Introduction

Thermoelectric generators have attracted considerable interest owing to the increasing demand for energy harvesting technologies1,2. In particular, flexible thermoelectric devices that can be deployed in diverse environments have significant potential for internet of things applications, such as remote sensing3,4,5,6. The figure of merit (ZT) of a thermoelectric device is a measure of its heat-to-electricity conversion performance. It is expressed as ZT = σS2 T κ−1 = PF κ−1, where σ, S, κ, PF, and T denote the electrical conductivity, Seebeck coefficient, thermal conductivity, power factor, and ambient temperature, respectively. Each parameter is influenced by the carrier density and scattering factors (phonon scattering, alloy scattering, etc.), creating a trade-off relationship among these parameters7,8,9,10,11. Consequently, when the ZT of a material is increased, its electronic and thermal transport properties need to be optimized. Narrow bandgap III–V compound semiconductors are promising candidates for achieving thermoelectric thin films that utilize micro-energy near room temperature (RT)12,13,14,15. However, the performance optimization of the III–V compound semiconductors needs considerable effort because of their large number of possible combinations16,17,18,19.

Recently, several innovative techniques have been developed based on machine learning; these techniques include high-dimensional-parameter search techniques such as Bayesian optimization (BO)20,21,22,23,24,25. The efficacy of BO has been demonstrated with thin-film thermoelectric materials such as Bi2Te326,27,28,29,30,31. BO may be particularly effective for multicomponent thermoelectric thin films with many parameters. Group III–V compound semiconductors are receiving increased attention mainly as single-crystal materials; however, from the perspective of thermoelectric applications, polycrystalline materials are preferable because they can utilize phonon scattering. Reports on the polycrystalline III–V compound thin films are limited but indicate that these compounds can be formed at relatively low temperatures32,33,34,35,36. These results indicate the possibility of fabricating a plastic-film-based III–V compound thermoelectric film. In this study, we propose a BO-based ZT optimization approach, focusing on Sn-doped polycrystalline In1−xGaxAs1−ySby thin films. These films provide a large search space with modifiable crystal and transport properties. We succeeded in improving ZT by nearly three times with only six cycles. Furthermore, we elucidated the pivotal guidelines for improving the ZT of the polycrystalline InGaAsSb thin films.

Results

Figure 1 shows a schematic diagram of the experimental cycle used in this study. The BO model learns the relationship between the previous experimental conditions and objective values and then predicts new experimental conditions that can lead to the highest degree of improvement. We repeated the following cycles: (i) thin-film deposition, (ii) thermoelectric property measurements, and (iii) BO recommendations.

Fig. 1: Schematic of the experimental cycles.
figure 1

The following cycle is repeated: (i) thin-film deposition, (ii) thermoelectric property measurements, and (iii) BO recommendations.

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Figure 2 shows the influence of the substrate temperature (Tsub) on the crystallinity of In1−xGaxAs1−ySby films not doped with Sn. The Ga-cell temperature (TGa-cell), As-cell temperature (TAs-cell), and Sb-cell temperature (TSb-cell) were set as 977 °C, 255 °C, and 430 °C, respectively, and the Sn-cell temperature (TSn-cell) was set to RT. These cell temperatures corresponded to those that yield approximately x = y = 0.5 at Tsub = 400 °C. As shown in the scanning electron microscopy (SEM) images in Fig. 2a–c, the surface morphology of the samples depended on Tsub. As Tsub varied, the grain size of the samples varied, ranging from approximately 100 nm to 500 nm. According to the energy dispersive X-ray (EDX) mapping, the composition of In1−xGaxAs1−ySby was uniform in these SEM images (Supplementary Fig. S1). We derived the composition ratio from the EDX spectra obtained from the samples. As shown in Fig. 2d, for Tsub ≤ 500 °C, the composition of In1−xGaxAs1−ySby remained largely consistent at x = y = 0.5. However, at Tsub = 600 °C, the proportion of Sb decreased. These results indicated that Sb tended to evaporate at high temperatures, with the resulting deficiency compensated by As. As shown in Fig. 2e, all samples exhibited three X-ray diffraction (XRD) patterns corresponding to polycrystalline InGaAsSb. Crystallization at temperatures as low as 100 °C is highly conducive to the development of the III–V compound films on plastic films29,30,31. The peaks shifted to higher angles as Tsub increased, which was attributed to the decrease in the lattice constant, likely due to the compositional changes in In1−xGaxAs1−ySby. Therefore, not only cell temperature but also Tsub influenced the composition of In1−xGaxAs1−ySby films, complicating the manual optimization of the experimental conditions.

