Impact of Graphene or Reduced Graphene Oxide on Performance of Thermoelectric Composites

Abstract

In recent years, worldwide research has been focused on clean and sustainable energy sources that can respond to the exponentially rising energy demands of humankind. The harvesting of unused heat in relation to automotive exhaustion, industrial processes, and home heating is one possible way of enabling the transformation from a fossil fuel-based society to a low-carbon socioeconomic epoch. Thermoelectric (TE) generators can convert heat to electrical energy thanks to high-performance TE materials that work via Seebeck effects when electricity appears between the cold part and the hot part of these materials. High figure of merit (ZT) TE material is characterized by high electrical conductivity and Seebeck coefficient, together with low thermal conductivity. This article aims to summarize ZT values reported for chalcogenides, skutterudites, and metal oxides with graphene (G) or reduced graphene oxide (rGO), and intends to understand the relationship between the addition of G-rGO to composites and ZT variation. In a majority of the publications, ZT value increases with the addition of G/rGO, although the relative growth of ZT varies for different material families, as well as inside the same group of materials, with it often being related not to a G/rGO amount but with the quality of the composite.

1. Introduction

In view of the current climate change problem, thermoelectric (TE) energy conversion is considered particularly attractive for harvesting electricity from solar heat or for recovering waste heat [1,2,3,4]. The use of waste heat as source of electrical energy in vehicles is also an attractive option for major automotive manufacturers, who actively pursue this technology to implement thermoelectric generators (TEGs) in car exhaust systems [5]. Moreover, it can significantly reduce the amount of CO₂ in industrial production processes. Furthermore, silent, reliable, and versatile TEGs without moving parts [6] can be used to power portable electronic devices as additional sources of energy.

Thus, TEGs hold a tantalizing promise of greater energy efficiency by providing a robust and clean option for waste heat recovery and its conversion into useful electrical energy through the Seebeck effect [7,8,9,10]. Moreover, their size can be easily varied, since TEGs consist of TE modules, which include multiple n- and p-type semiconductor couples connected electrically in series and thermally in parallel [11]. Both types of TE materials are widely studied and characterized by the dimensionless figure of merit at the absolute temperature, T:

$$ZT=\frac{\sigma \times S^2\times T}{k}$$

(1)

Accordingly, efficient TE materials should possess a great Seebeck coefficient, S, and a high electrical conductivity, σ, but a low thermal conductivity, k. Then, a high voltage related to the Seebeck coefficient can be generated by TE material placed in a temperature gradient. Electrical conductivity, σ, should be high to reduce the internal resistance of the material. Thermal conductivity of material, k, should be low to create a large temperature difference between the ends of the TE material.

However, σ is directly proportional to the carrier concentration, n, but Seebeck coefficient S, being proportional to n^−2/3, according to the Pisarenko relation for doped semiconductors [12], depends on the carrier concentration in the opposite way. Moreover, there is a direct relationship between σ and the electronic contribution to thermal conductivity following from σ/k~T [13,14]. Thus, an enhancement of the conversion efficiency is a major challenge for the implementation of TE energy conversion. Moreover, TE materials should also be stable under operating conditions, as well as having long life cycles, greater cost efficiency, and compatibility with existing technologies.

Nowadays, both p- and n-type of TE materials can show a high value of ZT that strongly depends on the material properties, such as stoichiometry/doping level, charge carrier concentration, and prevailing scattering mechanisms, as well as on processing methods/conditions [15,16]. The top ZT values are up to ~2.8 at 773 K [17] and ~2.6 at 923 K [18], reported for n-type Br-doped and p-type nanostructured SnSe, respectively. ZT up to ~2.2 at 915 K for n-type PbTe [19] and ~1.9 at 320 K for n-type Bi_0.5Sb_1.5Te were also reported [20]. All these systems belong to the family of chalcogenide TE materials. However, typically, ZT reported for other chalcogenides such as Bi₂Te₃ and Sb₂Te₃ [21], or for skutterudites such as CoSb-family materials [22], or for metal oxides, which are promising for high-T applications due to their robustness, is lower (<1.8) [23]. Among them, metal oxide TE materials possess a considerably smaller figure of merit so far, but they are more cost-effective and high-T stable than heavy metal alloys [24,25,26].

From the other side, graphene (G), a one-atom-thick sheet of carbon with a high electron mobility of 230,000 cm² V⁻¹ s⁻¹ and 125,000 cm² V⁻¹ s⁻¹ at 4.2 K and room T, respectively [27], is widely considered as a functional additive [28]. Moreover, its composites with different TE materials, particularly with polyaniline, poly(3,4-ethylenedioxythiophene) and other polymers are also studied [28]. However, typically, much less agglomerative graphene oxide (GO) that can be easily reduced by chemical or heat treatment, or already reduced graphene oxide (rGO), are used in a majority of reported composites because they are cheaper and easier to prepare than high quality monolayer graphene.

