With the advancement of nano-technology and push toward flexible electronics, the opportunity to generate electricity using solid-state devices has ushered tremendous research interest in improving the thermoelectric (TE) properties of flexible semiconducting materials. The majority of research done so far was focused on finding suitable doping schemes for all-organic flexible substrates or mixing organic and inorganic components to obtain flexible substrates with an optimized thermoelectric performance. Unfortunately, their performance is limited by their low power factor (PF) values and often suffers from degradation issues due to the organic component that limits them to low temperature applications. Here, through coupled microstructural and thermoelectric analysis, we show how to overcome these limitations by introducing a new inorganic GaAs flexible substrate with enhanced TE performance. We show that these flexible thin films are single-crystal-like biaxially textured with low angle grain boundary misalignment; and charge transport is dominated by multi- valley electron conduction. This results in a PF ∼1300 µW/mK2, the highest value for non-toxic inorganic flexible thin films and an estimated 3-fold enhancement in the figure of merit compared with bulk GaAs. We present the temperature-dependent experimental PF, mobility, and carrier concentration data coupled with the theoretical models to elucidate the charge transport characteristics of this new class of films. Moreover, these unique charge transport characteristics are material growth dependent, and thus, such novel thermoelectric properties are expected in different material systems.

Thermoelectric (TE) cooling and power generation is considered a good alternative compared with traditional technologies because of its direct solid-state energy conversion between heat and electricity. Unfortunately, till this date, such applications are limited to niche markets because of their low energy conversion efficiency. The TE efficiency is an increasing function of the materials’ dimensionless figure of merit ZT, which is defined as ZT = (S2σ/κ)T, where S, σ, κ, and T are the Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively.1 This illustrates the necessity of finely tuning these material properties to maximize S2σ(PF) and minimize κ in order to maximize ZT. Significant strides have been accomplished in the past two decades in maximizing ZT, by utilizing two main approaches: (a) reducing the lattice thermal conductivity “phonon engineering” and (b) enhancing the power factor (PF) via. “electronic-structure engineering.” Examples of phonon engineering include the lattice thermal conductivity reduction by utilization of point defects,2 grain boundaries,3 dislocations,4 nanoparticle structures,5 and lattice anharmonicity.6 Examples of electronic-structure engineering include band engineering,7 modulation doping,8,9 energy filtering,9,10 resonant levels,11 ionizations scattering,12 and band convergence.13 There is no single approach that significantly enhances ZT and a combination of these is usually needed.14 

Beyond low energy conversion efficiency, cost and utilization of toxic rare earth materials have also hindered the wide-scale technological applications of these TE materials. To circumvent this, recent trends have been geared toward inexpensive semiconductors such as silicon and GaAs, as well as organic materials. Using silicon as a potential TE material15 has spurred significant recent interest, because of its low cost and large knowledge in processing from the microelectronics industry. Unfortunately, it still has not proven to be viable. SiGe has also proven to be a promising prospect as TE material; however, its application is limited to high temperature operations.16 GaAs, on the other hand, has shown some prospect. Its cost is one of the biggest drawbacks compared with silicon, but significant work has been made to grow GaAs inexpensively17,18 and it is still more desirable than the state-of-the-art TE materials. GaAs itself should be a better TE material than silicon due to its higher mobility17 and lower thermal conductivity.19 Various efforts have been carried out to investigate the potential of GaAs20 based TE materials including thin film superlattices,21 resonant level doping,22,23 and nanowires.24 Koga et al. calculated enhancement in the ZT using carrier pocket engineering for GaAs/AlAs superlattices,21 reporting ten times higher ZT ∼ 0.082 than the bulk GaAs ZTbulk ∼ 0.0082 at Γ-valley minima in the conduction band. Pichanusakorn et al. focused on the resonant level N-doping to enhance the thermoelectric PF;23 however, their result showed decreased PF due to enhanced scattering and reduced electron mobility. More recently, Paul et al.25 and Zou et al.24 reported enhancement in the TE efficiency by utilizing tensile stress in uniaxial n-GaAs nanowire and by using thin GaAs nanowires, respectively. Paul et al. showed an increase in ZT by ∼1.14 times by applying 5% uniaxial tensile stress to 6 nm thick nanowire. Using density functional theory (DFT) and non-equilibrium Green’s function method, Zou et al. reported room temperature ZT as high as 1.34 for 1 nm thick nanowire, depicting an enhancement of 100-fold in comparison with bulk GaAs.

