−300 K300 \mathrm{~K}-500 \mathrm{~K}-300 \mathrm{~K} ) for 25 ps , and then equilibrated at 300 K for 2.5 ps to generate a GeOx/Ge(100)\mathrm{GeO}_{\mathrm{x}} / \mathrm{Ge}(100) surface as shown in Figure S6b. The GeOx/Ge(100)\mathrm{GeO}_{\mathrm{x}} / \mathrm{Ge}(100) surface was also expanded by a factor of 2 in the x - and y - directions to build a larger surface for Re-axFF-MD simulations.

3.3 GeOx/Ge(100)\mathrm{GeO}_{\mathrm{x}} / \mathrm{Ge}(100) and [Al2O3/GeOx]/Ge(100)\left[\mathrm{Al}_{2} \mathrm{O}_{3} / \mathrm{GeO}_{\mathrm{x}}\right] / \mathrm{Ge}(100) Interfaces

To investigate effects of Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} layer on oxygen diffusion from a GeOx\mathrm{GeO}_{\mathrm{x}} layer into a Ge-subsurface, we prepared GeOx/Ge(100)\mathrm{GeO}_{\mathrm{x}} / \mathrm{Ge}(100) and [Al2O3/GeOx]/Ge(100)\left[\mathrm{Al}_{2} \mathrm{O}_{3} / \mathrm{GeO}_{\mathrm{x}}\right] / \mathrm{Ge}(100) interfaces as shown in Figure S6c, d. In case of the GeOx/Ge(100)\mathrm{GeO}_{\mathrm{x}} / \mathrm{Ge}(100) interface, a 20.0A˚×20A˚×2.7A˚20.0 \AA \times 20 \AA \times 2.7 \AA of GeO2(100)\mathrm{GeO}_{2}(100) layer was placed on the top of Ge(100)\mathrm{Ge}(100) surface ( 20.0A˚×20.0A˚×15.6A˚20.0 \AA \times 20.0 \AA \times 15.6 \AA ). In addition, a 20.0A˚×20.0A˚×1.4A˚20.0 \AA \times 20.0 \AA \times 1.4 \AA of Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} bulk structure was placed on the top of the GeOx/Ge(100)\mathrm{GeO}_{\mathrm{x}} / \mathrm{Ge}(100) interface for the [Al2O3/GeOx]/Ge(100)\left[\mathrm{Al}_{2} \mathrm{O}_{3} / \mathrm{GeO}_{\mathrm{x}}\right] / \mathrm{Ge}(100) interface. Each part (i.e. Ge,GeO2\mathrm{Ge}, \mathrm{GeO}_{2}, and Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ) was initially separated by 2A˚2 \AA. Finally two prepared models were equilibrated at

Figure S6. System configurations of Ge surfaces for ReaxFF calculations: (a) Ge(100):H\mathrm{Ge}(100): \mathrm{H} surface; (b) GeOx/Ge(100)\mathrm{GeO}_{\mathrm{x}} / \mathrm{Ge}(100) surface; © GeOx/Ge(100)\mathrm{GeO}_{\mathrm{x}} / \mathrm{Ge}(100) interface; (d) [Al2O3/GeOx]/Ge(100)\left[\mathrm{Al}_{2} \mathrm{O}_{3} / \mathrm{GeO}_{\mathrm{x}}\right] / \mathrm{Ge}(100) interface.

300 K for 100 ps to stabilize the GeOx/Ge\mathrm{GeO}_{\mathrm{x}} / \mathrm{Ge} and [Al2O3/GeOx]/Ge\left[\mathrm{Al}_{2} \mathrm{O}_{3} / \mathrm{GeO}_{\mathrm{x}}\right] / \mathrm{Ge} interfaces.

SECTION 4. GE DANGLING BOND FORMATION ON HYDROGENATED GE

SURFACE

We expect that Ge-dangling bonds on the Ge:H\mathrm{Ge}: \mathrm{H} surface lead to a local TMA island growth. In other words, the Ge-dangling bonds provide a local center for non-conformal growth of Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} layer on the Ge:H\mathrm{Ge}: \mathrm{H} surface. To demonstrate how the Ge-dangling bonds on the Ge:H\mathrm{Ge}: \mathrm{H} surface can be generated, we evaluated a reaction profile for a H -atom to diffuse into a Ge-sublayer, subsequently resulting in a single Ge-dangling bond on the Ge:H surface by using the ReaxFF-NEB scheme. It was found that its reaction barrier is 0.68 eV , absorbing 0.39 eV energy for the entire reaction, but this reaction is energetically more favorable than H2\mathrm{H}_{2} desorption from 2Ge−H∗2 \mathrm{Ge}-\mathrm{H}^{*} species (see Figure S7). Thus, it can be suggested that the H -diffusion into the Ge-sublayer can occur at somewhat elevated temperatures, but this can be feasi-

Figure S7. ReaxFF-NEB calculations of H diffusion into Ge-sublayer and H2\mathrm{H}_{2} desorption from 2Ge−H∗2 \mathrm{Ge}-\mathrm{H}^{*} on the top surface. The yellow circles highlight the sites of Ge-dangling bond formation, obtained by H diffusion or H 2 desorption. The asterisk represents a surface species. The reaction stages are represented by IS (initial state), transition state (TS), and final state (FS), respectively.

ble at moderate conditions when compared to the H2\mathrm{H}_{2} desorption.

