Bayesian Optimization–Driven Design of Hydrogen Concentration in A‑Si/H Multilayers for Silicon Heterojunction Solar Cells

Abstract

Multilayer thin-film passivation structures provide high design flexibility but are inherently challenging to optimize due to the large number of process parameters and their coupled effects. In hydrogenated amorphous silicon (i-a-Si/H) passivation layers, hydrogen concentration plays a critical role in interfacial passivation and film quality, making it a physically meaningful parameter for systematic investigation. In this study, a three-layer i-a-Si/H passivation structure was examined as a representative example to verify an optimization approach that combines physical insight with Bayesian optimization. Rather than treating Bayesian optimization as a black-box search method, hydrogen concentration was explicitly incorporated into the experimental design. A comparative experiment was first conducted on the interfacial layer by varying hydrogen concentration over a wide range, followed by Bayesian optimization of the upper layers using hydrogen flow rate as the control variable. The results demonstrate that a graded hydrogen concentration profile is effective for passivation and validate the proposed approach as a practical framework for optimizing multilayer thin films.

1. Introduction

Multilayer thin-film structures provide significant design flexibility because optical, electrical, and interfacial properties can be tuned independently. Owing to this advantage, they have been widely used in applications such as solar cells, optoelectronic devices, and semiconductor devices. In photovoltaic applications, multilayer structures are commonly used in antireflection coatings, carrier-selective contacts, and absorber layers, enabling combinations of properties that are difficult to achieve with single-layer films. Such multilayer designs are therefore regarded as an effective strategy for incrementally improving device performance beyond the intrinsic limitations of the materials. − In silicon heterojunction (SHJ) solar cells, multilayer thin films also play a key role. Hydrogenated amorphous silicon (a-Si/H) has been commonly used as a passivation layer because it can effectively terminate dangling bonds at the surfaces of crystalline silicon. − However, a-Si/H itself is not a novel material, and its properties as a single layer have been extensively investigated over several decades. − Recently, it has been reported that multilayer configurations of intrinsic a-Si/H-based passivation layers can simultaneously improve interfacial quality, suppress epitaxial growth, and optimize carrier transport, leading to high-efficiency SHJ solar cells. − These studies indicate that even for well-established materials such as a-Si/H, multilayer design provides additional degrees of freedom for performance improvement. On the other hand, the high design freedom of multilayer thin films makes optimization intrinsically challenging. As the number of layers increases, the deposition conditions and compositional parameters grow rapidly, rendering conventional trial-and-error or exhaustive experimental approaches impractical. Moreover, because each layer often plays a different physical role, optimization based on a single performance metric can obscure the underlying physical interpretation. To address this challenge, Bayesian optimization (BO) has attracted attention as an efficient approach for exploring high-dimensional parameter spaces with a limited number of experiments. BO determines subsequent experimental conditions by balancing exploration and exploitation based on probabilistic regression models, and its effectiveness has been demonstrated in various thin-film and solar-cell-related processes. − In this study, multilayer thin-film optimization using BO is examined through a case study of intrinsic a-Si/H-based multilayer passivation films. Instead of aiming to further improve already highly optimized SHJ devices, intrinsic a-Si/H (i-a-Si/H) is adopted here as a representative and well-understood material system to evaluate the applicability of BO to multilayer thin films. By introducing simple modifications that account for material properties and the physical roles of individual layers, BO is used as an experimental design tool tailored for multilayer a-Si/H structures. Through this approach, we aim to demonstrate an efficient optimization framework and extract practical insights that can be applied to the design of multilayer thin-films in general.