Organic-based TE materials have also spurred significant attention lately26 not only due to the significant cost savings but also due to their flexibility, lightweight, ease of processing, and environmental safety. Traditional TE material and bulk semiconductors such as silicon and GaAs lack the mechanical flexibility compared with conductive polymers such as PEDOT:PSS (poly(3,4-ethlenedioxythiophene):polystyrene sulfonate) and PANI (polyaniline) based composites which show promising TE performance.27–29 Thermoelectric modules for daily wearables and internet of things (IoT) devices have ushered the development of flexible thermoelectrics devices. These wearables are powered by battery, requiring frequent recharges and are not suitable for long term bio-medical monitoring applications. Traditionally, researchers are drawn toward organic TE materials as they exhibit high PF and low intrinsic thermal conductivity which aids in improving the TE efficiency.30 However, they suffer from two main drawbacks, instability at high temperatures and being predominantly p-type. Notable studies include the work by Kim et al. who showed enhancement in the TE efficiency by engineered doping of PEDOT:PSS with ethylene glycol (EG) treatment and achieved a PF of 469 µWm−1K−2.27 Furthermore, Moriarty et al.31 showed enhancement in the power factor by using carbon nanotubes (CNTs) with stabilizers such as PEDOT:PSS and meso-tetra(4-carboxyphenyl) porphine (TCPP) to achieve a PF of 500 µWm−1K−2 for CNT-stabilized nanocomposite polymer. To overcome the challenge of organic flexible TE material being predominantly p-type, researchers combined flexible organic materials with high performance thermoelectric inorganic nanomaterials.32,33 The recent topical review by Yazdani and Pettes of the various chemistry based approaches encapsulates the recent trends and challenges in thermopower enhancement using such hybrid materials.34 There is recent work by Wan et al. where they reported PF of 904 µWm−1K−2, for n-type hybrid inorganic-organic superlattice of TiS2 and tetrabutylammonium hexyalmmonium composite suitable for room temperature applications exhibiting a ZT ∼ 0.2.35 However, these hybrids suffer from the same issue of instability at high temperature and performance degradation over time. The push to find new inorganic flexible TE has recently yielded materials that show a room temperature PF of 190 and 450 µWm−1K−2 for copper selenide, CuSe,36 and copper iodide, CuI,37 respectively, with high-temperature operation limit enforced by the thermal stability of the flexible polymeric substrate. Carbon nanotube based flexible thermoelectric with Ag2Te nanoparticles has been demonstrated to have a room temperature PF of 150 µWm−1K−2 with reduction in the electrical conductivity due to the phase change of Ag2Te leading to lowered power factor.33 Various paper-based thermoelectrics have been reported with lower power factor due to the reduced electrical conductivity which typically stems from the doping of the quantum dots during the fabrication.38 However, to be competitive in the commercial market, we need a material with high PF without affecting their thermal transport. The recent trends, challenges, and development of flexible thermoelectric devices have been thoroughly reviewed in various notable reviews.39 

In this work, we show for the first-time the potential of inorganic flexible films for high thermoelectric performance. We specifically show the properties of thin GaAs films grown by metalorganic chemical vapor deposition (MOCVD) on flexible metal foils that exhibit a single-crystal-like structure with low angle grain boundary misalignment <1° over long range (meters). The PF values of these new classes of flexible films are comparable to bulk single crystal and outperform state-of-the-art organic flexible TE materials. To understand the mechanisms behind the enhancement of the PF of these flexible films, in-depth temperature-dependent experiments on thermopower and charge transport were carried out and coupled with various theoretical models. The enhancement in the PF is attributed to the multi-valley conduction states which increase the contribution of the carrier; this increases the effective mass of the electron, resulting in the increased thermopower. Furthermore, we theoretically calculate the thermal conductivity of these films by considering the contribution of dislocation scattering which shows a reduction of 70% from the bulk thermal conductivity values resulting in a 3-fold enhancement in the figure of merit.

