Thermoelectric Characteristics of Bi2S3-Based Sandwich Materials

There are three related theories of thermoelectric operation that are popular among researchers. These are the Seebeck Effect, the Peltier Effect, and the Thomson Effect. TEG operation occurs when two poles experience a temperature difference that leads to the production of kinetic energy. TEG operation means that when one side of a metal is heated while the other side is cooled, the electrons surrounding the metal atoms on the hot side of the metal have more energy than the corresponding electrons on the cooler side. Thus, it is possible that the hot electrons will have more kinetic energy than the cooler electrons. Generally, these poles consist of two pairs of metal plates called P-type and N-type semiconductors. In principle, the use of this technique is not able to create a large voltage (V), even though various concepts of series or parallel circuits have been carried out which combine the two. This is affected by the connector or connecting material used to combine metal plates (poles) which are also made of metal. This situation influences the direction of stress created by the main material.

Firstly, introduced by Thomas Johan Seebeck in the 1820s, the system is defined as a mechanical system in which a temperature difference produces a voltage, known as the Seebeck effect [14]. A voltage gap (gap potential) can occur in the fusion of semiconductor poles which carry opposite temperature gradients (∆T). Temperature changes occur on both sides of the semiconductor plate where the substance is cooled or heated. This cold to hot change or vice versa, generates kinetic energy which creates an electrical voltage that can be utilized. The theory can be formulated as:

$S=-\frac{\Delta V}{\Delta T}$    (1)

The Seebeck effect (S) is the very basis of TEGs, wherein a temperature difference across a material induces an electric potential. For thermoelectric materials, the Seebeck coefficient measures voltage per unit temperature difference. A higher Seebeck coefficient improves voltage output for a given temperature gradient [19, 20]. Bi₂Te₃-based thermoelectric materials hold promise for their potential energy harvesting in thermal-to-electrical energy conversion and also for cooling. Doping with elements such as Sn in Bi₂Se₃ nanosheets has improved Seebeck coefficients and reduced thermal conductivity [21]. Other approaches include the introduction of dense dislocation arrays, dispersion of nano-SiC particles [22], and topological insulator boundary states studies in Bi₂Te₃ thin films for potential thermoelectric improvements [23]. These developments will lead to even higher values of ZT and optimized temperature ranges for both N-type and P-type materials in thermoelectric devices.

Thermoelectric simulations should consider the dimensions of the TEG as a problem-solving analysis and usually consist of elements P-legs and N-legs. When the process enters steady state, all the energy is transferred through the hot side pole and released at the cold side junction. It is characterized by constant temperature gradients and steady heat flows from hotter to colder poles. To define the power flowing through both sides (hot side and cold side) of the module, we can calculate according to study [24]:

$P_c=n\left[I T_h a-\frac{1}{2} I^2 R+K\left(T_h-T_c\right)\right]$    (2)

$P_h=n\left[I T_h a-\frac{1}{2} I^2 R+K\left(T_h-T_c\right)\right]$    (3)

To be able to calculate the power generated on both sides, we need to calculate the Seebeck coefficient ($a$). Meanwhile, in the derivation stage, it is possible to ignore heat loss and heat and electricity contact resistance. This step is enough to calculate the power passing through each module. The formulas for the $a$, thermoelectric resistance (R), and thermal conductivity (K) can be expressed as [25, 26]:

$a=\left(a_p-a_n\right)$    (4)

$R=\frac{\rho_{p L}}{A_p}-\frac{\rho_{n L}}{A_n}$     (5)

$K=\frac{1}{L}\left(K_p A_p+K_n A_n\right)$     (6)

Considering the external load resistance (R_L) and the current (I) generated in the system, the generated output power can be calculated as:

$P_h-P_c=W=I^2 R_2$    (7)

$I=\frac{a\left(T_{h-} T_c\right)}{R+R_L}$    (8)

TEG Module can be analyzing the efficiency offer as,

$\eta=\frac{\left(P_h-P_c\right)}{P_h}=\eta_c \frac{\beta}{(1-\beta)+(1+\beta)^2\left(Z T_h\right)^{-1} \eta_{c / 2}}$    (9)

Refer to single thermoelectric characteristic by using single leg with TE material, where $\beta=\frac{R_L}{R}, Z=\frac{a^2}{R K}=\frac{a^2}{P K}$, and considering efficiency formula $\eta=\frac{T_h-T_c}{T_h}$, it can be calculate that optimum efficiency at $\beta=\frac{R_L}{R}=\sqrt{1+Z \bar{T}}$ as follow:

$\eta_{\max }=\frac{T_{h-} T_c}{T_h}\left[\frac{\sqrt{1+Z \bar{T}}-1}{\sqrt{1+Z \bar{T}}-\frac{T_c}{T_h}}\right]$    (10)

$\bar{T}$ in this calculation means the average between $T_h$ and $T_c$.