Moreover, 3D network wrapping structures (or core-shell nanocomposites) with a shell layer of a few nm have been theoretically shown [29] and experimentally confirmed to strengthen the phonon scattering that could suppress thermal conductivity, and, thus, enhance ZT [30]. According to this model, if the secondary phase could be dispersed as a nanoscale shell layer on the grains of the matrix phase (core), the heat-carrying phonons would be effectively scattered; this is because of the enhanced interparticle and intraparticle boundary scattering with an increased number of interfaces [30]. An additional ZT enhancement is expected if the 3D network nanocomposite contains a wrapping phase that can scatter the phonons but maintain high electron transport. Furthermore, high electrical conductivity of the wrapping phase should be accompanied by a suitable band gap, matching with that of the matrix, to enhance the Seebeck coefficient, thus realizing an energy filtering effect in such a 3D wrapping structure. Zong et al. have shown that these demands can be satisfied using rGO as the wrapping phase because of its low thickness, high electrical conductivity (electron mobility), and band gap that can be tuned by the reduction degree (the oxygen ratio in rGO after chemical or/and thermal reduction of GO) [30]. In addition, besides the charge carrier mobility, a charge carrier density can also be enhanced in oxide TE materials by the carbon stimulated formation of oxygen vacancies [31]. Thus, a number of works were published over the last few years on G-rGO modified TE materials. In this article, a literature overview and discussion of TE performance on chalcogenides, skutterudites, and metal oxides with G-rGO additives are presented.

2. Current Achievements for Thermoelectric Materials with Graphene or Reduced Graphene Oxide

2.1. Chalcogenides

Among the chalcogenide family, Bi- and Te-based alloys are the most studied p- and n-type TE materials used in both bulk and thin film commercial applications [32]. That is because they possess a combination of relatively high Seebeck coefficient with great electrical conductivity and low thermal conductivity, which results in an elevated TE figure of merit (ZT).

In 2013, Liang et al. [33] and Dong et al. [34] first fabricated chalcogenide Bi₂Te₃ with G, and PbTe with rGO. Both research groups used a spark plasma sintering (SPS) process for the densification of the obtained TE materials. Moreover, in both cases the studied composites presented slightly decreasing relative densities when the G or rGO contents increased. Moreover, the grain sizes of the pristine ceramics were found to be larger than those of the composites, as can be seen in the scanning electron microscopy (SEM) images in Figure 1 for Bi₂Te₃, without and with graphene [33]. At the same time, the decrease in the grain size enhances the grain boundary phonon scattering, which is beneficial for the reduction in thermal conductivity [33]. The maximum ZT values were reported to increase from 0.16 to 0.21 at 475 K, with 0.2 vol.% G addition to Bi₂Te₃ [33], and from 0.12 to 0.7 at 670 K, with 5 wt.% GO addition to PbTe [34].

At the same time, in 2013, Chen et al. first studied Cu-based chalcogenide TE material CuInTe₂ in composite, with G obtained from expanded graphite with mass ratios of 80:1 and 40:1 [35]. The authors reported that, in incorporating G sheets into the CuInTe₂ matrix, thermal conductivity was successfully decreased, thus leading to an enhanced ZT of 0.4 at 700 K for CuInTe₂ composite, with G in 80:1 ratio, compared to 0.39 at 700 K for pristine CuInTe₂ [35]. Further, two Cu-based chalcogenide TE materials such as Cu₂SnSe₃ [36] and Cu₂ZnSnS₄ [37] were modified by G with different concentrations. The lattice thermal conductivity of these chalcogenides decreased in composites with a low G amount, effectively resulting from the phonon scattering by the graphene interface, similar to Bi₂Te₃ with G [33] or PbTe with GO [34]. However, when the fraction of graphene exceeds a certain value, the thermal conductivity of the composites starts to increase; this is because of an increase in the interface thickness instead of interface area due to the tendency to aggregation of graphene nanosheets reported in both these works [36,37]. The maximum figure of merit for Cu₂SnSe₃ with 0.25 vol.% G was 0.44 at 700 K [36], and ZT of 0.5 at 623 K was obtained for Cu₂ZnSnS₄ with 0.75 wt.% G [37].

Besides the SPS Bi₂Te₃ reported in 2013 by Liang et al. [33], in 2016, Agarwal et al. used simple mixing and pressing of commercial Bi₂Te₃ with 0.05 wt.% commercial G without sintering or other processing [38]. Investigating obtained composites by nanoscale atomic force microscopy, conductive atomic force microscopy, Kelvin probe force microscopy and scanning thermal microscopy, ZT was reported to be up to 0.92 at 402 K according to these local technique studies [38].

In addition to pristine Bi₂Te₃, its alloys Bi_xSb_yTe₃ (x = 0.36–0.5, y = 1.5–1.64) [39,40,41,42,43,44] and Bi₂Te_2.7Se_0.3 [45] were also modified by G or rGO and studied. All of them have shown enhanced ZT after the addition of G or GO, up to certain concentrations. ZT values for chalcogenides with G or rGO are presented in

Table 1. The composite preparation methods and conditions. The highest value of ZT (ZT_max) at the corresponding temperature (T_ZTmax), as well as the thermal conductivity (k), electrical conductivity (σ) and Seebeck coefficient (S) at that temperature reported for composites of chalcogenide TE materials with graphene or reduced graphene oxide.