GaAs thin films were grown on flexible metal substrates using a stationary reactor of a dual reactor MOCVD tool on the Ge single crystalline-like buffer layer which was grown in a roll-to-roll system discussed elsewhere.17 The tool has a traditional horizontal wafer-based quartz deposition chamber which accommodates 2” wafers with load lock and glove box for sample transfer. A custom-designed graphite susceptor was used to hold the flexible Ge substrates and to yield uniform heating of samples in the MOCVD reactor. Trimethylgallium (TMGa, Ga(CH3)3) and Arsine (AsH3) were used as Ga and As sources, respectively, and Silane (SiH4) was used as the dopant, with H2 as the carrier gas purified by a palladium cell. Chamber pressure was fixed at 20 Torr. The GaAs films were grown at 650 °C on wafer and flexible substrates, with a constant V/III ratio. Figure 1 shows the optical image of our flexible sample and the sample architecture of the GaAs thin film grown on the flexible metal substrates. The GaAs samples exhibited good mechanical robustness, adhesion, and displayed no sign of cracking during bending tests, indicative of small or no thermal mismatch and strain between the different epilayers.

FIG. 1.

Depicts the flexible GaAs sample, optical image and multilayer structural architecture on which the epitaxial GaAs thin films were grown.

FIG. 1.

Depicts the flexible GaAs sample, optical image and multilayer structural architecture on which the epitaxial GaAs thin films were grown.

Close modal

An undoped (intrinsic) GaAs buffer of ∼1 µm thickness was grown on the flexible Ge templates prior to growing the doped GaAs: Si layer to isolate the effect of the underlying Ge and oxide buffer layers from the top GaAs layer. The undoped buffer layer also played the role of a diffusion barrier, preventing Ge diffusion to the active GaAs: Si layer, and thus all the electrical properties characterized here are for the respective doped GaAs layers.17 Surface morphology, growth rate, and crystal structure were determined using focused ion beam cross-sections, Scanning Electron Microscopy (SEM), optical microscopy, and High Resolution X-ray Diffraction (HRXRD). Si-doped n-type GaAs was deposited by changing the SiH4 flow to achieve doping concentrations from 1017 to 1018 cm−3. Hall measurements were conducted using the Ecopia 5000 system from 77 to 350 K to confirm the carrier concentration and for temperature dependent electrical measurements. The samples characterized in this work are listed in (Table I), where samples F1-5 are flexible samples and W1 and W2 are wafer samples grown on the single crystal Si wafer.

TABLE I.

Different sample ID with respective doping concentration in cm−3.

Sample IDDoping concentration (cm−3)
W1 6.90 × 1016 
F1 4.11 × 1017 
W2 6.76 × 1017 
F2 1.39 × 1018 
F3 1.75 × 1018 
F4 1.95 × 1018 
F5 4.95 × 1018 
Sample IDDoping concentration (cm−3)
W1 6.90 × 1016 
F1 4.11 × 1017 
W2 6.76 × 1017 
F2 1.39 × 1018 
F3 1.75 × 1018 
F4 1.95 × 1018 
F5 4.95 × 1018 

Microstructural studies were carried using Scanning Electron Microscopy (SEM), X-Ray Diffraction (XRD), and Transmission Electron Microscopy (TEM), which included surface morphology and grain structure of the GaAs flexible films. The SEM images in Figs. 2(a)–2(e) show faceted surface morphology, as well as a layer-like grain structure with grain size distribution ranging from few hundreds of nanometers to few micrometers in all the samples. The average grain size for these samples was characterized in previous study;40 however, due to a large deviation of grain size within the sample, an average grain size of 2-4 μm was estimated. Sample F4 [depicted in Fig. 2(c)] showed an embedded AB grain structure. The in-plane and out-of-plane alignments of the grains were studied using XRD (111) pole figures and rocking curves and indicated good quality of the crystal alignment <1° over long range (meters) and biaxial texturing, as shown in the supplementary material Fig. S1. The TEM study showed an average dislocation density in the range of ∼108 cm−2 which were predominantly concentrated at the grain boundaries and consistent with previously published results for our samples.40 A detailed cross-sectional TEM image is shown in the supplementary material Fig. S2. More importantly, the flexibility of our GaAs sample enables roll-to-roll large-scale processing, using the industrially popular MOCVD technique to grow the film. Therefore, our unique template and processing conditions allow us to grow single-crystal-like structure GaAs substrates with low angle grain boundary misalignment <1° over long range (meters) suitable for wide temperature range TE applications including high temperatures.