Fig. 2: Crystal properties of the undoped InGaAsSb films.
figure 2

Scanning electron micrographs of the crystal at Tsub = (a) 100 °C, (b) 400 °C, and (c) 600 °C. (d) Composition ratio obtained from EDX analysis and (e) out-of-plane XRD patterns for Tsub = 100–600 °C. The gray areas indicate the peak positions corresponding to the 111, 220, and 311 orientations of the InGaAsSb crystal. The cell temperatures were fixed at TGa-cell = 977 °C, TAs-cell = 255 °C, and TSb-cell = 430 °C.

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Figure 3a, b shows the electrical and thermoelectric characteristics of the samples discussed above. As shown in Fig. 3a, the carrier concentration (n) significantly depends on Tsub, whereas the mobility (μ) exhibits minimal variations as Tsub increases. The crystal exhibits p-type behaviors at Tsub = 400 °C and 500 °C and n-type behaviors at all other temperatures. This reflects the behavior of the InAs–GaSb alloy, where InAs and GaSb are generally n-type and p-type semiconductors, respectively, at RT37,38. Considering the above results and the findings shown in Fig. 2d, the dependence of the conductivity type on Tsub can be elucidated as follows: at Tsub = 200 °C and 300 °C, the n-type InAs dominate the conductivity; at Tsub = 400 °C and 500 °C, partial replacement of InAs by GaSb results in a p-type conductivity; and at Tsub = 600 °C, Sb evaporates, causing the n-type InAs formation to dominate once again. As shown in Fig. 3b, the sign of S, which indicates the conductivity type, is consistent with the Hall effect measurement results. σ and PF reflect the behavior of n reaches a maximum at Tsub = 200 °C. Figure 3c, d shows the influence of the TSn-cell on the electrical and thermoelectric characteristics of the alloy at Tsub = 400 °C. According to the secondary ion mass spectrometry (SIMS) measurements, the concentrations of Sn in the In1−xGaxAs1−ySby films were 7.8 × 1019, 8.5 × 1020, and 6.3 × 1021 cm−3 at TSn-cell = 800 °C, 900 °C, and 1000 °C, respectively. As shown in Fig. 3c, all Sn-doped samples exhibit n-type conductivity, where n increases with increasing TSn-cell. This occurs because Sn acts as a donor in III–V compound semiconductors39,40. μ exhibits a peak at TSn-cell = 900 °C; this peak is typically observed in polycrystalline semiconductor thin films owing to the balance between grain boundaries and impurity scattering. As shown in Fig. 3d, the σ and PF peaks at TSn-cell = 900 °C reflect the balance between n and μ. In summary, the thermoelectric performance of In1−xGaxAs1−ySby thin films depends not only on the elemental composition of the III–V semiconductors but also on the substrate temperature and Sn doping levels. Based on these results, the Tsub and TSn-cell ranges were set to 100–600 °C and 600–1000 °C, respectively, for the BO of ZT.

Fig. 3: Electrical and thermoelectrical properties of the InGaAsSb films.
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The influence of Tsub on (a) n and μ and (b) σ, S, and PF of the samples fabricated without Sn addition. The influence of the TSn-cell on (c) n and μ and (d) σ, S, and PF at Tsub = 400 °C. The cell temperatures were fixed at TGa-cell = 977 °C, TAs-cell = 255 °C, and TSb-cell = 430 °C. The open and closed symbols denote p-type and n-type conduction, respectively, as shown in the inset in b.