2. Experimental Methods

2.1. Fabrication of Multilayer a-Si/H Passivation Films

Prior to describing the optimization procedure, the fabrication process and evaluation metrics for the a-Si/H passivation films are summarized as standard experimental procedures. Thei-a-Si/H films were deposited by plasma-enhanced chemical vapor deposition (PECVD). To enable accurate thickness control, the deposition rate of i-a-Si/H was determined in advance using test samples deposited on quartz glass substrates. Before deposition, the substrates were cleaned sequentially with acetone and methanol to remove organic contaminants. After cleaning, the i-a-Si/H films were deposited on one side of the quartz substrates by PECVD under representative process conditions. The film thickness was measured by a spectroscopic ellipsometer to estimate the deposition rate. Based on this rate, the deposition time for subsequent passivation films was adjusted to achieve the target thickness. To evaluate passivation performance, double-side-polished 6-in. n-type crystalline silicon (c-Si) wafers grown by the Czochralski method were used as substrates. The c-Si wafers had a (100) orientation, a thickness of 280 μm, and a resistivity of 1–5 Ω·cm. Prior to film deposition, the c-Si substrates were cleaned to remove native oxide and suppress surface contamination. The substrates were first immersed in a 2.5% HF solution for 1 min to remove the native oxide layer, followed by rinsing in ultrapure water for 1 min. To protect the surface from contamination before deposition, the substrates were subsequently immersed in a 2.5% H₂O₂ solution for 5 min to form a thin chemical oxide layer, and then rinsed again in ultrapure water for 1 min. Such an ultrathin oxide layer is known to play a beneficial role in silicon heterojunction structures. Specifically, it can suppress undesirable epitaxial growth of a-Si/H at the c-Si interface while maintaining excellent surface passivation and carrier transport properties. , Immediately after cleaning, the substrates were transferred into the PECVD chamber to minimize air exposure. Multilayer i-a-Si/H passivation films were deposited on both sides of the c-Si substrates. The passivation structure consisted of three intrinsic a-Si/H layers with thicknesses of 4, 3, and 3 nm, deposited sequentially on the c-Si interface. After completing deposition on one side, the chamber was vented with high-purity nitrogen, the substrates were flipped, and the same deposition sequence was applied to the opposite side. A schematic illustration of the fabricated three-layer passivation structure is shown in Figure .

1.

Schematic diagram of the three-layer i-a-Si/H passivation structure formed on both sides of a c-Si substrate. L1, L2, and L3 denote the first, second, and third passivation layers, respectively.

2.2. Evaluation Metrics for Passivation Performance and Film Properties

In this study, we introduce an effective performance indicator, denoted as F, to evaluate the passivation quality of the multilayer i-a-Si/H films. This indicator was derived from the conversion efficiency of solar cells, but it allows evaluation without fabricating complete solar cells, thereby significantly reducing the number of samples required for systematic optimization. In addition, device-level measurements are influenced by factors such as doped layers and electrodes, making it difficult to isolate the contribution of the passivation layer alone. To address these issues, an efficiency-related indicator was defined using the saturation current density (J ₀) and film thickness d, following previous studies. − The effective performance indicator F was calculated with the formula shown below. Here, the fill factor (FF) was approximated using empirical fitting functions derived from previously reported experimental data. In eqs and , d represents the numerical value of the film thickness measured in nanometers, and the fitting expressions are empirical formulas applicable when d is expressed in units of nm. The numerical coefficients were determined to ensure dimensional consistency and validity within the fitted thickness range.

$$F(d,J_0)=J_{\mathrm{s}\mathrm{c}}(d)\times V_{\mathrm{o}\mathrm{c}}(J_0)\times FF(d)$$ 1

$$FF=-0.06d^2+0.89d+72.14(0<d\le 18.2\mathrm{n}\mathrm{m})$$ 2

$$FF=94.93\exp (-0.03d)+13.48(18.2\mathrm{n}\mathrm{m}<d<100\mathrm{n}\mathrm{m})$$ 3

In this formulation, the open-circuit voltage (V _oc) was estimated from the saturation current density J ₀ using the ideal diode equation under open-circuit conditions. Assuming that the photogenerated current density is approximately equal to the short-circuit current density (J _ph ≈ J _sc), V _oc can be expressed as

$$V_{\mathrm{o}\mathrm{c}}=\frac{k_{\mathrm{B}}T}{q}\ln (\frac{J_{\mathrm{s}\mathrm{c}}}{J_0}+1)$$ 4

where k _B is the Boltzmann constant, T is the absolute temperature, and q is the elementary charge. Short-circuit current density (J _sc) was estimated from the optical transmittance of the films T(λ) and the air mass 1.5 global (AM1.5G) solar spectrum S _AM1.5G(λ), based on the Lambert–Beer law, using the following equations