FIG. 2.

Scanning Electron Microscopy (SEM) of the flexible GaAs: (a) Sample F2, (b) Sample F3, (c) Sample F4, and (d) Sample F5 with a carrier concentration of 1.39 × 1018, 1.75 × 1018, 1.95 × 1018, and 4.95 × 1018 cm−3, respectively.

FIG. 2.

Scanning Electron Microscopy (SEM) of the flexible GaAs: (a) Sample F2, (b) Sample F3, (c) Sample F4, and (d) Sample F5 with a carrier concentration of 1.39 × 1018, 1.75 × 1018, 1.95 × 1018, and 4.95 × 1018 cm−3, respectively.

Close modal

Temperature-dependent in-plane Hall measurement, RH, and resistivity were measured using the Van der Pauw method in a magnetic field 0.55 T. The Hall carrier concentration, nH and mobility were calculated from nH = 1/eRH and μH = RH/ρ, respectively. To measure the temperature dependent Seebeck coefficient, a setup reported elsewhere and similar to Ref. 41 was employed in a high vacuum (∼3.5 × 10−5 mbar) closed loop helium cryostat, as described in the supplementary material under the section of Seebeck setup and benchmarking. All the electrical contacts where confirmed to be ohmic for all the thermoelectric measurements.

To investigate the PF performance of the films, we first plot the electrical conductivity and Seebeck coefficient as a function of temperature (Fig. 3). Samples F1, F2, F3, F4, and F5 show an increasing electrical conductivity with increasing temperature indicating a semiconducting trend in the temperature range from 50 to 350 K [Fig. 3(a)]. The Seebeck coefficient, on the other hand, shows an increasing trend with increasing temperature for all samples [Fig. 3(b)].

FIG. 3.

(a) Temperature-dependent electrical conductivity and (b) temperature-dependent Seebeck coefficient of flexible GaAs samples.

FIG. 3.

(a) Temperature-dependent electrical conductivity and (b) temperature-dependent Seebeck coefficient of flexible GaAs samples.

Close modal

Traditionally, electrical conductivity and Seebeck coefficient have an inverse relationship for bulk materials, but the increasing trend with increasing temperature in both electrical conductivity and Seebeck coefficient indicates that either the samples are amorphous or that the energy filtering could be taking place in our samples. In the case of amorphous materials, the transport mechanism can be best described by Mott’s variable range hopping (VRH) model.42 Based on our structural characterization, our flexible samples exhibit high single-crystal-like quality with large biaxially textured grain boundaries which makes Mott’s VRH model not applicable. Despite the above argument, we fitted our temperature dependent data to Mott’s VRH model for 2D (Dimension) and 3D and found that the model failed to capture the transport.

To investigate if energy filtering effect is the case and to what extent, we carried out the analysis detailed below. Energy filtering occurs when hot electrons can traverse the energy barrier (grain boundary), while the cold electrons (electrons with low energy) get shunned, and this phenomenon is widely reported by others for other thermoelectric materials.43,44Figure 4(a) shows the carrier concentration dependent Seebeck coefficient (Pisarenko plot) for the flexible samples, wafer samples, and bulk samples taken from Ref. 45. The analytical calculation assuming various scattering mechanisms extracted and shown in Fig. 4(b) as a function of carrier concentration was considered to fit our experimental results.

FIG. 4.

(a) Theoretical Pisarenko plot of GaAs flexible and wafer substrate sample with varying scattering exponents at room temperature. The red diamond markers are from bulk Ref. 45, and the orange square markers are wafer sample depicting the thermopower fitted to a scattering exponent of r = 0.26. Black triangle markers represent the experimental thermopower of the flexible single-crystal-like GaAs samples. The theoretical fitting is shown by a green dashed line. (b) The relationship between the temperature scattering exponent r and hall carrier concentration.

FIG. 4.

(a) Theoretical Pisarenko plot of GaAs flexible and wafer substrate sample with varying scattering exponents at room temperature. The red diamond markers are from bulk Ref. 45, and the orange square markers are wafer sample depicting the thermopower fitted to a scattering exponent of r = 0.26. Black triangle markers represent the experimental thermopower of the flexible single-crystal-like GaAs samples. The theoretical fitting is shown by a green dashed line. (b) The relationship between the temperature scattering exponent r and hall carrier concentration.