SECTION 5. TMA AND H2O\mathrm{H}_{2} \mathrm{O} ADSORPTION ON HYDROGENATED GE SURFACE

As shown in Figure S8, ReaxFF-MD simulations at 500 K confirm that TMA and H2O\mathrm{H}_{2} \mathrm{O} molecules can preferably physisorb on the Ge-dangling (Ge-*) bond and Al(CH3)2\mathrm{Al}\left(\mathrm{CH}_{3}\right)_{2} site, respectively, rather than Ge-H* sites (at 0.5 ns ). It should also be noted that the physisorption of H2O\mathrm{H}_{2} \mathrm{O} molecules on the Ge-* site was not observed, indicating that H2O\mathrm{H}_{2} \mathrm{O} molecules primarily provide Al-O bonds rather than Ge-O bonds to fur-

Figure S8. Results of MD simulations at 500 K for (a) 80 TMA molecules on a H-terminated Ge(100)\mathrm{Ge}(100) surface with a single Ge-dangling bond; (b) 100H2O100 \mathrm{H}_{2} \mathrm{O} molecules on the H -terminated Ge(100)\mathrm{Ge}(100) surface with a Ge−Al(CH3)2∗\mathrm{Ge}-\mathrm{Al}\left(\mathrm{CH}_{3}\right)_{2}{ }^{*} site. ReaxFF-MD results confirm that TMA and H2O\mathrm{H}_{2} \mathrm{O} molecules preferably adsorb on the Ge-dangling and Ge−Al(CH3)2∗\mathrm{Ge}-\mathrm{Al}\left(\mathrm{CH}_{3}\right)_{2}{ }^{*} sites, respectively, rather than H-terminated Ge sites.
ther support the TMA island growth.

SECTION 6. SPECTROSCOPIC ELLIPSOMETRY

6.1 Spectroscopic Ellipsometry Modeling

In-situ spectroscopic ellipsometry (SE) was used to monitor the ALD processes in real time. In this measurement, linearly polarized white light (240−1000 nm)(240-1000 \mathrm{~nm}) is incident on the sample surface at an angle of 71∘71^{\circ}. The surface optical properties are obtained by measuring the changes in intensity and polarization state of the reflected light, as follows

rprs=tan⁡Ψ⋅eiΔ\frac{r_{p}}{r_{s}}=\tan \Psi \cdot e^{i \Delta}

where rpr_{p} and rsr_{s} are the Fresnel reflection coefficients for pp - and ss-polarizations, respectively, and Ψ\Psi and Δ\Delta are defined as ellipsometric angles. The optical constants ( n/kn / k or ε1/ε2\varepsilon_{1} / \varepsilon_{2} ) of a homogeneous structure (e.g. single-crystal substrate) can be simply extracted using the Fresnel equations. For multi-layer struc-

Table S2. The dielectric function of Ge substrate at T=270∘CT=270^{\circ} \mathrm{C} is fitted with general oscillators (Gen-Osc). εinf \varepsilon_{\text {inf }} is the contribution from the optical transitions at higher energies, Γ\Gamma is the peak broadening, E0E_{0} is the peak transition energy, AmpA m p is the transition amplitude, and EgE_{g} is the band gap of the corresponding optical transition.

tures, the interpretation of ellipsometric data requires model-based analysis and fitting, so as to obtain the optical constants of each individual layer.

Table S2 shows the optical model for Ge substrate at ALD process temperature of T=270∘CT=270^{\circ} \mathrm{C}. A combination of Tauc-Lorentz and four Lorentz oscillators was used. The Tauc-Lorentz (TL) oscillator is modeling through its contribution to the imaginary part of dielectric function (ε2)\left(\varepsilon_{2}\right), as follows

ε2(E)={AE⋅ΓE0(E−Eg)2(E2−Eg2)2+Γ2E2 for E>Eg0 for E≤Eg\varepsilon_{2}(E)= \begin{cases}\frac{A}{E} \cdot \frac{\Gamma E_{0}\left(E-E_{g}\right)^{2}}{\left(E^{2}-E_{g}^{2}\right)^{2}+\Gamma^{2} E^{2}} & \text { for } E>E_{g} \\ 0 & \text { for } E \leq E_{g}\end{cases}

where AA is the matrix element, EgE_{g} is the band gap, E0E_{0} is the peak transition energy and Γ□\Gamma \square is peak broadening factor for the corresponding optical transition. The contribution of the TL oscillator to real part of dielectric function (ε1)\left(\varepsilon_{1}\right) is obtained by the Kramers-Kronig integration of ε2\varepsilon_{2}, as follows