$$T(\lambda )=\exp [-\alpha (\lambda )d]$$ 5

$$Jsc=q{\int }_{{\lambda }_{\min }}^{{\lambda }_{\max }}\frac{S_{\mathrm{A}\mathrm{M}1.5\mathrm{G}}(\lambda )}{\frac{hc}{\lambda }}[1-T(\lambda )]\mathrm{d}\lambda$$ 6

where α­(λ) is the absorption coefficient, and standard values for amorphous silicon (a-Si/H) were used. q is the elementary charge, h is the Planck constant, and c is the velocity of light. The fill factor (FF) was approximated as a quadratic function of film thickness, based on the proportionality between electrical conductivity and thickness. − Although this approximation introduces some uncertainty, its influence on the present study is limited because the total thickness was fixed at 10 nm for all samples.

The functional relationship between the fill factor and thickness is illustrated in Figure .

2.

Relationship between the fill factor (FF) and i-a-Si/H thickness d. For the thin-film region (0 < d ≤ 18.2 nm), FF was approximated by a second-order polynomial function, whereas for the thicker-film region (18.2 < d ≤ 100 nm), FF was described by an exponential decay function.

To evaluate the multilayer passivation films, both passivation performance and material properties were measured. The saturation current density J ₀ was determined by quasi-steady-state photoconductance (QSSPC) measurements, which are widely used to evaluate surface passivation quality (Figure S1, Supporting Information). , Film thickness d was measured by spectroscopic ellipsometry to account for possible deviations from the target thickness determined by the deposition rate. The effective performance indicator F was then calculated from the measured J ₀ and d. It should be noted that F is defined based on several simplifying assumptions, which inevitably introduce uncertainties, and therefore F should not be interpreted as an absolute predictor of final device efficiency. Since the primary objective in this work is to establish an effective optimization framework and to elucidate the relationship between hydrogen distribution in multilayer i-a-Si/H films and passivation properties, the use of F provides a practical and sufficiently robust indicator for guiding the Bayesian optimization process.

In addition, the hydrogen concentration (C _H) in the films was evaluated by Fourier-transform infrared spectroscopy (FT-IR) to clarify the relationship between hydrogen incorporation and passivation performance. The infrared transmittance spectrum T(ω) was first normalized by the substrate transmittance T _s, followed by baseline correction. The baseline-corrected transmittance reduction ΔT(ω) was defined as the difference between the baseline and the normalized spectrum, representing the absorption associated with Si–H vibrational modes. Using ΔT(ω) and d, the absorption coefficient α­(ω) was calculated as

$$\alpha (\omega )=-\frac{1}{d}\{-2Ts+\sqrt{4{T_s}^2+{(1-T_s)}^2{(1+T_s)}^2{(\mathrm{\Delta }T)}^2}/{(1-T_s)}^2\mathrm{\Delta }T\}$$ 7

here, ω is the wavenumber (cm^–1), T _s is the transmittance factor of the substrate, and ΔT(ω) is the baseline-corrected transmittance reduction due to absorption in the film (Figure S2, Supporting Information). The absorption coefficient α­(ω) derived from FT-IR transmittance spectra can be overestimated, particularly for thin films, due to the neglect of interference and multiple reflection effects. To account for this, a correction method proposed by Maley et al. was applied.

Specifically, the corrected absorption coefficient α*­(ω) is given by

$${\alpha }^{*}(\omega )=\frac{\alpha (\omega )}{1.72-12\omega d}(\omega d<0.06)$$ 8

The total hydrogen density N _H (cm^–3) was then obtained by integrating α­(ω)/ω over the Si–H stretching-mode absorption region. In eq , A is a proportionality constant (calibration factor) that relates the integrated infrared absorption intensity to the hydrogen density.

$$N_{\mathrm{H}}=A\times \int \frac{\alpha (\omega )}{\omega }\mathbb{d}\omega$$ 9

Finally, the hydrogen concentration C _H (at. %) was calculated by normalizing N _H with the atomic density of crystalline silicon, 5.0 × 10²² cm^–3, and converting it into atomic percent.

$$C_{\mathrm{H}}=\frac{N_{\mathrm{H}}}{5.0\times {10}^{22}}\times 100(\mathrm{a}\mathrm{t}.\%)$$

In this analysis, the substrate transmittance factor T _s was assumed to be 0.53, corresponding to high-resistivity crystalline silicon. It should be noted that the atomic density used in this analysis corresponds to that of crystalline material and is therefore not strictly identical to that of the amorphous phase. This discrepancy may introduce an additional source of uncertainty in the hydrogen concentration estimation. It should be also noted that some uncertainty remains due to assumptions such as uniform film density and thickness. Therefore, the hydrogen concentration values should be interpreted with a certain degree of caution, particularly when comparing absolute values.