Close modal

The mathematical relationship between carrier concentration, n, and Seebeck coefficient, S, is determined by the Boltzmann Transport Equation (BTE),46 

n=12π2kBTmdħ232Fjη,j=1/2,
(1)

where η = Ef/kBT is the reduced Fermi energy, md is the density of states effective mass, and Fj(η) is the jth order Fermi integral. kB and ħ are the Boltzmann constant and Planck’s constant over 2π. The Seebeck coefficient can be analytically given by the following equation:

S=kber+5/2Fr+3/2ηr+3/2Fr+1/2ηη,
(2)

where the Seebeck coefficient depends on η and scattering exponent, r.

From Eq. (2), we can see that the value of the scattering exponent r is paramount to the value of the Seebeck coefficient, where the limits are r = −3/2 for acoustic phonon scattering, r = 3/2 for ionizations scattering, and in-between values for mixed scattering [Fig. 4(b)]. We first plot the values for single crystalline GaAs, both reference bulk and our wafer-grown samples [Fig. 4(a) red diamond and orange square markers, respectively]. From our fitting, we calculate a scattering exponent r = 0.26 [blue dashed-dotted line in Fig. 4(a)] which is in line with what has been reported in earlier studies23 indicating that mixed scattering is present. The scattering exponent for the flexible samples obtained from the temperature-dependent electrical conductivity graphs is tabulated in Table II, and they are in the range 0.04-0.41. These fall well within the scattering limit, indicating, similar to the single crystal samples, a mixed scattering exponent, i.e., by ionized impurities and acoustic phonons. As it is evident from [Fig. 4(a)], our flexible samples have higher Seebeck values which cannot be captured by choosing the extracted scattering exponents nor by the ionization scattering exponent, which gives the maximum theoretical Seebeck. This indicates that other phenomena are in play behind the enhanced thermopower for our flexible samples.

TABLE II.

Shows different parameters such as carrier concentration and mobility obtained via hall measurement and Seebeck coefficient (experimental values) and extracted values such as energy barrier or activation energy and scattering exponent parameter, r.

SampleCarrier concentrationMobilitySeebeck coefficientEnergy barrierScattering parameter
ID(cm−3)(cm2/Vs)(µV/K) (meV) (r)ms/mo
F1 4.11 × 1017 248 −430 15.3 0.335 0.26 
F2 1.39 × 1018 195 −287 9.6 0.042 0.24 
F3 1.75 × 1018 270 −380 12.2 0.3817 0.44 
F4 1.95 × 1018 130 −283 40.0 0.4064 0.21 
F5 4.95 × 1018 403 −168 5.3 0.066 0.16 
SampleCarrier concentrationMobilitySeebeck coefficientEnergy barrierScattering parameter
ID(cm−3)(cm2/Vs)(µV/K) (meV) (r)ms/mo
F1 4.11 × 1017 248 −430 15.3 0.335 0.26 
F2 1.39 × 1018 195 −287 9.6 0.042 0.24 
F3 1.75 × 1018 270 −380 12.2 0.3817 0.44 
F4 1.95 × 1018 130 −283 40.0 0.4064 0.21 
F5 4.95 × 1018 403 −168 5.3 0.066 0.16 

To further understand the source of thermopower enhancement, we studied the activation energy for conduction using the temperature dependent mobility data µ(T). The activation energy was extracted by plotting the logarithm of μH vs. temperature [see the supplementary material (Fig. S5) for details]. These activation energies range from 5 to 15 meV for samples F1, F2, F3, and F5 indicating shallow donor levels. However, sample F4 shows a higher activation energy of 40 meV, probably due to the enhanced electron scattering caused by the embedded AB grain structure, which is absent in the other sample showing higher mobility. Figure 5(a) also shows the different scattering processes that influence the electron mobility as a function of temperature. For samples F1-5, the combination of grain boundary and ionization scattering dominate in the temperature range below 250 K; and above that, the combination of ionization and acoustic phonon scattering is dominant. However, sample F4 shows predominantly grain boundary scattering in the low-temperature range and mixed type grain and ionization scattering above 250 K temperature. This trend for sample F4 can be attributed to the unique AB grain structure, resulting in reduced mobility at a carrier concentration of ∼1018 cm−3. To elucidate the reason for the variation in carrier scattering mechanism, we studied the temperature-dependent carrier concentration. Figure 5(b) shows the natural logarithm of carrier concentration vs. the reciprocal of temperature. For all the flexible samples, the carrier concentration shows a slight increase in the concentration as a function of increasing temperature in the range of 275-350 K and shows no temperature dependence in the range of 50-275 K. However, sample F4 shows decreasing carrier concentration as the temperature is increased, such unusual trend was recently reported for MgSbBiTe, where ionization scattering was attributed to such observation in the temperature-dependent carrier concentration.47 Since our sample F4 show mixed scattering, the atypical trend cannot be solely attributed to ionization scattering.