TE Material	G or rGO,	Method	T Range,	ZTmax (at TZTmax, K)	k at TZTmax,	σ at TZTmax,	S at TZTmax,	Ref.
	Used Amount		K	/Used G-rGO Amount	W/(m × K)	× 103 S/m	μV/K
Bi2Te3 ingots	G com.	SPS 350 °C	300–472	0.21 (472)/0.2 vol.%	2.2	75	−114	[33]
	0–2 vol.%	6 min 80 MPa
Bi2Te3 beads	GO by HM	HP 350 °C	RT	0.3 (RT)/1 wt.%	0.56	33	−160	[46]
	0–10 wt.%	10 min 50 MPa
Bi2Te3 NWs by WCSR	GO by HM	HP 350 °C	RT	0.4 (RT)/1 wt.%	0.48	41	−180	[46]
	0–10 wt.%	10 min 50 MPa
Bi2Te3 com.	G com.	Mix, press	300–480	0.92 (402)/0.05 wt.%	0.95	80	−145	[38]
	0, 0.05 wt.%	7 min, 2 MPa
Bi2Te2.7Se0.3 by exf.	G	SPS 420 °C	300–523	0.75 (360)/0.05 wt.%	1.1	75	−170	[45]
	0–0.1 wt.%	2 min, 30 MPa
Bi2Te2.7Se0.3 by US	G	SPS 420 °C	300–523	0.8 (400)/0.05 wt.%	0.95	60	−170	[45]
	0–0.1 wt.%	2 min, 30 MPa
Bi0.36Sb1.64Te3 ingots	rGO com.	SPS 480 °C	300–473	1.16 (393)/0.4 vol.%	1.26	1	195	[42]
	0–0.8 vol.%	3 min, 60 MPa
Bi0.4Sb1.6Te3 ingots	G by exf.	HP 350 °C	293–498	1.54 (440)/0.4 vol.%	0.8	74	200	[41]
	0–0.4 vol.%	1 h, 600 MPa
Bi0.44Sb1.56Te3 ingots	GO com.	SPS 480 °C	300–480	1.0 (400)/0.1 wt.%	1.1	75	190	[43]
	0–0.2 wt.%	5 min, 50 MPa
Bi0.48Sb1.52Te3 com.	G com.	HFIHS 370 °C	300–500	1.2 (375)/0.5 vol.%	0.7	55	215	[44]
	0–1 vol.%	35 MPa
Bi0.48Sb1.52Te3 ingots	G com.	SPS 420 °C	300–550	1.25 (320)/0.05 wt.%	1.1	100	230	[40]
	0–0.15 wt.%	10 min, 60 MPa
Bi0.5Sb1.5Te3 by MW-STS	G by MW-EGt,	SPS 390 °C	300–473	1.13 (360)/0.1 vol.%	0.7	55	200	[39]
	0–0.5 vol.%	3 min, 70 MPa
Bi0.5Sb1.5Te3 ingots	G by MW-EGt	SPS 480 °C	300–473	1.24 (360)/0.1 vol.%	0.8	57.5	230	[39]
	0, 0.1 vol.%	3 min, 70 MPa
Cu2SnSe3 ingots	GO com.	SPS 587 °C	300–700	0.44 (700)/0.25 vol.%	1.0	0.125	220	[36]
	0–1 vol.%	8min, 50 MPa
CuInTe2 ingots	G from EGt	SPS 500 °C	300–700	0.40 (700)/1.2 wt.%	1.25	13.5	225	[35]
	1.2, 2.4 wt.%	10 min, 60 MPa
Cu2ZnSnS4 by MW	G com.	HP 350 °C	300–700	0.5 (623)/0.75 wt.%	0.5	30	120	[37]
	0–1 wt.%	15 min, 80 MPa
PbTe in-situ	GO by HM	SPS 580 °C	300–670	0.7 (670)/5 wt.%	0.7	1.25	−250	[34]
	0–10 wt.%	5 min, 30 MPa

Here WCSR—wet-chemical synthetic route; com.—commercial; exf.—exfoliation; US—ultrasonication; MW—microwave (synthesis); STS—solvothermal synthesis; HM—Hummer’s method; Get—expanded graphite; SPS—spark plasma sintering; HP—hot-pressing; HFIHS—high frequency induction heated sintering.

and in Figure 2 for comparison. Table 1 shows also their thermal and electrical conductivities, as well as their Seebeck coefficient values.

As it turned out, the method of TE material preparation can also affect the ZT value. Particularly, Bi_0.5Sb_1.5Te₃ made using microwave-induced solvothermally synthesized Bi₂Te₃ and Sb₂Te₃ nanoplates with 0.1 vol.% G have shown a maximum ZT of 1.13 at 360 K, in comparison to ZT of 1.24 at 360 K for the same Bi_0.5Sb_1.5Te₃ obtained by a ball-milling process with the same amount of G [39].

At the same time, the composite of Bi₂Te₃ nanowires (NW) fabricated by a wet-chemical synthetic route (WCSR) with rGO can have slightly higher room-temperature ZT of 0.4 than that of 0.3 for a composite made of Bi₂Te₃ powder with the same 1 wt.% rGO [46], as can be seen in Table 1. Performance enhancement was connected to higher electrical conductivity and lower thermal conductivity of G-rGO composites with nanowires. Smaller dimensions of the NWs, and, thereby, a higher interface/boundary number in Bi₂Te₃-NW composite with G than this number in the Bi₂Te₃-powder composite with G, was suggested as an explanation for the low thermal conductivity [46].