ε1(E)=εinf +2πP∫εg∞ξε2(ξ)ξ2−E2dξ\varepsilon_{1}(E)=\varepsilon_{\text {inf }}+\frac{2}{\pi} P \int_{\varepsilon_{g}}^{\infty} \frac{\xi \varepsilon_{2}(\xi)}{\xi^{2}-E^{2}} d \xi

where εinf \varepsilon_{\text {inf }} is the contribution from the optical transitions at higher energies, and PP stands for the Cauchy principal of the integral. The Lorentz oscillator is described as

ε(E)=A⋅ΓE0E02−E2−iΓE\varepsilon(E)=A \cdot \frac{\Gamma E_{0}}{E_{0}^{2}-E^{2}-i \Gamma E}

where AA is the matrix element, E0E_{0} is the peak transition energy and Γ□\Gamma \square is peak broadening factor for the corresponding optical transition. To assess the fitting quality, an unweighted error function was used. Our model well fits the measured data (see Figure S8) with an error function of 2.975×10−32.975 \times 10^{-3}, which is well within the acceptable range of ≤1.0×10−2\leq 1.0 \times 10^{-2}.

Figure S8. (a) Experimental SE measurement (solid blue, Ψ\Psi; solid red, Δ\Delta ) with the incident angle of 71∘71^{\circ}, and the best-fit curves (black dash) for Ge substrate at T=270∘CT=270^{\circ} \mathrm{C}. (b) Extracted dielectric functions for Ge at T=270∘CT=270^{\circ} \mathrm{C}.

All the amorphous oxide films (GeOx,Al2O3\left(\mathrm{GeO}_{\mathrm{x}}, \mathrm{Al}_{2} \mathrm{O}_{3}\right., and HfO2\mathrm{HfO}_{2} ) grown in our processes have high band gaps beyond the spectral range ( 1.24−5.17eV1.24-5.17 \mathrm{eV} ), so a Cauchy dispersion was used to describe their optical constants, as shown in Table S2. The Cauchy dispersion is modeling through refractive index ( nn ) and assuming k=0k=0, as follows

n(λ)=An+Bnλ2+Cnλ4 and k(λ)=0n(\lambda)=A_{n}+\frac{B_{n}}{\lambda^{2}}+\frac{C_{n}}{\lambda^{4}} \quad \text { and } \quad k(\lambda)=0

Table S3. The refractive index ( nn ) of GeOn,Al2O3\mathrm{GeO}_{n}, \mathrm{Al}_{2} \mathrm{O}_{3} and HfO2\mathrm{HfO}_{2} deposited by ALD at T=270∘C\mathrm{T}=270^{\circ} \mathrm{C} are fitted with Cauchy model. CnC_{n} term has trivial contribution, so is not included in the fitting. Since the band gaps of the three oxides are beyond the spectrum range (1.24−5.18eV)(1.24-5.18 \mathrm{eV}), the oxides are considered as transparent with extinction coefficient k=0k=0.

where An,BnA_{n}, B_{n}, and CnC_{n} are the Cauchy fit parameters and λ\lambda is the wavelength in nm .

6.2 Ellipsometry for Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ALD Baseline

Figure S9a shows the in-situ SE monitoring for coalesced Al2O3ALD\mathrm{Al}_{2} \mathrm{O}_{3} \mathrm{ALD} on Al2O3(30 nm)/SiO2(25\mathrm{Al}_{2} \mathrm{O}_{3}(30 \mathrm{~nm}) / \mathrm{SiO}_{2}(25 nm)/Si\mathrm{nm}) / \mathrm{Si}. This deposition serves as the ALD baseline. The coalesced Al2O3ALD\mathrm{Al}_{2} \mathrm{O}_{3} \mathrm{ALD} is linear, with a growth per cycle (GPC) of ∼0.86A˚/\sim 0.86 \AA / cycle. The extracted ratio of Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} growth to TMA adsorption is estimated to be ∼0.4\sim 0.4 (see Figure S9b). The GPC/TMA adsorption for the Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ALD on the Ge:H surface is

Figure S9. (a) In-situ SE monitoring of Al2O3ALD\mathrm{Al}_{2} \mathrm{O}_{3} \mathrm{ALD} on Al2O3(30 nm)/SiO2(25 nm)/Si\mathrm{Al}_{2} \mathrm{O}_{3}(30 \mathrm{~nm}) / \mathrm{SiO}_{2}(25 \mathrm{~nm}) / \mathrm{Si}. (b) Extracted ratio of Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} growth to TMA adsorption as a function of growth cycle for Al2O3ALD\mathrm{Al}_{2} \mathrm{O}_{3} \mathrm{ALD} on Al2O3(30 nm)/SiO2(25 nm)/Si\mathrm{Al}_{2} \mathrm{O}_{3}(30 \mathrm{~nm}) / \mathrm{SiO}_{2}(25 \mathrm{~nm}) / \mathrm{Si}. © Extracted ratio of GPC to TMA adsorption as a function of growth cycle for Al2O3ALD\mathrm{Al}_{2} \mathrm{O}_{3} \mathrm{ALD} on the Ge: H surface.

shown in Figure S9c. The large uncertainty in Figure S9c is a result of the low signal to noise ratio in the initial nucleation delay.