FIG. 5.

(a) shows the temperature dependence of various scattering mechanisms such as grain boundary scattering or exponential dependency, expEBkBT, ionization scattering, T3/2, and acoustic phonon scattering, T−3/2. (b) Natural logarithm of the carrier concentration vs. reciprocal of the temperature.

FIG. 5.

(a) shows the temperature dependence of various scattering mechanisms such as grain boundary scattering or exponential dependency, expEBkBT, ionization scattering, T3/2, and acoustic phonon scattering, T−3/2. (b) Natural logarithm of the carrier concentration vs. reciprocal of the temperature.

Close modal

To better understand the electrical Hall measurement, thermopower measurement, and fit to our Pisarenko plot, we extracted the Fermi level by calculating both two-band model and single-band model, as explained in our earlier studies.48 The total Seebeck coefficient and the respective contribution from electrons and holes can be described by the two-band Seebeck model equation shown below,

S=Senμe+Shpμhnμe+pμh,
(3)

where n and p are the electrons and hole concentration, respectively, and μe and μh are the electron and hole mobility, respectively.

The individual contributions of electron, Se, and hole, Sh, Seebeck are described by the following Eqs. (4) and (5):

Se=kBere+52Fre+32ηere+32Fre+12ηeηe,
(4)
Sh=kBerh+52Frh+32ηhrh+32Frh+12ηhηh,
(5)

where kB is Boltzmann’s constant, where Fj is the Fermi Dirac integral of order j,

Fjη=0yjdye(yη)+1,
(6)

where ηe = Ef/kBT is the reduced Fermi energy for electrons and Ef is the Fermi energy for the electron carrier and ηh = Efh/kBT = −(Ef + Eg)/kBT is the reduced Fermi energy for holes, and Efh is the Fermi energy for the hole carrier.

Energy band gap of GaAs is Eg ∼ 1.521 eV, and its temperature dependence was obtained from the empirical equation (7), 49 

EgT=Eg0αe(Θ/T)1.
(7)

The Seebeck coefficient is dependent on the electron/hole energy according to τe/p = τoEre(h) here both re(h) and τo are two constant and re(h) gives the scattering rate of electron and hole.

The electron and hole concentrations were calculated using the following equation:

n(h)=4πh3(2me(h)*kBT)3/2F12ηe(h).
(8)

We first extract the Fermi energy Ef using two solutions for the two-band model and one solution for the single band model. Figure S6 (see the supplementary material) shows the solutions which correspond to two different regimes, one transition regime, and another highly degenerate regime. Since the intrinsic carrier concentration for GaAs50 is ni ∼ 2.35 × 106 cm−3, and our doping concentrations are more than 1017 cm−3; the highly degenerate solution from the single band model can be used to extract the fermi energy for our samples.