As can be seen from Figure 2, the highest ZT of 1.54 at 440 K was reported by Li et al. for Bi_0.4Sb_1.6Te₃, with 0.4 vol.% exfoliated G [41]. Other p-type Bi_xSb_yTe₃ chalcogenides with G-rGO have shown lower ZT values with a visible peak at a relatively low T, up to 400 K [39,40,42,43,44], in contrast to p-type composites of Cu-based chalcogenides (Cu₂SnSe₃, CuInTe₂ and Cu₂ZnSnS₄) and G-rGO [35,36,37], with ZT continuously increasing up to the limit of the measured T range of 650–700 K. At the same time, reported n-type chalcogenide TE materials with G-rGO have also shown dissimilarities in the temperature variation of ZT. Evident low-T peak is detected for Bi₂Te_2.7Se_0.3 [45] and for Bi₂Te₃ [38], while no peak is seen for SPS densified Bi₂Te₃ with G [33], or for PbTe with GO [34].

2.2. Skutterudites

Skutterudites with a general formula of MX₃ (M = Co, Rh, or Ir; X = P, As, or Sb) have an open frame (“cagey”) structure with a body-centered cubic unit cell and a network of corner-sharing octahedra, each of which consists of one M atom in the center and six X atoms vertices [47,48]. Such a structure has motivated works on filling the cages with diverse atoms, in conjunction with the routine substitutional doping efforts, to tailor specific application functions described in many articles, including reviews [22,49]. Another strategy to enhance the TE performance of materials such as skutterudites involves the incorporation of a secondary phase, particularly 2D graphene or reduced graphene oxide, into the core-shell nanocomposites with 3D network wrapping structures [30]. Among the composites of skutterudites with G or rGO, materials such as pristine CoSb₃ [50] and related Yb_0.27Co₄Sb₁₂ [30], Ce_0.85Fe₃CoSb₁₂ [51], and La_0.8Ti_0.1Ga_0.1Fe₃CoSb₁₂ [52] were reported.

In 2013, Feng et al. first reported p-type nanocomposite with GO added to CoSb₃ during the solvothermal process, performed at 290 °C for 12 h [50]. After hot pressing under 80 MPa at 600 °C for 2 h, the CoSb₃ bulk hybrid with rGO has shown homogeneously embedded graphene in the nanostructured CoSb₃ matrix (see Figure 3a,b). The obtained ZT value of 0.81 at 800 K for CoSb₃ with 1.5 wt.% GO was found to be more than twice as high as that of bare CoSb₃ [50]. Reported enhancement of ZT for CoSb₃ with the addition of a small G amount was attributed to significantly increased carrier’s concentration and their mobility, and, thereby, electrical conductivity. Moreover, the well dispersed graphene in the nanostructured CoSb₃ matrix prepared by solvothermal route also contributed to the diminished lattice thermal conductivity [50]. In addition, ZT ≈ 0.45 at 650 K was reported for CoSb₃ also prepared by a solvothermal process with 1 wt.% commercial G, but at lower temperature of 240 °C during 24 h, with further sintering at 500 °C by Yadav et al. [53].

The highest ZT of 1.52 at 850 K was reported by Zong et al., for SPS densified composite of n-type Yb_0.27Co₄Sb₁₂ skutterudite, prepared by conventional solid-state melting method and 0.72 vol.% GO [30]. SEM (see Figure 3c) and transmission electron microscopy (TEM) analysis (see Figure 3d) revealed that rGO embedded in boundaries of Yb_0.27Co₄Sb₁₂ was wrapped and 3–5 nm thick. Thus, 3D-rGO network wrapping architecture dramatically reduced the lattice thermal conductivity due to enhanced interparticle and intraparticle phonon scattering effects, and simultaneously enhanced the Seebeck coefficient due to the energy filtering effect of the grain boundary semiconductive rGO layer with nanometer thickness, resulting in high ZT [30]. Moreover, both when GO was added to Ce_0.85Fe₃CoSb₁₂ [51] and when G was grown in-situ by plasma-enhanced chemical vapor deposition (PECVD) in La_0.8Ti_0.1Ga_0.1Fe₃CoSb₁₂ [52], the values of ZT increased in comparison to pure CoSb₃ or CoSb₃ with G or rGO, as can be seen in

Table 2. The composite preparation method and conditions, the highest value of ZT (ZT_max) at the corresponding temperature (T_ZTmax), as well as the thermal conductivity (k), electrical conductivity (σ) and Seebeck coefficient (S) at that temperature reported for composites of skutterudite TE materials with graphene or reduced graphene oxide.

