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Title: Topology Optimization of Multimaterial Thermoelectric Structures
Abstract A large amount of energy from power plants, vehicles, oil refining, and steel or glass making process is released to the atmosphere as waste heat. The thermoelectric generator (TEG) provides a way to reutilize this portion of energy by converting temperature differences into electricity using Seebeck phenomenon. Because the figures of merit zT of the thermoelectric materials are temperature-dependent, it is not feasible to achieve high efficiency of the thermoelectric conversion using only one single thermoelectric material in a wide temperature range. To address this challenge, the authors propose a method based on topology optimization to optimize the layouts of functional graded TEGs consisting of multiple materials. The multimaterial TEG is optimized using the solid isotropic material with penalization (SIMP) method. Instead of dummy materials, both the P-type and N-type electric conductors are optimally distributed with two different practical thermoelectric materials. Specifically, Bi2Te3 and Zn4Sb3 are selected for the P-type element while Bi2Te3 and CoSb3 are employed for the N-type element. Two optimization scenarios with relatively regular domains are first considered with one optimizing on both the P-type and N-type elements simultaneously, and the other one only on single P-type element. The maximum conversion efficiency could reach 9.61% and more » 12.34% respectively in the temperature range from 25 °C to 400 °C. CAD models are reconstructed based on the optimization results for numerical verification. A good agreement between the performance of the CAD model and optimization result is achieved, which demonstrates the effectiveness of the proposed method. « less
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Journal of Mechanical Design
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National Science Foundation
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  1. Abstract

    Over 50% of the energy from power plants, vehicles, oil refining, and steel or glass making process is released to the atmosphere as waste heat. As an attempt to deal with the growing energy crisis, the solid-state thermoelectric generator (TEG), which converts the waste heat into electricity using Seebeck phenomenon, has gained increasing popularity. Since the figures of merit of the thermoelectric materials are temperature dependent, it is not feasible to achieve high efficiency of the thermoelectric conversion using only one single thermoelectric material in a wide temperature range. To address this challenge, this paper proposes a method based on topology optimization to optimize the layouts of functional graded TEGs consisting of multiple materials. The objective of the optimization problem is to maximize the output power and conversion efficiency as well. The proposed method is implemented using the Solid Isotropic Material with Penalization (SIMP) method. The proposed method can make the most of the potential of different thermoelectric materials by distributing each material into its optimal working temperature interval. Instead of dummy materials, both the P and N-type electric conductors are optimally distributed with two different practical thermoelectric materials, namely Bi2Te3 & PbTe for P-type, and Bi2Te3 & CoSb3more »for N-type respectively, with the yielding conversion efficiency around 12.5% in the temperature range Tc = 25°C and Th = 400°C. In the 2.5D computational simulation, however, the conversion efficiency shows a significant drop. This could be attributed to the mismatch of the external load and internal TEG resistance as well as the grey region from the topology optimization results as discussed in this paper.

