Te-Embedded Nanocrystalline PbTe Thick Films: Structure and Thermoelectric Properties Relationship

: The Te-embedded PbTe nanocrystallline thick ﬁlms (i.e., 50 µ m) were electrodeposited, where the fraction and average grain size of PbTe and Te phases were tuned by adjusting the applied potential followed by post thermal treatment. The crystal grain boundary and Te nano-inclusion in the ﬁlms played critical roles in their thermoelectric properties. The Te-embedded PbTe thick ﬁlm with the average grain size of around 100 nm showed lower energy barrier height (E B = 0.023 eV) than thick ﬁlms with the average grain size of a few tens of nm (E B = 0.11). Although decrease in the energy barrier reduced the Seebeck coefﬁcient, however, it enhanced the electrical conductivity, which resulted in an increase in power factor (PF). The highest power factor was 183 µ w K − 2 cm − 1 , achieved at the energy barrier of 0.023 eV.


Introduction
Heat is the natural by-product of the energy conversion processes. Of the~4 × 10 20 J of energy the USA consumes every year, greater than 60% is wasted in the form of heat [1][2][3]. Thus, waste heat recovery is a crucial step to improve the energy conversion and utilization efficiency. Thermoelectric (TE) materials, which can directly convert waste heat into energy, have been extensively researched for this purpose. The efficiency of a thermoelectric device can be presented by the thermoelectric-figure-of-merit called ZT = S 2 σT/κ, where S, σ, T, and κ are the Seebeck coefficient, electrical conductivity, temperature, and thermal conductivity, respectively. Two different approaches have been utilized to enhance the ZT of thermoelectric materials, which include the finding of proper thermoelectric materials with suitable carrier concentration values, n, since three interdependent thermoelectric parameters (S, σ, and κ) are functional to the carrier concentration [4]. In addition, nanoengineering of thermoelectric materials (e.g., dimension, superlattices, and second phase-inclusion) has been highlighted as the way to decouple the thermoelectric parameters [5][6][7][8][9][10][11][12][13].
Thermal management of miniaturized electronic components led to need of solidstate micro-coolers and generators. Therefore, fabrication of micro-thermoelectric devices, which typically are based on thin-and thick-films, has drawn a significant amount of attention lately [14]. Especially, the film-based thermoelectric devices have been shown to have many advantages over conventional bulk thermoelectric modules because of their compact size and flexibility. In addition, a micro-thermoelectric device is able to operate under smaller temperature gradients with fast response time, which allow the handling of a wider range of thermal and power management microelectronic systems [14][15][16][17][18]. The electrodeposition has a low operating and facility cost and high deposition rate, which is suitable for commercial application. Additionally, the electrodeposition is able to have selective deposition, which allows easy patterning for small sized-features as well as reduction of waste materials [19]. Various types of micro-thermoelectric devices mostly consisted of Bi 2 Te 3 alloys (n-type) and Sb 2 Te 3 alloys (p-type) were fabricated using the electrodeposition technique [20]. However, approaches to enhance the thermoelectric efficiency were limited to changes of device configuration and heat flow direction, therefore, it is important to combine nano-engineering to manipulate the charge transfer mechanism to further enhance the thermoelectric efficiency.
Using the electrodeposition process, precise control over the chemical composition and microstructure (e.g., crystallinity, crystal structure, preferred orientation, and the attainment of nano-inclusions and/or intermetallic phases) yields improved thermoelectric properties. Additionally, for lead telluride, nanoengineering can also introduce phonon scattering and quantum confinement effect to optimize the thermoelectric properties [9][10][11]. Lead telluride (PbTe) is a known candidate for mid-range temperature thermoelectrics showing the great performance at temperature range between 400 and 600 K. The electrodeposition method has been also applied for a synthesis of the PbTe thin films in acidic media [21][22][23][24][25][26][27][28]. However, the acidic baths have their drawbacks such as a low deposition-rate and mass transfer limited reaction due to low solubility of Te ions [29]. On the other hand, the solubility of Te ions (i.e., TeO 3 2− ) is much higher in an alkaline solution. The electrodeposition of PbTe films in alkaline solution was investigated by several groups [29][30][31][32][33][34]. Unfortunately, all of these works demonstrated the few-micron thick PbTe films and only few works investigated their thermoelectric performance. Therefore, it is meaningful to thoroughly investigate the thermoelectric performance of PbTe thick films along with systematical engineering their crystallinity properties for its thermoelectric performance enhancement.