Figure S7 (see the supplementary material) shows the temperature dependent Fermi level for samples F2, F4, and F5. The extracted Ef showed that typical semiconductor trend, i.e., decrease in the Ef as a function of temperature. Our room temperature Ef was calculated to be ∼10 meV below the conduction band minima (CBM) for samples F2 and F4 and ∼60 meV above the CBM for sample F5. This is expected since sample F5 is doped at a higher level that samples F2 and F4. In the highly degenerate regime for bulk GaAs, Ef is calculated to be ∼60 meV in the CBM, with an electron effective mass of ∼0.06751 and a carrier concentration of roughly 1018 cm−3. Using the bulk single crystal electron effective mass in our single band model with the extracted Fermi level yielded a carrier concentration below the measured carrier concentration n from the Hall data. To match the calculated carrier concentration with the experimentally determined value from Hall measurement, the electron effective mass was treated as a tunable parameter52 and the fitted values are tabulated in Table II. We found that an average effective mass of mS*/mo = 0.27 best fits our experimental room temperature Seebeck values, as shown in [Fig. 4(a)]. In the degenerate limit, S is directly proportional to mS* and scattering exponent r, thus having an increased effective mass, helps reach the experimental Seebeck values in the Pisarenko plot plotted at room temperature for our flexible samples. Having a higher effective mass indicates that other conduction band valleys (Γ, L, and X) of GaAs play a vital role in the thermopower enhancement. At high temperature, which enhances the Seebeck values and as the temperature is lowered, the multi-valley conduction is reduced, thus reducing the Seebeck. This occurs because the Fermi level is obtained by the distribution of energy of electrons and holes, and for our flexible sample, the upper conduction band gets populated by the electron at higher temperature resulting in multi-valley states giving us enhanced S. More recently, Tang et al. showed that high thermoelectric performance in TE material originated from such multi-valley conduction, high mobility, and high effective mass.52 

Our thermopower measurement and theoretical analysis validate the contribution of other conduction band valleys for GaAs flexible films in enhancing the thermopower and thereby the power factor for this TE material. Figure 6 shows the PF comparison of our flexible GaAs samples with various state-of-the-art flexible organic (blue box), inorganic (orange box), and hybrid films (red box). It is evident that our samples at high enough carrier concentrations are outperforming most of the state of the art flexible systems27,29,31,35–37,53,54 and opens up the potential application of all inorganic TE material in the flexible market, offering the chemical stability in high-temperature operation, ease of processing compared with organic TE materials.

FIG. 6.

Shows the comparison of various power factor, S2σ for flexible GaAs F1-5 sample with the various state-of-the-art flexible organic (blue box), inorganic (orange box), and hybrid films (red box). We observe that organic flexible TE materials have lower power factor compared to inorganic and hybrid TE systems. The organic flexible system shown are OF1: PANI/CSA-doping in m-cresol,53 OF2: PANI/graphene nanoplatelets,54 OF3: PEDOT:VVPPTos,29 OF4: PEDOT:PSS treated with EG27, and OF5: CNT/PEDOT stabilized with TCPP.31 The inorganic flexible system CuSe,36 CuI,37 and hybrid system HF1: TiS2 Superlattice35 have power factor lower than our flexible GaAs sample F3 and F5.

FIG. 6.

Shows the comparison of various power factor, S2σ for flexible GaAs F1-5 sample with the various state-of-the-art flexible organic (blue box), inorganic (orange box), and hybrid films (red box). We observe that organic flexible TE materials have lower power factor compared to inorganic and hybrid TE systems. The organic flexible system shown are OF1: PANI/CSA-doping in m-cresol,53 OF2: PANI/graphene nanoplatelets,54 OF3: PEDOT:VVPPTos,29 OF4: PEDOT:PSS treated with EG27, and OF5: CNT/PEDOT stabilized with TCPP.31 The inorganic flexible system CuSe,36 CuI,37 and hybrid system HF1: TiS2 Superlattice35 have power factor lower than our flexible GaAs sample F3 and F5.