6.3 Calculation for TMA Adsorption Density

To obtain TMA adsorption density on Ge:H surface, we firstly need to verify the same parameter for Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ALD baseline. Assuming 3.0 g/cm33.0 \mathrm{~g} / \mathrm{cm}^{3} for Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} density, 13{ }^{13} the density of Al atom is ρ=\rho= 3.54×1022/cm33.54 \times 10^{22} / \mathrm{cm}^{3}. Then the areal density of Al atom is ρ2/3=1.08×1015/cm2\rho^{2 / 3}=1.08 \times 10^{15} / \mathrm{cm}^{2}, and the monolayer thickness of AlO1.5\mathrm{AlO}_{1.5} is ρ1/3=3.04A˚\rho^{1 / 3}=3.04 \AA. The baseline GPC of ∼0.86A˚\sim 0.86 \AA corresponds to 0.28 monolayer of AlO1.5\mathrm{AlO}_{1.5}, so we have an areal density of 0.28×ρ2/3=3.05/nm20.28 \times \rho^{2 / 3}=3.05 / \mathrm{nm}^{2} for Al atoms deposited in one ALD cycle. Since one TMA molecule contributes one Al atom, the TMA adsorption density =3.05/nm2=3.05 / \mathrm{nm}^{2} for the baseline.

In Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ALD on Ge:H surface (Figure 3b in the main text), the very initial TMA adsorption level obtained by in-situ SE was ∼0.37A˚,∼17%\sim 0.37 \AA, \sim 17 \% of the baseline, that is 3.05×17%≈0.5/nm23.05 \times 17 \% \approx 0.5 / \mathrm{nm}^{2}. If we assume that TMA adsorption only occurs at all Ge-* sites, Ge-* density is ∼0.5/nm2\sim 0.5 / \mathrm{nm}^{2}.

6.4 Real-time Raw Ellipsometry Data of Ψ\Psi and Δ\Delta for Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ALD

Figure S10, S11 show the raw ellipsometry data of Ψ\Psi and Δ\Delta for Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ALD on Ge:H and GeOx(5\mathrm{GeO}_{\mathrm{x}}(5 A˚)/Ge(100)\AA) / \mathrm{Ge}(100) surfaces, respectively. Due to the small film thickness, the small changes of Ψ\Psi and Δ\Delta are better demonstrated as a function of time at certain wavelengths (300.2, 501.1, 701.4 and 900.4 nm ). Compared to the amplitude change of the reflected light (characterized by Ψ\Psi ), the phase change (charac-

Figure S10. Raw SE data of (a) Ψ\Psi and (b) Δ\Delta at different cycles of Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ALD on Ge:H surface. Real-time raw SE data of © Ψ\Psi and (d) Δ\Delta at various wavelengths (300.2, 501.1, 701.4 and 900.4 nm ).
terized by Δ\Delta ) is more sensitive to the film thickness.

Figure S11. Raw SE data of (a) Ψ\Psi and (b) Δ\Delta at different cycles of Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ALD on GeO4(5A˚)/Ge(100)\mathrm{GeO}_{4}(5 \AA) / \mathrm{Ge}(100) surface. Real-time raw SE data of © Ψ\Psi and (d) Δ\Delta at various wavelengths (300.2, 501.1, 701.4 and 900.4 nm ).

SECTION 7. ELLINGHAM DIAGRAM

Figure S12 shows the Ellingham diagram calculations for Al,Si,Ga,Ge\mathrm{Al}, \mathrm{Si}, \mathrm{Ga}, \mathrm{Ge}, and As in reaction with O2( g)\mathrm{O}_{2}(\mathrm{~g}). The calculations were based on Reference 14. From the diagram, Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} is the most stable phase,

Figure S12. Ellingham calculations for As2O3,GeO2,Ga2O3\mathrm{As}_{2} \mathrm{O}_{3}, \mathrm{GeO}_{2}, \mathrm{Ga}_{2} \mathrm{O}_{3} and Al2O3\mathrm{Al}_{2} \mathrm{O}_{3}, respectively.
while the other oxides can be potentially reduced by Al.