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  2. Resonant tunneling diodes (RTDs) have come full-circle in the past 10 years after their demonstration in the early 1990s as the fastest room-temperature semiconductor oscillator, displaying experimental results up to 712 GHz and fmax values exceeding 1.0 THz [1]. Now the RTD is once again the preeminent electronic oscillator above 1.0 THz and is being implemented as a coherent source [2] and a self-oscillating mixer [3], amongst other applications. This paper concerns RTD electroluminescence – an effect that has been studied very little in the past 30+ years of RTD development, and not at room temperature. We present experiments and modeling of an n-type In0.53Ga0.47As/AlAs double-barrier RTD operating as a cross-gap light emitter at ~300K. The MBE-growth stack is shown in Fig. 1(a). A 15-μm-diam-mesa device was defined by standard planar processing including a top annular ohmic contact with a 5-μm-diam pinhole in the center to couple out enough of the internal emission for accurate free-space power measurements [4]. The emission spectra have the behavior displayed in Fig. 1(b), parameterized by bias voltage (VB). The long wavelength emission edge is at  = 1684 nm - close to the In0.53Ga0.47As bandgap energy of Ug ≈ 0.75 eV at 300 K.more »The spectral peaks for VB = 2.8 and 3.0 V both occur around  = 1550 nm (h = 0.75 eV), so blue-shifted relative to the peak of the “ideal”, bulk InGaAs emission spectrum shown in Fig. 1(b) [5]. These results are consistent with the model displayed in Fig. 1(c), whereby the broad emission peak is attributed to the radiative recombination between electrons accumulated on the emitter side, and holes generated on the emitter side by interband tunneling with current density Jinter. The blue-shifted main peak is attributed to the quantum-size effect on the emitter side, which creates a radiative recombination rate RN,2 comparable to the band-edge cross-gap rate RN,1. Further support for this model is provided by the shorter wavelength and weaker emission peak shown in Fig. 1(b) around = 1148 nm. Our quantum mechanical calculations attribute this to radiative recombination RR,3 in the RTD quantum well between the electron ground-state level E1,e, and the hole level E1,h. To further test the model and estimate quantum efficiencies, we conducted optical power measurements using a large-area Ge photodiode located ≈3 mm away from the RTD pinhole, and having spectral response between 800 and 1800 nm with a peak responsivity of ≈0.85 A/W at  =1550 nm. Simultaneous I-V and L-V plots were obtained and are plotted in Fig. 2(a) with positive bias on the top contact (emitter on the bottom). The I-V curve displays a pronounced NDR region having a current peak-to-valley current ratio of 10.7 (typical for In0.53Ga0.47As RTDs). The external quantum efficiency (EQE) was calculated from EQE = e∙IP/(∙IE∙h) where IP is the photodiode dc current and IE the RTD current. The plot of EQE is shown in Fig. 2(b) where we see a very rapid rise with VB, but a maximum value (at VB= 3.0 V) of only ≈2×10-5. To extract the internal quantum efficiency (IQE), we use the expression EQE= c ∙i ∙r ≡ c∙IQE where ci, and r are the optical-coupling, electrical-injection, and radiative recombination efficiencies, respectively [6]. Our separate optical calculations yield c≈3.4×10-4 (limited primarily by the small pinhole) from which we obtain the curve of IQE plotted in Fig. 2(b) (right-hand scale). The maximum value of IQE (again at VB = 3.0 V) is 6.0%. From the implicit definition of IQE in terms of i and r given above, and the fact that the recombination efficiency in In0.53Ga0.47As is likely limited by Auger scattering, this result for IQE suggests that i might be significantly high. To estimate i, we have used the experimental total current of Fig. 2(a), the Kane two-band model of interband tunneling [7] computed in conjunction with a solution to Poisson’s equation across the entire structure, and a rate-equation model of Auger recombination on the emitter side [6] assuming a free-electron density of 2×1018 cm3. We focus on the high-bias regime above VB = 2.5 V of Fig. 2(a) where most of the interband tunneling should occur in the depletion region on the collector side [Jinter,2 in Fig. 1(c)]. And because of the high-quality of the InGaAs/AlAs heterostructure (very few traps or deep levels), most of the holes should reach the emitter side by some combination of drift, diffusion, and tunneling through the valence-band double barriers (Type-I offset) between InGaAs and AlAs. The computed interband current density Jinter is shown in Fig. 3(a) along with the total current density Jtot. At the maximum Jinter (at VB=3.0 V) of 7.4×102 A/cm2, we get i = Jinter/Jtot = 0.18, which is surprisingly high considering there is no p-type doping