In this study, the nanocrystalline PbTe thick (i.e., 50 µm) films with Te inclusions were electrodeposited in alkaline solution with high deposition-rate (>100 µm/h) at different applied potentials. Depending on the growth rate, the initial volume fraction of the PbTe phase and its grain size were differed in the as-deposited films. The crucial factors (e.g., grain size, inclusion of a secondary phase) to determine the thermoelectric property of the Te embedded PbTe were found by comparison of electrical and thermoelectric properties as a function of the volume fraction of PbTe and the grain size. The thermoelectric properties (e.g., electrical conductivity, mobility, carrier concentration, Seebeck coefficient, and power factor (PF)) at room temperature were correlated with the barrier height (E B ).

Materials and Method
All the solutions were prepared by dissolving various amounts of lead nitrate (Pb(NO 3 ) 2 , Fisher Chemical, Hampton, NH, USA), ethylenediaminetetraacetic acid disodium salt (Na 2 H 2 EDTA, Fisher Chemical, Hampton, NH, USA), tellurium dioxide (TeO 2 , 99+%, Acros Organics, Waltham, MA, USA) in sodium hydroxide solutions (NaOH, 10 N, Fisher Chemical) and pH of the solutions were adjusted by NaOH. All the electrodeposition experiments were performed in a conventional three-electrode cell using a rotating disk electrode (RDE) (6.4 mm in diameter gold coated copper rods embedded in a cylindrical Teflon holder) as working electrodes, platinum coated titanium stripe as counter electrode, and saturated Ag/AgCl as reference electrode. All the solutions are deaerated by bubbling N 2 for 40 min [35]. The PbTe thick films (approx. 50 µm) were electrodeposited at different applied potential (i.e., −0.9, −0.95, −1.0 and −1.05 V vs. sat. Ag/AgCl) in the solution with 550 mM [TeO 3 2− ], 100 mM [Pb(NO 3 ) 2 ], and [EDTA 4− ]/[Pb 2+ ] of 7.5 at pH of 12.3 and temperature of 23 • C. The process for electrodeposition of PbTe were the same as our previous publication [36].
For electrical and thermoelectric characterization, the thick films were detached from the Au/Cu substrate and transferred to a non-conductive epoxy substrate (Loctite, epoxy instant mix). The entire film was successfully transferred without cracking [37]. The final dimensions of the sample for characterization were around 0.4 × 0.4 cm 2 to fit the van der Pauw configuration for Hall measurement. The morphology, composition and crystal orientation of the thick PbTe films were studied by field emission-scanning electron microscopy (FE-SEM, FEI NNS450, Hillsboro, OR, USA), energy dispersive X-ray (EDS, FEI NNS450) and X-ray diffraction (XRD, PANalytical Empyrean, Malvern, UK). The samples were annealed at 200 • C for 2 and 10 h in 5% H 2 + 95% N 2 environment. During the annealing process, the temperature was ramped up at 5 • C/min. The sample was naturally cooled down to room temperature. The electrical conductivity, Hall mobility, and carrier concentration of the film were examined using a custom-made Hall measurement system by the van der Pauw configuration with four-point probes. The Seebeck coefficient was investigated by a custom-made Seebeck measurement system [38,39].

Results and Discussion
The four PbTe thick films (50 µm) were electrodeposited at different applied potentials resulting in different deposition rates (i.e., 115, 138, 167 and 163 µm/h), respectively. It is expected that the crystal structure and crystallinity would be different due to different growth rates. Additionally, the applied potential had effects not only on the growth rate, but also on the nucleation rate, where normally high overpotential results in high nucleation rates [40][41][42]. The nucleation rate of alloy as a function of applied overpotential have been expressed as the following equation: where J is the nucleation rate, η is overpotential, n A and n B are number of atoms for element A and B, z is number of critical nuclei, q = α A z A or α B z B , α is ion transition coefficient, k is Boltzmann's constant, T is temperature and e is elementary electric charge [42]. Based on this, the appropriate applied overpotential would lead to the films consisted of the small crystal size.