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We investigated the influence of the In1−xGaxAs1−ySby composition on κ. Figure 4 illustrates the dependence of κ on the composition of an Sn-free sample at Tsub = 400 °C. Compositional alloying decreased κ, which could be reasonably attributed to enhanced alloy scattering. The introduction of In and Sb was particularly effective at reducing κ, which agreed with that they were relatively heavy metallic elements. At x = y = 0.5, κ reached a low value of 1.05 W m−1 K−1. At Tsub = 100 °C, the κ of the sample was 0.57 W m−1 K−1 at x = y = 0.5. These results indicated that crystallinity decreased with decreasing Tsub, which also decreased κ. In contrast, κ was independent of TSn-cell within the experimental conditions of this study. This behavior was consistent with the fact that Sn was added at the doping level. Based on the above findings and previous studies7,8, we fitted κ to the experimental results using six parameters (WInAs, WGaAs, WInSb, WGaSb, a, κ0) as follows:

$$\begin{array}{ll}\kappa =\left[\right.{W}_{{\rm{InAs}}}(1{\rm{-}}x)(1{\rm{-}}y)+{W}_{{\rm{GaAs}}}(1{\rm{-}}x)y+{W}_{{\rm{InSb}}}x(1{\rm{-}}y)\\\qquad+\,{W}_{{\rm{GaSb}}}{xy}\left.\right]^{{\rm{-}}1}+a{T}_{{\rm{sub}}}+{\kappa }_{0}.\end{array}$$
(1)
Fig. 4: Influence of the composition of the Sn-free In1−xGaxAs1−ySby films on κ at Tsub = 400 °C.
figure 4

The blue dots represent the measured values, and the curved surface shows the fitting result.

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We executed BO using a Gaussian process regression (GPR) algorithm and the characteristics of the samples prepared under five random conditions (1st–5th cycles) within the search range, which were set as the initial points. The next proposed conditions were predicted to lead to the maximum value of the expected improvement (EI). Figure 5a–e shows the GPR results from the 19th experiment. The figures show the ZT and EI cutting planes and the next proposed condition; these are 5-parameter functions. In this manner, BO optimizes all five parameters simultaneously, as shown in Table 1. As shown in Fig. 5f, the measured and predicted ZT (ZTpred) increase, and the condition variation distance decreases with increasing cycle number. We defined the condition variation distance as the Euclidean distance between the normalized parameters under the previous and subsequent proposed conditions. The ZT and EI values converged to high and small values, respectively, with large fluctuations (Supplementary Fig. S2). The heatmaps of ZTpred corresponding to cross-sections of two parameters under the experimental conditions clearly showed the areas where high ZT was expected (Supplementary Fig. S3). These results indicated that the BO process converged. All samples in this BO cycle were the n-type. The p-type region was not suitable for thermoelectric applications owing to its significantly low σ; hence, exploring this region using the optimization model was deduced to provide the limited value. At the 11th cycle, the sample exhibited a maximum ZT of 0.033, at which Tsub = 205 °C, TGa-cell = 860 °C, TAs-cell = 220 °C, TSb-cell = 350 °C, and TSn-cell = 640 °C. The sample exhibited a composition of x = 0.13 and y = 0.04, a Sn concentration of 9.6 × 1018 cm−3, a κ of 1.76 W m−1 K−1, and a PF of 150.3 μW m−1 K−2. After the 12th cycle, ZTpred and EI exhibited relatively high values, where a finer search in the vicinity of optimal conditions was carried out. As shown in Table 1, among the cell temperatures, the variation in TSb-cell was relatively large, which indicated that the other parameters, such as TGa-cell and TAs-cell, had a more significant influence on ZT. A comparison between the maximum initial points revealed that an approximately threefold improvement in ZT (from an initial value of 0.013) was achieved within only 6 cycles. Notably, BO proposed a low substrate temperature (Tsub = 205 °C), which could potentially facilitate the deposition of InGaAsSb thermoelectric films on plastic substrates and further expand the applicability of this material.

Fig. 5: BO process.
figure 5

a–e Predicted value of ZT (solid red), 95% confidence interval (light red), condition (solid green), and EI (solid blue) at the 19th cycle as a function of (a) Tsub, (b) TGa-cell, (c) TAs-cell, (d) TSb-cell, and (e) TSn-cell. f ZT (red solid red), ZTpred (red dashed line), and distance (blue solid line) with respect to the number of cycles.