The Thomson effect became the next development theory, introduced for the first time by an English physicist named William Thomson (1854). The core of this concept lies in the use of a single plate of material that has a temperature difference along its current circuit. This concept allows you to measure the current flowing through the plate and the amount of heat loss caused by the temperature difference. This distinguishes it from his previous two concepts.

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(a) Seebeck effect

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(b) Peltier effect

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(c) Thomson effect demonstration

Figure 1. Thermoelectric working principle [14]

Numerical modeling and simulations are used in this study as detailed prediction methods for TE performance. The design framework for the proposed idea plan was created using the Solidwork software application, and the numerical analysis was performed using the ANSYS software application. This application is widely used by researchers for modeling studies in various fields such as materials, CFD, stress, torsion, FEM and others [27-30]. References for setting the input parameters for this modeling are given in Table 1. These parameters serve as a reference for possible variations to find the best performance. To explain the thermoelectric concept, a geometric adjustment is required as seen in Figure 1. The development of this model is the result of an analysis of previous studies using different material types, different temperature regimes, stacked with the material sandwich concept. Materials (Cu₂Se+; BiTe+) (Bi₂S₃-; CuFeS-) were used for leg 1 and (PbSe+; BiTe+) (Bi₂S₃-; AgInSe-) were used for leg 2 with a temperature range (ΔT) of 300–1000K. The module height plays an important role in supplying the moving energy in the thermoelectric circuit, being the part to be analyzed.

Table 1. Simulation variation set-up

In this study, a new thermoelectric module structure is designed. Dimension plays important role to the result performance. It predicts absorb area to produce energy, further it should suite with the installation device. Through electrodes, the P and N type legs were thermally coupled in series (as opposed to electrically in parallel), as shown in Figure 2. The geometries under investigation consisted rectangular shape as standard leg geometry chosen. Furthermore, Table 2 shows the module dimension requirement of this numerical study. Simplified calculation and evaluation of the generator's thermoelectric properties. It was discovered that thermoelectric materials have thermal conductivity, and it was investigated how temperature fields cause the diffusion of thermoelectric material carriers from high temperature to low temperature.

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Figure 2. Schematic thermoelectric module

Table 2. Module dimension

This numerical simulation modeling goes through several stages, one of which is meshing. This meshing stage is carried out with a hexagonal mesh shape. The size element is set to capture the phenomena that occur. In the copper and ceramic parts, the mesh size is made at a thickness of 0.01 mm and 0.05 mm respectively, while in the leg part it is made with a size of 0.1 mm with a global mesh size of 0.1 mm [31].

4.1 Power output

Analysis of power generation was done by mathematical calculations. Modeling was carried out step by step considering the running process according to the specifications. Temperature raw material data was categorized according to data collection criteria under the same constraints. In order to get perfect comparison results, a simulation was repeated to see the visibility of the data while still considering the material specifications and the designed geometric model. Data analysis is performed critically and carefully to minimize various aspects of possible errors. The output power produced by the module is shown in Figure 4. It can be clearly seen that the difference in the sandwich material of the thermoelectric legs affects the output. Configuration A1 gives better results than configuration A2. However, they both show the same trend line trend pattern. The height of the modules that produce the best performance in configurations A1 and A2 equals t=10 mm. However, module A shows a more optimal performance effect.

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Figure 4. Power output (A) Module A1, (B) Module A2, (C) Module A1 vs Module A2

Output power is the basis of the first consideration when choosing a TEG [35]. In principle, the temperature distribution (ΔT) can also be widened by excessive leakage. This condition can have a direct impact on material conditions such as: warping, stress, and even damage to other components. Every material can experience degradation of properties as a result of the shock of flowing heat [36]. The worst risk is causing the device to not function. Sufficiency of power is another factor so that it can be installed on certain objects. Optimal selection of modules with good thermal conductivity minimizes the occurrence of Joule heating (temperature rise due to current flowing through the circuit). The performance trend results show that the material is of safe specification. This result is suitable for use as a low to medium power generator. 

Figure 5 shows the relationship between current and generated power. This module provides an interesting and diverse set of criteria. We can use the A1-10 mm configuration for low current TEG with large power. Simultaneously we can use A2-10 mm and A1-15 to achieve large currents with optimum power. A2 is the lowest specification of the configuration displayed. The displayed power output gives a positive outlook and has a significant impact according to the thermoelectric instrument in operation. The optimum power that can be generated is 27.385 Watt, while the optimum current that can be achieved is 700 mA. One of the CuFeS- containing A1 building materials has a relatively low thermoelectric power as shown in Figure 6, but the sandwich diffusion process with other materials does not affect the performance degradation. A2 contains a PbSe+ constituent material, while A2-20 has low performance. The most optimum module height to produce maximum power is at 10 mm, both A1 and A2. The presence of the AgInSe- component in A2 shows that a low electric resistivity value can decrease the performance of the power generated.

The thermal conductivity value also affects the voltage generated. Higher thermal conductivity has a greater impact on the voltage that can be generated. The A1-10 configuration provides maximum performance, this is in line with the supporting material properties that have good thermal conductivity. In contrast, the A2-20 module has the lowest output, but is still within the ideal voltage range. This graphic makes it clear that the designed module is suitable for further development.