As shown in Figure 1, the four electrodeposited films are compact based on the crosssection SEM image (Figure 1a-d, top row) with slightly different surface morphology (Figure 1a-d, bottom row). At the applied potential of −0.90 and −0.95 V vs. sat. Ag/AgCl, the surface morphology is nodular (Figure 1a,b), while at the applied potential of −1.0 V vs. sat. Ag/AgCl (Figure 1c), the surface was smoother. Moreover, at the applied potential of −1.05 V the surface morphology became rougher, which may be caused by further reduction of Te at higher applied potential [36,43]. The composition of the four films determined by EDS analysis showed that it was independent of the applied potential (i.e., Pb content of 47 at.%) [36] due to under potential deposition (UPD) deposition mechanism [30,31]. The XRD patterns of as-deposited PbTe films are shown in Figure 2. Further adjustment of the crystallinity of the films were achieved by thermal treatment in a reductive atmosphere (i.e., 95 vol.% N2 + 5 vol.% H2). The thermal treatment process was carried out in a reductive atmosphere to prevent the oxidation of PbTe during the treatment. The an-  The XRD patterns of as-deposited PbTe films are shown in Figure 2. Further adjustment of the crystallinity of the films were achieved by thermal treatment in a reductive atmosphere (i.e., 95 vol.% N 2 + 5 vol.% H 2 ). The thermal treatment process was carried out in a reductive atmosphere to prevent the oxidation of PbTe during the treatment. The annealing process was carried out at 200 • C for 2 and 10 h. The deposition rate increase from 120 to about 160 µm h −1 when applied potential changed from −0.9 to −1.05 V. According to Equation (1) and Buttler-Volmer's equation, both nucleation rate and grain growth rate is enhanced dramatically by applied potential. Namely, the grain size of PbTe turned out to be almost the same with dominant crystal orientation of (111) ( Figure 2) and nano-crystalline structure. For Tellurium, the preferred orientation is (111). When the annealing process was carried out for 10 h, there was a contamination issue that the copper, which is a substrate material being used as the counter electrode, was diffused into the PbTe films electrodeposited −1.00 and −1.05 V ( Figure S1a). However, PbTe samples electrodeposited at −0.90 and −0.95 V did not show copper diffusion ( Figure  S1a). The XRD patterns of the electrodeposited PbTe thick films match with the standard reference data (JCPDS-International Center for Diffraction Data, for Te No. 36-1452 and PbTe No. 38-1435). The un-indexed peak at 29.5 degree is attributed to the reflection of a frequency doubling radiation wave [44]. According to these XRD data, the electrodeposited films consisted of crystallized Te and PbTe with dominant orientation of (111) for both Te and PbTe phases. During the thermal treatment, the films were further crystallized which was identified by the decrease in FWHM of XRD peaks compared to as-deposited films. For the Te phase, because of its anisotropic hexagonal structure (i.e., six spiral chains at each corner and one in the center bound together via van der Waals forces) Te crystal normally has preferred orientation of (001) [45][46][47]. The fact that (111) orientation was dominant in Te crystal probably because it was surrounded by PbTe which had preferred orientation of (111). Two sets of information were extracted from the XRD data: When the annealing process was carried out for 10 h, there was a contamination issue that the copper, which is a substrate material being used as the counter electrode, was diffused into the PbTe films electrodeposited −1.00 and −1.05 V ( Figure S1a). However, PbTe samples electrodeposited at −0.90 and −0.95 V did not show copper diffusion ( Figure  S1a). The XRD patterns of the electrodeposited PbTe thick films match with the standard reference data (JCPDS-International Center for Diffraction Data, for Te No. 36-1452 and PbTe No. 38-1435). The un-indexed peak at 29.5 degree is attributed to the reflection of a frequency doubling radiation wave [44]. According to these XRD data, the electrodeposited films consisted of crystallized Te and PbTe with dominant orientation of (111) for both Te and PbTe phases. During the thermal treatment, the films were further crystallized which was identified by the decrease in FWHM of XRD peaks compared to as-deposited films. For the Te phase, because of its anisotropic hexagonal structure (i.e., six spiral chains at each corner and one in the center bound