2.3. Experimental Workflow and Optimization Procedure

The overall experimental workflow for passivation-film optimization is summarized in Figure .

3.

Overall experimental workflow for passivation-film optimization.

First, the influence of PECVD process parameters on C _H was investigated to identify parameters with a strong impact on film properties. Understanding parameter sensitivity enables more efficient optimization by focusing on dominant variables rather than indiscriminately exploring the entire parameter space. The parameters for the film deposition were determined based on a ref and several samples were fabricated over a wide parameter range. The parameter ranges investigated in this study are summarized in Table , and the sample conditions used in the nuclear reaction analysis (NRA) measurements to examine the contribution of each process parameter to C _H are listed in Table . In this technique, a high-energy ion beam ¹⁵N⁺ is incident on the sample, and hydrogen atoms are detected via a nuclear reaction to result in γ-rays emission. The yield of the emitted γ-rays is proportional to the local hydrogen concentration. Depth profiling is achieved by varying the incident ion energy, which changes the penetration depth of the ions in the sample due to energy-loss processes. As a result, the hydrogen concentration can be obtained as a function of depth. It should be noted that NRA was primarily used to investigate the depth-dependent hydrogen distribution, whereas FT-IR was employed for systematic comparison of hydrogen concentration across the sample set used in the Bayesian optimization.

1. Range of PECVD Process Parameters Investigated in this Study for i-a-Si/H Deposition.

	temperature, T (°C)	hydrogenated flow rate, QH2 (sccm)	pressure, P (Pa)
maximum value	300	200	99
minimum value	210	50	30

2. Representative PECVD Deposition Conditions Used to Examine the Influence of Process Parameters on Hydrogen Concentration in i-a-Si/H Films.

	T (°C)	Q H2 (sccm)	P (Pa)
median	250	125	65
high H2	250	200	65
high P	250	125	99
high T	300	125	65

Although the absolute values obtained from the two techniques may differ, consistent trends were observed, supporting the validity of the conclusions.

Based on this preliminary analysis, a comparative experiment was conducted for the first passivation layer by varying C _H over a wide range while fixing the deposition conditions of the second and third layers. This approach was adopted to identify the C _H range most suitable for the interfacial layer, where suppression of epitaxial growth and defect termination are particularly important. It should be noted that complete elimination of hydrogen dilution was not feasible in the present setup and remains a subject for future investigation. Subsequently, BO was applied to the second and third passivation layers. Five initial samples were fabricated under randomly selected deposition conditions, and the corresponding F values were used as the initial data set for BO. The PECVD process parameters were treated as input variables, and F was defined as the objective function. At each iteration, BO was used to propose the next deposition condition, after which a new sample was fabricated and evaluated. This cycle was repeated to efficiently search for deposition conditions that maximize F. To further improve optimization efficiency, prior experimental data were incorporated through transfer learning. In the previous data set, carrier lifetimes corresponding to various deposition parameters had been measured. These data were converted into J ₀ using eq and then used to estimate the variance of F for similar process conditions.

$$\frac{1}{{\tau }_{\mathrm{e}\mathrm{f}\mathrm{f}}}=\frac{1}{{\tau }_{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}}+\frac{2J_0}{q{n_i}^{2}W}(N_A+\mathrm{\Delta }n)$$ 10

where τ_eff is the effective carrier lifetime, τ_bulk is the bulk carrier lifetime, J ₀ is the saturation current density, q is the elementary charge, n is the carrier density, W is the sample thickness, and N _A is the acceptor concentration. For simplicity and consistency across samples, J ₀ was estimated at a fixed excess carrier density Δn of 1 × 10¹⁶ cm^–3. This approach allows for a straightforward comparison of passivation quality among samples, although it does not fully capture the injection-level dependence of recombination. The obtained variance information was used to tune the hyperparameters of the kernel function employed in BO, enabling more reliable estimation of the expected value and uncertainty. The overall optimization flow, including sample fabrication, evaluation, and BO-assisted condition selection, is summarized in Figure .