TE Material	G-rGO,	Method	T Range,	ZTmax (at TZTmax, K)	k at TZTmax,	σ at TZTmax,	S at TZTmax,	Ref.
	Used Amount		K	/Used G-rGO Amount	W/m × K	×103 S/m	μV/K
CoSb3 by STS	GO by HM	HP, 600 °C	300–850	0.61 (800)/1.5 wt.%	1	4.5	100	[50]
	0, 1.5 wt.%	2 h, 80 MPa
CoSb3 by STS	G	CSM, 500 °C	300–700	0.45(650)/2 wt./%	1.75	11.9	45	[53]
	1 wt.%	5 h, 10−5 Torr
Ce0.85Fe3CoSb12 ingots	GO by HM	SPS 600 °C	300–800	1.06 (700)/1.4 vol.%	1.85	80	180	[51]
	0–2.8 vol.%	15 min, 55 MPa
La0.8Ti0.1Ga0.1Fe3CoSb12 ingots	G by PECVD	HP 650 °C	300–800	1 (723)/ -	2	70	190	[52]
		1 h, 90 MPa
Yb0.27Co4Sb12 ingots	Wrapped rGO	SPS 627 °C	300–850	1.52 (850)/0.72 vol.%	3	150	−195	[30]
	0–3.6 vol.%	10 min, 60 MPa

Here STS—solvothermal synthesis; CS—chemical synthesis; HM—Hummer’s method; PECVD—plasma-enhanced chemical vapor deposition; HP—hot-pressing; CSM—conventional sintering method; SPS—spark plasma sintering.

and in Figure 4.

Figure 4 presents that all the reported skutterudite materials combined with G-rGO show increase of ZT with the temperature. Moreover, p-type materials can show a peak of ZT at 700–800 K in contrast to the only reported n-type skutterudite Yb_0.27Co₄Sb₁₂ with rGO that presented no peak or saturation up to 850 K. In addition, the highest ZT reported for p-type (Ce,Fe)CoSb₁₂ with rGO (ZT of 1.06 at 700 K for Ce_0.85Fe₃CoSb₁₂ [51]) is very close to ZT obtained for more complex multicomponent p-type skutterudites without addition of G or rGO such as (La,Ce,Fe)CoSb₁₂ (ZT of 1.15 at 748 K in La_0.68Ce_0.22Fe_3.5Co_0.5Sb₁₂ [54]) or (Ca,Ce,Nb,Fe)CoSb₁₂ (ZT of 1.1 at 748 K for Ca_0.35Ce_0.35Nd_0.35Fe_3.5Co_0.5Sb₁₂ [55]). Moreover, the highest ZT value of 1.52 at 850 K reported for unique n-type skutterudite Yb_0.27Co₄Sb₁₂ with rGO [45] is not far from ZT of 1.8 at 823 K reported for the more complicated n-type (Sr,Ba,Yb)_yCo₄Sb₁₂ with 0.91 wt.% In_0.4Co₄Sb₁₂ [56]. Thus, TE performance similar to that of complex skutterudites can be obtained by adding G or rGO to simpler structures.

2.3. Metal Oxides

In contrast to chalcogenides, skutterudites or other TE materials, metal oxides are not so deeply studied yet and there are only few well known p-type materials such as Na_xCoO₂ and Ca₃Co₄O_9+δ, which have been found very promising especially in high T range, benefiting from their layered structure. BiCuSeO as well as n-type CaMnO₃- and SrTiO₃-based materials are also among the most studied TE oxides [57,58,59]. There are several reports since 2015 on the influence of G-rGO on n-type SrTiO₃- or ZnO-based materials, TiO₂ or BaTiO₃ [31,60,61,62,63,64,65,66,67,68,69], summarized in

Table 3. The composite preparation method and conditions. The highest value of ZT (ZT_max) at the corresponding temperature (T_ZTmax), as well as the thermal conductivity (k), electrical conductivity (σ) and Seebeck coefficient (S) at that temperature, reported for composites of metal oxide TE materials with graphene or reduced graphene oxide.

TE Material	G-rGO,	Method	T Range,	ZTmax (at TZTmax, K)	k at TZTmax,	σ at TZTmax,	S at TZTmax,	Ref.
	Used Amount		K	/Used G-rGO Amount	W/m × K	×103 S/m	μV/K
SrTiO3 com.	GO by HM	SPS 1200 °C	300–760	0.09 (760)/0.64 vol.%	3	3	−375	[31]
	0, 0.64 vol.%	5 min, 60 MPa
SrTiO3 by SSS	GO	SPS 1300 °C	300–723	0.05 (673)/0.7 wt.%	3.5	2.5	−350	[60]
	0–4 wt.%	15 min, 60 MPa
La0.067Sr0.9TiO3 by SSS	G by exf.	CSM 1437 °C	273–1033	0.42 (273)/0.6 wt.%	1.8	200	−120	[61]
	0–1 wt.%	24 h
SrTi0.90Nb0.10O3 by SSS	GO by HM	CSM 1570 °C	315–1160	0.24 (1160)/0.6 wt.%	3.5	5	−200	[62]
	0, 0.6 wt.%	10 h
Sr0.98Ti0.90Nb0.10O3 by SSS	GO by HM	CSM 1570 °C	315–1160	0.29 (1160)/0.6 wt.%	3	5	−200	[62]
	0, 0.6 wt.%	10 h
Sr0.98Ti0.85Nb0.15O3 by SSS	GO by HM	CSM 1570 °C	315–1160	0.27 (1160)/0.6 wt.%	3.1	10	−180	[62]
	0, 0.6 wt.%	10 h
Sr0.93Ti0.90Nb0.10O3 by HTS	GO by HM	SPS 1300 °C	300–800	0.22 (800) /0.6 wt.%	3	0.2	−200	[63]
	0–1 wt.%	80 MPa
SrTi0.85Nb0.15O3 by SSS	GO by HM	SPS 1427 °C	300–1200	0.5 (1200)/1.5 wt.%	3.5	45	−190	[64]
	0–2 wt.%	7 min, 50 MPa
Sr0.8L0.67Ti0.8Nb0.2O3 by SSS	G by exf.	SPS 1200 °C	300–1000	0.07 (1000)/1 wt.%	2.2	2	−220	[65]
	0–1 wt.%	5 min, 50 MPa
ZnO com.	G com.	SPS 900 °C	273–1073	0.04 (1073)/1 wt.%	7	4	−220	[66]
	0–2 wt.%	5 min, 70 MPa
Zn0.98Al0.02O by CS	GO by HM	HP 900 °C	273–1173	0.28 (1173)/1.5 wt.%	2.5	75	−95	[67]
	0–3.5 wt.%	2 h, 75MPa
TiO2 com.	GO com.	SPS 900 °C	300–1100	0.064 (1050)/4 wt.%	1.2	5	−100	[68]
	0–4 wt.%	5 min, 50 MPa
BaTiO3 com.	GO by HM	SPS 1100 °C	300–600	0.08 (600)/1.7 wt.%	2.5	0.25	−380	[69]
	1.5–4 wt.%	1 min, 80 MPa