together via van der Waals forces) Te crystal normally has preferred orientation of (001) [45][46][47]. The fact that (111) orientation was dominant in Te crystal probably because it was surrounded by PbTe which had preferred orientation of (111). Two sets of information were extracted from the XRD data: one is the grain size of PbTe and Te, which is calculated by Scherrer equation [48], where the instrument peak broadening was corrected by substrate, and the stress-induced peak broadening from was corrected using Williamson-Hall analysis [49,50]; the other one is the quantitative information of crystalline PbTe and Te phases. This information was extracted by phase identification and estimation of the quantity of all identified phases of a mixture, which was realized using software (i.e., HighScore). The crystallite size and phase fraction of PbTe and Te, were plotted as a function of thermal treatment time ( Figure 3). As the annealing time increased, the diffraction percentage of PbTe increased from 66 to 86% for the film electrodeposited at −0.9 V, 74 to 90% for the film electrodeposited at −0.95 V, 74 to 94% for the film electrodeposited at −1.0 V, and 52% to 96% for the film electrodeposited at −1.05 V. As expected, the average grain size of PbTe increased with increased in thermal treatment time.  [51][52][53][54][55][56][57][58]. If this is the reason, after annealing the Te/(Te + Pb) ratio would decrease, however the data in Figure S1a showed that the Te/(Te + Pb) ratio remained constant, which indicated that Te evaporation is not the reason for the decrease of Te grain. The Ostwald ripening process, in which larger particles grow while smaller particles shrink, is a thermodynamically-driven spontaneous process because larger particles are more energetically stable [59][60][61]. In the Te-rich PbTe system, PbTe compound formation have a Gibbs free energy of −69.5 kJ/mol, which is thermodynamically favorable [62]. Moreover, Te has hexagonal crystal structure contains six spiral chains at each corner and one in the center, and the spiral chains are bound together via van der Waals forces [45], which are much weaker forces compared to chemical bond of Pb-Te. As a consequence, the possible explanation for decrease of Te grain size is that: the Te nanocrystal, which was relatively small amount, was embedded in the PbTe crystals, when the PbTe crystal grains started to growth, it may consume the Te atoms to fill its crystal imperfection and vacancy during the annealing process. Rojas-Chavez et al. also reported this phenomenon during PbTe milling. Their results show that during milling process, smaller particles and quantum dots are eventually dissolved completely to lower the total energy surface energy. They also mentioned that the formation of larger particles can be attributed to atom migration due to detachment of the atoms from amorphous zones [63].
For the two samples deposited at −1.0 and −1.05 V, Te grains increased slightly after annealing. In the nanocrystalline PbTe film, the dominant charge transfer mechanism would be significantly affected because its grain size changes as well as the interfaces as two different phases are formed. The energy barrier height of thick films was calculated using temperature-dependent electrical conductivity data ( Figure S2) based on the Equation (2): where σ is electrical conductivity, k is Boltzmann's constant, T is temperature and E b is energy barrier height [64,65]. The plot used to extract energy barrier height was shown in Figure S3. The energy barrier was influenced by grain size of the PbTe phase. According to literatures, the energy barrier from the dislocations at the grain boundaries can be ranged from 0.01 to 0.1 eV [66,67]. The difference of the initial energy barrier heights of the asdeposited films were distinctive (i.e., 0.11, 0.04, 0.16 and 0.08 eV for the film deposited at −0.9, −0.95, −1.0 and −1.05 V vs. Ag/AgCl, respectively as shown in Figure 4), which might be caused by crystal imperfection and vacancy formed at different growth rate ( Figure 4). The difference in the energy barrier between samples became smaller after annealing (e.g., 0.02, 0.023, 0.037 and 0.016 eV for the film deposited at −0.9, −0.95, −1.0 and −1.05 V vs. Ag/AgCl, respectively, after annealed at 200 • C for 10 h). This is because the PbTe films tend to approach thermodynamically stable crystal structures after annealing so that the difference of energy barrier height of the films was diminished after annealing.