in the device. When combined with the Auger-limited r of 0.41 and c ≈ 3.4×10-4, we find a model value of IQE = 7.4% in good agreement with experiment. This leads to the model values for EQE plotted in Fig. 2(b) - also in good agreement with experiment. Finally, we address the high Jinter and consider a possible universal nature of the light-emission mechanism. Fig. 3(b) shows the tunneling probability T according to the Kane two-band model in the three materials, In0.53Ga0.47As, GaAs, and GaN, following our observation of a similar electroluminescence mechanism in GaN/AlN RTDs (due to strong polarization field of wurtzite structures) [8]. The expression is Tinter = (2/9)∙exp[(-2 ∙Ug 2 ∙me)/(2h∙P∙E)], where Ug is the bandgap energy, P is the valence-to-conduction-band momentum matrix element, and E is the electric field. Values for the highest calculated internal E fields for the InGaAs and GaN are also shown, indicating that Tinter in those structures approaches values of ~10-5. As shown, a GaAs RTD would require an internal field of ~6×105 V/cm, which is rarely realized in standard GaAs RTDs, perhaps explaining why there have been few if any reports of room-temperature electroluminescence in the GaAs devices. [1] E.R. Brown,et al., Appl. Phys. Lett., vol. 58, 2291, 1991. [5] S. Sze, Physics of Semiconductor Devices, 2nd Ed. 12.2.1 (Wiley, 1981). [2] M. Feiginov et al., Appl. Phys. Lett., 99, 233506, 2011. [6] L. Coldren, Diode Lasers and Photonic Integrated Circuits, (Wiley, 1995). [3] Y. Nishida et al., Nature Sci. Reports, 9, 18125, 2019. [7] E.O. Kane, J. of Appl. Phy 32, 83 (1961). [4] P. Fakhimi, et al., 2019 DRC Conference Digest. [8] T. Growden, et al., Nature Light: Science & Applications 7, 17150 (2018). [5] S. Sze, Physics of Semiconductor Devices, 2nd Ed. 12.2.1 (Wiley, 1981). [6] L. Coldren, Diode Lasers and Photonic Integrated Circuits, (Wiley, 1995). [7] E.O. Kane, J. of Appl. Phy 32, 83 (1961). [8] T. Growden, et al., Nature Light: Science & Applications 7, 17150 (2018).« less
  3. This work evaluates wearable thermoelectric (TE) devices consisting of nanocomposite thermoelectric materials, aluminum nitride ceramic headers, and a flexible and stretchable circuit board. These types of wearable systems are part of a broader effort to harvest thermal energy from the body and convert it into electrical energy to power wearable electronics. Thermoelectric generators are made of p-type (Bi,Sb)2Te3 and n-type Bi2(Te,Se)3. The nanocomposite thermoelectric materials investigated in this research address the two fundamental challenges for body heat harvesting. The first challenge is related to the unavailability of high zT n-type materials near the body temperature. The second challenge is related to the thermoelectric power factor. To improve the zT, one has to increase the power factor simultaneously while reducing the thermal conductivity. Our nanocomposites result in enhancement of the TE power factor along with the reduction of the thermal conductivity. The fundamental reason is a nanoscale effect that happens only when the energy distribution function of the carriers does not relax to that of the bulk material in the crystallites. Ten p-type and ten n-type nanocomposite ingots were synthesized and characterized in this research. All ingots were characterized versus their thermoelectric properties and they all showed similarly enhanced properties. Ourmore »nanocomposites, compared to commercial materials, have better zT and thermal resistivity by 40% and 75% for p-type, respectively, and 15% and 140% for n-type. Compared to the state-of-the-art materials, our nanocomposites produce significantly higher power due to their optimized properties for the body temperature.« less
  4. All-solid-state batteries (ASSBs) have garnered increasing attention due to the enhanced safety, featuring nonflammable solid electrolytes as well as the potential to achieve high energy density. 1 The advancement of the ASSBs is expected to provide, arguably, the most straightforward path towards practical, high-energy, and rechargeable batteries based on metallic anodes. 1 However, the sluggish ion transmission at the cathode-electrolyte (solid/solid) interface would result in the high resistant at the contact and limit the practical implementation of these all solid-state materials in real world batteries. 2 Several methods were suggested to enhance the kinetic condition of the ion migration between the cathode and the solid electrolyte (SE). 3 A composite strategy that mixes active materials and SEs for the cathode is a general way to decrease the ion transmission barrier at the cathode-electrolyte interface. 