SECTION 8. ATOMIC FORCE MICROSCOPY

Atomic force microscopy (AFM) was used to characterize the surface morphology of Ge(100)\mathrm{Ge}(100) surfaces at different chemistry states. Figure 13a and b shows the relative height signals before and after

Figure S13. AFM morphology for (a) before and (b) after 16 cycles of Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ALD on GeOx(5A˚)/Ge(100)\mathrm{GeO}_{\mathrm{x}}(5 \AA) / \mathrm{Ge}(100). The surface roughness is represented by the root mean square (RMS) of relative height signal.

16 cycles of Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ALD on GeOx(5A˚)/Ge(100)\mathrm{GeO}_{\mathrm{x}}(5 \AA) / \mathrm{Ge}(100), respectively.

SECTION 9. ELECTRICAL CHARACTERIZATION

Figure S14a shows the design of Ge-MOSCap devices used to test the electrical performance of [Al2O3/GeOx]/Ge(100)\left[\mathrm{Al}_{2} \mathrm{O}_{3} / \mathrm{GeO}_{\mathrm{x}}\right] / \mathrm{Ge}(100) interface. Figure S14b shows the process flow of fabricating MOSCap devices. A GeOx\mathrm{GeO}_{\mathrm{x}} layer ( 5A˚5 \AA ) was applied to form superior dielectric/semiconductor interface that showed low interface trap density (D0).Al2O3\left(D_{0}\right) . \mathrm{Al}_{2} \mathrm{O}_{3} deposition intermixed with GeOx\mathrm{GeO}_{\mathrm{x}} and thereafter stabilized the interface. A high-k dielectric of HfO2(24A˚,k∼20)\mathrm{HfO}_{2}(24 \AA, \mathrm{k} \sim 20) was used to suppress the gate leakage current (JG)\left(J_{G}\right). A 60 nm Ni layer was deposited as the gate electrode with matching work function (5.04 5.35 eV) to p-Ge

Figure S14. (a) The structural schematic and the function of each individual layer for Ge-MOSCap devices of Ni(60 nm)/HfO2(24A˚)/[Al2O3\mathrm{nm}) / \mathrm{HfO}_{2}(24 \AA) /\left[\mathrm{Al}_{2} \mathrm{O}_{3}\right. (varied cycles) /GeO4(5A˚)p−Ge(100)/ \mathrm{GeO}_{4}(5 \AA) \mathrm{p}-\mathrm{Ge}(100); the only variable in the structure was the cycle number of Al2O3\mathrm{Al}_{2} \mathrm{O}_{3} ALD. (b) The process flow for the fabrication of Ge-MOSCap devices. © The setup of measurement impedance of MOSCap devices.
(4.43 4.47 eV ). A shadow mask was used to define the pattern of the Ni electrodes (Figure S14c).

SECTION 10. REAXFF REACTIVE FORCE FIELD FOR GE/AL/C/H/O

INTERACTIONS

The ReaxFF reactive force field for Ge/Al/C/H/O\mathrm{Ge} / \mathrm{Al} / \mathrm{C} / \mathrm{H} / \mathrm{O} interactions was developed as follows:

11.97271 .00004 .000010 .5217131 .42004 .20276 .01200 .0000
-1.00000 .0000128 .98918 .789523 .92980 .83810 .85630 .0000
-4.00003 .03651 .03386 .29982 .57910 .00000 .00000 .00000
X -0.10002 .00001 .00802 .00000 .000000 .0100 -0.10006 .0000
10.00002 .50004 .000000 .000000 .00005 .00009999 .99990 .00000
-0.10000 .0000 -2.37008 .741013 .36400 .66900 .97450 .0000
-11.00002 .74661 .03382 .00002 .87930 .000000 .00000 .00000
15 ! Nr of bonds; Edis1;LPpen;n.u.;pbe1;pbo5;13corr;pbo6 pbe2;pbo3;pbo4;n.u.;pbo1;pbo2;ovcorr
11158.200499.189778.0000−0.7738−0.45501.000037.61170.4147\begin{array}{llllllllll}1 & 1 & 158.2004 & 99.1897 & 78.0000 & -0.7738 & -0.4550 & 1.0000 & 37.6117 & 0.4147\end{array} 0.4590−0.10009.16281.0000−0.07776.72681.00000.00000.4590-0.1000 \quad 9.1628 \quad 1.0000-0.0777 \quad 6.7268 \quad 1.0000 \quad 0.0000
12169.47600.00000.0000−0.60830.00001.00006.00000.7652\begin{array}{llllllllll}1 & 2 & 169.4760 & 0.0000 & 0.0000 & -0.6083 & 0.0000 & 1.0000 & 6.0000 & 0.7652\end{array} 5.22901.00000.00001.0000−0.05006.91360.00000.00005.2290 \quad 1.0000 \quad 0.0000 \quad 1.0000-0.0500 \quad 6.9136 \quad 0.0000 \quad 0.0000
22153.39340.00000.0000−0.46000.00001.00006.00000.7300\begin{array}{llllllllll}2 & 2 & 153.3934 & 0.0000 & 0.0000 & -0.4600 & 0.0000 & 1.0000 & 6.0000 & 0.7300\end{array} 6.25001.00000.00001.0000−0.07906.05520.00000.00006.2500 \quad 1.0000 \quad 0.0000 \quad 1.0000-0.0790 \quad 6.0552 \quad 0.0000 \quad 0.0000
13158.6946107.458323.3136−0.4240−0.17431.000010.82091.0000\begin{array}{llllllllll}1 & 3 & 158.6946 & 107.4583 & 23.3136 & -0.4240 & -0.1743 & 1.0000 & 10.8209 & 1.0000\end{array} 0.5322−0.31137.00001.0000−0.14475.24500.00000.00000.5322-0.3113 \quad 7.0000 \quad 1.0000-0.1447 \quad 5.2450 \quad 0.0000 \quad 0.0000
23160.00000.00000.0000−0.57250.00001.00006.00000.5626\begin{array}{llllllllll}2 & 3 & 160.0000 & 0.0000 & 0.0000 & -0.5725 & 0.0000 & 1.0000 & 6.0000 & 0.5626\end{array} 1.11501.00000.00000.0000−0.09204.27900.00000.00001.1150 \quad 1.0000 \quad 0.0000 \quad 0.0000-0.0920 \quad 4.2790 \quad 0.0000 \quad 0.0000
33142.2858145.000050.82930.2506−0.10001.000029.75030.6051\begin{array}{llllllllll}3 & 3 & 142.2858 & 145.0000 & 50.8293 & 0.2506 & -0.1000 & 1.0000 & 29.7503 & 0.6051\end{array} 0.3451−0.10559.00001.0000−0.12255.50001.00000.00000.3451-0.1055 \quad 9.0000 \quad 1.0000-0.1225 \quad 5.5000 \quad 1.0000 \quad 0.0000
14124.66510.00000.00000.8374−0.30000.000036.00000.0100\begin{array}{llllllllll}1 & 4 & 124.6651 & 0.0000 & 0.0000 & 0.8374 & -0.3000 & 0.0000 & 36.0000 & 0.0100\end{array} 1.8311−0.350025.00001.0000−0.23374.66030.00000.00001.8311-0.3500 \quad 25.0000 \quad 1.0000-0.2337 \quad 4.6603 \quad 0.0000 \quad 0.0000
2488.13570.00000.0000−0.6715−0.30000.000036.00000.0208\begin{array}{llllllllll}2 & 4 & 88.1357 & 0.0000 & 0.0000-0.6715 & -0.3000 & 0.0000 & 36.0000 & 0.0208\end{array} 9.9192−0.350025.00001.0000−0.10145.52680.00000.00009.9192-0.3500 \quad 25.0000 \quad 1.0000-0.1014 \quad 5.5268 \quad 0.0000 \quad 0.0000
34175.25170.00000.0000−0.8707−0.30000.000036.00000.0100\begin{array}{llllllllll}3 & 4 & 175.2517 & 0.0000 & 0.0000-0.8707 & -0.3000 & 0.0000 & 36.0000 & 0.0100\end{array} 0.9278−0.350025.00001.0000−0.11834.65330.00000.00000.9278-0.3500 \quad 25.0000 \quad 1.0000-0.1183 \quad 4.6533 \quad 0.0000 \quad 0.0000