Here com.—commercial; SSS—solid-state synthesis; HTS—hydrothermal synthesis; CS—chemical synthesis; HM—Hummer’s method; exf.—exfoliation; SPS—spark plasma sintering; CSM—conventional sintering method; HP—hot-pressing.

and presented in Figure 5, but there is no available report on p-type metal oxide TEs modified by G-rGO.

A composite of commercial powder of pure SrTiO₃ with rGO densified by SPS was studied by Feng et al., which reported a ZT value of 0.09 at 760 K for 0.64 vol.% GO [31]. That is higher than the ZT of 0.05 at 673 K reported for the similar composite densified by SPS, but with SrTiO₃ powder obtained by conventional solid-state reaction method and mixed with 0.7 wt.% GO by Rahman et al. [60]. However, in both cases, the authors reported significantly enhanced ZT after the addition of GO. Feng et al. also reported that room-T electrical conductivity of SrTiO₃ densified in vacuum by SPS increases from 18 S/m to 1633 S/m, after the addition of rGO and without any additional reducing process [31]. Based on electron energy-loss spectroscopy analysis and low-angle annular dark field imaging, Feng et al. concluded that rGO in composite with SrTiO₃ serves as a carbon source that promotes the formation of oxygen vacancies via a mild reaction with oxygen atoms on the surface of SrTiO₃ grains, and that is the reason behind the highly increased carrier density for SrTiO₃ with rGO [31].

Moreover, although the pristine SrTiO₃ was doped by many different elements, such as La, Nd, Sm, Gd, Dy, Y, Er Pr, Yb, Ta, Nb, etc., to enhance ZT [57,59], the G-rGO effect on ZT was studied only on SrTiO₃ doped by La, incorporated at Sr-site [61], or by Nb in Ti-position [62,63], or simultaneously doped by La and Nb [65]. In general, the ZT of Nb- and simultaneously La,Nb-doped SrTiO₃ composites with G-rGO were found to increase with the temperature, and the highest ZT values were reported at the highest measured T of these composites without an obvious peak (see Figure 5).

The addition of 0.6 wt.% GO to SrTi_0.90Nb_0.10O₃, prepared by the conventional method, leads to ZT of 0.24 at 1160 K, as was reported by Okhay et al. [62]. At the same time, almost zero ZT was detected by Dey et al. for SPS SrTi_0.85Nb_0.15O₃ with 0.5 wt.% GO; that was significantly enhanced, however, to 0.5 at 1200 K by further increase of GO amounts up to 1.5 wt.% [64]. Considering Sr vacancy as a defect that can serve for phonon scattering, and thus decrease thermal conductivity and increase ZT, Okhay et al. studied composites of rGO with nonstoichiometric Nb-doped SrTiO₃ with 2 mol.% Sr vacancies, achieving the highest ZT of 0.29 at 1160 K for Sr_0.98Ti_0.90Nb_0.10O₃ with 0.6 wt.% GO [62]. Following that direction, Wu et al. increased Sr deficiency to 7 mol.%, thus obtaining a ZT of 0.22 at 800 K for Sr_0.93Ti_0.90Nb_0.10O₃ + 0.6 wt.% GO nominal composition [63]. However, such high Sr deficiency should result not only in the formation of Sr vacancies but in the segregation of the titanium oxide secondary phase [70].