Coatings 2021, 11, x FOR PEER REVIEW 7 of 14 ure 4). The difference in the energy barrier between samples became smaller after annealing (e.g., 0.02, 0.023, 0.037 and 0.016 eV for the film deposited at −0.9, −0.95, −1.0 and −1.05 V vs. Ag/AgCl, respectively, after annealed at 200 °C for 10 h). This is because the PbTe films tend to approach thermodynamically stable crystal structures after annealing so that the difference of energy barrier height of the films was diminished after annealing.  The carrier concentration, mobility and electrical conductivity as a function of energy barrier were plotted in Figure 5. The results showed that the carrier concentration does not have significant trend as a function of energy barrier height (Figure 5a). The increased carrier concentration of Te-embedded PbTe films can result from multiple reasons. For example, the excessed Te in the PbTe acted as acceptor, and the grain boundary may also contribute the increase of hole concentration [68]. Strauss et al. reported that the carrier concentration at of Te-saturated PbTe was typically about 3 × 10 18 cm −3 and the maximum carrier concentration according to his data was 8 × 10 18 cm −3 , additionally he claimed that the carrier concentration of Te-saturated PbTe can barely go below 10 17 cm −3  [70]. The mobility decreased significant as energy barrier increased (Figure 5b). The mobility can be presented by the following equations: where µ is mobility, L is grain size, e is elementary electric charge and m* is effective mass [64]. The relatively high mobility of 587 cm 2 V −1 s −1 was achieved at low energy barrier range of about 0.02 eV, and the lowest mobility of 1.4 × 10 −3 cm 2 ·V −1 s −1 was obtained when energy barrier is 0. 16    The carrier concentration, mobility and electrical conductivity as a function of ene barrier were plotted in Figure 5. The results showed that the carrier concentration d not have significant trend as a function of energy barrier height (Figure 5a). The increa carrier concentration of Te-embedded PbTe films can result from multiple reasons. example, the excessed Te in the PbTe acted as acceptor, and the grain boundary may contribute the increase of hole concentration [68]. Strauss et al. reported that the car concentration at of Te-saturated PbTe was typically about 3 × 10 18 cm −3 and the maxim carrier concentration according to his data was 8 × 10 18 cm −3 , additionally he claimed the carrier concentration of Te-saturated PbTe can barely go below 10 17 cm −3 at room t perature, even after long-term annealing. [69] Allgaier et al. also reported the carrier c centration of p-type PbTe had a carrier concentration range of 4.85 × 10 17 to 1.67 × 10 19 c [70] The mobility decreased significant as energy barrier increased (Figure 5b). The bility can be presented by the following equations:   The electrical conductivity followed the same trend as mobility behavior when changing the energy barrier height, which can be expressed by following equation: where σ is electrical conductivity and p is average carrier concentration. Additionally, the Equations (3) and (4) was utilized base on the assumption that when E b is not much smaller than kT [64]. According to the equation, the larger energy barrier height (E b ) leads to smaller electrical conductivity (σ). The best electrical conductivity (140 and 115 S cm −1 ) was achieved when the films showed the lowest energy barrier heights of about 0.02 eV for the films deposited at −0.9 and −0.95 V. The mobility and the electrical conductivity of the as-deposited sample at −0.9 V is larger than expected, which may be caused by a lower effective mass according to Equations (3) and (4). The as-deposited film at −0.9 V have an energy barrier of 0.11 eV, compared the samples have been annealed for 2 h with energy barrier of 0.06 eV, the as-deposited sample is supposed to have lower mobility and electrical conductivity. The bulk p-type PbTe has electrical conductivity higher than 10 3 S cm −1 at carrier concentration range of 10 19 cm −3 at room temperature [72,73]. There are few studies reported the Cu doped PbTe. The results in this study showed that the thick films with Cu contamination have relatively high carrier concentration, and relatively low mobility and electrical conductivity. The two films deposited at −1.0 and −1.05 V have relatively low electrical conductivity (i.e., 13.7 and 11.7 S cm −1 , respectively) after annealing for 10 h, which possibly because the formation of CuTe as a result of Cu diffusion during the annealing process. Introduction of the energy barrier by Te nano-inclusion and grain boundaries reduced the electrical conductivity of PbTe, which is consistent with the Equation (4). Compared to bulk Te-rich PbTe without other doping elements (Table 1), the electrodeposited Te-rich PbTe films have relatively high electrical conductivity and carrier concentration, but relatively low carrier mobility after annealing [38,39]. Table 1. Summary of electrical and thermoelectric properties of Te-rich PbTe.

Ref.