4.

The flowchart illustrates the entire experiment using Bayesian Optimization (BO). It is important to note that the substrate temperature was fixed while optimizing the second and third layers.

3. Results and Discussion

3.1. Influence of PECVD Parameters on Hydrogen Concentration

Before applying optimization, the influence of PECVD process parameters on C _H in i-a-Si/H films was investigated using nuclear reaction analysis (NRA). Figure shows the hydrogen depth profiles measured for films deposited under different conditions.

5.

Nuclear reaction analysis (NRA) γ-ray yield spectra of i-a-Si/H films deposited under different PECVD conditions. The spectra were measured as a function of incident N-ion energy, which corresponds to the probing depth in the film. “Median” denotes the reference condition using median values of the investigated parameter ranges, while “high H₂”, “high P”, and “high T” represent samples deposited with increased hydrogen flow rate, chamber pressure, and substrate temperature, respectively, with all other parameters fixed. A lower γ-ray yield indicates a reduced hydrogen concentration in the film.

In these measurements, the vertical axis represents C _H, while the horizontal axis corresponds to the depth from the film surface. To systematically examine parameter sensitivity, a reference condition (denoted as “median”) was defined using the median values of the investigated parameter ranges. For the other samples, only one deposition parameter was increased from the default condition at a time, while the remaining parameters were fixed. The specific combinations of Q _H2 and chamber P used for this analysis are summarized in Table . As shown in Figure , increasing any of the investigated parameters resulted in a decrease in C _H in the film, indicating a negative correlation between C _H and each process parameter. Among them, Q _H2 exhibited the strongest influence, where an increase in flow rate led to the most pronounced reduction in C _H. This counterintuitive trend can be attributed to enhanced hydrogen abstraction and etching effects under high hydrogen flux conditions, which suppress net hydrogen incorporation into the growing film. Based on these results, the deposition parameters to be treated as optimization variables in subsequent experiments were selected, as summarized in Table . It should be noted that the temperature for the second and third layers was fixed at 280 °C.

3. Deposition Parameters for Each Passivation Layer, Indicating Fixed and Variable Conditions Used in This Study.

	T (°C)	P (Pa)	Q H2 (sccm)
L1	210	99–30	50–200
L2	280	50	50–200
L3	280	50	50–200

In particular, Q _H2 and P were selected as key variables for the first passivation layer in order to cover a wide range of C _H. For the second and third layers, Bayesian optimization was performed within the experimental parameter range, and Q _H2, which has the strongest influence on hydrogen incorporation, was chosen as the optimization variable to ensure efficient exploration.

3.2. Comparative Experiment for the First Passivation Layer

Using the results of Sect. 3.1, a comparative experiment was conducted to determine the optimal C _H for the first passivation layer. In Table , the grayscale bar indicates the relative C _H, ranging from porous to dense, and clarifies how each parameter set maps onto the hydrogen content in the deposited films.

4. PECVD Deposition Conditions for the L1 Passivation Layer (i-a-Si/H) and the Corresponding Hydrogen Concentrations C _H obtained for Each Sample.

	porous				dense
Q H2 (sccm)	200	200	100	50	50
P (Pa)	99	30	60	99	30
C H (at %)	29	21	17	16	13

The deposition conditions were selected to cover a wide range of C _H while fixing the conditions of the second and third layers. Figure shows the relationship between C _H and the effective performance indicator F for the first-layer samples.

6.

Relationship between C _H and F in the L1 measured by FTIR.