On the other hand, a ZT of 0.36 at 1023 K was reported by Lin et al. for Sr-deficient La-doped strontium titanate La_0.067Sr_0.9TiO₃ with 0.6 wt.% G, obtained by exfoliation of graphite [61]. The high ZT value is accompanied by the highest electrical conductivity and the lowest thermal conductivity in Table 3. The observed enhancement of electrical conductivity in La-doped SrTiO₃ with graphene loading was explained by the formation of a percolation network and the graphene-facilitated reduction of La-doped SrTiO₃ at the grain boundaries, resulting in faster electronic transport. Similar to other TE materials, Lin et al. also posited that the introduction of G lead to significant reduction in grain size of the nanocomposites from 2.2 μm for pristine La-doped SrTiO₃ to 412 nm when 0.6 wt.% G was added. Such nanotexturing introduces significant lattice scattering and, hence, reduces the thermal conductivity of the composite [61]. However, the reason for the decrease in thermal conductivity on cooling below 500 K reported by Lin et al., for La_0.067Sr_0.9TiO₃ with 0.6 wt.% G, and thereby for room temperature ZT with a value of 0.42, is still unclear, since no other report on graphene-modified SrTiO₃-based TE materials, including that from the same group [65], has presented such variation.

Moreover, although both La-doped SrTiO₃ and Nb-doped SrTiO₃ with G-rGO present in Figure 5 and Table 3 rather high ZT, from 0.22 to 0.5, either the addition of solvent-derived flakes of graphene nanoplatelets to or the mixing GO prepared by the modified Hammer method with Sr_0.8La_0.067Ti_0.8Nb_0.2O_3-δ composition, was reported to lead to ZT that does not exceed 0.07 at 1000 K [65].

In addition to the described above metal oxide TE materials, Chen et al. reported a ZT of 0.28 at 1173 K for Al-doped ZnO with 1.5 wt.% GO [67], which is much higher than 0.04 at 1073 K reported for pure ZnO with 1 wt.% G [66], or even 0.064 at 1050 K for TiO₂ with 4 wt.% GO [68] and 0.08 at 600 K for BaTiO₃ with 1.7 wt.% GO [69].

In summary, according to the aforementioned reports, the ZT of TE materials tends to be enhanced by G-rGO addition. However, the systematic studies of the G-rGO concentration influence on the TE performance of composite materials show that ZT decreases after the application of a certain concentration of G or rGO, for all material types. Such an optimal concentration of G-rGO, at which the highest ZT can be achieved, is individual for each composite and is reported to be between 0.1 and 1.4 vol.% (for chalcogenide Bi_0.5Sb_1.5Te₃ [37] and for skutterudite Ce_0.85Fe₃CoSb₁₂ [51], respectively) or from 0.05 to 4 wt.% (for chalcogenide Bi₂Te_2.7Se_0.3 [45] or Bi_0.48Sb_1.52Te₃ [40] and for metal oxide TiO₂ [68], respectively). However, the trend is general, and it deserves a comparative consideration involving all ZT components in the next section.

3. Relationship between the Thermoelectric Performance of Materials and the Presence of Graphene or Reduced Graphene Oxide

According to Equation (1) for the dimensionless figure of merit, ZT depends on electrical and thermal conductivity, as well as on the value of the Seebeck coefficient. As it was described above, the Seebeck coefficient decreases with increase in charge carrier concentration. Thus, a high S can be observed in dielectric materials, such as undoped metal oxide, particularly SrTiO₃. After the addition of G-rGO to insulating pure SrTiO₃, its electrical conductivity increases and absolute value of S decreases as can be seen in Figure 6a, as reported by Rahman et al. [60] and supported by Wu et al. [63]. However, σ of SrTiO₃ can be significantly increased not only by the addition of G-rGO but also by Nb or La doping process [61,62,64]. Then, the addition of G-rGO to an already semiconductive material, such as heavily doped SrTiO₃, chalcogenides and skutterudites, does not lead to serious variations of S, as shown in Figure 6b–d, respectively, although they could be slightly enhanced in the case of Yb_0.27Co₄Sb₁₂ skutterudite (see Figure 6d) due to the energy filtering effect [30].

In accordance with the abovementioned statements, the electrical conductivity σ of rather resistive metal oxides is significantly enhanced after G-rGO addition, as can be seen in Figure 7a, in comparison to less notable changes of σ for initially conductive chalcogenides or skutterudites, as shown in Figure 8a. Moreover, there are several studies on chalcogenides (Bi_0.44Sb_1.56Te₃ [43], Bi_0.5Sb_1.5Te₃ [44]) and skutterudites (Yb_0.27Co₄Sb₁₂ [30], Ce_0.85Fe₃CoSb₁₂ [51]), with a reported decrease in electrical conductivity after the addition of G-rGO. In these articles, the authors stressed that the G-rGO nm-layer located between the grains can grow and form agglomerates, with increasing rGO content that leads to decreased charge carrier mobility and, thereby, electrical conductivity because of the boundary scattering effect. At the same time, both the carrier concentration and its mobility were typically increased with the addition of G-rGO in the metal oxides (see Figure 7b,c, respectively). However, in the case of the chalcogenides or skutterudites, the carrier concentration was reported only to change insignificantly, while the mobility of the carriers was not strongly raised in general with the increase of rGO content (see Figure 8b).

According to Figure 9, reported values of the thermal conductivity tend to decrease at least until a certain amount of G-rGO as for undoped SrTiO₃ (see Figure 9a) [60] as for donor-doped SrTiO₃ (see Figure 9b) [62], chalcogenide (see Figure 9c) [42] or skutterudite (see Figure 9d) [30] composites. Such a decrease can be related to the enhanced interface phonon scattering, which is due both to the secondary phase of G-rGO at the grain boundaries of TE materials and to the enlarged number of grain boundaries caused by grain growth inhibition by G-rGO addition. Thus, thermal conductivity shows rather common behavior with G-rGO addition for all three TE material systems overviewed here, in contrast to electrical conductivity and the Seebeck coefficient.