Close modal

Beyond high PF, we need to have low κ to achieve a high figure of merit. κ = Σiκi, and i = e, l for κe—electronic thermal conductivity and κl—lattice thermal conductivity. The electronic thermal conductivity can be obtained from the Wiedemann-Franz law, κe = LσT, where L is defined by the Lorenz number ∼2.88 × 10−8 WΩK−2, σ is the electrical conductivity, and T is the absolute temperature. The highest electronic thermal conductivity for our samples is 0.07 Wm−1K−1. However, the lattice conductivity for single crystal GaAs has high thermal conductivity of κl = 50 Wm−1K−155 making it difficult to achieve high ZT. It is well known that grains and dislocation play a huge role in reducing the lattice thermal conductivity of polycrystalline material, and in Fig. 7(a), we carry out theoretical calculations based on a modified Callaway model (see the supplementary material for details) to predict what is the expected reduction in the thermal conductivity of our samples. Grain size is widely known to affect thermal conductivity, but Luo et al.56 showed that grain boundary in the order of 100s of nanometers to a few micrometers, similar to our grain size, is not able to reduce the lattice thermal conductivity in GaAs films. However, Clark et al. showed that κl can be as low as 14.5 Wm−1K−1 in 1 µm thick films.19 They did not perform detailed structural characterizations and theoretical calculation of their films but attributed their low thermal conductivity to the characteristics length of 1 µm thick sample which dominated the scattering. Based on our as well as Luo et al. theoretical calculations, boundary scattering due to 1 µm length scale cannot be the only source of thermal conductivity reduction in the GaAs sample reported by Clark et al. [black dashed line in Fig. 7(a)]. Even grain size as small as 200 nm [black dashed line in Fig. 7(a)] is not enough to reduce the thermal conductivity values reported by Clark et al. Either the grain size in their films is much smaller or other defects dominate the phonon scattering in their films. It has been shown that dislocations can have bigger impact in reducing the thermal conductivity than grains.57 As stated earlier, our films have a dislocation density of ∼108 cm−2 and based on this, we are able to predict a reduction of 70% from the bulk thermal conductivity by including the dislocation scattering in our modified Callaway model [green dotted line in Fig. 7(a)]. This reduction in the thermal transport in our flexible samples results in ZT values of ∼0.024, a 3-fold increase compared with bulk GaAs21 samples. We illustrate this in Fig. 7(b) which depicts the comparison of the temperature dependent ZT values for our flexible samples F2, F4, and F5 compared with bulk GaAs, other state-of-the-art organic and hybrid systems. We observe that due to the enhanced PF values, our samples can outperform all organic PEDOT samples27,30 and some hybrid samples58 even though we exhibit higher estimated thermal conductivity. Unfortunately, due to the comparable PF and higher thermal conductivity, we cannot outperform other hybrid systems such as the screen-printed Bi0.5Sb1.5Te358 TE system and powder Bi2Te3—PEDOT:PSS.59 On the other hand, similar fabrication techniques could be applied to other system of material such as SiGe to enhance the figure of merit as we expect the enhanced charge transport properties to behave similar to the flexible GaAs films reported in this work.

FIG. 7.

(a) shows the temperature-dependent thermal conductivity of GaAs for bulk GaAs,55 theoretical fitting for a boundary, and dislocation scattering with a dislocation density40 of 108 cm−2. (b) shows the temperature dependent figure of merit of sample F2, F4, and F5 compared with the state-of-the-art flexible TE organic material system.30 The secondary axis marked in red shows the inorganic-organic flexible screen-printed Bi0.5Sb1.5Te358 TE system and inorganic-polymer composite (powder Bi2Te3 - PEDOT:PSS).59 

FIG. 7.

(a) shows the temperature-dependent thermal conductivity of GaAs for bulk GaAs,55 theoretical fitting for a boundary, and dislocation scattering with a dislocation density40 of 108 cm−2. (b) shows the temperature dependent figure of merit of sample F2, F4, and F5 compared with the state-of-the-art flexible TE organic material system.30 The secondary axis marked in red shows the inorganic-organic flexible screen-printed Bi0.5Sb1.5Te358 TE system and inorganic-polymer composite (powder Bi2Te3 - PEDOT:PSS).59 

Close modal

In summary, thermoelectric measurements were performed on flexible single-crystal-like biaxially textured thin film of GaAs to obtain the temperature-dependent Seebeck coefficient and Hall measurements at varying Si doping levels. Microstructural analysis coupled with detailed thermoelectric analysis using various theoretical models was utilized to elucidate the enhancement in power factor for these n-GaAs flexible films. We report a PF ∼1300 µW/mK2, the highest value for the non-toxic thin film inorganic flexible films and far superior than organic hybrid state-of-the-art flexible thermoelectric material. This study revealed that multi-conduction band plays an important role in enhancing the thermopower of our samples, and theoretical thermal conductivity modeling revealed the possible reduction in the thermal transport by threading dislocations, aiding in a possible 3-fold enhancement in the figure of merit.

See supplementary material for details on the structural characterization using XRD, TEM for the flexible GaAs samples. Additional information on the thermoelectric measurement setup, Fermi level calculation and thermal transport model is included.

A.M., P.D. and V.S. acknowledge financial support from the University of Houston.

There are no conflicts to declare.

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