4465.77420.00000.0000−0.4111−0.30000.000016.00000.2955\begin{array}{llllllllll}4 & 4 & 65.7742 & 0.0000 & 0.0000-0.4111 & -0.3000 & 0.0000 & 16.0000 & 0.2955\end{array} 2.8637−0.419714.30851.0000−0.19934.87570.00000.00002.8637-0.4197 \quad 14.3085 \quad 1.0000-0.1993 \quad 4.8757 \quad 0.0000 \quad 0.0000
5595.100363.019330.00000.1000−0.30001.000016.00000.0755\begin{array}{llllllllll}5 & 5 & 95.1003 & 63.0193 & 30.0000 & 0.1000-0.3000 & 1.0000 & 16.0000 & 0.0755\end{array} 0.1062−0.64206.18111.0000−0.06028.17210.00000.00000.1062-0.6420 \quad 6.1811 \quad 1.0000-0.0602 \quad 8.1721 \quad 0.0000 \quad 0.0000
25197.25650.00000.0000−0.49490.00001.00006.00000.5000\begin{array}{llllllllll}2 & 5 & 197.2565 & 0.0000 & 0.0000-0.4949 & 0.0000 & 1.0000 & 6.0000 & 0.5000\end{array} 14.07001.00000.00001.0000−0.08225.09480.00000.000014.0700 \quad 1.0000 \quad 0.0000 \quad 1.0000-0.0822 \quad 5.0948 \quad 0.0000 \quad 0.0000
35179.466927.303743.3991−0.4799−0.30001.000036.00000.1561\begin{array}{llllllllll}3 & 5 & 179.4669 & 27.3037 & 43.3991 & -0.4799 & -0.3000 & 1.0000 & 36.0000 & 0.1561\end{array} 9.5978−0.60315.84401.0000−0.15905.81441.00000.00009.5978-0.6031 \quad 5.8440 \quad 1.0000-0.1590 \quad 5.8144 \quad 1.0000 \quad 0.0000
15161.461847.670843.3991−1.0000−0.30001.000036.00000.0421\begin{array}{llllllllll}1 & 5 & 161.4618 & 47.6708 & 43.3991-1.0000-0.3000 & 1.0000 & 36.0000 & 0.0421\end{array} 10.0094−1.255614.07261.0000−0.06616.59651.00000.000010.0094-1.2556 \quad 14.0726 \quad 1.0000-0.0661 \quad 6.5965 \quad 1.0000 \quad 0.0000
45139.68850.00000.0000−0.4520−0.20000.000016.00000.5199\begin{array}{llllllllll}4 & 5 & 139.6885 & 0.0000 & 0.0000-0.4520 & -0.2000 & 0.0000 & 16.0000 & 0.5199\end{array} 8.1108−0.200015.00001.0000−0.11084.07290.00000.00008.1108-0.2000 \quad 15.0000 \quad 1.0000-0.1108 \quad 4.0729 \quad 0.0000 \quad 0.0000
10 ! Nr of off-diagonal terms; Edisc;Ro;gamma;vigma;rpi;rpi2
120.12391.40049.84671.1210−1.0000−1.0000\begin{array}{llllllllll}1 & 2 & 0.1239 & 1.4004 & 9.8467 & 1.1210 & -1.0000 & -1.0000\end{array} 130.11561.85209.83171.28541.13521.0706\begin{array}{llllllllll}1 & 3 & 0.1156 & 1.8520 & 9.8317 & 1.2854 & 1.1352 & 1.0706\end{array} 230.02831.288510.91900.9215−1.0000−1.0000\begin{array}{llllllllll}2 & 3 & 0.0283 & 1.2885 & 10.9190 & 0.9215 & -1.0000 & -1.0000\end{array} 140.33931.468312.53621.4713−1.0000−1.0000\begin{array}{llllllllll}1 & 4 & 0.3393 & 1.4683 & 12.5362 & 1.4713 & -1.0000 & -1.0000\end{array} 240.06161.484611.65041.6956−1.0000−1.0000\begin{array}{llllllllll}2 & 4 & 0.0616 & 1.4846 & 11.6504 & 1.6956 & -1.0000 & -1.0000\end{array} 340.37451.81799.73591.4165−1.0000−1.0000\begin{array}{llllllllll}3 & 4 & 0.3745 & 1.8179 & 9.7359 & 1.4165 & -1.0000 & -1.0000\end{array} 250.06561.393913.61701.2520−1.0000−1.0000\begin{array}{llllllllll}2 & 5 & 0.0656 & 1.3939 & 13.6170 & 1.2520 & -1.0000 & -1.0000\end{array} 350.10091.748412.45271.77701.3682−1.0000\begin{array}{llllllllll}3 & 5 & 0.1009 & 1.7484 & 12.4527 & 1.7770 & 1.3682 & -1.0000\end{array} 150.26551.909711.18861.99831.3682−1.0000\begin{array}{llllllllll}1 & 5 & 0.2655 & 1.9097 & 11.1886 & 1.9983 & 1.3682 & -1.0000\end{array} 450.20002.100011.50001.9916−1.0000−1.0000\begin{array}{llllllllll}4 & 5 & 0.2000 & 2.1000 & 11.5000 & 1.9916 & -1.0000 & -1.0000\end{array} 67!Nr of angles;at1;at2;at3;Thetao,n;ka;kbr;pv1;pv2 \begin{array}{llllllllll}67 & ! \mathrm{Nr} \text { of angles;at1;at2;at3;Thetao,n;ka;kbr;pv1;pv2 }\end{array} 11159.057330.70290.76060.00000.71806.29331.1244\begin{array}{llllllllll}1 & 1 & 1 & 59.0573 & 30.7029 & 0.7606 & 0.0000 & 