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Table 1 Summary of the parameters used in BO. The predicted values of ZT (ZTpred) and EI, the BO model outputs, are also shown for each cycle.
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We systematically organized the sample properties (σ, S, PF, and ZT) as functions of n. As shown in Fig. 6a, b, σ and S increase and decrease, respectively, as n increases. This is a typical behavior exhibited by semiconductor materials. As shown in Fig. 6c, PF has a maximum at approximately n = 1018–1019 cm−3, reflecting the delicate balance between σ and S. As shown in Fig. 6d, ZT also attains its maximum value in the same n range, reflecting the characteristics of PF. A common challenge with BO is the lack of physical insight into the process of optimizing parameters. Therefore, we analyzed the experimental ZT values in terms of the In1−xGaxAs1−ySby composition, Tsub, and TSn-cell. As shown in Fig. 6e, f, achieving a high ZT relies upon three critical factors: a high compositional presence of In and As, low Tsub, and low TSn-cell. This behavior can be interpreted as follows. The incorporation of In increases σ, and the addition of a modest quantity of Sb coupled with a reduced Tsub decreases κ. Furthermore, a decrease in TSn-cell increases S. In reality, the parameters such as σ, S, and κ are entangled in intricate trade-offs; nonetheless, the current BO framework adaptively optimizes these parameters using minimal experimental iterations.

Fig. 6: Thermoelectric properties of In1−xGaxAs1−ySby obtained via BO.
figure 6

The dependence of (a) σ, (b) S, (c) PF, and (d) ZT on n. The color of the dots indicates the cycle number. Composition-dependent ZT of the samples (e) not doped with Sn and (f) at Tsub = 400 °C.

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Discussion

We proposed III–V compound semiconductor thin films as thermoelectric thin films and improved the performance of Sn-doped In1−xGaxAs1−ySby using machine learning. BO was suitable for the rapid identification of the growth conditions that maximized ZT (0.033), and the maximum value of ZT was approximately three times greater than that of the initial sample. This outcome demonstrated the efficacy of the BO model in understanding the fundamental behaviors of the thermoelectric properties of III–V compound semiconductors. The GPR algorithm, which employed material properties as inputs, conclusively revealed that high In composition and low Tsub were particularly effective at increasing ZT. The optimal substrate temperature (Tsub = 205 °C) showed the potential for depositing InGaAsSb thermoelectric thin films onto plastic substrates. Therefore, we demonstrated the efficacy of BO in enhancing the properties of multicomponent thermoelectric materials characterized by diverse and intricate parameter relationships.

Methods

Sample preparation with BO optimization

Sn-doped In1−xGaxAs1−ySby films (thickness: 500 nm) were deposited onto SiO2 glass substrates using a vacuum evaporation system equipped with Knudsen cells. Using BO, we investigated the optimum cell temperatures for Ga, As, Sb, and Sn (TGa-cell = 820–970 °C, TAs-cell = 150–225 °C, TSb-cell = 300–450 °C, and TSn-cell = 600–1000 °C) and the substrate temperature (Tsub = 100–600 °C). The In-cell temperature was varied from 635 °C to 775 °C depending on the TGa-cell used to maintain a film thickness of 500 nm. The deposition time was fixed at 1 h. We executed BO using a GPR algorithm in the Python library GPyOpt41,42,43, with EI as the acquisition function. The 1st–5th cycles of BO training data were randomly created.

Sample evaluation

The samples were examined using a SEM (Hitachi-high-tech SU7000, voltage: 15 kV). In the SEM system, the compositions of In1−xGaxAs1−ySby were determined from the EDX spectra obtained in 25 μm squares. SIMS measurements were conducted to determine the Sn concentration using a PHI ADEPT1010 instrument. The out-of-plane XRD patterns were obtained using a diffractometer (Rigaku SmartLab) equipped with a Ge monochromator (wavelength: 1.54 Å) and a Cu-Kα radiation source (voltage: 40 kV, current: 30 mA). The incident angle was varied from 20 ° to 60 ° in steps of 0.01 °. Hall effect measurements were obtained via the van der Pauw method using a Lake Shore M91-EV system, where n and μ were averaged over ten measurements for each sample. The σ and S values were measured using a ZEM-3 system, in which Ag paste was used to fix the sample to a ceramic stage44,45. The cross-plane κ was measured using a PicoTherm PicoTR.