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Figure 5. Power output vs. Ampere

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Figure 6. Power output vs. electric voltage

4.2 Efficiency

Figure 7 shows the designed model efficiency data. Material composition can significantly improve efficiency. The geometric design is suitable for conducting electricity with temperature differences between 300° and 1000°K. The chart confirms that the designed module configuration has a positive impact on increasing power output and is suitable for manufacturing. Although TEG efficiency is generally lower than other energy sources, its use remains popular. The main reason for the numerous studies related to this is that the tool can withstand extreme conditions without any special precautions [8]. Choosing a material with good thermal conductivity helps increase TEG efficiency. Furthermore, the choice of N-type or P-type material affects the ability to absorb temperature, improving efficiency [24].

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Figure 7. Efficiency

4.3 Compatibility

Compatibility analysis is used to check the eligibility of modules for using as TEG configurations. Figure 8 shows the estimated material compatibility of N-type and P-type. Both have different compatibility factors, but the difference is greater than 2, indicating a normal criterion. The s-factor and z addition play an important role in the efficient operation of TEGs and are very reasonable criteria for choosing TE materials designed for a particular engineered device. At the N pole, Bi₂S₃ is known to fail to reach the optimum temperature, but the trend is decreasing. On the other hand, CuFeS- in the graph actually gives a positive interaction. The condition of the chart shows the variations in the trend of the changing data for both N-type and P-type. Simulation data show that the TE material can be used as a leg-TEG configuration.

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Figure 8. Compatibility factor of material (a) N-type, (b) P-type

4.4 Temperature distribution

The module flow temperature indicates a thermal degradation of heat per unit volume. The resulting internal heat plays an important role in determining the amount of contact resistance in the binderies during the process. Figure 9 shows that the distribution is influenced by the constituent materials used. Module thickness affects the color degradation that occurs. With increasing material thickness, the temperature on the cold side of the TEG will be reduced due to increasing thermal resistance of the thickness. In effect, this spreads the temperature gradient across the thickness to make it much more gradual, hence making the distribution of heat somewhat much more uniform and avoiding hotspots. This is not meant to imply 'normal', but rather a more smooth and controlled temperature gradient. Those data performed, was analyzed by using ANSYs software, where it’s the temperature distribution was generated using finite element analysis, commonly used to simulate thermoelectric heat transfer and thermal effects.

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Figure 9. Temperature distribution

The combination of F10, there appears to be a proper distribution of temperature gradient with respect to the module. This even distribution could arise due to the inherent good thermal conductivity in the layers Cu₂Se and BiTe, allowing heat to pass through with relatively less hindrance. On the cold side, the presence of Bi₂S₃ and Cu₂FeS introduces some resistances that could balance the thermoelectric efficiency to hold more heat on the hot side and maintain the gradient.

According to G10, the temperature distribution remains very close to the previous one, but with a little twist: substitution including PbSe and AgInSe could contribute to an increase in thermal resistance at some interfaces, which, in turn, might improve the thermoelectric effect due to a reduction in heat leakage. Consequently, there is an increased temperature gradient in certain regions of the thermoelement, which would be helpful for power generation since this increases the effective temperature difference across the thermoelectric elements.

In the case of J15, the thermal distribution in this configuration is uniform, similar to F10. It may indicate that the thermal properties are consistent within the layers of Cu₂Se and BiTe. This can be an indication that the involved combination serves well for heat transfer without losing much thermoelectric gradient. Further, H15 is also similar to G10 in giving a temperature distribution that is more variant, with a great drop of temperature across the thermoelectric layers. Perhaps this could be due to increased thermal resistance caused by the presence of AgInSe and its different thermal properties, which is good for maintaining a strong temperature gradient.

It can be observed from these simulations that all the different configurations give different effects to the temperature distribution and further affect the thermoelectric efficiency. The configurations with AgInSe and Bi₂S₃ have higher gradients, which means higher thermal resistance and thus should help in the thermoelectric effect. In turn, combinations such as Cu₂Se+BiTe have less disparate heat flow that could be appropriate for applications needing balanced thermal dissipation. Further, this analysis supports the potential of Bi₂S₃-based sandwich materials in enhancing TEG performance by carefully selecting material pairing to maximize temperature gradient retention along with energy conversion efficiency.

According to the explained data, the design of the TEG structure uses sandwich model combined with Bi2S3 material. This model has several advantages, including: minimalist structure, simplified shape, and an energy efficiency rate which tends to be 4.2% higher compared to previous research [14]. Furthermore, this design characteristic has possible production requirement, which mean relevant to industry demand for fabrication in large scale.

This work was supported by the Lembaga Penelitian dan Pengabdian kepada Masyarakat (LPPM) Universitas Sebelas Maret (UNS) (Grant No.: 194.2/UN27.22/PT.01.03/2024).