ZT was also found to be usually enhanced by G-rGO addition until a certain amount, as shown in Section 2. For further analysis, we have used the published data to calculate the relative increase of ZT as a ratio between the figure of merit difference for TE material without G-rGO (ZT_{max without G-rGO}), and its composite with G-rGO (ZT_{max with G-rGO}) in relation to ZT_{max without G-rGO}:

$$Relative increase of ZT=\frac{Z{T}_{ max with G-rGO}-Z{T}_{ max without G-rGO}}{Z{T}_{ max without G-rGO}}\times 100\%$$

(2)

Calculated values of the increment of ZT for chalcogenide, metal oxide and skutterudite TE materials are presented in

Table 4. The highest ZT values of chalcogenide materials before and after G-rGO addition, ordered from the lowest to highest ZT values of TE materials without G-rGO, and calculated relative increase of ZT.

TE Material	ZTmax		Relative Increase of ZT, %	Ref.
	without G-rGO	with G-rGO
Cu2ZnSnS4	0.11	0.5	355	[37]
PbTe	0.12	0.7	483	[34]
Bi2Te3	0.145	0.21	44	[33]
Cu2SnSe3	0.24	0.44	83	[36]
Bi2Te3	0.68	0.92	23	[38]
Bi2Te2.7Se0.3	0.65	0.8	15	[45]
Bi2Te2.7Se0.3	0.65	0.75	35	[45]
Bi0.5Sb1.5Te3	0.78	1.13	45	[39]
Bi0.48Sb1.52Te3	0.9	1.25	39	[40]
Bi0.5Sb1.5Te3	0.98	1.24	27	[39]
Bi0.44Sb1.56Te3	1.0	1.0	0	[43]
Bi0.36Sb1.64Te3	1.01	1.16	15	[42]
Bi0.4Sb1.6Te3	1.4	1.54	15	[41]
Bi0.48Sb1.52Te3	1.04	1.2	10	[44]

,

Table 5. The highest ZT values of skutterudite materials before and after G-rGO addition, ordered from the lowest to highest ZT values of TE materials without G-rGO, and calculated relative increase of ZT.

TE Material	ZTmax		Relative Increase of ZT, %	Ref.
	without G-rGO	with G-rGO
CoSb3	0.26	0.61	135	[50]
La0.8Ti0.1Ga0.1Fe3CoSb12	0.75	1	33	[52]
Ce0.85Fe3CoSb12	0.8	1.06	33	[51]
Yb0.27Co4Sb12	1.25	1.52	22	[30]

and

Table 6. The highest ZT values of metal oxide materials before and after G-rGO addition, ordered from the lowest to highest ZT values of TE materials without G-rGO, and calculated relative increase of ZT.

TE Material	ZTmax		Relative Increase of ZT, %	Ref.
	without G-rGO	with G-rGO
SrLa0.67Ti0.8Nb0.2O3	0.0002	0.07	34900	[65]
TiO2	0.0003	0.064	21233	[68]
ZnO	0.005	0.04	700	[66]
SrTiO3	0.009	0.09	900	[31]
SrTiO3	0.02	0.05	150	[60]
Sr0.8L0.67Ti0.8Nb0.2O3	0.02	0.07	250	[65]
SrTi0.85Nb0.15O3	0.02	0.5	2400	[64]
Zn0.98Al0.02O	0.035	0.28	700	[67]
Sr0.93Ti0.9Nb0.1O3	0.12	0.22	83	[63]
La0.067Sr0.9TiO3	0.12	0.42	250	[61]
SrTi0.90Nb0.10O3	0.17	0.24	41	[62]
Sr0.98Ti0.85Nb0.15O3	0.22	0.27	23	[62]
Sr0.98Ti0.90Nb0.10O3	0.27	0.29	7	[62]

and summarized in Figure 10.

It is obviously seen in Figure 10 that the lowest relative increase of ZT is calculated for the composites with the highest initial ZT before the addition of G-rGO and vice versa. In the case that the materials have shown very low ZT before the addition of G-rGO, their composite with graphene or reduced graphene oxide can show a high increment of ZT. Moreover, such a tendency can be found in all chalcogenide, skutterudite or metal oxide TE materials (see Figure 10). Thus, the fabrication of TE composites using the addition of up to 5 wt.% or 1.4 vol.% G or rGO can be an alternative, but not incremental method, for the preparation of high-performance TE materials.

4. Conclusions

Analyzing the available data on chalcogenide-, skutterudite- and metal oxide-based composites with graphene or reduced graphene oxide, it is possible to conclude that the addition of rather low amount of G-rGO is able to increase their final ZT, mainly enhancing the phonon scattering at grain boundaries of all these materials and increasing the charge carrier concentration and mobility in some of them, particularly in oxide thermoelectrics. However, that is mainly valid in the case of TE materials with low initial ZT. When TE material is already nanostructured and possesses high electrical conductivity, such an addition does not enhance ZT significantly. Thus, G-rGO works mainly as an optimizer of the intrinsic performance of TE materials.