0.7180 & 6.2933 & 1.1244\end{array} 1265.775814.52346.24810.00000.56650.00001.6255\begin{array}{llllllllll}1 & 2 & 65.7758 & 14.5234 & 6.2481 & 0.0000 & 0.5665 & 0.0000 & 1.6255\end{array} 21270.260725.22023.73120.00000.00500.00002.7500\begin{array}{llllllllll}2 & 1 & 2 & 70.2607 & 25.2202 & 3.7312 & 0.0000 & 0.0050 & 0.0000 & 2.7500\end{array} 11349.68117.17134.38890.00000.717110.26611.0463\begin{array}{llllllllll}1 & 1 & 3 & 49.6811 & 7.1713 & 4.3889 & 0.0000 & 0.7171 & 10.2661 & 1.0463\end{array} 21365.000013.88155.05830.00000.49850.00001.4900\begin{array}{llllllllll}2 & 1 & 3 & 65.0000 & 13.8815 & 5.0583 & 0.0000 & 0.4985 & 0.0000 & 1.4900\end{array} 31377.747340.17182.9802−25.30631.6170−46.13152.2503\begin{array}{llllllllll}3 & 1 & 3 & 77.7473 & 40.1718 & 2.9802 & -25.3063 & 1.6170 & -46.1315 & 2.2503\end{array} 1210.00003.41107.73500.00000.00000.00001.0400\begin{array}{llllllllll}1 & 2 & 1 & 0.0000 & 3.4110 & 7.7350 & 0.0000 & 0.0000 & 0.0000 & 1.0400\end{array} 1220.00000.00006.00000.00000.00000.00001.0400\begin{array}{llllllllll}1 & 2 & 2 & 0.0000 & 0.0000 & 6.0000 & 0.0000 & 0.0000 & 0.0000 & 1.0400\end{array} 1230.000025.00003.00000.00001.00000.00001.0400\begin{array}{llllllllll}1 & 2 & 3 & 0.0000 & 25.0000 & 3.0000 & 0.0000 & 1.0000 & 0.0000 & 1.0400\end{array} 2220.000027.92135.86350.00000.00000.00001.0400\begin{array}{llllllllll}2 & 2 & 2 & 0.0000 & 27.9213 & 5.8635 & 0.0000 & 0.0000 & 0.0000 & 1.0400\end{array} 2230.00008.57443.00000.00000.00000.00001.0421\begin{array}{llllllllll}2 & 2 & 3 & 0.0000 & 8.5744 & 3.0000 & 0.0000 & 0.0000 & 0.0000 & 1.0421\end{array} 3230.000015.00002.89000.00000.00000.00002.8774\begin{array}{llllllllll}3 & 2 & 3 & 0.0000 & 15.0000 & 2.8900 & 0.0000 & 0.0000 & 0.0000 & 2.8774\end{array} 13173.531244.72750.73540.00003.00000.00001.0684\begin{array}{llllllllll}1 & 3 & 1 & 73.5312 & 44.7275 & 0.7354 & 0.0000 & 3.0000 & 0.0000 & 1.0684\end{array} 13379.476136.37011.89430.00000.735167.67773.0000\begin{array}{llllllllll}1 & 3 & 3 & 79.4761 & 36.3701 & 1.8943 & 0.0000 & 0.7351 & 67.6777 & 3.0000\end{array} 13270.188020.95620.38640.00000.00500.00001.6924\begin{array}{llllllllll}1 & 3 & 2 & 70.1880 & 20.9562 & 0.3864 & 0.0000 & 0.0050 & 0.0000 & 1.6924\end{array} 23285.80009.84532.27200.00002.86350.00001.5800\begin{array}{llllllllll}2 & 3 & 2 & 85.8000 & 9.8453 & 2.2720 & 0.0000 & 2.8635 & 0.0000 & 1.5800\end{array} 23375.693550.00002.00000.00001.00000.00001.1680\begin{array}{llllllllll}2 & 3 & 3 & 75.6935 & 50.0000 & 2.0000 & 0.0000 & 1.0000 & 0.0000 & 1.1680\end{array} 33380.732430.45540.99530.00001.631050.00001.0783\begin{array}{llllllllll}3 & 3 & 3 & 80.7324 & 30.4554 & 0.9953 & 0.0000 & 1.6310 & 50.0000 & 1.0783\end{array} 134104.609427.23249.05490.00002.32140.00001.1378\begin{array}{llllllllll}1 & 3 & 4 & 104.6094 & 27.2324 & 9.0549 & 0.0000 & 2.3214 & 0.0000 & 1.1378\end{array} 23490.000011.12124.33790.00003.00000.00003.0000\begin{array}{llllllllll}2 & 3 & 4 & 90.0000 & 11.1212 & 4.3379 & 0.0000 & 3.0000 & 0.0000 & 3.0000\end{array} 33443.628011.07506.62000.00003.00000.00001.0100\begin{array}{llllllllll}3 & 3 & 4 & 43.6280 & 11.0750 & 6.6200 & 0.0000 & 3.0000 & 0.0000 & 1.0100\end{array} 43464.551310.59871.04710.00003.00000.00001.6045\begin{array}{llllllllll}4 & 3 & 4 & 64.5513 & 10.5987 & 1.0471 & 0.0000 & 3.0000 & 0.0000 & 1.6045\end{array}

3232.1200−3.58001.450019.50003232.1200-3.58001 .450019 .5000

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