3 The active material concentration in the cathode is reduced as much as the SE portion increases by which the energy density of the ASSB is restricted. In addition, the mixing approach generally accompanies lattice mismatches between the cathode active materials and the SE, thus providing only limited improvements, which is imputed by random contacts between the cathode active materials and the SE during the mixingmore »process. Implementing high-pressure for the electrode and electrolyte of ASSB in the assembling process has been verified is a but effective way to boost the ion transmission ability between the cathode active materials and the SE by decreasing the grain boundary impedance. Whereas the short-circuit of the battery would be induced by the mechanical deformation of the electrolyte under high pressure. 4 Herein, we demonstrate a novel way to address the ion transmission problem at the cathode-electrolyte interface in ASSBs. Starting from the cathode configuration, the finite element method (FEM) was employed to evaluate the current concentration and the distribution of the space charge layer at the cathode-electrolyte interface. Hierarchical three-dimensional (HTD) structures are found to have a higher Li + transfer number (t Li+ ), fewer free anions, and the weaker space-charge layer at the cathode-electrolyte interface in the resulting FEM simulation. To take advantage of the HTD structure, stereolithography is adopted as a manufacturing technique and single-crystalline Ni-rich (SCN) materials are selected as the active materials. Next, the manufactured HTD cathode is sintered at 600 °C in an N 2 atmosphere for the carbonization of the resin, which induces sufficient electronic conductivity for the cathode. Then, the gel-like Li 1.4 Al 0.4 Ti 1.6 (PO 4 ) 3 (LATP) precursor is synthesized and filled into the voids of the HTD structure cathode sufficiently. And the filled HTD structure cathodes are sintered at 900 °C to achieve the crystallization of the LATP gel. Scanning transmission electron microscopy (STEM) is used to unveil the morphology of the cathode-electrolyte interface between the sintered HTD cathode and the in-situ generated electrolyte (LATP). A transient phase has been found generated at the interface and matched with both lattices of the SCN and the SE, accelerating the transmission of the Li-ions, which is further verified by density functional theory calculations. In addition, Electron Energy Loss Spectroscopy demonstrates the preserved interface between HTD cathode and SEs. Atomic force microscopy is employed to measure the potential image of the cross-sectional interface by the peak force tapping mode. The average potential of modified samples is lower than the sample that mix SCN and SEs simply in the 2D planar structure, which confirms a weakened space charge layer by the enhanced contact capability as well as the ion transmission ability. To see if the demonstrated method is universally applicable, LiNi 0.8 Co 0.1 Mn 0.1 O 2 (NCM811) is selected as the cathode active material and manufactured in the same way as the SCN. The HTD cathode based on NCM811 exhibits higher electrochemical performance compared with the reference sample based on the 2D planar mixing-type cathode. We believe such a demonstrated universal strategy provides a new guideline to engineer the cathode/electrolyte interface by revolutionizing electrode structures that can be applicable to all-solid-state batteries. Figure 1. Schematic of comparing of traditional 2D planar cathode and HTD cathode in ASSB Tikekar, M. D. , et al. , Nature Energy (2016) 1 (9), 16114 Banerjee, A. , et al. , Chem Rev (2020) 120 (14), 6878 Chen, R. , et al. , Chem Rev (2020) 120 (14), 6820 Cheng, X. , et al. , Advanced Energy Materials (2018) 8 (7) Figure 1« less
  5. Thermoelectric materials could play a crucial role in the future of wearable electronic devices. They can continuously generate electricity from body heat. For efficient operation in wearable systems, in addition to a high thermoelectric figure of merit, zT, the thermoelectric material must have low thermal conductivity and a high Seebeck coefficient. In this study, we successfully synthesized high-performance nanocomposites of n-type Bi2Te2.7Se0.3, optimized especially for body heat harvesting and power generation applications. Different techniques such as dopant optimization, glass inclusion, microwave radiation in a single mode microwave cavity, and sintering conditions were used to optimize the temperature-dependent thermoelectric properties of Bi2Te2.7Se0.3. The effects of these techniques were studied and compared with each other. A room temperature thermal conductivity as low as 0.65 W/mK and high Seebeck coefficient of −297 μV/K were obtained for a wearable application, while maintaining a high thermoelectric figure of merit, zT, of 0.87 and an average zT of 0.82 over the entire temperature range of 25 °C to 225 °C, which makes the material appropriate for a variety of power generation applications.