The results suggest that a positive correlation between F and C _H within the investigated range although the trend is not monotonic, and the highest F value was obtained for the sample with the highest C _H. This behavior indicates that a hydrogen-rich first layer is effective in improving F, owing to its superior passivation quality presumably by the suppression of epitaxial growth at the c-Si interface. However, it is unrealistic to assume that F continues to improve indefinitely with increasing C _H. The existence of an optimal hydrogen concentration is expected, and identifying this maximum remains an important subject for future investigation. Previous studies have reported that higher hydrogen concentrations promote void formation, leading to reduced film density and suppression of Si–Si bond formation. , In particular, it has been reported that film density decreases linearly with hydrogen concentration below approximately 14%, whereas above this threshold, the decrease becomes more pronounced and is attributed to void formation rather than isolated vacancies. In the present study, all investigated samples exhibited C _H values exceeding 14%, suggesting that void-induced density reduction played a dominant role in suppressing epitaxial growth and improving passivation performance.

3.3. Bayesian Optimization for the Second and Third Passivation Layers

Following the determination of the first-layer condition, Bayesian optimization was applied to determine Q _H2 for the second and third passivation layers. In this optimization, Q _H2 was restricted to values ≥ 40 sccm due to operational limitations of the PECVD system, which prevent stable plasma discharge at lower flow rates. Table summarizes the PECVD deposition conditions, specifically Q _H2 for the second and third layers, together with the corresponding F values obtained in each experimental iteration. Figures and show the expected-value surface of F as a function of Q _H2 for the second and third layers and the evolution of F with the number of experiments, respectively.

5. PECVD L1 L2 Passivation Layer (i-a-Si/H) Deposition Conditions and Corresponding Simplified Efficiency F .

number of experiments	Q H2 (sccm) (L1)	Q H2 (sccm) (L2)	F (%)
1	89	170	16.73
2	76	48	17.61
3	153	47	17.43
4	172	153	17.12
5	42	197	18.31
6	40	40	20.39
7	200	40	17.42
8	200	200	17.12
9	132	200	17.30
10	46	40	20.01
11	40	79	20.79
12	40	116	19.95
13	40	56	20.81
14	40	69	21.55
15	40	61	22.38

7.

Expected-value surface of F as a function of the hydrogen flow rates Q _H2 for L1 and L2. The explored parameter space was restricted to Q _H2 ≥ 40 sccm due to operational limitations of the PECVD system.

8.

Change in max F over the number of experiments.

After the initial sampling, BO successfully identified deposition conditions that maximize F within only ten additional experiments. As shown in Table , samples deposited under relatively low Q _H2 tended to exhibit higher F values. The expected-value surface in Figure also predicts a region of high F in the lower-left area of the parameter space, corresponding to lower Q _H2 values for both layers. In Figure , a color bar indicating C _H is overlaid on the parameter space. This color scale was constructed by measuring C _H at several representative points using FT-IR and assuming a linear relationship between hydrogen flow rate Q _H2 and C _H within the investigated range. It should be noted that the linear relationship used here does not fully capture the complexity of the underlying physical plasma processes. Due to this simplification, the following discussion on C _H should be interpreted as general trends rather than precise quantitative evaluation. By correlating C _H with F using this visualization, it is evident that the highest F values were obtained at relatively high C _H values. The deposition temperature for the second and third layers was fixed at 280 °C based on previous reports indicating stable passivation performance in this temperature range although it is known that lowering deposition temperature or P can further increase hydrogen incorporation into a-Si/H films. The optimal conditions for the second and third layers are located near the boundary of the explored parameter space. This suggests that further improvement in performance may be achievable by extending the parameter range. However, such an extension is not straightforward in practice, as the accessible parameter space is constrained by the stability of the PECVD process. In particular, stable plasma generation imposes limitations on the minimum hydrogen flow rate and other deposition conditions. Therefore, the present optimization results should be interpreted within the experimentally accessible parameter space, where reliable and reproducible film deposition can be ensured. Within this practical constraint, the proposed optimization framework successfully identified conditions that significantly improve the passivation performance.

3.4. Optimized Deposition Conditions and Film Quality

Finally, the optimized deposition parameters obtained through the comparative experiment and Bayesian optimization are summarized in Table .

6. Optimized PECVD Deposition Conditions for the Three-Layer Passivation Structure (i-a-Si/H), Including Hydrogen Flow Rate (Q_H2), Chamber Pressure (P), Substrate Temperature (T), Film Thickness (d), and Hydrogen Concentration (C _H) for Each Layer.