Year Grain Size The Seebeck coefficient of four films were plotted as a function of the electrical conductivity. As shown in Figure 6a, the as-deposited films consisted of tens of nanometer-sized grains had the larger Seebeck coefficient values which is expected due to interdependency between Seebeck coefficient and electrical conductivity. As the films were annealed longer, the Seebeck coefficient decreased and the electrical conductivity increased at the same time. The calculated power factor (PF) showed the best values in the films annealed for 10 h where the films show the lowest barrier heights (Figure 6b). The highest power factor (183 µW K −2 m −1 ) was achieved at energy barrier of 0.023 eV. However, at even higher conductivity, Seebeck coefficient will decrease, hence the power factor will reach a peak and start decreasing. For the bulk p-type PbTe materials doped with 0.3% Na, the Seebeck coefficient is 120 µV K −1 , and the electrical conductivity is about 2000 S cm −1 at room temperature [84]. Compared to the sample in this study, the Seebeck coefficient of the samples in the study is higher for the as-deposited thick films. However, the electrical conductivity of the thick films study in this study is lower than the bulk PbTe materials even after annealed for 10 h. Popescu et al. calculated the effect of the energy barrier on electrical conductivity, the results showed that higher energy barrier would result in lower electrical conductivity and lower Seebeck coefficient. Their results showed that the maximum thermoelectric power factor was achieved at the energy barrier of 0.095 eV [85]. Accordingly, in order to apply the nanocrysatlline PbTe thick films for thermoelectric applications, instead of the nano-inclusion of second phase, the engineering of grain size of single-phase PbTe films would be promising. even higher conductivity, Seebeck coefficient will decrease, hence the power factor will reach a peak and start decreasing. For the bulk p-type PbTe materials doped with 0.3% Na, the Seebeck coefficient is 120 µ V K −1 , and the electrical conductivity is about 2000 S cm −1 at room temperature. [84] Compared to the sample in this study, the Seebeck coefficient of the samples in the study is higher for the as-deposited thick films. However, the electrical conductivity of the thick films study in this study is lower than the bulk PbTe materials even after annealed for 10 h. Popescu et al. calculated the effect of the energy barrier on electrical conductivity, the results showed that higher energy barrier would result in lower electrical conductivity and lower Seebeck coefficient. Their results showed that the maximum thermoelectric power factor was achieved at the energy barrier of 0.095 eV [85]. Accordingly, in order to apply the nanocrysatlline PbTe thick films for thermoelectric applications, instead of the nano-inclusion of second phase, the engineering of grain size of single-phase PbTe films would be promising.

Conclusions
Nanocrystalline PbTe thick films were electrodeposited in alkaline solution with high deposition-rates (i.e., >100 µ m/h). By adjusting the growth rate, the initial fraction of PbTe phase and its grain size were controlled whereas the formation of a secondary Te embedded phase was controlled by film composition. As-deposited PbTe thick films were thermal treated with a control of various temperature and duration to tailor the crystal structure and crystallinity. The thermoelectric properties (i.e., Seebeck coefficient and electrical conductivity, and power factor (PF)) of these films were measured at room temperature and correlated to their crystal structure, average grain size, and the fraction of Te phase. Additionally, the energy barrier heights (EB) were determined from the temperature dependent electrical conductivity. The highest PF of 183 μW K −2 cm −1 with a Seebeck coefficient of 125 µ V K −1 and electrical conductivity of 116 S cm −1 were observed from Te embedded PbTe thick films with the average grain size of 100 nm.

Conclusions
Nanocrystalline PbTe thick films were electrodeposited in alkaline solution with high deposition-rates (i.e., >100 µm/h). By adjusting the growth rate, the initial fraction of PbTe phase and its grain size were controlled whereas the formation of a secondary Te embedded phase was controlled by film composition. As-deposited PbTe thick films were thermal treated with a control of various temperature and duration to tailor the crystal structure and crystallinity. The thermoelectric properties (i.e., Seebeck coefficient and electrical conductivity, and power factor (PF)) of these films were measured at room temperature and correlated to their crystal structure, average grain size, and the fraction of Te phase. Additionally, the energy barrier heights (E B ) were determined from the temperature dependent electrical conductivity. The highest PF of 183 µW K −2 cm −1 with a Seebeck coefficient of 125 µV K −1 and electrical conductivity of 116 S cm −1 were observed from Te embedded PbTe thick films with the average grain size of 100 nm.