	Q H2 (sccm)	P (Pa)	T (°C)	d (nm)	C H (%)
L1	50	30	210	4	29
L2	40	40	280	3	24
L3	61	40	280	3	22

Compared with conventional single-layer passivation films, which typically exhibit hydrogen concentrations of approximately 20%, the optimized multilayer structure shows consistently higher C _H across all layers.

This result is consistent with previous studies reporting that hydrogen-rich passivation layers are effective for dangling-bond termination at the c-Si interface. The optimized three-layer passivation structure derived in this study is schematically illustrated in Figure . The graded C _H profile suggests distinct physical roles of the individual layers. It should be noted that the corresponding microstructural features (e.g., porous or dense characteristics) are inferred qualitatively from the hydrogen concentration, rather than being directly measured or rigorously classified. Despite this limitation, the observed hydrogen distribution provides useful insight into the relationship between layer structure and passivation performance, and highlights the effectiveness of combining comparative experiments with Bayesian optimization for multilayer thin-film design.

9.

Schematic illustration of the optimized three-layer i-a-Si/H passivation structure, showing the graded hydrogen concentration profile and the corresponding microstructural features. In the middle panel, the larger and smaller circles represent silicon and hydrogen atoms, respectively. In the right panel, the highlighted circles indicate void-like regions. These illustrations are intended to provide a qualitative visualization of the inferred structure based on hydrogen concentration and do not represent quantitative structural characterization.

Finally, we note that the proposed framework has the potential to be extended toward more autonomous optimization schemes. − By integrating automated film deposition systems with characterization techniques, it would be possible to construct a closed-loop optimization process driven by Bayesian optimization. In particular, recent advances in robotics-assisted materials synthesis and measurement suggest that fully autonomous optimization of multilayer thin films could be realized in the future. Such an approach would significantly accelerate the exploration of high-dimensional parameter spaces and enable more efficient discovery of optimal structures.

4. Conclusions

We developed an optimization strategy for a three-layer i-a-Si/H passivation structure to improve surface passivation performance. For the first passivation layer, where prior knowledge was available, a comparative experiment was conducted by systematically varying the hydrogen concentration over a wide range to identify favorable conditions. In contrast, for the second and third layers, where the physical roles and optimal conditions were less well understood, Bayesian optimization was applied using Q _H2 as the primary control variable. As a result, the optimized three-layer passivation structure exhibited relatively high hydrogen concentrations, with a gradual decrease from the first layer toward the upper layers. This graded hydrogen concentration profile suggests that a hydrogen-rich and relatively porous structure at the c-Si interface is effective in suppressing epitaxial growth, while denser upper layers with lower hydrogen concentration contribute to reducing bulk defects and maintaining film quality. These findings demonstrate that combining comparative experiments with Bayesian optimization is an effective approach for designing multilayer passivation structures and provide practical guidelines for the rational optimization of complex thin-film systems.

Glossary

Abbreviations

SHJ

silicon heterojunction.

PECVD

plasma-enhanced chemical vapor deposition.

NRA

nuclear reaction analysis.

BO

Bayesian optimization.

FT-IR

Fourier-transform infrared spectroscopy.

a-Si

H, hydrogenated amorphous silicon

i-a-Si

H, intrinsic hydrogenated amorphous silicon

c-Si

crystalline silicon

QSSPC

quasi-steady-state photoconductance

AM1.5G

air mass 1.5 global

HF

hydrofluoric acid

Voc

open-circuit voltage

Jsc

short-circuit current density

FF

fill factor

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsami.6c01687.

• Method for determining J ₀ using QSSPC measurements and an example of FT-IR baseline correction (PDF)

S.K. conceived the study, performed the experiments, and wrote the original manuscript. Y.K., K.K., and N.U. supervised the project and provided critical feedback, and N.U. reviewed and edited the manuscript. T.O., M.W., and K.F. contributed to the experimental design and data interpretation. S.F. assisted with data analysis and visualization. All authors discussed the results and approved the final version of the manuscript.

This work was supported by the New Energy and Industrial Technology Development Organization (NEDO), Japan, under Grant No. JPNP25011. This work is partially supported by Nagoya University Research Fund.

The authors declare no competing financial interest.